基于参数依赖齐次多项式的时变系统稳定性分析(英文)

基于齐次多项式Lyapunov函数这一新工具研究了时变不确定系统鲁棒稳定性问题.针对常见的含参数时变且有界连续可微线性系统的最大稳定区域问题,首先构造常用的参数依赖二次Lyapunov函数,进而给出一个时变系统稳定的充分条件.然后,通过构造适合的参数依赖齐次Lyapunov函数,并利用齐次多项式矩阵表示方法,最终以线性不等式的形式给出系统全局渐近稳定的一个充分条件.数值仿真结果表明齐次Lyapunov函数方法得到的结论对于某些系统比之前类似文献具有更小的保守性.     

Parent-Child Relationships from the Child’S Point of View

The authors examined the distributional properties of 3 improvement-over-chance, I, effect sizes each derived from linear and quadratic predictive discriminant analysis and from logistic regression analysis for the 2-group univariate classification. These 3 classification methods (3 levels) were studied under varying levels of data conditions, including population separation (3 levels), variance pattern (3 levels), total sample size (3 levels), and prior probabilities (5 levels). The results indicated that the decision of which effect size to choose is primarily determined by the variance pattern and prior probabilities. Some of the I indices performed well for some small sample cases and quadratic predictive discriminant analysis I tended to work well with extreme variance heterogeneity and differing prior probabilities.     

Power of Latent Growth Modeling for Detecting Group Differences in Linear Growth Trajectory Parameters

This simulation study focused on the power for detecting group differences in linear growth trajectory parameters within the framework of structural equation modeling (SEM) and compared the latent growth modeling (LGM) approach to the more traditional repeated-measures analysis of variance (ANOVA) approach. Several patterns of group differences in linear growth trajectories were considered. SEM growth modeling consistently showed higher statistical power for detecting group differences in the linear growth slope than repeated-measures ANOVA. For small group differences in the growth trajectories, large sample size (e.g., N > 500) would be required for adequate statistical power. For medium or large group differences, moderate or small sample size would be sufficient for adequate power. Some future research directions are discussed.     

Group‐Difference Effect Sizes: Gauging the Practical Importance of Findings from Group‐Experimental Research

Effect sizes are powerful tools for evaluating the practical importance of study findings that should be considered in the context of study characteristics such as participants, dependent variables, and comparison condition. In this article, we discuss how group‐difference effect sizes are used to gauge the practical importance of group experimental studies. We first define different types of group‐difference effect sizes and discuss how they can provide valuable information for research consumers. Second, we present guidelines for interpreting group‐difference effect sizes. Third, we discuss important contextual variables that should be taken into account when interpreting group‐difference effect sizes reported in the literature. Last, we provide two examples of how group‐difference effect sizes have been used in the learning disabilities research base.     

Non-interior continuation algorithm for solving system of inequalities over symmetric cones

As a basic mathematical structure,the system of inequalities over symmetric cones and its solution can provide an effective method for solving the startup problem of interior point method which is used to solve many optimization problems.In this paper,a non-interior continuation algorithm is proposed for solving the system of inequalities under the order induced by a symmetric cone.It is shown that the proposed algorithm is globally convergent and well-defined.Moreover,it can start from any point and only needs to solve one system of linear equations at most at each iteration.Under suitable assumptions,global linear and local quadratic convergence is established with Euclidean Jordan algebras.Numerical results indicate that the algorithm is efficient.The systems of random linear inequalities were tested over the second-order cones with sizes of 10,100,,1 000 respectively and the problems of each size were generated randomly for 10 times.The average iterative numbers show that the proposed algorithm can generate a solution at one step for solving the given linear class of problems with random initializations.It seems possible that the continuation algorithm can solve larger scale systems of linear inequalities over the secondorder cones quickly.Moreover,a system of nonlinear inequalities was also tested over Cartesian product of two simple second-order cones,and numerical results indicate that the proposed algorithm can deal with the nonlinear cases.     

Programs for the promotion of family wellness and the prevention of child maltreatment: a meta-analytic review

OBJECTIVE: The objectives were to determine the effectiveness of programs in promoting family wellness and preventing child maltreatment and to identify factors that moderate program success. METHOD: Meta-analysis, employing a 3-step model testing procedure, was used to review 56 programs designed to promote family wellness and prevent child maltreatment. RESULTS: The effect sizes for proactive interventions were larger at follow-up than at post-assessment, while the effect sizes for reactive interventions were higher at post-assessment than follow-up. The lowest effect sizes for home visitation programs on child maltreatment were for programs with 12 or fewer visits and less than a 6-month duration. Intensive family preservation programs with high levels of participant involvement, an empowerment/strengths-based approach, and a component of social support had higher effect sizes than programs without those elements. Also, both home visitation and intensive family preservation interventions achieved higher effect sizes with participants of mixed socioeconomic status (SES) than participants with low SES. CONCLUSIONS: The total mean weighted effect size was .41, indicating that outcomes for the intervention group exceed 66% of those in control/comparison groups. The findings from this review demonstrated that child maltreatment can be prevented and that family wellness can be promoted.     

Testing Factorial Invariance With Unbalanced Samples

In testing the factorial invariance of a measure across groups, the groups are often of different sizes. Large imbalances in group size might affect the results of factorial invariance studies and lead to incorrect conclusions of invariance because the fit function in multiple-group factor analysis includes a weighting by group sample size. The implication is that violations of invariance might not be detected if the sample sizes of the 2 groups are severely unbalanced. In this study, we examined the effects of group size differences on results of factorial invariance tests, proposed a subsampling method to address unbalanced sample size issue in factorial invariance studies, and evaluated the proposed approach in various simulation conditions. Our findings confirm that violations of invariance might be masked in the case of severely unbalanced group size conditions and support the use of the proposed subsampling method to obtain accurate results for invariance studies.     

Enumeration Index Performance in Generalized Growth Mixture Models: A Monte Carlo Test of Muthén’s (2003) Hypothesis

Relatively few empirical studies have examined the performance of enumeration indices in correctly identifying longitudinal population heterogeneity when present, and these studies have produced mixed results. In light of these findings, Muthén (2003) suggested that the inclusion of time-invariant (antecedent) and time-varying (concurrent) covariates, as well as allowing the extracted growth mixture classes to predict a distal outcome (consequent covariate), could improve the performance of enumeration indices. This Monte Carlo simulation study examined the performance of a large set of enumeration indices within these generalized growth mixture model (GGMM) conditions, as suggested by Muthén, by manipulating 4 design conditions: (a) sample size, (b) separation distance between adjacent latent growth trajectories, (c) growth trajectory membership proportions, and (d) the amount of mixture model variance explained by the covariates. The findings suggest: (a) at smaller (N = 500) sample sizes, enumeration indices were much more likely to select an incorrect model than the correct one, (b) at larger (N = 3,000) sample sizes, correct model identification occurred only in the largest separation distance and trajectory membership equality conditions, and (c) the inclusion of covariates had a negligible effect at smaller sample sizes, but covariate inclusion had a more favorable effect on data generation model identification in the largest sample size, largest trajectory separation distance, and equal trajectory membership proportions conditions. Suggestions for researchers and future empirical study possibilities are discussed.     

Teaching and learning floating and sinking: A meta-analysis

Floating and sinking (FS) is a key topic in science education, both at primary and secondary levels. The interpretation of FS phenomena, however, is challenging due to the difficulty of the scientific concepts and explanatory models involved (e.g., density, buoyancy), along with students' everyday experiences, which conflict with scientific explanations. Consequently, many studies over the last few decades have investigated how FS could be taught effectively to students of different ages while utilizing multiple teaching approaches. This meta-analysis summarizes findings from 69 intervention studies on teaching FS conducted between 1977 and 2021. Over all studies, we estimated a mean effect size of g = 0.85 (95% CI = 0.71, 0.99). This large effect size demonstrates that, although FS is a challenging concept, teaching FS is effective even in elementary school. Moreover, in a moderator analysis, we investigate the effect of intervention characteristics, students' age, as well as study design, and assessment features on the mean study effect size. To analyze the effect of these moderator variables, we use a three-level hierarchical meta-regression model for dealing with multiple effect sizes from single studies. We found two intervention characteristics that explain variance in study effect sizes: longer lasting interventions result in larger effect sizes and interventions where hands-on experiments are applied are more effective than those utilizing virtual experiments. Furthermore, studies with a treatment-control group comparison have significantly smaller effect sizes than studies with a pre-post design. We discuss the implications of our findings regarding the moderator variables for effective teaching of FS and further research on FS.     

Detecting Appropriate Trajectories of Growth in Latent Growth Models: The Performance of Information-Based Criteria

Latent growth modeling (LGM) is a popular and flexible technique that may be used when data are collected across several different measurement occasions. Modeling the appropriate growth trajectory has important implications with respect to the accurate interpretation of parameter estimates of interest in a latent growth model that may impact educational policy decisions. A Monte Carlo simulation study was conducted to examine the accuracy of six information-based criteria (i.e., AIC, CAIC, AICC, BIC, nBIC, and HQIC) when selecting among various growth trajectories modeled using LGM under different sample size, number of time points, and growth trajectory scenarios. The accuracy of the information criteria generally improved as sample size increased. The cubic and linear growth models were distinguished most accurately by the information criteria. All of the nonlinear models were more easily distinguished as the number of time points increased. The comparative performance of the six information criteria was dependent upon the manipulated conditions. Implications of the findings are discussed.     

Delay-dependent robust control for uncertain discrete singular systems with time-varying delay

The design problem of delay-dependent robust control For uncertain discrete singular systems with time-varying delay is addressed in this paper. The uncertainty is assumed to be norm-bounded. By establishing a finite sum inequality based on quadratic terms, a new delay-dependent robust stability condition is derived and expressed in terms of linear matrix inequalities （LMIs）. A suitable robust state feedback control law is presented, which guarantees that the resultant closed-loop system is regular, causal and stable for all admissible uncertainties. Numerical examples are given to demonstrate the applicability of the proposed method.     

Efficiency of digital and non-digital educational games: A comparative meta-analysis and a meta-thematic analysis

Abstract

The present article attempts to reinterpret the findings of most recent studies investigating effect of using games for teaching purposes. A methodological approach combining a meta-analysis of quantitative data with qualitative ones was adopted in order to present the broadest picture of the current research on educational use of games. To this end, we conducted a meta-analysis of 180 effect size comparisons out of 154 empirical studies on the effect of both digital and non-digital games on academic achievement conducted during the period from 2004 to 2019 in order to determine the overall effect size of using games for teaching various subjects. The overall sample size of the studies included a total number of 12800 participants. Some moderator analyses were also carried out to determine the exact efficiency of educational games in terms of student levels, durations of implementation of game activities, school subjects in which games were used, class sizes, kinds of games and achievement tests used. The findings suggest that educational games have a positive effect on academic achievement and this effect is at a medium level (g?=?0.695). The highest effect sizes were observed in foreign language courses (g?=?0.87), small (less than 50) class sizes (g?=?0.87), and in non-digital games (g?=?0.90). Moreover, we conducted a meta-thematic analysis based on document analysis of qualitative studies in order to further consolidate the findings of the meta-analysis. The meta-thematic dimension of our study reveals cognitive contributions as well as drawbacks of game-based teaching, and provides suggestions for conducting educational games in a better way.     

Statistical Power of the Multiple Domain Latent Growth Model for Detecting Group Differences

The latent growth model (LGM) in structural equation modeling (SEM) may be extended to allow for the modeling of associations among multiple latent growth trajectories, resulting in a multiple domain latent growth model (MDLGM). While the MDLGM is conceived as a more powerful multivariate analysis technique, the examination of its methodological performance is very limited. Hence, the present study compared the power of the MDLGM with that of a set of univariate LGMs for detecting group differences in growth rates over time using a Monte Carlo study with a two-group and two-domain design. The results indicated that there were different scenarios where the power rates for the MDLGM were greater than that of the set of LGMs (and vice versa) due to a joint function of the two domains’ intercorrelation size and the group difference effect size.     

一类非线性系统的广义预测控制

对于时延的非线性系统,将其等价为含有纯滞后的时变线性系统,利用三次样条函数逼近时变参数,利用渐消记忆递推最小二乘法在线辨识多项式的参数以实现时变参数估计,将基于Hammerstein模型的非线性系统线性化.最后运用广义预测控制策略实现对该系统的仿真,结果表明被控对象在广义预测控制算法的控制下系统闭环稳定性好、稳态误差小.     

Power Computations for Polynomial Change Models in Block-Randomized Designs

Education experiments frequently assign students to treatment or control conditions within schools. Longitudinal components added in these studies (e.g., students followed over time) allow researchers to assess treatment effects in average rates of change (e.g., linear or quadratic). We provide methods for a priori power analysis in three-level polynomial change models for block-randomized designs. We discuss unconditional models and models with covariates at the second and third level. We illustrate how power is influenced by the number of measurement occasions, the sample sizes at the second and third levels, and the covariates at the second and third levels.     

PowerUp!: A Tool for Calculating Minimum Detectable Effect Sizes and Minimum Required Sample Sizes for Experimental and Quasi-Experimental Design Studies

Abstract

This paper and the accompanying tool are intended to complement existing supports for conducting power analysis tools by offering a tool based on the framework of Minimum Detectable Effect Sizes (MDES) formulae that can be used in determining sample size requirements and in estimating minimum detectable effect sizes for a range of individual- and group-random assignment design studies and for common quasi-experimental design studies. The paper and accompanying tool cover computation of minimum detectable effect sizes under the following study designs: individual random assignment designs, hierarchical random assignment designs (2-4 levels), block random assignment designs (2-4 levels), regression discontinuity designs (6 types), and short interrupted time-series designs. In each case, the discussion and accompanying tool consider the key factors associated with statistical power and minimum detectable effect sizes, including the level at which treatment occurs and the statistical models (e.g., fixed effect and random effect) used in the analysis. The tool also includes a module that estimates for one and two level random assignment design studies the minimum sample sizes required in order for studies to attain user-defined minimum detectable effect sizes.     

Sample Size Requirements in Single- and Multiphase Growth Mixture Models: A Monte Carlo Simulation Study

Just as growth mixture models are useful with single-phase longitudinal data, multiphase growth mixture models can be used with multiple-phase longitudinal data. One of the practically important issues in single- and multiphase growth mixture models is the sample size requirements for accurate estimation. In a Monte Carlo simulation study, the sample sizes required for using these models are investigated under various theoretical and realistic conditions. In particular, the relationship between the sample size requirement and the number of indicator variables is examined, because the number of indicators can be relatively easily controlled by researchers in many multiphase data collection settings such as ecological momentary assessment. The findings not only provide tangible information about required sample sizes under various conditions to help researchers, but they also increase understanding of sample size requirements in single- and multiphase growth mixture models.     

木炭颗粒对水溶液中Cd2+和Cr3+质量浓度的影响

目的及方法:采用室内模拟试验,研究木炭不同粒径和用量及不同吸附时间对水溶液中Cd2+和Cr3+质量浓度的影响。结果:木炭粒径为0.25 mm时,溶液中的Cd2+、Cr3+质量浓度最高;粒径大于0.25 mm时,Cd2+、Cr3+质量浓度随着粒径增大而减小;粒径小于0.25 mm时,Cd2+、Cr3+质量浓度随着粒径减小而减小,表明只有在粒径小于0.25 mm时,粒径越小,吸附效果越好。木炭用量达到20 g.L-1时,水溶液中Cd2+、Cr3+剩余质量浓度显著低于对照,且随着用量增加,Cd2+、Cr3+剩余质量浓度有所降低;木炭用量为40 g.L-1时,第1天至第4天,4种不同浓度Cr3+水溶液中,Cr3+质量浓度随着时间的递增而递减,随后随着时间的推移,Cr3+质量浓度呈小幅增长趋势。结论:使用木炭对水溶液中的重金属离子浓度进行吸附,需要对粒径大小、用量、吸附时间等因素进行优化,才能保证吸附效果。     

Mean Effects of Test Accommodations for ELLs and Non‐ELLs: A Meta‐Analysis of Experimental Studies

The objective was to examine the impact of different types of accommodations on performance in content tests such as mathematics. The meta‐analysis included 14 U.S. studies that randomly assigned school‐aged English language learners (ELLs) to test accommodation versus control conditions or used repeated measures in counter‐balanced order. Individual effect sizes (Glass's d) were calculated for 50 groups of ELLs and 32 groups of non‐ELLs. Individual effect sizes for English language and native language accommodations were classified into groups according to type of accommodation and timing conditions. Means and standard errors were calculated for each category. The findings suggest that accommodations that require extra printed materials need generous time limits for both the accommodated and unaccommodated groups to ensure that they are effective, equivalent in scale to the original test, and therefore more valid owing to reduced construct‐irrelevant variance. Computer‐administered glossaries were effective even when time limits were restricted. Although the Plain English accommodation had very small average effect sizes, inspection of individual effect sizes suggests that it may be much more effective for ELLs at intermediate levels of English language proficiency. For Spanish‐speaking students with low proficiency in English, the Spanish test version had the highest individual effect size (+1.45).     

二次损失下带约束增长曲线模型的线性容许Minimax估计

在二次损失下,讨论了带等式约束的增长曲线模型的参数阵在适当的线性估计类中是线性Minimax容许估计的充分必要条件.