Approximate IPA: Trading Unbiasedness for Simplicity

When Perturbation Analysis (PA) yields unbiased sensitivity estimators for expected-value performance functions in discrete event dynamic systems, it can be used for performance optimization of those functions. However, when PA is known to be unbiased, the complexity of its estimators often does not scale with the system's size. The purpose of this paper is to suggest an alternative approach to optimization which balances precision with computing efforts by trading off complicated, unbiased PA estimators for simple, biased approximate estimators. Furthermore, we provide guidelines for developing such estimators, that are largely based on the Stochastic Flow Modeling framework. We suggest that if the relative error (or bias) is not too large, then optimization algorithms such as stochastic approximation converge to a (local) minimum just like in the case where no approximation is used. We apply this approach to an example of balancing loss with buffer-cost in a finite-buffer queue, and prove a crucial upper bound on the relative error. This paper presents the initial study of the proposed approach, and we believe that if the idea gains traction then it may lead to a significant expansion of the scope of PA in optimization of discrete event systems.Comment: 8 pages, 8 figure

Eksperimentasi Model Pembelajaran Kooperatif Tipe Nht Dengan Pmr Dan Tsts Dengan Pmr Ditinjau Dari Kemandirian Belajar Siswa

The objective of this research was to investigate the effect of the learning models on learning achievement in mathematics viewed from self regulated learning. The learning models compared were cooperative learning model of the NHT type by using realistic mathematics approach, TSTS type by using realistic mathematics approach and the conventional learning model. The type of the research was a quasi experimental research. The population was all of the students in grade VIII of State Junior Secondary Schools of district of Eastern Lombok in academic year 2013/2014. The size of the sample was 308 students consisted of 104 in experimental class 1, 104 in experimental class 2, and 100 in control class. The instruments used were mathematics achievement test on the topic of geometry and questionnaire of self regulated learning. The data was analyzed by using two way analysis of variance with unbalanced cells. The conclusions of the research were as follows. (1) The cooperative learning model of the NHT type with the realistic mathematics approach resulted in alearning achievement equally well as the cooperative learning model of the TSTS type with realistic mathematics approach. The cooperative learning model of the NHT type and the cooperative learning model of the TSTS type with realistic mathematics approach provided better learning achievement than the conventional learning, (2) The students with the high self regulated learning had a better learning achievement in mathematics than those with the moderate and low self regulated learning categories, and the students with the moderate self regulated learning had a better learning achievement in mathematics than those with the low self regulated learning, (3) There was an interaction among learning models and the catagories of self regulated learning on learning achievement in mathematics

The study of the structure of anxiety in athletes

Objective: to study the structure of disorders caused by anxiety in athletes. Materials and methods: the objects of the first task of the research were different terminological definitions and classifications of anxiety disorders. Comparative analysis of the definitions and concepts used in psychology, physiology, sports medicine, theory and methodology of physical education has been carried out. The second task was to determine the leading factors characterizing the psychological status of athletes, and to give them the descriptive characteristics. A factor analysis was conducted on the results of testing 79 athletes of combat sports (34 men, 45 women) using the M Luscher color test and the integrative anxiety test by AP Bizyuk, LI Wasserman, BV Iovlev. Results: Luscher's test scores (total deviation from the autogenous rate, mental performance, vegetative coefficient) explained only 14.5% of the total variance. Simultaneously, the indicator of situational anxiety from Luscher's test was not included in any factor. The informativeness of more detailed integrative anxiety test was significantly higher: its indicators were included in 3 factors, explaining totally 49.5% of the total variance, as well as in the general factor, which explains 33% of the total variance. Conclusions: the emotional component (emotions which cause situational anxiety) contributes largely to the total anxiety level, some smaller contribution accounts for the social components (fear of condemnation, dependence on the opinions of others), finally, the personal anxiety contributes to it even less

Algorithm for switching-time optimization in hybrid dynamical systems

Abstract — We consider the problem of minimizing a cost functional defined on the state trajectory of a switchedmode dynamical system with respect to the switching times. Following the derivation, in recent years, of various results concerning the gradient of the cost functional, we present a suitable algorithm, based on gradient projection, for computing local minima. Utilizing the problem’s special structure, we prove a convenient formula for the direction of descent, and apply the Armijo procedure for computing the step size. A potential extension to the optimal mode-insertion problem is discussed, and numerical examples are provided