The averaging method is one of the most powerful methods used to analyse differential equations appearing in the study of nonlinear problems. The idea behind the averaging method is to replace the original equation by an averaged equation with simple structure and close solutions. A large number of practical problems leads to differential equations with discontinuous right-hand sides. In a rigo...

In this paper we present the greedy step averaging(GSA) method, a parameter-free stochastic optimization algorithm for a variety of machine learning problems. As a gradient-based optimization method, GSA makes use of the information from the minimizer of a single sample’s loss function, and takes average strategy to calculate reasonable learning rate sequence. While most existing gradient-based...

Power electronic converters are non-linear time-dependent systems whose exact analysis without the use of computers is very difficult, and even using computer softwares requires a long time. Use of the state space averaging method, as will be mentioned, in addition to simplifying the analysis procedure which is a result of converting a time-dependent system to a time-independent one, reduces th...

Fuzzy risk analysis, as a powerful tool to address uncertain information, can provide an appropriate method for risk analysis. However, the previous fuzzy risk analysis methods still have some weaknesses. To overcome the weaknesses of existing fuzzy risk analysis methods, a novel method for ranking generalized fuzzy numbers is proposed for addressing fuzzy risk analysis problems. In the propose...

This study evaluates alternative groundwater models with different recharge and geologic components at the northern Yucca Flat area of the Death Valley Regional Flow System (DVRFS), USA. Recharge over the DVRFS has been estimated using five methods, and five geological interpretations are available at the northern Yucca Flat area. Combining the recharge and geological components together with a...

In a recent paper, Bubeck, Lee, and Singh introduced a new first order method for minimizing smooth strongly convex functions. Their geometric descent algorithm, largely inspired by the ellipsoid method, enjoys the optimal linear rate of convergence. We show that the same iterate sequence is generated by a scheme that in each iteration computes an optimal average of quadratic lower-models of th...

Control of underactuated mechanisms is one of major research topics in control engineering and robotics. A manipulator with free joints is one of such the systems and its control is di cult via ordinary nonlinear control methods. In this paper, we discuss control of free-joint manipulators whose rst joint is only actuated and the others are free joints. We apply the averaging method to analysis...

Averaging is one of the basic methods of statistical analysis of experimental data where the response of the system is periodic or quasi-periodic. As long as the noise are Gaussian, the standard averaging leads to good results and effective noise reduction. However, when the distortions have impulsive nature, then such an approach leads to a deterioration of the system. In this case the robust ...

This paper considers the problem of combining multiple models to achieve a prediction accuracy not much worse than that of the best single model for least squares regression. It is known that if the models are mis-specified, model averaging is superior to model selection. Specifically, let n be the sample size, then the worst case regret of the former decays at the rate of O(1/n) while the wors...

Stimulus-locked, response-locked, and ERP-locked averaging are effective methods for reducing artifacts in ERP analysis. However, they suffer from a magnifying-glass effect: they increase the resolution of specific ERPs at the cost of blurring other ERPs. Here we propose an extremely simple technique-binning trials based on response times and then averaging-which can significantly alleviate the...