Non-uniform Randomized Sampling for Multivariate Approximation by High Order Parzen Windows

2011 ◽  
Vol 54 (3) ◽  
pp. 566-576
Author(s):  
Xiang-Jun Zhou ◽  
Lei Shi ◽  
Ding-Xuan Zhou
Keyword(s):  
Density Function ◽  
High Order ◽  
Multivariate Approximation ◽  
Probability Measures ◽  
Multivariate Functions ◽  
Uniform Sampling ◽  
Randomized Sampling ◽  
Parzen Windows ◽  
Sampling Points ◽  
Non Uniform Sampling

AbstractWe consider approximation of multivariate functions in Sobolev spaces by high order Parzen windows in a non-uniform sampling setting. Sampling points are neither i.i.d. nor regular, but are noised from regular grids by non-uniform shifts of a probability density function. Sample function values at sampling points are drawn according to probability measures with expected values being values of the approximated function. The approximation orders are estimated by means of regularity of the approximated function, the density function, and the order of the Parzen windows, under suitable choices of the scaling parameter.

High order Parzen windows and randomized sampling

2008 ◽  
Vol 31 (4) ◽  
pp. 349-368 ◽  
Author(s):  
Xiang-Jun Zhou ◽  
Ding-Xuan Zhou
Keyword(s):  
High Order ◽  
Randomized Sampling ◽  
Parzen Windows

scholarly journals A Coupled Sampling Design for Parameter Estimation in Microalgae Growth Experiment: Maximizing the Benefits of Uniform and Non-Uniform Sampling

Water ◽  
2021 ◽  
Vol 13 (21) ◽  
pp. 2996
Author(s):  
Hao Li ◽  
Enze Zhang
Keyword(s):  
Parameter Estimation ◽  
Confidence Interval ◽  
Prior Knowledge ◽  
Sampling Design ◽  
Parameter Estimates ◽  
Parameter Distribution ◽  
Model Parameters ◽  
Uniform Sampling ◽  
Sampling Points ◽  
Non Uniform Sampling

As an important primary producer in aquatic ecosystems, the various parameters within the mathematical models are used to describe the growth of microalgae and need to be estimated by carefully designed experiments. Non-uniform sampling has proved to generate a deliberately optimized sampling temporal schedule that can benefit parameter estimation. However, the current non-uniform sampling method depends on prior knowledge of the nominal values of the model parameters. It also largely ignores the uncertainty associated with the nominal values, thus inducing unacceptable parameter estimates. This study focuses on the uncertainty problem and describes a new sampling design that couples the traditional uniform and non-uniform sampling schedules to benefit from the merits of both methods. Based on D-optimal design, we first derive the non-uniform optimal sampling points by maximizing the determinant of the Fisher information matrix. Then the confidence interval around the non-uniform sampling points is determined by Monte Carlo simulations based on the prior knowledge of parameter distribution. Finally, we wrap the non-uniform sampling points with the uniform sampling points within the confidence interval to obtain the ultimate optimal experimental design. Scenedesmus obliquus, whose growth curve follows a four-parameter model, was used as a case study. Compared with the traditional sampling design, the simulation results show that our proposed coupled sampling schedule can partly eliminate the uncertainty in parameter estimates caused by fixed systematic errors in observations. Our coupled sampling can also retain some advantages belonging to non-uniform sampling, in exploiting information maximization and managing the cost of sampling.

scholarly journals Non-uniform sampling in pulse dipolar spectroscopy by EPR: the redistribution of noise and the optimization of data acquisition

2021 ◽  
Author(s):  
Anna G. Matveeva ◽  
Victoria N. Syryamina ◽  
Vyacheslav M. Nekrasov ◽  
Michael K. Bowman
Keyword(s):  
Data Acquisition ◽  
Spectroscopy Data ◽  
Distance Spectrum ◽  
Uniform Sampling ◽  
Increased Sensitivity ◽  
Non Uniform Sampling

Non-uniform schemes for collection of pulse dipole spectroscopy data can decrease and redistribute noise in the distance spectrum for increased sensitivity and throughput.

scholarly journals An Optimized Triggering Algorithm for Event-Triggered Control of Networked Control Systems

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1262
Author(s):  
Sunil Kumar Mishra ◽  
Amitkumar V. Jha ◽  
Vijay Kumar Verma ◽  
Bhargav Appasani ◽  
Almoataz Y. Abdelaziz ◽  
...  
Keyword(s):  
Control Systems ◽  
Networked Control Systems ◽  
Networked Control ◽  
Pendulum System ◽  
Uniform Sampling ◽  
Inverted Pendulum System ◽  
Event Triggering ◽  
Non Uniform Sampling ◽  
System States ◽  
Event Triggered

This paper presents an optimized algorithm for event-triggered control (ETC) of networked control systems (NCS). Initially, the traditional backstepping controller is designed for a generalized nonlinear plant in strict-feedback form that is subsequently extended to the ETC. In the NCS, the controller and the plant communicate with each other using a communication network. In order to minimize the bandwidth required, the number of samples to be sent over the communication channel should be reduced. This can be achieved using the non-uniform sampling of data. However, the implementation of non-uniform sampling without a proper event triggering rule might lead the closed-loop system towards instability. Therefore, an optimized event triggering algorithm has been designed such that the system states are always forced to remain in stable trajectory. Additionally, the effect of ETC on the stability of backstepping control has been analyzed using the Lyapunov stability theory. Two case studies on an inverted pendulum system and single-link robot system have been carried out to demonstrate the effectiveness of the proposed ETC in terms of system states, control effort and inter-event execution time.

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