Sample Numbers and Optimal Lagrange Interpolation of Sobolev Spaces W_(1)^(r)

This paper investigates the optimal recovery of Sobolev spaces W_(1)^(r)[-1,1],r∈N in the space L_(1)[-1,1].They obtain the values of the sampling numbers of W_(1)^(r)[-1,1]in L_(1)[-1,1]and show that the Lagrange interpolation algorithms based on the extreme points of Chebyshev polynomials are optimal algorithms.Meanwhile,they prove that the extreme points of Chebyshev polynomials are optimal Lagrange interpolation nodes.

Designing Adaptive Multiple Dependent State Sampling Plan for Accelerated Life Tests

A novel adaptive multiple dependent state sampling plan(AMDSSP)was designed to inspect products from a continuous manufacturing process under the accelerated life test(ALT)using both double sampling plan(DSP)and multiple dependent state sampling plan(MDSSP)concepts.Under accelerated conditions,the lifetime of a product follows the Weibull distribution with a known shape parameter,while the scale parameter can be determined using the acceleration factor(AF).The Arrhenius model is used to estimate AF when the damaging process is temperature-sensitive.An economic design of the proposed sampling plan was also considered for the ALT.A genetic algorithm with nonlinear optimization was used to estimate optimal plan parameters to minimize the average sample number(ASN)and total cost of inspection(TC)under both producer’s and consumer’s risks.Numerical results are presented to support the AMDSSP for the ALT,while performance comparisons between the AMDSSP,the MDSSP and a single sampling plan(SSP)for the ALT are discussed.Results indicated that the AMDSSP was more flexible and efficient for ASN and TC than the MDSSP and SSP plans under accelerated conditions.The AMDSSP also had a higher operating characteristic(OC)curve than both the existing sampling plans.Two real datasets of electronic devices for the ALT at high temperatures demonstrated the practicality and usefulness of the proposed sampling plan.

Fault Diagnosis of 5G Networks Based on Digital Twin Model

Fault diagnosis of 5G networks faces the challenges of heavy reliance on human experience and insufficient fault samples and relevant monitoring data.The digital twin technology can realize the interaction between virtual space and physical space through the fusion of model and data,providing a new paradigm for fault diagnosis.In this paper,we first propose a network digital twin model and apply it to 5G network diagnosis.We then use an improved Average Wasserstein GAN with Gradient Penalty(AWGAN-GP)method to discover and predict failures in the twin network.Finally,we use XGBoost algorithm to locate the faults in physical network in real time.Extensive simulation results show that the proposed approach can significantly increase fault prediction and diagnosis accuracy in the case of a small number of labeled failure samples in 5G networks.

Key parameter optimization and analysis of stochastic seismic inversion

Stochastic seismic inversion is the combination of geostatistics and seismic inversion technology which integrates information from seismic records, well logs, and geostatistics into a posterior probability density function （PDF） of subsurface models. The Markov chain Monte Carlo （MCMC） method is used to sample the posterior PDF and the subsurface model characteristics can be inferred by analyzing a set of the posterior PDF samples. In this paper, we first introduce the stochastic seismic inversion theory, discuss and analyze the four key parameters： seismic data signal-to-noise ratio （S/N）, variogram, the posterior PDF sample number, and well density, and propose the optimum selection of these parameters. The analysis results show that seismic data S/N adjusts the compromise between the influence of the seismic data and geostatistics on the inversion results, the variogram controls the smoothness of the inversion results, the posterior PDF sample number determines the reliability of the statistical characteristics derived from the samples, and well density influences the inversion uncertainty. Finally, the comparison between the stochastic seismic inversion and the deterministic model based seismic inversion indicates that the stochastic seismic inversion can provide more reliable information of the subsurface character.

Spatial Distribution Pattern and Sampling Technique of Spring Wheat Aphid

[ Objective] The aim was to study the spatial distribution pattern and field sampling method of aphid population in spring wheat. [ Method] The aphid quantity in tested wheat field was calculated, the field distribution pattern of wheat aphid was calculated by using aggregated index method, the aggregated reason was analyzed and the field theoretical sampling number was ascertained. [ Result] The wheat aphid population showed aggregation distribution and negative binomial distribution, and such aggregation distribution was induced by interaction of its behavior and environmental factors. The field theoretical sampling number of wheat aphid was related to sample variance and permissible error; the less the sam- ple variance [ S^2 ） was, the less the permissible error [ d＇） was, the bigger the theoretical sampling number without replacement was; when the initial population numbers were different, the theoretical sampling numbers were also different; after the permissible error being set, the bigger the sample variance （ S^2 ） was, the bigger the theoretical sampling number was. [ Conclusion] This study supplied scientific basis for prediction and field control of wheat aphid.

On Spatial Distribution Pattern of Broccoli Clubroot Disease and and the Sampling Technique

[Objective] To further improve the prediction and forecast and continuous control ability of broccoli clubroot disease. [Methods] The spatial distribution pattern of diseased or infected plants was analyzed using the least square method, fre- quency distribution, aggregation index, m＊-m regression analysis and Taylor＇s pow- er law model. [Result] The field distribution of broccoli plants with clubroot disease tended to be aggregated distribution, m＇-m regression analysis showed that the el- ementary composition of the spatial distribution of diseased or infected plants was individual colony, the individuals attracted each other; the disease had obvious dis- ease focus in the field, and the individual colony showed uniform distribution pattern in the field. Taylor＇s power law showed that the spatial pattern of individual dis- eased or infected plant with clubroot disease tended to be uniform distribution with the increase of the density. On the basis of this, Iwao optimal theoretical sampling model and sequential sampling model were established, namely N =273.954 1/m- 59.698 5, To （N）=0.368 4N±1.926 8√N, respectively, it meant that when surveying N plants, if the accumulative incidence rate exceeded upper bound, the field can be set as control object; if the accumulative incidence rate didn＇t reach lower bound, it can be set as uncontrol field; if the accumulative incidence rate was between upper bound and lower bound, it should be surveyed continuously until the maximum sample size （mo=0.368 4） appeared, that was, the disease incidence was 15%, so the sampling number should be 684 plants. [Conclusion] The research results had very important instructive meaning for disease control.

Impacts of the sampling design on the abundance index estimation of Portunus trituberculatus using bottom trawl

In the survey of fishery resources,the sampling design will directly impact the accuracy of the estimation of the abundance.Therefore,it is necessary to optimize the sampling design to increase the quality of fishery surveys.The distribution and abundance of fisheries resource estimated based on the bottom trawl survey data in the Changjiang River(Yangtze River)Estuary-Hangzhou Bay and its adjacent waters in 2007 were used to simulate the"true"situation.Then the abundance index of Portunus trituberculatus were calculated and compared with its true index to evaluate the impacts of different sampling designs on the abundance estimation.Four sampling methods(including fixed-station sampling,simple random sampling,stratified fixed-station sampling,and stratified random sampling)were simulated.Three numbers of stations(9,16 and 24)were assumed for the scenarios of fixed-station sampling and simple random sampling without stratification.While 16 stations were assumed for the scenarios with stratification.Three reaction distances(1.5 m,3 m and 5 m)of P.trituberculatus to the bottom line of trawl were also assumed to adapt to the movement ability of the P.trituberculatus for different ages,seasons and substrate conditions.Generally speaking,compared with unstratified sampling design,the stratified sampling design resulted in more accurate abundance estimation of P.trituberculatus,and simple random sampling design is better than fixed-station sampling design.The accuracy of the simulated results was improved with the increase of the station number.The maximum relative estimation error(REE)was 163.43%and the minimum was 49.40%for the fixed-station sampling scenario with 9 stations,while 38.62%and 4.15%for 24 stations.With the increase of reaction distance,the relative absolute bias(RAB)and REE gradually decreased.Resource-intensive area and the seasons with high density variances have significant impacts on simulation results.Thus,it will be helpful if there are prior information or pre-survey results about density distribution.The current study can provide reference for the future sampling design of bottom trawl of P.trituberculatus and other species.

Impacts of sampling design on the abundance estimation of Portunus trituberculatus using crab pots

Fishery-independent surveys can provide high-quality data and support fishery assessment and management.Optimization of sampling design is crucial to increase the quality of fishery surveys.Crab pots are important fishing gears used to catch crabs.We analyzed the impacts of sampling design of crab pots on the abundance of Portunus trituberculatus in the Changjiang(Yangtze)River estuary to the Hangzhou Bay and its adjacent waters in East China Sea.The crab pots were cylindrical,240 mm in height and 600 mm in diameter of the iron ring.Our sampling designs(including fixed-station sampling,simple random sampling,stratified fixed-station sampling,and stratified random sampling),three number of stations(9,16,and 24),and three numbers of crab pots(500,1000,and 3000)were simulated and compared with the“true”abundance that obtained from bottom trawl surveys in the study area in 2007.The scenarios with 16 stations were set in stratification as a control group for comparison with unstratified designs.Results show that simple random sampling can obtain more stable results than fixed-station sampling in the abundance estimation of P.trituberculatus.In addition,stratified sampling resulted in more accurate abundance than unstratified sampling.The accuracy of the simulated results improved with the increase of the number of stations.No remarkable differences in the results were found among the scenarios of different number of crab pots at each station.However,resource-intensive areas exerted great impacts on simulation results.Thus,prior information or pre-survey results about resource abundance and density distribution are necessary.This study may serve as a reference for future sampling designs of crab pots of P.trituberculatus and other species.

Optimal Recovery of Functions on the Sphere on a Sobolev Spaces with a Gaussian Measure in the Average Case Setting

In this paper, we study optimal recovery （reconstruction） of functions on the sphere in the average case setting. We obtain the asymptotic orders of average sampling numbers of a Sobolev space on the sphere with a Gaussian measure in the Lq （S^d-1） metric for 1 ≤ q ≤ ∞, and show that some worst-case asymptotically optimal algorithms are also asymptotically optimal in the average case setting in the Lq （S^d-1） metric for 1 ≤ q ≤ ∞.