SOLVING SYSTEMS OF PHASELESS EQUATIONS VIA RIEMANNIAN OPTIMIZATION WITH OPTIMAL SAMPLING COMPLEXITY

A Riemannian gradient descent algorithm and a truncated variant are presented to solve systems of phaseless equations|Ax|^(2)=y.The algorithms are developed by exploiting the inherent low rank structure of the problem based on the embedded manifold of rank-1 positive semidefinite matrices.Theoretical recovery guarantee has been established for the truncated variant,showing that the algorithm is able to achieve successful recovery when the number of equations is proportional to the number of unknowns.Two key ingredients in the analysis are the restricted well conditioned property and the restricted weak correlation property of the associated truncated linear operator.Empirical evaluations show that our algorithms are competitive with other state-of-the-art first order nonconvex approaches with provable guarantees.

Spatial Variability of Soil Properties at Capulin Volcano,New Mexico,USA:Implications for Sampling Strategy

Non-agricultural lands are surveyed sparsely in general.Meanwhile,soils in these areas usually exhibit strong spatial variability which requires more samples for producing acceptable estimates.Capulin Volcano National Monument,as a typical sparsely-surveyed area,was chosen to assess spatial variability of a variety of soil properties,and furthermore,to investigate its implications for sampling design.One hundred and forty one composited soil samples were collected across the Monument and the surrounding areas.Soil properties including pH,organic matter content,extractable elements such as calcium (Ca),magnesium (Mg),potassium (K),sodium (Na),phosphorus (P),sulfur (S),zinc (Zn),and copper (Cu),as well as sand,silt,and clay percentages were analyzed for each sample.Semivariograms of all properties were constructed,standardized,and compared to estimate the spatial variability of the soil properties in the area.Based on the similarity among standardized semivariograms,we found that the semivariograms could be generalized for physical and chemical properties,respectively.The generalized semivariogram for physical properties had a much greater sill value (2.635) and effective range (7 500 m) than that for chemical properties.Optimal sampling density (OSD),which is derived from the generalized semivariogram and defines the relationship between sampling density and expected error percentage,was proposed to represent,interpret,and compare soil spatial variability and to provide guidance for sample scheme design.OSDs showed that chemical properties exhibit a stronger local spatial variability than soil texture parameters,implying more samples or analysis are required to achieve a similar level of precision.

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.

Free clustering optimal particle probability hypothesis density(PHD) filter

As to the fact that it is difficult to obtain analytical form of optimal sampling density and tracking performance of standard particle probability hypothesis density(P-PHD) filter would decline when clustering algorithm is used to extract target states,a free clustering optimal P-PHD(FCO-P-PHD) filter is proposed.This method can lead to obtainment of analytical form of optimal sampling density of P-PHD filter and realization of optimal P-PHD filter without use of clustering algorithms in extraction target states.Besides,as sate extraction method in FCO-P-PHD filter is coupled with the process of obtaining analytical form for optimal sampling density,through decoupling process,a new single-sensor free clustering state extraction method is proposed.By combining this method with standard P-PHD filter,FC-P-PHD filter can be obtained,which significantly improves the tracking performance of P-PHD filter.In the end,the effectiveness of proposed algorithms and their advantages over other algorithms are validated through several simulation experiments.

Distributed model predictive control based on adaptive sampling mechanism

In this work,an adaptive sampling control strategy for distributed predictive control is proposed.According to the proposed method,the sampling rate of each subsystem of the accused object is determined based on the periodic detection of its dynamic behavior and calculations made using a correlation function.Then,the optimal sampling interval within the period is obtained and sent to the corresponding sub-prediction controller,and the sampling interval of the controller is changed accordingly before the next sampling period begins.In the next control period,the adaptive sampling mechanism recalculates the sampling rate of each subsystem’s measurable output variable according to both the abovementioned method and the change in the dynamic behavior of the entire system,and this process is repeated.Such an adaptive sampling interval selection based on an autocorrelation function that measures dynamic behavior can dynamically optimize the selection of sampling rate according to the real-time change in the dynamic behavior of the controlled object.It can also accurately capture dynamic changes,meaning that each sub-prediction controller can more accurately calculate the optimal control quantity at the next moment,significantly improving the performance of distributed model predictive control(DMPC).A comparison demonstrates that the proposed adaptive sampling DMPC algorithm has better tracking performance than the traditional DMPC algorithm.

Optimizing the atmospheric sampling sites using fuzzy mathe-matic methods

A new approach applying fuzzy mathematic theorems, including the Primary Matrix Element Theorem and the Fisher Classification Method, was established to solve the optimization problem of atmospheric environmental sampling sites. According to its basis, an application in the optimization of sampling sites in the atmospheric environmental monitoring was discussed. The method was proven to be suitable and effective. The results were admitted and applied by the Environmental Protection Bureau (EPB) of many cities of China. A set of computer software of this approach was also completely compiled and used.

Optimization of the Sampling Method for Genetic Variation Survey in Maize Populations Using SSR Markers

In this study, single-plant DNA sampling method, multi-plant leaf-mixing DNA sampling method, and single-plant DNA-mixing sampling method were adopted, to analyze the genetic variations of Meng A population and C population 1 using SSR markers and establish the optimal technological system for analyzing genetic diversity of maize populations. DNA samples in different treatments were amplified using 34 SSR primers which were uniformly distributed in ten chromosomes of maize. Polyacrylamidc gel electrophoresis was performed to analyze the polymorphism information content and genetic similarity coefficient of 60 individuals and compare the numbers of alleles amplified from DNA samples in different treatments. The results indicated that Meng A population and C population 1 both had relatively abundant genetic variations and the established technological system could be applied in researches of maize genetic diversity. Extracting DNA samples from mixed leaves of 12 individuals with five replications is the best sampling method, which could achieve similar results to mixed DNA samples of 12 individuals. This sampling method can be applied to analyze the genetic relationship among a large number of maize populations, which can not only reduce the workload, but also significantly improve the efficiency.

Optimization on the Impeller of a Low-specific-speed Centrifugal Pump for Hydraulic Performance Improvement

In order to widen the high-efficiency operating range of a low-specific-speed centrifugal pump, an optimization process for considering efficiencies under 1.0Qd and 1.4Qd is proposed. Three parameters, namely, the blade outlet width b2, blade outlet angle β2, and blade wrap angle φ, are selected as design variables. Impellers are generated using the optimal Latin hypercube sampling method. The pump efficiencies are calculated using the software CFX 14.5 at two operating points selected as objectives. Surrogate models are also constructed to analyze the relationship between the objectives and the design variables. Finally, the particle swarm optimization algorithm is applied to calculate the surrogate model to determine the best combination of the impeller parameters. The results show that the performance curve predicted by numerical simulation has a good agreement with the experimental results. Compared with the efficiencies of the original impeller, the hydraulic efficiencies of the optimized impeller are increased by 4.18% and 0.62% under 1.0Qd and 1.4Qd, respectively. The comparison of inner flow between the original pump and optimized one illustrates the improvement of performance. The optimization process can provide a useful reference on performance improvement of other pumps, even on reduction of pressure fluctuations.

Optimization of stratification scheme for a fishery-independent survey with multiple objectives

Fishery-independent surveys are often used for collecting high quality biological and ecological data to support fisheries management. A careful optimization of fishery-independent survey design is necessary to improve the precision of survey estimates with cost-effective sampling efforts. We developed a simulation approach to evaluate and optimize the stratification scheme for a fishery-independent survey with multiple goals including estimation of abundance indices of individual species and species diversity indices. We compared the performances of the sampling designs with different stratification schemes for different goals over different months. Gains in precision of survey estimates from the stratification schemes were acquired compared to simple random sampling design for most indices. The stratification scheme with five strata performed the best. This study showed that the loss of precision of survey estimates due to the reduction of sampling efforts could be compensated by improved stratification schemes, which would reduce the cost and negative impacts of survey trawling on those species with low abundance in the fishery-independent survey. This study also suggests that optimization of a survey design differed with different survey objectives. A post-survey analysis can improve the stratification scheme of fishery-independent survey designs.

The Simulation of Five Tropical Cyclones by Sample Optimization of Ensemble Forecasting Based on the Observed Track and Intensity

The quality of ensemble forecasting is seriously affected by sample quality.In this study,the distributions of ensemble members based on the observed track and intensity of tropical cyclones(TCs)were optimized and their influence on the simulation results was analyzed.Simulated and observed tracks and intensities of TCs were compared and these two indicators were combined and weighted to score the sample.Samples with higher scores were retained and samples with lower scores were eliminated to improve the overall quality of the ensemble forecast.For each sample,the track score and intensity score were added as the final score of the sample with weight proportions of 10 to 0,9 to 1,8 to 2,7 to 3,6 to 4,5 to 5.These were named as“tr”,“91”,“82”,“73”,“64”,and“55”,respectively.The WRF model was used to simulate five tropical cyclones in the northwestern Pacific to test the ability of this scheme to improve the forecast track and intensity of these cyclones.The results show that the sample optimization effectively reduced the track and intensity error,“55”usually had better performance on the short-term intensity prediction,and“tr”had better performance in short-term track prediction.From the overall performance of the track and intensity simulation,“91”was the best and most stable among all sample optimization schemes.These results may provide some guidance for optimizing operational ensemble forecasting of TCs.

Impacts of sample size for stomach content analysis on the estimation of ecosystem indices

This study used Ecopath model of the Jiaozhou Bay as an example to evaluate the effect of stomach sample size of three fish species on the projection of this model. The derived ecosystem indices were classified into three categories:(1) direct indices, like the trophic level of species, influenced by stomach sample size directly;(2)indirect indices, like ecology efficiency(EE) of invertebrates, influenced by the multiple prey-predator relationships;and(3) systemic indices, like total system throughout(TST), describing the status of the whole ecosystem. The influences of different stomach sample sizes on these indices were evaluated. The results suggest that systemic indices of the ecosystem model were robust to stomach sample sizes, whereas specific indices related to species were indicated to be with low accuracy and precision when stomach samples were insufficient.The indices became more uncertain when the stomach sample sizes varied for more species. This study enhances the understanding of how the quality of diet composition data influences ecosystem modeling outputs. The results can also guide the design of stomach content analysis for developing ecosystem models.

STACKING SEQUENCE OPTIMIZA-TION OF LAMINATED COMPOSITE CYLINDER SHELL FOR MAXIMAL BUCKLING LOAD

A new optimization method for the optimization of stacking of composite glass fiber laminates is developed. The fiber orientation and angle of the layers of the cylindrical shells are sought considering the buckling load. The proposed optimization algorithm applies both finite element analysis and the mode-pursuing sampling （MPS）method. The algorithms suggest the optimal stacking sequence for achieving the maximal buckling load. The procedure is implemented by integrating ANSYS and MATLAB. The stacking sequence designing for the symmetric angle-ply three-layered and five-layered composite cylinder shells is presented to illustrate the optimization process, respectively. Compared with the genetic algorithms, the proposed optimization method is much faster and efficient for composite staking sequence plan.

SAMPLE OPTIMIZATION OF ENSEMBLE FORECAST TO SIMULATE TROPICAL STORMS(MERBOK, MAWAR, AND GUCHOL) USING THE OBSERVED TRACK

Nowadays,ensemble forecasting is popular in numerical weather prediction(NWP).However,an ensemble may not produce a perfect Gaussian probability distribution due to limited members and the fact that some members significantly deviate from the true atmospheric state.Therefore,event samples with small probabilities may downgrade the accuracy of an ensemble forecast.In this study,the evolution of tropical storms(weak typhoon)was investigated and an observed tropical storm track was used to limit the probability distribution of samples.The ensemble forecast method used pure observation data instead of assimilated data.In addition,the prediction results for three tropical storm systems,Merbok,Mawar,and Guchol,showed that track and intensity errors could be reduced through sample optimization.In the research,the vertical structures of these tropical storms were compared,and the existence of different thermal structures was discovered.One possible reason for structural differences is sample optimization,and it may affect storm intensity and track.

Non-destructive method of small sample sets for the maize moisture content measurement during filling based on NIRS

In maize breeding,limitations on sampling quantity and associated costs for measuring maize grain moisture during filling are imposed by factors like the planting area of new varieties,maize plant density,effective experimental spikes,and other conditions.However,the conventional method of detecting moisture content in maize grains is slow,damages seeds,and necessitates many sample sets,particularly for high moisture content determination.Thus,a strong demand exists for a non-destructive quantitative analysis model of maize moisture content using a small sample set during grain filling.The Bayes-Merged-Bootstrap(BMB)sample optimization method,which built upon the Bayes-Bootstrap sampling method and the concept of merging,was proposed.A critical concern in dealing with small samples is the relationship between data distribution,minimum sample value,and sample size,which has been thoroughly analyzed.Compared to the Bayes-Bootstrap sample selection method,the BMB method offers distinct advantages in the optimized selection of small samples for non-destructive detection.The quantitative analysis model for maize grain moisture content was established based on the support vector machine regression.Results demonstrate that when the optimal resampling size is 1000 times or more than the original sample size using the BMB method,the model exhibits strong predictive capabilities,with a determination coefficient(R2)>0.989 and a relative prediction determination(RPD)>2.47.The results of the 3 varieties experiment demonstrate the generality of the model.Therefore,it can be applied effectively in practical maize breeding and determining grain moisture content during maize machine harvesting.

Optimization of sampling frequency for routine river water quality monitoring

Sampling frequency is an important factor to be considered during the design of a water monitoring network,and the cost-effective selection of possible ways and means for the optimization of sampling frequency is still needed.This paper introduces water pollution index deviation ratio comparison(WPI DRC),a procedure for the optimization of sampling frequency for a routine river water quality monitoring system.Sampling frequency optimized using WPI DRC at monitoring station X5 in the mainstream of Xiangjiang River is compared with that established using the traditional Statistical Algorithm method.The result of comparison indicates that WPI DRC is more feasible than the traditional one.And then,the sampling frequencies for other 16 monitoring stations also have been optimized,and the results show the sampling frequencies of all the stations except that X4 are reduced,and there is no unacceptable difference between water quality evaluation results at 17 stations before and after the optimization.Therefore,it is concluded that WPI DRC is an effective optimization process with operable results,which can be used to fulfill the requirement of practical monitoring work.

Contribution to sample failure probability plot and its solution by Kriging method

To analyze the effect of the region of the model inputs on the model output,a novel concept about contribution to the sample failure probability plot(CSFP) is proposed based on the contribution to the sample mean plot(CSM) and the contribution to the sample variance plot(CSV).The CSFP can be used to analyze the effect of the region of the model inputs on the failure probability.After the definition of CSFP,its property and the differences between CSFP and CSV/CSM are discussed.The proposed CSFP can not only provide the information about which input affects the failure probability mostly,but also identify the contribution of the regions of the input to the failure probability mostly.By employing the Kriging model method on optimized sample points,a solution for CSFP is obtained.The computational cost for solving CSFP is greatly decreased because of the efficiency of Kriging surrogate model.Some examples are used to illustrate the validity of the proposed CSFP and the applicability and feasibility of the Kriging surrogate method based solution for CSFP.

A novel cooperative mid-course guidance scheme for multiple intercepting missiles

In the interception engagement,if the target movement information is not accurate enough for the mid-course guidance of intercepting missiles,the interception mission may fail as a result of large handover errors.This paper proposes a novel cooperative mid-course guidance scheme for multiple missiles to intercept a target under the condition of large detection errors.Under this scheme,the launch and interception moments are staggered for different missiles.The earlier launched missiles can obtain a relatively accurate detection to the target during their terminal guidance,based on which the latter missiles are permitted to eliminate the handover error in the mid-course guidance.A significant merit of this scheme is that the available resources are fully exploited and less missiles are needed to achieve the interception mission.To this end,first,the design of cooperative handover parameters is formulated as an optimization problem.Then,an algorithm based on Monte Carlo sampling and stochastic approximation is proposed to solve this optimization problem,and the convergence of the algorithm is proved as well.Finally,simulation experiments are carried out to validate the effectiveness of the proposed cooperative scheme and algorithm.

Error Rate Estimation in Quantum Key Distribution with Finite Resources

The goal of quantum key distribution(QKD) is to generate secret key shared between two distant players,Alice and Bob. We present the connection between sampling rate and erroneous judgment probability when estimating error rate with random sampling method, and propose a method to compute optimal sampling rate, which can maximize final secure key generation rate. These results can be applied to choose the optimal sampling rate and improve the performance of QKD system with finite resources.

Estimation of optimum sample size allocation:An illustration with body mass index for evaluating the effect of a dietetic supplement

In many medical researches,it is needed to determine the optimal sample size allocation in a heterogeneous population.This paper proposes the algorithm for optimal sample size allocation.We consider the optimal allocation problem as an optimization problem and the solution is obtained by using Bisection,Secant,Regula-Falsi and other numerical methods.The performance of the algorithm for different numerical methods are analyzed and evaluated in terms of computing time,number of iterations and gain in accuracy using stratification.The efficacy of algorithm is evaluated for the response in terms of body mass index(BMI)to the dietetic supplement with diabetes mellitus,HIV/AIDS and cancer post-operatory recovery patients.