The linearity of the master stability function

2021 ◽  
Author(s):  
Janarthanan Ramadoss ◽  
Karthikeyan Rajagopal ◽  
Hayder Natiq ◽  
Iqtadar Hussain
Keyword(s):  
Root Mean Square Error ◽  
Network Topology ◽  
Coupled Oscillators ◽  
Local Stability ◽  
Mean Square ◽  
Single Variable ◽  
Stability Function ◽  
Master Stability Function ◽  
Straight Line ◽  
Variable Coupling

Abstract The master stability function (MSF) is an approach to evaluate the local stability of the synchronization in coupled oscillators. Computing the MSF of a network according to its parameters results in a curve whose shape is dependent on the nodes’ dynamics, network topology, coupling function, and coupling strength. This paper calculates the MSF of networks of two diffusively coupled oscillators by considering different single variable and multi-variable couplings. Then, the linearity of the MSF is investigated by fitting a straight line to the MSF curve, and the root mean square error is obtained. It is observed that the multi-variable coupling with equal coefficients on all variables results in a linear MSF regardless of the dynamics of the nodes.

The Design and Experiment of a Two-Dimensional Position Sensitive Detecting (PSD) Sensor Based on Avalanche Breakdown

2014 ◽  
Vol 609-610 ◽  
pp. 1094-1099
Author(s):  
Yuan Yuan Shan ◽  
Ming Qin ◽  
Sheng Qi Chen
Keyword(s):  
Root Mean Square Error ◽  
Comsol Multiphysics ◽  
Process Conditions ◽  
Avalanche Breakdown ◽  
Mean Square ◽  
Two Dimensional ◽  
Pn Junction ◽  
Straight Line ◽  
Psd Sensor ◽  
Position Sensitive

A two-dimensional position sensitive detecting sensor (PSD) based on avalanche breakdown is introduced in this paper. The structure of the sensor is designed under the assumption that the breakdown of the PN junction in the sensor occurs at the bottom of the PN junction. The breakdown structure and characteristics of the sensor are simulated by Medici software and the doping structure and process conditions are calculated by Tsuprem4 software. By using COMSOL Multiphysics, we obtained current allocation of the straight and right angle type electrodes, which is corresponding to the optimal structure. In simulation, the root mean square error of the rectangular-shaped electrode and the straight line-shaped electrode are 0.198, 0.145 respectively. Experiment results show that in the 50% photosensitive area with the center as the origin, the rectangular-shaped electrode error is much smaller than a straight line-shaped electrode and fits in to linear relationship better. But the error of the angle the boundary of the electrode is significantly worse than the line-shaped electrode.

SYNCHRONIZATION STABILITY IN COUPLED OSCILLATOR ARRAYS: SOLUTION FOR ARBITRARY CONFIGURATIONS

2000 ◽  
Vol 10 (02) ◽  
pp. 273-290 ◽  
Author(s):  
LOU PECORA ◽  
TOM CARROLL ◽  
GREGG JOHNSON ◽  
DOUG MAR ◽  
KENNETH S. FINK
Keyword(s):  
Coupled Oscillators ◽  
Stability Function ◽  
Crucial Issue ◽  
Asymptotic Results ◽  
Coupled Oscillator ◽  
Master Stability Function ◽  
Synchronization Problem ◽  
Oscillator Arrays ◽  
The Stability ◽  
General Guidance

The stability of the state of motion in which a collection of coupled oscillators are in identical synchrony is often a primary and crucial issue. When synchronization stability is needed for many different configurations of the oscillators the problem can become computationally intense. In addition, there is often no general guidance on how to change a configuration to enhance or diminsh stability, depending on the requirements. We have recently introduced a concept called the Master Stability Function that is designed to accomplish two goals: (1) decrease the numerical load in calculating synchronization stability and (2) provide guidance in designing coupling configurations that conform to the stability required. In doing this, we develop a very general formulation of the identical synchronization problem, show that asymptotic results can be derived for very general cases, and demonstrate that simple oscillator configurations can probe the Master Stability Function.

scholarly journals Estimation of Apple Flowering Frost Loss for Fruit Yield Based on Gridded Meteorological and Remote Sensing Data in Luochuan, Shaanxi Province, China

2021 ◽  
Vol 13 (9) ◽  
pp. 1630
Author(s):  
Yaohui Zhu ◽  
Guijun Yang ◽  
Hao Yang ◽  
Fa Zhao ◽  
Shaoyu Han ◽  
...  
Keyword(s):  
Remote Sensing ◽  
Root Mean Square Error ◽  
Mean Square Error ◽  
Root Mean Square ◽  
Minimum Temperature ◽  
Price Regulation ◽  
Flowering Period ◽  
Mean Square ◽  
Prevention Measures ◽  
Agricultural Insurance

With the increase in the frequency of extreme weather events in recent years, apple growing areas in the Loess Plateau frequently encounter frost during flowering. Accurately assessing the frost loss in orchards during the flowering period is of great significance for optimizing disaster prevention measures, market apple price regulation, agricultural insurance, and government subsidy programs. The previous research on orchard frost disasters is mainly focused on early risk warning. Therefore, to effectively quantify orchard frost loss, this paper proposes a frost loss assessment model constructed using meteorological and remote sensing information and applies this model to the regional-scale assessment of orchard fruit loss after frost. As an example, this article examines a frost event that occurred during the apple flowering period in Luochuan County, Northwestern China, on 17 April 2020. A multivariable linear regression (MLR) model was constructed based on the orchard planting years, the number of flowering days, and the chill accumulation before frost, as well as the minimum temperature and daily temperature difference on the day of frost. Then, the model simulation accuracy was verified using the leave-one-out cross-validation (LOOCV) method, and the coefficient of determination (R2), the root mean square error (RMSE), and the normalized root mean square error (NRMSE) were 0.69, 18.76%, and 18.76%, respectively. Additionally, the extended Fourier amplitude sensitivity test (EFAST) method was used for the sensitivity analysis of the model parameters. The results show that the simulated apple orchard fruit number reduction ratio is highly sensitive to the minimum temperature on the day of frost, and the chill accumulation and planting years before the frost, with sensitivity values of ≥0.74, ≥0.25, and ≥0.15, respectively. This research can not only assist governments in optimizing traditional orchard frost prevention measures and market price regulation but can also provide a reference for agricultural insurance companies to formulate plans for compensation after frost.

MASTER STABILITY FUNCTIONS FOR SYNCHRONIZED COUPLED SYSTEMS

1999 ◽  
Vol 09 (12) ◽  
pp. 2315-2320 ◽  
Author(s):  
LOUIS M. PECORA ◽  
THOMAS L. CARROLL
Keyword(s):  
Simple Form ◽  
Coupled Systems ◽  
Stability Function ◽  
Coupled Oscillator ◽  
Synchronous State ◽  
Master Stability Function ◽  
Stability Functions ◽  
The Stability

We show that many coupled oscillator array configurations considered in the literature can be put into a simple form so that determining the stability of the synchronous state can be done by a master stability function which solves, once and for all, the problem of synchronous stability for many couplings of that oscillator.

scholarly journals Low Cost Automatic Reconstruction of Tree Structure by AdQSM with Terrestrial Close-Range Photogrammetry

Forests ◽  
2021 ◽  
Vol 12 (8) ◽  
pp. 1020
Author(s):  
Yanqi Dong ◽  
Guangpeng Fan ◽  
Zhiwu Zhou ◽  
Jincheng Liu ◽  
Yongguo Wang ◽  
...  
Keyword(s):  
Root Mean Square Error ◽  
Mean Square Error ◽  
Root Mean Square ◽  
Low Cost ◽  
Reference Value ◽  
Tree Height ◽  
Point Clouds ◽  
Tree Structure ◽  
Mean Square ◽  
Tree Model

The quantitative structure model (QSM) contains the branch geometry and attributes of the tree. AdQSM is a new, accurate, and detailed tree QSM. In this paper, an automatic modeling method based on AdQSM is developed, and a low-cost technical scheme of tree structure modeling is provided, so that AdQSM can be freely used by more people. First, we used two digital cameras to collect two-dimensional (2D) photos of trees and generated three-dimensional (3D) point clouds of plot and segmented individual tree from the plot point clouds. Then a new QSM-AdQSM was used to construct tree model from point clouds of 44 trees. Finally, to verify the effectiveness of our method, the diameter at breast height (DBH), tree height, and trunk volume were derived from the reconstructed tree model. These parameters extracted from AdQSM were compared with the reference values from forest inventory. For the DBH, the relative bias (rBias), root mean square error (RMSE), and coefficient of variation of root mean square error (rRMSE) were 4.26%, 1.93 cm, and 6.60%. For the tree height, the rBias, RMSE, and rRMSE were—10.86%, 1.67 m, and 12.34%. The determination coefficient (R2) of DBH and tree height estimated by AdQSM and the reference value were 0.94 and 0.86. We used the trunk volume calculated by the allometric equation as a reference value to test the accuracy of AdQSM. The trunk volume was estimated based on AdQSM, and its bias was 0.07066 m3, rBias was 18.73%, RMSE was 0.12369 m3, rRMSE was 32.78%. To better evaluate the accuracy of QSM’s reconstruction of the trunk volume, we compared AdQSM and TreeQSM in the same dataset. The bias of the trunk volume estimated based on TreeQSM was −0.05071 m3, and the rBias was −13.44%, RMSE was 0.13267 m3, rRMSE was 35.16%. At 95% confidence interval level, the concordance correlation coefficient (CCC = 0.77) of the agreement between the estimated tree trunk volume of AdQSM and the reference value was greater than that of TreeQSM (CCC = 0.60). The significance of this research is as follows: (1) The automatic modeling method based on AdQSM is developed, which expands the application scope of AdQSM; (2) provide low-cost photogrammetric point cloud as the input data of AdQSM; (3) explore the potential of AdQSM to reconstruct forest terrestrial photogrammetric point clouds.

scholarly journals Rapid Biochemical Methane Potential Evaluation of Anaerobic Co-Digestion Feedstocks Based on Near Infrared Spectroscopy and Chemometrics

Energies ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1460
Author(s):  
Jinming Liu ◽  
Changhao Zeng ◽  
Na Wang ◽  
Jianfei Shi ◽  
Bo Zhang ◽  
...  
Keyword(s):  
Infrared Spectroscopy ◽  
Variable Selection ◽  
Root Mean Square Error ◽  
Least Squares ◽  
Mean Square Error ◽  
Near Infrared Spectroscopy ◽  
Near Infrared ◽  
Mean Square ◽  
Biochemical Methane Potential ◽  
Methane Potential

Biochemical methane potential (BMP) of anaerobic co-digestion (co-AD) feedstocks is an essential basis for optimizing ratios of materials. Given the time-consuming shortage of conventional BMP tests, a rapid estimated method was proposed for BMP of co-AD—with straw and feces as feedstocks—based on near infrared spectroscopy (NIRS) combined with chemometrics. Partial least squares with several variable selection algorithms were used for establishing calibration models. Variable selection methods were constructed by the genetic simulated annealing algorithm (GSA) combined with interval partial least squares (iPLS), synergy iPLS, backward iPLS, and competitive adaptive reweighted sampling (CARS), respectively. By comparing the modeling performances of characteristic wavelengths selected by different algorithms, it was found that the model constructed using 57 characteristic wavelengths selected by CARS-GSA had the best prediction accuracy. For the validation set, the determination coefficient, root mean square error and relative root mean square error of the CARS-GSA model were 0.984, 6.293 and 2.600, respectively. The result shows that the NIRS regression model—constructed with characteristic wavelengths, selected by CARS-GSA—can meet actual detection requirements. Based on a large number of samples collected, the method proposed in this study can realize the rapid and accurate determination of the BMP for co-AD raw materials in biogas engineering.

scholarly journals Quality of wood in the stands of poplar clones

2008 ◽  
Vol 54 (No. 1) ◽  
pp. 9-16
Author(s):  
R. Petráš ◽  
J. Mecko ◽  
V. Nociar
Keyword(s):  
Root Mean Square Error ◽  
Systematic Error ◽  
Mean Square Error ◽  
Statistical Tests ◽  
Mean Square ◽  
Poplar Clones ◽  
Mean Diameter ◽  
Empirical Material ◽  
Relative Root

The results obtained in research on the quality of raw timber by means of the structure of assortments for the stands of poplar clones Robusta and I-214 are presented in the paper. Models for an estimation of the structure of basic assortments of poplar stands were constructed separately for each clone in dependence on mean diameter, quality of stems, and damage to stems in the stand. The clone Robusta has higher proportions of higher-quality assortments than the clone I-214. The accuracy of models was determined on empirical material. It was confirmed by statistical tests that the models did not have a systematic error. The relative root mean-square error for main assortments of the clone I-214 is 15–27% and Robusta 13–24%.

Comparison of Thresholding and Edge Detection Segmentation Techniques

2013 ◽  
Vol 860-863 ◽  
pp. 2783-2786
Author(s):  
Yu Bing Dong ◽  
Hai Yan Wang ◽  
Ming Jing Li
Keyword(s):  
Image Segmentation ◽  
Root Mean Square Error ◽  
Edge Detection ◽  
Mean Square Error ◽  
Root Mean Square ◽  
Experimental Results ◽  
Mean Square ◽  
Segmentation Method ◽  
Segmentation Algorithms

Edge detection and thresholding segmentation algorithms are presented and tested with variety of grayscale images in different fields. In order to analyze and evaluate the quality of image segmentation, Root Mean Square Error is used. The smaller error value is, the better image segmentation effect is. The experimental results show that a segmentation method is not suitable for all images segmentation.

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