面向人脑功能划分的人工水母搜索优化算法

doi:10.3778/j.issn.1673-9418.2201012

计算机科学与探索 ›› 2022, Vol. 16 ›› Issue (8): 1829-1841.DOI: 10.3778/j.issn.1673-9418.2201012

面向人脑功能划分的人工水母搜索优化算法

赵学武¹, 王红梅¹, 刘超慧¹, 李玲玲⁺(), 薄树奎¹, 冀俊忠²

1. 郑州航空工业管理学院智能工程学院，郑州 450046
2. 北京工业大学信息学部计算机学院，北京 100124

收稿日期:2022-01-05 修回日期:2022-04-08 出版日期:2022-08-01 发布日期:2022-08-19
通讯作者: +E-mail: 373413349@qq.com.
作者简介:赵学武（1983—），男，河南南阳人，博士，讲师，硕士生导师，CCF会员，主要研究方向为数据挖掘、机器学习、脑科学。
王红梅（1976—），女，河南镇平人，硕士，副教授，主要研究方向为数据库技术、多媒体技术。
刘超慧（1981—），男，河南项城人，硕士，副教授，硕士生导师，主要研究方向为机器学习、资源推荐。
李玲玲（1973—），女，河南开封人，博士，教授，教育部新世纪人才奖获得者，主要研究方向为计算机视觉、模式识别。
薄树奎（1976—），男，河北唐山人，博士，教授，主要研究方向为信息提取、模式识别、图像处理。
冀俊忠（1969—），男，博士，教授，博士生导师，主要研究方向为机器学习、计算智能、生物信息学、脑科学。
基金资助:
河南省科技攻关项目(202102210164);河南省科技攻关项目(202102210341);河南省科技攻关项目(212102210077);河南省科技攻关项目(202102210399);河南省科技攻关项目(212102210518);河南省科技攻关项目(222102210292);河南省科技攻关项目(192102210283);国家自然科学基金(U1904119);河南省高等学校重点科研项目基础研究计划(21A520047);河南省高等学校重点科研项目基础研究计划(20A520041);河南省高等学校重点科研项目基础研究计划(20A520040);国家大学生创新创业训练计划项目(202110485023);河南省教育科学十三五规划项目(2020YB0149)

Artificial Jellyfish Search Optimization Algorithm for Human Brain Functional Parcellation

ZHAO Xuewu¹, WANG Hongmei¹, LIU Chaohui¹, LI Lingling⁺(), BO Shukui¹, JI Junzhong²

1. School of Intelligent Engineering, Zhengzhou University of Aeronautics, Zhengzhou 450046, China
2. College of Computer in Faculty of Information Technology, Beijing University of Technology, Beijing 100124, China

Received:2022-01-05 Revised:2022-04-08 Online:2022-08-01 Published:2022-08-19
About author:ZHAO Xuewu, born in 1983, Ph.D., lecturer, M.S. supervisor, member of CCF. His research interests include data mining, machine learning and brain science.
WANG Hongmei, born in 1976, M.S., associate professor. Her research interests include database technology and multimedia technology.
LIU Chaohui, born in 1981, M.S., associate professor, M.S. supervisor. His research interests include machine learning and resource recommendation.
LI Lingling, born in 1973, Ph.D., professor, a winner of new century talent by the Ministry of Education of China. Her research interests include computer vision and pattern recognition.
BO Shukui, born in 1976, Ph.D., professor. His research interests include information extraction, pattern recognition and image processing.
JI Junzhong, born in 1969, Ph.D., professor, Ph.D. supervisor. His research interests include machine learning, computational intelligence, bio-informatics and brain science.
Supported by:
the Key Technologies Research and Development Program of Henan Province(202102210164);the Key Technologies Research and Development Program of Henan Province(202102210341);the Key Technologies Research and Development Program of Henan Province(212102210077);the Key Technologies Research and Development Program of Henan Province(202102210399);the Key Technologies Research and Development Program of Henan Province(212102210518);the Key Technologies Research and Development Program of Henan Province(222102210292);the Key Technologies Research and Development Program of Henan Province(192102210283);the National Natural Science Foundation of China(U1904119);the Basic Research Plan of Key Scientific Research Projects of Henan Universities(21A520047);the Basic Research Plan of Key Scientific Research Projects of Henan Universities(20A520041);the Basic Research Plan of Key Scientific Research Projects of Henan Universities(20A520040);the National College Students’ Innovation and Entrepreneurship Training Program(202110485023);the 13th Five Year Plan of Educational Science in Henan Province(2020YB0149)

摘要/Abstract

摘要：

人脑功能划分是揭示人脑功能分离性的重要方式。然而，现有的大多数划分方法因不能较好地处理功能磁共振影像（fMRI）数据的高维性和低信噪比性，表现出搜索能力较弱和划分结果较差的问题。为了减轻此问题，提出一种基于人工水母搜索优化（AJSO）的人脑功能划分方法。该方法首先基于预处理的fMRI数据计算功能相关矩阵，并将其映射到低维空间。然后将食物编码为由多个功能簇中心构成的聚类解，利用改进型人工水母搜索优化算法搜索更优的食物，采用融入迭代停滞的时间控制机制调控人工水母执行主动运动或被动运动，以提高全局搜索能力;针对主动运动设计适应度引导的步长确定策略，增强人工水母搜索的科学性和针对性。最后根据最小距离原则得到相关矩阵中每行数据的簇标，并将其映射到相应的体素上。在真实fMRI数据上的实验表明：与其他一些划分方法相比，新方法不仅拥有较高的搜索能力，而且可得到具有更好空间结构和更强功能一致性的划分结果。这项研究将人工水母搜索优化算法应用于人脑功能划分，提供了一种更有效的人脑功能划分方法。

关键词: 人脑功能划分, 人工水母搜索优化算法（AJSO）, 融入迭代停滞的时间控制机制, 适应度引导的步长确定策略, 海马

Abstract:

Human brain function parcellation is an important way to reveal the separation of brain functions. However, most of the existing parcellation methods can not deal with the high dimension and low signal-to-noise ratio of functional magnetic resonance imaging (fMRI) data, so they show the problem of weaker search ability and poorer parcellation results. To alleviate this problem, a human brain functional parcellation method based on artificial jellyfish search optimization (AJSO) algorithm is proposed. Firstly, a functional correlation matrix is calculated based on the preprocessed fMRI data and mapped to a low-dimensional space. Then, a food is encoded as a cluster solution composed of multiple functional cluster centers and the improved AJSO is used to search for better food. The time control mechanism integrated with iterative stagnation is used to control the artificial jellyfish to perform active or passive motion, so as to improve the global search ability. Step size determination strategy guided by fitness is designed for active movement to enhance scientific and targeted search of artificial jellyfish. Finally, according to the principle of minimum distance, the cluster label of each row data in the correlation matrix is obtained and mapped to the corresponding voxels. Experiments on real fMRI data show that compared with other partitioning methods, the new method not only has higher searching ability, but also can obtain better spatial structures and stronger functional consistency. In this study, artificial jellyfish search optimization algorithm is applied to brain functional parcellation, which provides a more effective method of brain functional parcellation.

Key words: human brain functional parcellation, artificial jellyfish search optimization (AJSO) algorithm, time control mechanism with iteration stagnation, fitness-guided step size determination strategy, hippocampus

中图分类号:

TP311

赵学武, 王红梅, 刘超慧, 李玲玲, 薄树奎, 冀俊忠. 面向人脑功能划分的人工水母搜索优化算法[J]. 计算机科学与探索, 2022, 16(8): 1829-1841.

ZHAO Xuewu, WANG Hongmei, LIU Chaohui, LI Lingling, BO Shukui, JI Junzhong. Artificial Jellyfish Search Optimization Algorithm for Human Brain Functional Parcellation[J]. Journal of Frontiers of Computer Science and Technology, 2022, 16(8): 1829-1841.

图/表 11

参考文献 38

[1]	EICKHOFF S B, YEO B T T, GENON S. Imaging-based parcellations of the human brain[J]. Nature Reviews Neuroscience, 2018, 19(11): 672-686.
[2]	赵学武, 冀俊忠, 梁佩鹏. 面向fMRI数据的人脑功能划分[J]. 科学通报, 2016, 61(18): 2035-2052.
	ZHAO X W, JI J Z, LIANG P P. The human brain functional parcellation based on fMRI data[J]. Chinese Science Bulletin, 2016, 61(18): 2035-2052.
[3]	KIM J H, LEE J M, JO H J, et al. Defining functional SMA and pre-SMA subregions in human MFC using resting state fMRI: functional connectivity-based parcellation method[J]. NeuroImage, 2010, 49(3): 2375-2386.
[4]	CAUDA F, D’AGATA F, SACCO K, et al. Functional connectivity of the insula in the resting brain[J]. NeuroImage, 2011, 55(1): 8-23.
[5]	JUNG W H, JANG J H, PARK J W, et al. Unravelling the intrinsic functional organization of the human striatum: a parcellation and connectivity study based on resting-state FMRI[J]. PLoS One, 2014, 9(9): e106768.
[6]	BOUKHDHIR A, ZHANG Y, MIGNOTTE M, et al. Unrave-ling reproducible dynamic states of individual brain functional parcellation[J]. Network Neuroscience, 2021, 5(1): 28-55.
[7]	LIU X, EICKHOFF S B, CASPERS S, et al. Functional parcellation of human and macaque striatum reveals human-specific connectivity in the dorsal caudate[J]. NeuroImage, 2021, 235: 118006.
[8]	BLUMENSATH T, JBABDI S, GLASSER M F, et al. Spatially constrained hierarchical parcellation of the brain with resting-state fMRI[J]. NeuroImage, 2013, 76: 313-324.
[9]	CRADDOCK R C, JAMES G A, HOLTZHEIMER III P E, et al. A whole brain fMRI atlas generated via spatially constrained spectral clustering[J]. Human Brain Mapping, 2012, 33(8): 1914-1928.
[10]	NEBEL M B, JOEL S E, MUSCHELLI J, et al. Disruption of functional organization within the primary motor cortex in children with autism[J]. Human Brain Mapping, 2014, 35(2): 567-580.
[11]	MEJIA A F, NEBEL M B, SHOU H, et al. Improving reliability of subject-level resting-state fMRI parcellation with shrinkage estimators[J]. NeuroImage, 2015, 112: 14-29.
[12]	REN Y, GUO L, GUO C C. A connectivity-based parcellation improved functional representation of the human cerebellum[J]. Scientific Reports, 2019, 9(1): 1-12.
[13]	HU Y, LI X, WANG L, et al. T-distribution stochastic neighbor embedding for fine brain functional parcellation on rs-fMRI[J]. Brain Research Bulletin, 2020, 162(9): 199-207.
[14]	CHENG H, LIU J. Concurrent brain parcellation and connectivity estimation via co-clustering of resting state fMRI data: a novel approach[J]. Human Brain Mapping, 2021, 42(8): 2477-2489.
[15]	RYALI S, CHEN T, SUPEKAR K, et al. A parcellation scheme based on von Mises-Fisher distributions and Markov random fields for segmenting brain regions using resting-state fMRI[J]. NeuroImage, 2013, 65: 83-96.
[16]	HONNORAT N, EAVANI H, SATTERTHWAITE T D, et al. GraSP: geodesic graph-based segmentation with shape priors for the functional parcellation of the cortex[J]. NeuroImage, 2015, 106: 207-221.
[17]	JANSSEN R J, JYLÄNKI P, KESSELS R P C, et al. Probabilistic model-based functional parcellation reveals a robust, fine-grained subdivision of the striatum[J]. NeuroImage, 2015, 119: 398-405.
[18]	赵学武, 冀俊忠, 姚垚. 基于免疫克隆选择算法搜索GMM的脑岛功能划分[J]. 浙江大学学报(工学版), 2017, 51(12): 2320-2331.
	ZHAO X W, JI J Z, YAO Y. Insula functional parcellation by searching Gaussian mixture model (GMM) using immune clonal selection (ICS) algorithm[J]. Journal of Zhejiang University (Engineering Science), 2017, 51(12): 2320-2331.
[19]	BLUMENSATH T, BEHRENS T E J, SMITH S M. Resting-state FMRI single subject cortical parcellation based on region growing[C]// Proceedings of the 15th International Conference on Medical Image Computing and Computer-Assisted Intervention, Nice, Oct 1-5, 2012. Berlin: Springer, 2012: 188-195.
[20]	BELLEC P, PERLBARG V, JBABDI S, et al. Identification of large-scale networks in the brain using fMRI[J]. NeuroImage, 2006, 29(4): 1231-1243.
[21]	BLUMENSATH T, JBABDI S, GLASSER M F, et al. Spatially constrained hierarchical parcellation of the brain with resting-state fMRI[J]. NeuroImage, 2013, 76: 313-324.
[22]	HALE J R, MAYHEW S D, MULLINGER K J, et al. Comparison of functional thalamic segmentation from seed-based analysis and ICA[J]. NeuroImage, 2015, 114: 448-465.
[23]	NOMI J S, FARRANT K, DAMARAJU E, et al. Dynamic functional network connectivity reveals unique and overlapping profiles of insula subdivisions[J]. Human Brain Mapping, 2016, 37(5): 1770-1787.
[24]	DUFF E P, TRACHTENBERG A J, MACKAY C E, et al. Task-driven ICA feature generation for accurate and interpretable prediction using fMRI[J]. NeuroImage, 2012, 60(1): 189-203.
[25]	KAZEMIVASH B, CALHOUN V D. BPARC:a novel spatio-temporal (4D) data-driven brain parcellation scheme based on deep residual networks[C]// Proceedings of the 2020 IEEE 20th International Conference on Bioinformatics and Bioengineering, Cincinnati, Oct 26-28, 2020. Piscataway: IEEE, 2020: 1071-1076.
[26]	FAN L, ZHONG Q, QIN J, et al. Brain parcellation driven by dynamic functional connectivity better capture intrinsic network dynamics[J]. Human Brain Mapping, 2021, 42(5): 1416-1433.
[27]	MISHRA A, ROGERS B P, CHEN L M, et al. Functional connectivity-based parcellation of amygdala using self-organized mapping: a data driven approach[J]. Human Brain Mapping, 2014, 35(4): 1247-1260.
[28]	GRANDE-BARRETO J. Partial volume segmentation in magnetic resonance imaging (MRI)[D]. Puebla: National Institute for Astrophysics Optics and Electronics, 2017.
[29]	CHOU J S, TRUONG D N. A novel metaheuristic optimizer inspired by behavior of jellyfish in ocean[J]. Applied Mathematics and Computation, 2021, 389(2): 125535.
[30]	ABDEL-BASSET M, MOHAMED R, ABOUHAWWASH M, et al. An improved jellyfish algorithm for multilevel thresholding of magnetic resonance brain image segmentations[J]. Computers, Materials and Continua, 2021, 68(3): 2961-2977.
[31]	FARHAT M, KAMEL S, ATALLAH A M, et al. Optimal power flow solution based on jellyfish search optimization considering un certainty of renewable energy sources[J]. IEEE Access, 2021, 9: 100911-100933.
[32]	朱佳莹, 高茂庭. 融合粒子群与改进蚁群算法的AUV路径规划算法[J]. 计算机工程与应用, 2021, 57(6): 267-273.
	ZHU J Y, GAO M T. AUV path planning based on particle swarm optimization and improved ant colony optimization[J]. Computer Engineering and Applications, 2021, 57(6): 267-273.
[33]	胡晓敏, 王明丰, 张首荣, 等. 用于文本聚类的新型差分进化粒子群算法[J]. 计算机工程与应用, 2021, 57(4): 61-67.
	HU X M, WANG M F, ZHANG S R, et al. New differential evolution with particle swarm optimization algorithm for text clustering[J]. Computer Engineering and Applications, 2021, 57(4): 61-67.
[34]	张晗, 杨继斌, 张继业, 等. 基于多种群萤火虫算法的车载燃料电池直流微电网能量管理优化[J]. 中国电机工程学报, 2021, 41(3): 13-19.
	ZHANG H, YANG J B, ZHANG J Y, et al. Multiple-population firefly algorithm-based energy management strategy for vehicle-mounted fuel cell DC microgrid[J]. Proceedings of the CSEE, 2021, 41(3): 13-19.
[35]	章呈瑞, 柯鹏, 尹梅. 改进人工蜂群算法及其在边缘计算卸载的应用[J]. 计算机工程与应用, 2022, 58(7): 150-161.
	ZHANG C R, KE P, YIN M. Improved artificial bee colony algorithm and its application in edge computing offloading[J]. Computer Engineering and Applications, 2022, 58(7): 150-161.
[36]	ZHANG Y, CASPERS S, FAN L, et al. Robust brain parcellation using sparse representation on resting-state fMRI[J]. Brain Structure and Function, 2015, 220(6): 3565-3579.
[37]	CHENG H, WU H, FAN Y. Optimizing affinity measures for parcellating brain structures based on resting state fMRI data: a validation on medial superior frontal cortex[J]. Journal of Neuroscience Methods, 2014, 237(11): 90-102.
[38]	WANG J, JU L, WANG X. An edge-weighted centroidal voronoi tessellation model for image segmentation[J]. IEEE Transactions on Image Processing, 2009, 18(8): 1844-1858.

Image	Sequence	TR/ms	No_s	FOV	No_v
F.Img	EPI	2 000	33	200×200	200
S.Img	MPRAGE	2 530	144	256×256	1

Image	Sequence	TR/ms	No_s	FOV	No_v
F.Img	EPI	2 000	33	200×200	200
S.Img	MPRAGE	2 530	144	256×256	1

K	SC	AJSO	IAJSO	SAJSO	ISAJSO
2	72 234.77±4.37E-11	72 233.47±0	72 232.89±0	72 232.57±0	72 231.50±0
3	61 362.75±5.64E-01	61 358.00±8.06E-02	61 345.10±7.96E-02	61 101.62±1.41E-02	60 913.33±1.23E-02
4	50 915.47±1.94E-01	50 836.03±6.27E-02	50 761.07±1.03E-02	50 681.75±1.25E-02	50 648.13±9.58E-02
5	44 318.16±6.90E-01	43 933.13±4.09E-02	43 875.30±2.26E-02	44 820.60±2.17E-02	43 882.83±5.59E-02
6	40 282.39±6.81E-01	40 142.90±2.09E-03	40 089.67±2.99E-03	40 107.03±7.69E-03	40 083.43±1.02E-03
7	38 630.60±1.43E-02	38 381.83±1.14E-03	37 877.73±1.19E-03	37 143.86±1.14E-03	37 114.07±1.38E-04
8	35 277.22±1.35E-02	34 625.00±2.51E-04	34 513.73±1.97E-04	34 529.80±2.96E-04	34 497.03±1.76E-04
9	33 769.14±7.19E-02	32 984.13±2.47E-04	32 916.53±2.15E-04	32 967.47±2.85E-04	32 905.37±2.66E-05

K	SC	AJSO	IAJSO	SAJSO	ISAJSO
2	72 234.77±4.37E-11	72 233.47±0	72 232.89±0	72 232.57±0	72 231.50±0
3	61 362.75±5.64E-01	61 358.00±8.06E-02	61 345.10±7.96E-02	61 101.62±1.41E-02	60 913.33±1.23E-02
4	50 915.47±1.94E-01	50 836.03±6.27E-02	50 761.07±1.03E-02	50 681.75±1.25E-02	50 648.13±9.58E-02
5	44 318.16±6.90E-01	43 933.13±4.09E-02	43 875.30±2.26E-02	44 820.60±2.17E-02	43 882.83±5.59E-02
6	40 282.39±6.81E-01	40 142.90±2.09E-03	40 089.67±2.99E-03	40 107.03±7.69E-03	40 083.43±1.02E-03
7	38 630.60±1.43E-02	38 381.83±1.14E-03	37 877.73±1.19E-03	37 143.86±1.14E-03	37 114.07±1.38E-04
8	35 277.22±1.35E-02	34 625.00±2.51E-04	34 513.73±1.97E-04	34 529.80±2.96E-04	34 497.03±1.76E-04
9	33 769.14±7.19E-02	32 984.13±2.47E-04	32 916.53±2.15E-04	32 967.47±2.85E-04	32 905.37±2.66E-05

K	K-means	HC	GMM	SC	SSC
2	-0.226 5±1.49E-01	0.029 4±3.47E-18	0.071 3±3.36E-01	0.404 4±5.55E-03	-1.051 5±4.44E-16
3	-1.078 2±4.07E-01	-0.544 1±3.33E-16	-0.800 0±4.98E-01	-0.382 3±2.78E-02	-1.463 2±0
4	-1.730 4±3.75E-01	-1.536 8±0	-1.239 0±4.65E-01	-1.205 9±2.22E-02	-2.602 9±4.44E-16
5	-2.245 3±3.58E-01	-1.955 9±8.88E-16	-1.787 1±4.67E-01	-2.029 4±1.34E-02	-3.617 6±2.66E-15
6	-2.693 9±4.19E-01	-2.544 1±1.33E-15	-2.307 0±4.06E-01	-2.438 7±1.32E-02	-4.644 6±4.55E-02
7	-3.129 9±4.22E-01	-2.852 9±4.44E-16	-2.580 1±4.53E-01	-2.323 5±1.33E-02	-4.703 9±1.97E-02
8	-3.522 5±3.87E-01	-3.308 8±2.22E-15	-2.974 6±4.75E-01	-2.808 8±2.22E-02	-5.360 8±1.10E-01
9	-3.681 1±3.35E-01	-3.551 5±8.88E-16	-3.301 5±3.68E-01	-3.092 2±1.28E-02	-5.524 0±1.78E-02
K	AJSO	IAJSO	SAJSO	ISAJSO
2	0.404 4±2.78E-05	0.404 4±2.78E-05	0.404 4±1.90E-05	0.404 4±1.03E-05
3	-0.367 7±4.01E-04	-0.345 6±5.65E-04	-0.338 2±8.97E-04	-0.316 2±6.33E-04
4	-1.188 0±6.48E-03	-1.184 3±7.81E-03	-1.167 2±8.39E-03	-1.117 6±1.04E-03
5	-1.723 4±2.70E-03	-1.618 6±2.79E-03	-1.697 8±2.58E-03	-1.455 9±2.49E-03
6	-2.102 5±3.05E-03	-1.879 4±3.29E-03	-2.097 3±3.35E-03	-1.994 1±2.93E-03
7	-2.198 5±2.13E-03	-2.139 7±2.93E-03	-2.007 0±2.65E-03	-1.977 9±2.82E-03
8	-2.658 1±2.69E-03	-2.602 7±3.68E-03	-2.551 5±3.06E-03	-2.492 6±3.54E-03
9	-3.051 5±4.21E-03	-3.007 4±3.76E-03	-2.963 2±3.86E-03	-2.933 8±2.70E-03

面向人脑功能划分的人工水母搜索优化算法

Artificial Jellyfish Search Optimization Algorithm for Human Brain Functional Parcellation

RichHTML

PDF

可视化

摘要/Abstract

引用本文

使用本文

图/表 11

参考文献 38

相关文章 1

编辑推荐

Metrics

K	K-means	HC	GMM	SC	SSC
2	0.798 9±3.32E-02	0.757 4±1.11E-16	0.703 8±1.31E-01	0.909 4±0	0.601 1±0
3	0.824 5±7.79E-02	0.881 1±5.55E-16	0.810 0±7.10E-02	0.901 2±4.44E-04	0.737 5±4.20E-16
4	0.846 6±4.09E-02	0.881 9±3.33E-16	0.830 6±4.92E-02	0.910 6±5.73E-03	0.771 2±3.14E-16
5	0.865 9±2.77E-02	0.888 7±1.11E-16	0.854 5±3.22E-02	0.892 7±4.34E-03	0.678 6±2.22E-16
6	0.872 8±2.59E-02	0.883 6±3.33E-16	0.867 4±3.12E-02	0.895 3±7.88E-03	0.657 2±4.50E-03
7	0.873 3±2.58E-02	0.895 0±6.66E-16	0.873 1±3.04E-02	0.911 1±1.01E-03	0.736 5±2.20E-03
8	0.877 1±2.25E-02	0.893 7±5.55E-16	0.888 1±1.38E-02	0.907 1±3.32E-03	0.729 1±1.22E-02
9	0.889 5±1.53E-02	0.897 4±5.55E-16	0.891 2±1.51E-02	0.909 4±4.62E-03	0.739 4±1.76E-03
K	AJSO	IAJSO	SAJSO	ISAJSO
2	0.909 4±5.55E-16	0.909 4±5.55E-16	0.910 0±1.28E-03	0.911 2±5.15E-04
3	0.901 4±8.47E-04	0.902 1±1.03E-04	0.902 5±1.74E-04	0.902 6±1.09E-04
4	0.911 7±5.30E-04	0.912 5±6.40E-04	0.912 6±5.06E-04	0.914 6±6.62E-04
5	0.896 4±1.03E-02	0.898 9±1.34E-04	0.897 5±1.76E-04	0.905 8±1.04E-04
6	0.902 1±1.37E-03	0.906 4±4.54E-03	0.906 2±1.59E-03	0.909 5±1.25E-03
7	0.912 5±1.20E-03	0.913 6±1.56E-03	0.898 6±8.95E-03	0.912 4±1.39E-03
8	0.912 3±1.50E-03	0.913 7±1.37E-03	0.891 4±1.33E-03	0.921 5±1.41E-03
9	0.913 2±1.74E-03	0.913 9±4.27E-03	0.913 7±5.47E-03	0.916 1±1.45E-03