Volume 26 Issue 9
. 
Turn off MathJax
Article Contents
Article Navigation >  Applied Mathematics and Mechanics  > 2005  >  26(9): 1083-1090
SHEN En-hua, CAI Zhi-jie, GU Fan-ji. Mathematical Foundation of C0 Complexity[J]. Applied Mathematics and Mechanics, 2005, 26(9): 1083-1090.
Citation: SHEN En-hua, CAI Zhi-jie, GU Fan-ji. Mathematical Foundation of C0 Complexity[J]. Applied Mathematics and Mechanics, 2005, 26(9): 1083-1090.
shu

Mathematical Foundation of C0 Complexity

  • 1.

    School of Life Science, Research Center for Brain Science, Institute of Brain Science, Fudan University, Shanghai 200433, P. R. China;

  • Received Date: 2003-07-18
  • Rev Recd Date: 2005-05-20
  • Publish Date: 2005-09-15
    Abstract
  • For many continuous bio-medical signals with both strong nonlinearity and non-stationarity,two criterions were proposed for their complexity estimation:1)Only short data set is enough for robust estimation;2)No over-coarse graining preprocessing,such as transferring the original signal into a binary time series,is needed.C0 complexity measure proposed by us previously is one of such measures.However,it lacked solid mathematical foundation and thus its use was limited.A modified version of this measure is proposed,and some important properties are proved rigorously.According to these properties,this measure can be considered as an index of randomness of time series in some senses,and thus also a quantitative index of complexity under the meaning of randomness finding complexity.Compared with other similar measures,this measure seems more suitable for estimating a large quantity of complexity measures for a given task,such as studying the dynamic variation of such measures in sliding windows of a long process,owing to its fast speed for estimation.
    • FullText(HTML)
  • loading
    • References(9)
  • [1]
    吴祥宝，徐京华.复杂性和脑功能[J].生物物理学报,1991,7(1):103—106.
    [2]
    孟欣,沈恩华,陈芳,等.脑电图复杂度分析中的粗粒化问题Ⅰ: 过分粗粒化和三种复杂度的比较[J].生物物理学报,2000,16(4):701—706.
    [3]
    Chen F,Xu J,Gu F,et al.Dynamic process of information transmission complexity in human brains[J].Biological Cybernetics,2000,83(4):355—366. doi: 10.1007/s004220000158
    [4]
    杨斯环，杨秦飞，石继明，等.不同生理状态时脑电时间序列的三种复杂度计算比较[J].生物物理学报,1996,12(3)：437—440.
    [5]
    Rapp P E,Schmah T I.Dynamical analysis in clinical practice[A].In: Lehnertz K,Arnhold J,Grassberger P,et al，Eds.Chaos in Brains[C].Singapore:World Scientific,2000,52—62,
    [6]
    Lempel A,Ziv J.On complexity of finite sequences[J].IEEE Transactions on Information Theory,1976,IT22(1):75—81.
    [7]
    Pincus S M.Approximate entropy as a measure of system complexity[J].Proceedings of the National Academy of Sciences of the United States of America,1991,88(6):2297—2301. doi: 10.1073/pnas.88.6.2297
    [8]
    Gu F,Shen E,Meng X,et al.Higher order complexity of time series[J].The International Journal of Bifurcation and Chaos,2004,14(8):2979—2990. doi: 10.1142/S021812740401093X
    [9]
    Lehnertz K,Elger C E.Can epileptic seizures be predicted? Evidence from nonlinear time series analysis of brain electrical activity[J].Physical Review Letters,1998,80(22):5019—5022. doi: 10.1103/PhysRevLett.80.5019
    • Relative Articles
    • Supplements(0)
    • Cited By
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索
    Get Citation
    PDF
    XML

    Article Metrics

    Article views (2261) PDF downloads(813) Cited by()
    Proportional views
    Related
    Contact Us

    Copyright © Editorial Department of Applied Mathematics and Mechanics渝ICP备11007697号-3

    address：P.O. Box 90, Chongqing Jiaotong University, No.66 Xuefu Road, Nan'an District, Chongqing, 400074, P.R.ChinaPostcode：400074

    Phone/Fax: 023-62652450　

    Email: amm1980@vip.163.com； amm1980@163.com； applmathmech@cqjtu.edu.cn

    Journal Online
    Email alert RSS

    Supported by: Beijing Renhe Information Technology Co. Ltd  

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return