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　　Despite these advantages，traditional feedback identification

theories often suffer from the opinion that they usually address

two-variate time-series data and are inappropriate for large-scale

networks because of their practical and theoretical

limitations.Data acquisition is difficult or connective

entanglements are fearing，which might hinder their applications to

very large datasets， as occur more and more frequently nowadays.

Now this is not the case，as many new experimental techniques， for

example，real-time PCR，

immunofluorescence，microarray，multi-electrode array and EEG;can now

provide such time-series data in a cost efficient manner. Also a

multi-variate time-series analysis theory has undergone a great

development.The new theoretical contribution much helps to find the

feedback loops in large-scale networks.

1 Introduction

1.1 Systems Biology andIts Objective

1.2 Biological Feedback Loops

1.3 Identification Methods ofBiological Feedback Loops

1.4 0utline ofthe Book

2 Non-causallmpulse Response Component Methods

2.1 Basic Concepts about the Stochastic Process

2.2 Correlation Identification Methods

2.3 SpectralFactorAnalysis

2.4 Identification Algorithm of the NIRCM

2.5 Perturbation Methods

2.6 Factors Affecting the Identification Precision

3 Multi-step Granger Causality Methods

3.1 Multivariate Time-Series Analysis

3.2 Finite-order Vector Autoregressive Model and Its

Corresponding Infinite-order Vector Moving Average Model 

3.3 Estimation ofVAR Coefficients 

3.4 Granger Causality and Multi-step Causality.

3.4.1 Granger Causalitylnference Between the 2-partitioned

Variate Sets

3.4.2 Granger Causality Between a Pair of Variate Sets 

3.4.3 Testing Multi-step Granger Causality Between a Pair of

Variate Sets

3.5 Identification Algorithm of the MSGCM

4 Synthetic Spike NeuraI Networks and Their Dynamical Network

Behaviors

4.1 Spike Neural Networks

4.2 Typical Network Behaviors

4.3 Synchronized Bursting Behavior and Feedback Mechanism

4.4 Feedback Motifs ofNetworks

4.5 Dynamical Characteristics of Network Motifs

5 Application of Feedback Loop Identification Methods to

Synthetic Spike Neural Networks

6 Feedback Loop Identifications for Biological Cultured Neural

Networks 

7 Summary

Appendix

Bibliography

　　董朝轶，男，汉族，1976年7月出生内蒙古包头市人，韩国高丽大学控制与机器人专业哲学博士（Ph.D.），内蒙古工业大学副教授，“控制理论与控制工程”专业硕士生导师。长期从事系统生物学、生物信息学、复杂系统与控制等领域的研究丁作，曾在韩国首尔国立大学系统生物学实验室、韩国科学技术院系统生物学与生物激发的工程学实验室从事“生物神经网络动态主旨辨识”研究。目前，主持*留学回国人员科研启动基金、内蒙古教育厅重点项目、内蒙古自然科学基金面上项目各1项。以作者发表论文16篇，其中，SCI检索4篇；EI检索6篇。作者的主要研究方向有：生物复杂网络建模、仿真与生物网络内部动态模体辨识研究；飞行器动态建模、仿真和飞行控制策略研究。

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