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.
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
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