Sampling Artifacts Of Granger Causality And The Reliable Reconstruction Of Neuronal Network Connectivity

In neuroscience,one of the key issues is to understand how neurons connected with one another to perform computation.Due to the limitation of technique,in experiments,it is difficult to uncover the neuronal network connectivity.On the other hand,due to the development of recording techniques,we now have greater ability than past to acquire the data of neuronal activities.Therefore,an inverse problem is under active investigations that how we can reconstruct the underlying neuronal network connectivity from the recordings of neuronal activities.Based on the analysis of discrete time series,Granger Causality(GC)is widely applied to the neuronal network reconstruction.However,because most physical quantities measured in experiments are continuous in time,one should sample them discretely in order to perform GC analysis.Therefore,how sampling(e.g.,sampling interval length)could influence the GC analysis and how to sample in order to obtain a reliable GC analysis are important issues in applications.In this thesis,we undertake a thorough discussion and a detailed theoretical analysis of these issues,and propose strategies for a reliable GC neuronal network reconstruction.Our analysis of sampling and the reliability of GC not only can be applied to the neuronal network dynamics,but also can be extended to more general dynamic systems.Our work has following innovation and contribution.(i)We analyze in detail how sampling interval length influences the GC value and the reliability of GC analysis.(ii)Base on the neuronal network dynamics,we observe and explain the scaling paradox,propose the GC normalization.(iii)We propose the sampling strategy to obtain a reliable GC analysis,which could help to use correctly the GC analysis in experiments.(iv)We extend the GC analysis to the nonuniformly sampled data,thus are able to obtain a reliable GC analysis at a low sampling rate.(v)We analyze in detail the theoretical properties of spectrum of I&F dynamics,propose the covariance truncation and power-law tail fitting approaches of spectral processing,thereby obtain a reliable and accurate GC analysis.