Brain functional integration can be investigated by the statistical models of the information flows traveling among brain regions (Friston, 2002). It has been recently shown that complex social processes are supported by different brain networks (Park and Friston, 2013), such as motives behind human altruism (Hein et al., 2016). Currently, much of our understanding of the directional connectivity among brain regions comes from the mathematical modeling of brain networks (Friston, 2002). For example, the classical Granger causality analysis (GCA) estimates the directional connectivity via an autoregressive model (Ding et al., 2006), and the dynamic causal modeling (DCM) approximates the dynamic interaction between brain areas with a bilinear model (Friston et al., 2003). However, one possible over-simplification in some scenarios is that the noise process in neural signal has been assumed to follow a time invariant model. As the spike train of a neuron is typically close to Poisson processes in their timing, the variance thus increases linearly with the signal (Gerstein and Mandelbrot, 1964). In addition, such signal-dependent noise (SDN) has been demonstrated to be functionally important, for example, as an optimal control strategy for motor planning (Harris and Wolpert, 1998). However, in presence of the SDN in the blood-oxygen-level dependent (BOLD) signal recorded from the fMRI experiments (Luo et al., 2013), neither the classical GCA nor the DCM is applicable, as both models assuming a constant-level of variance for the brain signal. Therefore, we have proposed an adaptation of the classical GCA to model the SDN, and be thus sensitive to the variance-affected interactions that other methods would miss (Luo et al., 2011, 2013).
- Qiang Luo(#), Pan Baobao(#), Huaguang Gu, Molly Simmonite, Susan Francis, Peter Liddle, Lena Palaniyappan(*). Effective connectivity of the salience network in schizophrenia: task-negative to task-positive transition, under review, 2018. (Code to replicate the results; Data can be avaliable by application to Prof Peter Liddle https://www.nottingham.ac.uk/medicine/people/peter.liddle after evaluation according an established procedure and the IRB.)
- Pan Baobao(#), Qiang Luo(#)(*), Huaguang Gu(*), Yi-Na Ma, Meghana A. Bhatt, Terry Lohrenz, Colin F. Camerer, Jian-Feng Feng, P. Read Montague, Dynamic effective connectivity reveals an in-default wiring for prosociality and an on-demand circuit for deception in the brain, under review, 2018. (Code and Data to replicate the results)
- Luo Qiang(#), Ma Yina(#), Bhatt Meghana A. (#), Montague P. Read(*), Feng Jianfeng(*), The Functional Architecture of the Brain Underlies Strategic Deception in Impression Management, Frontiers in Human Neuroscience, 2017, 11, 513.
- Pu, W(#)，Luo, Q(#)，Palaniyappan, L(#)，Xue, Z，Yao, S，Feng, J(*)，Liu, Z(*)，Failed cooperative, but not competitive, interaction between large-scale brain networks impairs working memory in schizophrenia.，Psychological Medicine，2016，46（6）：1211-24.
- Qiang Luo(#)，Tian Ge，Fabian Grabenhorst，Edmund Rolls(*)，Jianfeng Feng(*)，Attention-dependent modulation of cortical taste circuits revealed by granger causality with signal-dependent noise，PLoS Computational Biology，2013，9（10）.
- Luo, Qiang(#)，Lu, Wenlian(#)，Cheng, Wei(#)，Valdes-Sosa, Pedro A.，Wen, Xiaotong，Ding, Mingzhou，Feng, Jianfeng(*)，Spatio-temporal Granger causality: A new framework，NeuroImage，2013，79：241-263.
- Qiang Luo(#)，Tian Ge，Jianfeng Feng(*)，Granger causality with signal-dependent noise，NeuroImage，2011，57（4）：1422-1429.