At the point of a second order phase transition also termed as a critical point, systems display long range order and their macroscopic behaviors are independent of the microscopic details making up the system. Due to these properties, it has long been speculated that biological systems that show similar behavior despite having very different microscopics, may be operating near a critical point. Recent methods in neuroscience are making it possible to explore whether criticality exists in neural networks. Despite being large in size, many data sets are still only a minute sample of the neural system and methods towards expanding these data sets have to be considered in order to study the existence of criticality. In this work we develop an analytical method of expanding a dataset to the large N limit so that statements about the critical nature of the data set could be made. We also show using a particular dataset analyzed computationally in literature that expanding data sets keeping the moments of the original data set need not lead to unique values of the critical temperature when the large N limit is considered analytically, despite the mirage of them appearing to do so when analyzed computationally. This suggests that not all available data sets from experiments are amenable for understanding the critically of the underlying system.
Optimal Griffiths Phase in Heterogeneous Human Brain Networks: Brain Criticality Embracing Stability and Flexibility across Individuals
Lanzhou University（兰州大学）；Instituto de Ciencias Físicas (ICIFI-CONICET), Center for Complex Systems and Brain Sciences (CEMSC3), Escuela de Ciencia y Tecnología, Universidad Nacional de Gral. San Martín（国立圣马丁大学科学技术学院复杂系统与脑科学中心）；Department of Physics, Centre for Nonlinear Studies, Beijing-Hong Kong-Singapore Joint Centre for Nonlinear and Complex Systems (Hong Kong), Institute of Computational and Theoretical Studies, Hong Kong Baptist University（香港浸会大学物理系非线性研究中心计算与理论研究所）；Life Science Imaging Centre, Hong Kong Baptist University（香港浸会大学生命科学成像中心）
