TY - CHAP
T1 - Statistical models of neural activity, criticality, and Zipf's law
AU - Sorbaro, Martino
AU - Herrmann, J. Michael
AU - Hennig, Matthias H.
PY - 2019/7/24
Y1 - 2019/7/24
N2 - In this overview, we discuss the connections between the observations of critical dynamics in neuronal networks and the maximum entropy models that are often used as statistical models of neural activity, focusing in particular on the relation between "statistical" and "dynamical" criticality. We present examples of systems that are critical in one way, but not in the other, exemplifying thus the difference of the two concepts. We then discuss the emergence of Zipf laws in neural activity, verifying their presence in retinal activity under a number of different conditions. In the second part of the chapter we review connections between statistical criticality and the structure of the parameter space, as described by Fisher information. We note that the model-based signature of criticality, namely the divergence of specific heat, emerges independently of the dataset studied; we suggest this is compatible with previous theoretical findings.
AB - In this overview, we discuss the connections between the observations of critical dynamics in neuronal networks and the maximum entropy models that are often used as statistical models of neural activity, focusing in particular on the relation between "statistical" and "dynamical" criticality. We present examples of systems that are critical in one way, but not in the other, exemplifying thus the difference of the two concepts. We then discuss the emergence of Zipf laws in neural activity, verifying their presence in retinal activity under a number of different conditions. In the second part of the chapter we review connections between statistical criticality and the structure of the parameter space, as described by Fisher information. We note that the model-based signature of criticality, namely the divergence of specific heat, emerges independently of the dataset studied; we suggest this is compatible with previous theoretical findings.
KW - quantitative biology - neurons and cognition
KW - condensed matter - disordered systems and neural networks
KW - nonlinear sciences - adaptation and self-organizing systems
U2 - 10.1007/978-3-030-20965-0_13
DO - 10.1007/978-3-030-20965-0_13
M3 - Chapter (peer-reviewed)
SN - 9783030209643
T3 - Springer Series on Bio- and Neurosystems
SP - 265
EP - 287
BT - The Functional Role of Critical Dynamics in Neural Systems
A2 - Tomen, Nergis
A2 - Herrmann, J. Michael
A2 - Ernst, Udo
PB - Springer
ER -