P037 Maximum-entropy-based metrics for quantifying critical dynamics in spiking neuronal data.
Pedro V. Carelli,*1, Felipe Serafim1, Mauro Copelli1
1Departmento de Física, Universidade Federal de Pernambuco, Recife, Brasil
*Email: pedro.carelli@ufpe.br
Introduction An important working hypothesis to investigate brain activity is whether it operates in a critical regime[1,2]. Recently, maximum-entropy phenomenological models have emerged as an alternative way of identifying critical behavior in neuronal data sets[3]. In the present work, we investigate the signatures of criticality from a firing rate-based maximum-entropy approach on data sets generated by computational models, and we compare them to experimental results. Methods We simulate critical and noncritical spiking neuronal models [4] and generate spiking time series. Then, following Mora et al [3], a Boltzmann-like distribution is defined. We consider as observable the firing rates Kt, and constrain the probability distribution in two different times, Pu(Kt,Kt+u), obtaining the energy function. We then solve an inverse problem to fit the model parameters to the data statistics. Once the model is adjusted to describe the data, we can perform statistical physics analysis, and the signatures of criticality are obtained from the divergence of the model's generalized specific heat. Results We found that the maximum entropy approach consistently identifies critical behavior around the phase transition in models and rules out criticality in models without phase transition. The maximum-entropy-model results are compatible with results for cortical data from urethane-anesthetized rats [4] and human MEG. Discussion
We detect signatures of criticality in different brain data sets by employing a maximum entropy approach based on neuronal population firing rates. This method diverges from conventional techniques that depend on estimating critical exponents through power law distributions of neuronal avalanche sizes and durations. It proves especially useful in scenarios where traditional markers of criticality derived from neuronal avalanches are either methodologically unreliable or yield ambiguous results. Our results providefurther support for criticality in the brain.
Acknowledgements We thankfully acknowledge the funding from CNPq, FACEPE, CAPES and FINEP.
References 1. Beggs JM, Plenz D. Neuronal avalanches in neocortical circuits. Journal of neuroscience. 2003 3;23(35):11167-77. 2. FONTENELE, A. J. et al. Criticality between cortical states. PHYSICAL REVIEW LETTERS, v. 122, p. 208101, 2019. 3. Mora T, Deny S, Marre O. Dynamical criticality in the collective activity of a population of retinal neurons. Physical review letters. 2015 Feb 20;114(7):078105. 4. SERAFIM, F. et al. Maximum-entropy-based metrics for quantifying critical dynamics in spiking neuron data. Phys Rev E, v. 110, p. 024401, 2024.
