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Complex systems are typically characterized as an intermediate situation between a complete regular structure and a random system. Brain signals can be studied as a striking example of such systems: cortical states can range from highly synchronous and ordered neuronal activity (with higher spiking variability) to desynchronized and disordered regimes (with lower spiking variability). It has been recently shown, by testing independent signatures of criticality, that a phase transition occurs in a cortical state of intermediate spiking variability. Here, we use a symbolic information approach to show that, despite the monotonical increase of the Shannon entropy between ordered and disordered regimes, we can determine an intermediate state of maximum complexity based on the Jensen disequilibrium measure. More specifically, we show that statistical complexity is maximized close to criticality for cortical spiking data of urethane-anesthetized rats, as well as for a network model of excitable elements that presents a critical point of a non-equilibrium phase transition., 8 pages, 6 figures

Since the first measurements of neuronal avalanches, the critical brain hypothesis has gained traction. However, if the brain is critical, what is the phase transition? For several decades, it has been known that the cerebral cortex operates in a diversity of regimes, ranging from highly synchronous states (with higher spiking variability) to desynchronized states (with lower spiking variability). Here, using both new and publicly available data, we test independent signatures of criticality and show that a phase transition occurs in an intermediate value of spiking variability, in both anesthetized and freely moving animals. The critical exponents point to a universality class different from mean-field directed percolation. Importantly, as the cortex hovers around this critical point, the avalanche exponents follow a linear relation that encompasses previous experimental results from different setups and is reproduced by a model., NPAD/UFRN. A. J. F., N. A. P. V., T. F., L. A. A. A,L. D. P., S. R., P. V. C., and M. C. acknowledge supportfrom CAPES (Grants No. 88887.131435/2016-00 andPROEX 534/2018, No. 23038.003382/2018-39),FACEPE (Grant No. APQ 0826-1.05/15) and CNPq(Grants No. 310712/2014-9, No. 301744/2018-1,No. 425329/2018-6, No. 308775/2015-5, No. 249991/2013-6, and No. 408145/2016-1). This article was pro-duced as part of the activities of FAPESP Research,InnovationandDisseminationCenterforNeuromathematics (Grant No. 2013/07699-0, S. PauloResearch Foundation). C. S.-C. and B. C. acknowledgesupport from FCT (Grants No. SFRH/BD/51992/2012and No. SFRH/BD/98675/2013) and PAC-MEDPERSYST Project No. POCI-01-0145-FEDER-016428 (Portugal 2020); A. J. R. received support from anFCT Investigator Fellowship (IF/00883/2013) and acknowl-edges the Janssen Neuroscience Prize (first edition) and theBIAL Foundation Grant No. 30/2016

FACEPE Funções cerebrais decorrem da interação de um grande número de neurônios. Sendo o cérebro um sistema não linear e complexo, a obtenção de modelos que descrevam adequadamente o comportamento coletivo de circuitos neurais não é uma tarefa trivial. Uma das hipóteses que vem ganhando destaque na literatura é a de que a dinâmica do cérebro se encontra próxima a um ponto crítico. Alguns trabalhos mostraram que modelos de máxima entropia que levam em conta apenas a interação por pares (modelos tipo Ising) eram capazes explicar padrões de atividade global em dados de retina de invertebrados e fatias de córtex in vitro. Além disso estes modelos permitem obter assinaturas de criticalidade nas redes neurais estudadas. Nesta dissertação, realizamos experimentos in vivo onde registramos longos períodos da atividade cortical espontânea de ratos anestesiados. Os registros foram feitos utilizando tanto matrizes de multieletrodos de fios de tungstênio quanto eletrodos de silício de alta densidade (silicon probes). Implementamos um algoritmo para ajustar um modelo de máxima entropia que leva em conta a interação por pares entre os elementos do modelo e validamos o algoritmo com dados simulados. Finalmente apresentamos os resultados utilizando o modelo de máxima entropia para analisar os dados experimentais medidos com ambos os tipos de eletrodos. Brain functions arise from the interaction of a large number of neurons. Since the brain is a nonlinear and complex system, obtaining models that adequately describe the collective behavior of neural circuits is not a trivial task. One of the hypotheses that has gained prominence in the literature is that the dynamics of the brain is close to a critical point. Some studies have shown that maximum entropy models that take into account only the interaction by pairs (Ising type models) were able to explain patterns of global activity in retinal data of invertebrates and in vitro cortex slices. In addition, these models allow to obtain criticality signatures in the studied neural networks. In this dissertation, we performed in vivo experiments where we recorded long periods of spontaneous cortical activity of anesthetized rats. The records were made using both tungsten wire multi-electrode arrays and silicon probes. We implemented an algorithm to fit a maximum entropy model that takes into account the paired interaction between the elements of the model and validate the algorithm with simulated data. Finally we present the results using the maximum entropy model to analyze the experimental data measured with both types of electrodes.