Multi-class oscillating systems of interacting neurons

Susanne Ditlevsen and Eva Löcherbach

We consider multi-class systems of interacting nonlinear Hawkes processes modeling several large families of neurons and study their mean field limits. As the total number of neurons goes to infinity we prove that the evolution within each class can be described by a nonlinear limit differential equation driven by a Poisson random measure, and state associated central limit theorems. We study situations in which the limit system exhibits oscillatory behavior, and relate the results to certain piecewise deterministic Markov processes and their diffusion approximations.

The maximum size of a non-trivial intersecting uniform family that is not a subfamily of the Hilton-Milner family

Jie Han and Yoshiharu Kohayakawa

The celebrated Erdos–Ko–Rado theorem determines the maximum size of a k-uniform intersecting family. The Hilton–Milner theorem determines the maximum size of a k-uniform intersecting family that is not a subfamily of the so-called Erdos–Ko–Rado family. In turn, it is natural to ask what the maximum size of an intersecting k-uniform family that is neither a subfamily of the Erdos–Ko–Rado family nor of the Hilton–Milner family is. For k ≥ 4, this was solved (implicitly) in the same paper by Hilton–Milner in 1967. We give a different and simpler proof, based on the
shifting method, which allows us to solve all cases k ≥ 3 and characterize all extremal families achieving the extremal value.

Self-Organized Supercriticality and Oscillations in Networks of Stochastic Spiking Neurons

Ariadne A. Costa, Ludmila Brochini and Osame Kinouchi

Networks of stochastic spiking neurons are interesting models in the area of Theoretical Neuroscience, presenting both continuous and discontinuous phase transitions. Here we study fully connected networks analytically, numerically and by computational simulations. The neurons have dynamic gains that enable the network to converge to a stationary slightly supercritical state (self-organized supercriticality or SOSC) in the presence of the continuous transition. We show that SOSC, which presents power laws for neuronal avalanches plus some large events, is robust as a function of the main parameter of the neuronal gain dynamics. We discuss the possible applications of the idea of SOSC to biological phenomena like epilepsy and dragon king avalanches. We also find that neuronal gains can produce collective oscillations that coexists with neuronal avalanches, with frequencies compatible with characteristic brain rhythms.

NES: a free software to manage data from neuroscience experiments

Neuroscientists perform complex experiments aiming to reach a more effective understanding on the functioning of the brain and the treatment of pathologies. Each research laboratory uses different techniques and methodologies to produce and to analyze its findings. In this scenario, the Research, Innovation and Dissemination Center for Neuromathematics (NeuroMat) has developed the Neuroscience Experiments System (NES), a free software to manage data from neuroscience experiments. This web-based system is meant to assist researchers in their data collecting routine throughout a neuroscience experiment, integrating data records from different types such as clinical, electrophysiological, and behavioral. Furthermore, it provides a unified repository (database) for the experimental data of an entire research laboratory, group, or project.

Electrophysiological Evidence That the Retrosplenial Cortex Displays a Strong and Specific Activation Phased with Hippocampal Theta during Paradoxical (REM) Sleep

Bruna Del Vechio Koike, Kelly Soares Farias, Francesca Billwiller, Daniel Almeida-Filho, Paul-Antoine Libourel, Alix Tiran-Cappello, Régis Parmentier, Wilfredo Blanco, Sidarta Ribeiro, Pierre-Herve Luppi and Claudio Marcos Queiroz

It is widely accepted that cortical neurons are similarly more activated during waking and paradoxical sleep (PS; aka REM) than during slow-wave sleep (SWS). However, we recently reported using Fos labeling that only a few limbic cortical structures including the retrosplenial cortex (RSC) and anterior cingulate cortex (ACA) contain a large number of neurons activated during PS hypersomnia. Our aim in the present study was to record local field potentials and unit activity from these two structures across all vigilance states in freely moving male rats to determine whether the RSC and the ACA are electrophysiologically specifically active during basal PS episodes. We found that theta power was significantly higher during PS than during active waking (aWK) similarly in the RSC and hippocampus (HPC) but not in ACA. Phase–amplitude coupling between HPC theta and gamma oscillations strongly and specifically increased in RSC during PS compared with aWK. It did not occur in ACA. Further, 68% and 43% of the units recorded in the RSC and ACA were significantly more active during PS than during aWK and SWS, respectively. In addition, neuronal discharge of RSC but not of ACA neurons increased just after the peak of hippocampal theta wave. Our results show for the first time that RSC neurons display enhanced spiking in synchrony with theta specifically during PS. We propose that activation of RSC neurons specifically during PS may play a role in the offline consolidation of spatial memories, and in the generation of vivid perceptual scenery during dreaming.




The Research, Innovation and Dissemination Center for Neuromathematics is hosted by the University of São Paulo and funded by FAPESP (São Paulo Research Foundation).


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