Publications

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.

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.

Hawkes processes with variable length memory and an infinite number of components

Pierre Hodara and Eva Löcherbach

In this paper we propose a model for biological neural nets where the activity of the network is described by Hawkes processes having a variable length memory. The particularity in this paper is that we deal with an infinite number of components. We propose a graphical construction of the process and build, by means of a perfect simulation algorithm, a stationary version of the process. To implement this algorithm, we make use of a Kalikow-type decomposition technique. Two models are described in this paper. In the first model, we associate to each edge of the interaction graph a saturation threshold that controls the influence of a neuron on another. In the second model, we impose a structure on the interaction graph leading to a cascade of spike trains. Such structures, where neurons are divided into layers, can be found in the retina.

Counting results for sparse pseudorandom hypergraphs II

Yoshiharu Kohayakawa, Guilherme Oliveira Mota, Mathias Schacht and Anusch Taraz

We present a variant of a universality result of Rödl (1986) for sparse, 3-uniform hypergraphs contained in strongly jumbled hypergraphs. One of the ingredients of our proof is a counting lemma for fixed hypergraphs in sparse “pseudorandom” hypergraphs, which is proved in the companion paper (Counting results for sparse pseudorandom hypergraphs I).

Coupled variability in primary sensory areas and the hippocampus during spontaneous activity

Nivaldo A. P. de Vasconcelos, Carina Soares-Cunha, Ana João Rodrigues, Sidarta Ribeiro and Nuno Sousa

The cerebral cortex is an anatomically divided and functionally specialized structure. It includes distinct areas, which work on different states over time. The structural features of spiking activity in sensory cortices have been characterized during spontaneous and evoked activity. However, the coordination among cortical and sub-cortical neurons during spontaneous activity across different states remains poorly characterized. We addressed this issue by studying the temporal coupling of spiking variability recorded from primary sensory cortices and hippocampus of anesthetized or freely behaving rats. During spontaneous activity, spiking variability was highly correlated across primary cortical sensory areas at both small and large spatial scales, whereas the cortico-hippocampal correlation was modest. This general pattern of spiking variability was observed under urethane anesthesia, as well as during waking, slow-wave sleep and rapid-eye-movement sleep, and was unchanged by novel stimulation. These results support the notion that primary sensory areas are strongly coupled during spontaneous activity.

Can somatosensory electrical stimulation relieve spasticity in post-stroke patients? A TMS pilot study

Peres A.S.C., Souza V.H., Catunda J.M.Y., Mazzeto-Betti K.C., Santos-Pontelli T.E.G., Vargas C.D., Baffa O., de Araújo D.B., Pontes-Neto O.M., Leite J.P. and Garcia M.A.C.

Evidence suggests that somatosensory electrical stimulation (SES) may decrease the degree of spasticity from neural drives, although there is no agreement between corticospinal modulation and the level of spasticity. Thus, stroke patients and healthy subjects were submitted to SES (3 Hz) for 30' on the impaired and dominant forearms, respectively. Motor evoked potentials induced by single-pulse transcranial magnetic stimulation were collected from two forearm muscles before and after SES. The passive resistance of the wrist joint was measured with an isokinetic system. We found no evidence of an acute carry-over effect of SES on the degree of spasticity.

Anticipated synchronization in neuronal circuits unveiled by a phase-response-curve analysis

Fernanda S. Matias, Pedro V. Carelli, Claudio R. Mirasso and Mauro Copelli

Anticipated synchronization (AS) is a counterintuitive behavior that has been observed in several systems. When AS occurs in a sender-receiver configuration, the latter can predict the future dynamics of the former for certain parameter values. In particular, in neuroscience AS was proposed to explain the apparent discrepancy between information flow and time lag in the cortical activity recorded in monkeys. Despite its success, a clear understanding of the mechanisms yielding AS in neuronal circuits is still missing. Here we use the well-known phase-response-curve (PRC) approach to study the prototypical sender-receiver-interneuron neuronal motif. Our aim is to better understand how the transitions between delayed to anticipated synchronization and anticipated synchronization to phase-drift regimes occur. We construct a map based on the PRC method to predict the phase-locking regimes and their stability. We find that a PRC function of two variables, accounting simultaneously for the inputs from sender and interneuron into the receiver, is essential to reproduce the numerical results obtained using a Hodgkin-Huxley model for the neurons. On the contrary, the typical approximation that considers a sum of two independent single-variable PRCs fails for intermediate to high values of the inhibitory coupling strength of the interneuron. In particular, it loses the delayed-synchronization to anticipated-synchronization transition.

Information transmission and criticality in the contact process

Marzio Cassandro, Antonio Galves and Eva Löcherbach

In the present paper, we study the relation between criticality and information transmission in the one-dimensional contact process with infection parameter λ. To do this we define the {\it sensitivity} of the process to its initial condition. This sensitivity increases for values of λ ‹ λc, the value of the critical parameter. The main point of the present paper is that we show that actually it continues increasing even after λc and only starts decreasing for sufficiently large values of λ. This provides a counterexample to the common belief that associates maximal information transmission to criticality.

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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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