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).

“Inside the Brain,” a NeuroMat-supported exhibition at the University of São Paulo Museum of Veterinary Anatomy

The University of São Paulo Museum of Veterinary Anatomy will launch in the short-run the exhibition “Inside the Brain,” curated by NeuroMat investigator André Frazão Helene. The goal of the exhibition, which will be held permanently in the museum, is to stress the role of the anatomy (form) and neural activity (function) in how the brain works. The exhibition is supported by FAPESP (via NeuroMat), the University of São Paulo “Pró- Reitoria de Cultura e Extensão Universitária,” the Laboratory of Cognitive Processes, and the User Group Wikimedia in Brazil.

Video: Inside the brain

Movie on the exhibition "Por dentro do cérebro", at the University of São Paulo.

Production: Giulia Ebohon.

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.




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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