Tight Hamilton cycles in random hypergraphs

Peter Allen, Julia Böttcher, Yoshiharu Kohayakawa, Yury Person

We give an algorithmic proof for the existence of tight Hamilton cycles in a random r-uniform hypergraph with edge probability p=n^{-1+eps} for every eps>0. This partly answers a question of Dudek and Frieze [Random Structures Algorithms], who used a second moment method to show that tight Hamilton cycles exist even for p=omega(n)/n (r>2) where omega(n) tends to infinity arbitrary slowly, and for p=(e+o(1))/n (r>3). The method we develop for proving our result applies to related problems as well.

Increase in hippocampal theta oscillations during spatial decision making

Hindiael Belchior, Vítor Lopes dos Santos, Adriano B. L. Tort, Sidarta Ribeiro

The processing of spatial and mnemonic information is believed to depend on hippocampal theta oscillations (5–12 Hz). However, in rats both the power and the frequency of the theta rhythm are modulated by locomotor activity, which is a major confounding factor when estimating its cognitive correlates. Previous studies have suggested that hippocampal theta oscillations support decision-making processes. In this study, we investigated to what extent spatial decision making modulates hippocampal theta oscillations when controlling for variations in locomotion speed. We recorded local field potentials from the CA1 region of rats while animals had to choose one arm to enter for reward (goal) in a four-arm radial maze. We observed prominent theta oscillations during the decision-making period of the task, which occurred in the center of the maze before animals deliberately ran through an arm toward goal location. In speed-controlled analyses, theta power and frequency were higher during the decision period when compared to either an intertrial delay period (also at the maze center), or to the period of running toward goal location. In addition, theta activity was higher during decision periods preceding correct choices than during decision periods preceding incorrect choices. Altogether, our data support a cognitive function for the hippocampal theta rhythm in spatial decision making.

Body maps inside the brain

This month Claudia Vargas and Maria Luiza Rangel published the text titled "Os mapas do corpo no cérebro" (Body maps inside the brain) at the "Museu do Amanhã" official website. Vargas is the technical consultant of the museum's exhibition "Sport & Brain", which can be seen until October 2. Vargas is also a NeuroMat co-principal investigator, one of FAPESP's Research, Innovation and Dissemination centers, hosted by the University of São Paulo (USP). Text by Claudia Domingues Vargas & Maria Luiza Rangel, 08/2016. (In Portuguese.)

Stochastic Induction of Long-Term Potentiation and Long-Term Depression

G. Antunes, A. C. Roque & F. M. Simoes-de-Souza

Long-term depression (LTD) and long-term potentiation (LTP) of granule-Purkinje cell synapses are persistent synaptic alterations induced by high and low rises of the intracellular calcium ion concentration ([Ca2+]), respectively. The occurrence of LTD involves the activation of a positive feedback loop formed by protein kinase C, phospholipase A2, and the extracellular signal-regulated protein kinase pathway, and its expression comprises the reduction of the population of synaptic AMPA receptors. Recently, a stochastic computational model of these signalling processes demonstrated that, in single synapses, LTD is probabilistic and bistable. Here, we expanded this model to simulate LTP, which requires protein phosphatases and the increase in the population of synaptic AMPA receptors. Our results indicated that, in single synapses, while LTD is bistable, LTP is gradual. Ca2+ induced both processes stochastically. The magnitudes of the Ca2+ signals and the states of the signalling network regulated the likelihood of LTP and LTD and defined dynamic macroscopic Ca2+ thresholds for the synaptic modifications in populations of synapses according to an inverse Bienenstock, Cooper and Munro (BCM) rule or a sigmoidal function. In conclusion, our model presents a unifying mechanism that explains the macroscopic properties of LTP and LTD from their dynamics in single synapses.

NIRA - NeuroMat Individual Report of Activities

The NeuroMat Individual Report of Activities (NIRA) is a system that can be used by Research, Innovation and Dissemination Centers (RIDCs) supported by the São Paulo Research Foundation (FAPESP). Its goal is to assist in preparing the annual report of activities, a document that is submitted annually to FAPESP.

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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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