Andressa Cerqueira, Aurélien Garivier and Florencia Leonardi
In this paper, we propose a perfect simulation algorithm for the Exponential Random Graph Model, based on the Coupling from the past method of Propp and Wilson (1996). We use a Glauber dynamics to construct the Markov Chain and we prove the monotonicity of the ERGM for a subset of the parametric space. We also obtain an upper bound on the running time of the algorithm that depends on the mixing time of the Markov chain.
We study the modified log-Sobolev inequality for a class of pure jump Markov processes that describe the interactions between brain neurons. In particular, we focus on a finite and compact process with degenerate jumps inspired by the model introduced by Galves and Löcherbach. As a result, we obtain concentration properties for empirical approximations of the process.
Fernando Borges, Paulo Protachevicz, Rodrigo Pena, Ewandson Lameu, Guilherme Higa, Fernanda Matias, Alexandre Kihara, Chris Antonopoulos, Roberto de Pasquale, Antonio Roque, Kelly Iarosz, Peng Ji and Antonio Batista
Self-sustained activity in the brain is observed in the absence of external stimuli and contributes to signal propagation, neural coding, and dynamic stability. It also plays an important role in cognitive processes. In this work, by means of studying intracellular recordings from CA1 neurons in rats and results from numerical simulations, we demonstrate that self-sustained activity presents high variability of patterns, such as low neural firing rates and activity in the form of small-bursts in distinct neurons. In our numerical simulations, we consider random networks composed of coupled, adaptive exponential integrate-and-fire neurons. The neural dynamics in the random networks simulates regular spiking (excitatory) and fast spiking (inhibitory) neurons. We show that both the connection probability and network size are fundamental properties that give rise to self-sustained activity in qualitative agreement with our experimental results. Finally, we provide a more detailed description of self-sustained activity in terms of lifetime distributions, synaptic conductances, and synaptic currents.
Rafael B. Stern, Matheus Silva d'Alencar, Yanina L. Uscapi, Marco D. Gubitoso, Antonio C. Roque, André F. Helene and Maria Elisa Pimentel Piemonte
Background: People with Parkinson's disease (PD) display poorer gait performance when walking under complex conditions than under simple conditions. Screening tests that evaluate gait performance changes under complex walking conditions may be valuable tools for early intervention, especially if allowing for massive data collection.
Mauricio Girardi-Schappo, Ludmila Brochini, Ariadne A. Costa, Tawan T. A. Carvalho and Osame Kinouchi
Recent experiments suggested that a homeostatic regulation of synaptic balance leads the visual system to recover and maintain a regime of power-law avalanches. Here we study an excitatory/inhibitory (E/I) meanfield neuronal network that has a critical point with power-law avalanches and synaptic balance. When shortterm depression in inhibitory synapses and firing threshold adaptation are added, the system hovers around the critical point. This homeostatically self-organized quasicritical (SOqC) dynamics generates E/I synaptic current cancellation in fast timescales, causing fluctuation-driven asynchronous-irregular (AI) firing. We present the full phase diagram of the model without adaptation varying external input versus synaptic coupling. This system has a rich dynamical repertoire of spiking patterns: synchronous regular (SR), asynchronous regular (AR), synchronous irregular (SI), slow oscillations (SO), and AI. It also presents dynamic balance of synaptic currents, since inhibitory currents try and compensate excitatory currents over time, resulting in both of them scaling linearly with external input. Our model thus unifies two different perspectives on cortical spontaneous activity: both critical avalanches and fluctuation-driven AI firing arise from SOqC homeostatic adaptation and are indeed two sides of the same coin.
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