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The dynamic membrane potential threshold, as one of the essential properties of a biological neuron, is a spontaneous regulation mechanism that maintains neuronal homeostasis, i.e., the constant overall spiking firing rate of a neuron. As…

Robotics · Computer Science 2023-06-21 Jianchuan Ding , Bo Dong , Felix Heide , Yufei Ding , Yunduo Zhou , Baocai Yin , Xin Yang

Cortical circuits exhibit high levels of response diversity, even across apparently uniform neuronal populations. While emerging data-driven approaches exploit this heterogeneity to infer effective models of cortical circuit computation…

Neurons and Cognition · Quantitative Biology 2025-11-06 Mohammadreza Soltanipour , Stefan Treue , Fred Wolf

It has long been known that neurons in the brain are not physiologically homogeneous. In response to current stimulus, they can fire several distinct patterns of action potentials that are associated with different physiological classes…

Dynamical Systems · Mathematics 2017-05-30 Abdelmalik Moujahid , Alicia D'Anjou , Manuel Graña

The quadratic adaptive integrate-and-fire model (Izhikecih 2003, 2007) is recognized as very interesting for its computational efficiency and its ability to reproduce many behaviors observed in cortical neurons. For this reason it is…

Dynamical Systems · Mathematics 2012-11-07 Jonathan Touboul

Hippocampal neurons exhibit precise phase locking to network oscillations, but the computational principle governing this temporal precision is still unclear. Neural information is conveyed jointly by firing rates and spike timing, but…

Neurons and Cognition · Quantitative Biology 2026-03-23 Reza Ahmadvand , Sara Safura Sharif , Yaser Mike Banad

The dynamical responses of complex neuronal networks to external stimulus injected on a \emph{single} neuron are investigated. Stimulating the largest-degree neuron in the network, it is found that as the intensity of the stimulus…

Chaotic Dynamics · Physics 2016-04-13 Mengjiao Chen , Weijie Lin , Hengtong Wang , Wei Ren , Xingang Wang

In this work, we propose to catch the complexity of the membrane potential's dynamic of a motoneuron between its spikes, taking into account the spikes from other neurons around. Our approach relies on two types of data: extracellular…

Statistics Theory · Mathematics 2021-08-03 Anna Bonnet , Charlotte Dion , François Gindraud , Sarah Lemler

Air hockey demands split-second decisions at high puck velocities, a challenge we address with a compact network of spiking neurons running on a mixed-signal analog/digital neuromorphic processor. By co-designing hardware and learning…

The time elapsed model describes the firing activity of an homogeneous assembly of neurons thanks to the distribution of times elapsed since the last discharge. It gives a mathematical description of the probability density of neurons…

Analysis of PDEs · Mathematics 2011-09-16 Khashayar Pakdaman , Benoît Perthame , Delphine Salort

A fundamental problem in neuroscience is to characterize the dynamics of spiking from the neurons in a circuit that is involved in learning about a stimulus or a contingency. A key limitation of current methods to analyze neural spiking…

Methodology · Statistics 2017-09-29 Yingzhuo Zhang , Noa Malem-Shinitski , Stephen A Allsop , Kay Tye , Demba Ba

Optical imaging of genetically encoded calcium indicators is a powerful tool to record the activity of a large number of neurons simultaneously over a long period of time from freely behaving animals. However, determining the exact time at…

Applications · Statistics 2021-03-08 Tong Shen , Kevin Johnston , Gyorgy Lur , Michele Guindani , Hernando Ombao , Zhaoxia Yu

Regular firing neurons can be seen as oscillators. The phase-response curve (PRC) describes how such neurons will respond to small excitatory perturbations. Knowledge of the PRC is important as it is associated to the excitability type of…

Neurons and Cognition · Quantitative Biology 2010-01-05 Benjamin Torben-Nielsen , Marylka Uusisaari , Klaus M. Stiefel

Humans perform remarkably well in many cognitive tasks including pattern recognition. However, the neuronal mechanisms underlying this process are not well understood. Nevertheless, artificial neural networks, inspired in brain circuits,…

Neurons and Cognition · Quantitative Biology 2018-06-28 Gianluca Susi , Luis Anton Toro , Leonides Canuet , Maria Eugenia Lopez , Fernando Maestu , Claudio R. Mirasso , Ernesto Pereda

Experiments suggest that cerebral cortex gains several functional advantages by operating in a dynamical regime near the critical point of a phase transition. However, a long-standing criticism of this hypothesis is that critical dynamics…

Neurons and Cognition · Quantitative Biology 2020-09-30 Kathleen Finlinson , Woodrow L. Shew , Daniel B. Larremore , Juan G. Restrepo

The relationship between a neuron's complex inputs and its spiking output defines the neuron's coding strategy. This is frequently and effectively modeled phenomenologically by one or more linear filters that extract the components of the…

Neurons and Cognition · Quantitative Biology 2011-11-02 Michael Famulare , Adrienne L. Fairhall

Neural networks are complex algorithms that loosely model the behaviour of the human brain. They play a significant role in computational neuroscience and artificial intelligence. The next generation of neural network models is based on the…

Neural and Evolutionary Computing · Computer Science 2020-05-29 Ifeatu Ezenwe , Alok Joshi , KongFatt Wong-Lin

We prove the existence of a phase transition for a stochastic model of interacting neurons. The spiking activity of each neuron is represented by a point process having rate $1 $ whenever its membrane potential is larger than a threshold…

Probability · Mathematics 2018-08-15 P. A. Ferrari , A. Galves , I. Grigorescu , E. Löcherbach

The experimental study of neural networks requires simultaneous measurements of a massive number of neurons, while monitoring properties of the connectivity, synaptic strengths and delays. Current technological barriers make such a mission…

Neurons and Cognition · Quantitative Biology 2016-01-12 Amir Goldental , Pinhas Sabo , Shira Sardi , Roni Vardi , Ido Kanter

We consider a model of interacting neurons where the membrane potentials of the neurons are described by a multidimensional piecewise deterministic Markov process (PDMP) with values in ${\mathbb R}^N, $ where $ N$ is the number of neurons…

Statistics Theory · Mathematics 2016-10-04 Pierre Hodara , Nathalie Krell , Eva Löcherbach

Neural networks are able to extract information from the timing of spikes. Here we provide new results on the behavior of the simplest neuronal model which is able to decode information embedded in temporal spike patterns, the so called…

Disordered Systems and Neural Networks · Physics 2015-06-17 Carlo Baldassi , Alfredo Braunstein , Riccardo Zecchina
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