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Synaptic connections in neuronal circuits are modulated by pre- and post-synaptic spiking activity. Heuristic models of this process of synaptic plasticity can provide excellent fits to results from in-vitro experiments in which pre- and…
We study the capacity of Hodgkin-Huxley neuron in a network to change temporarily or permanently their connections and behavior, the so called spike timing-dependent plasticity (STDP), as a function of their synchronous behavior. We…
Biological systems represent time from microseconds to years. An important gap in our knowledge concerns the mechanisms for encoding time intervals of hundreds of milliseconds to minutes that matter for tasks like navigation, communication,…
We study the synchronization of two model neurons coupled through a synapse having an activity-dependent strength. Our synapse follows the rules of Spike-Timing Dependent Plasticity (STDP). We show that this plasticity of the coupling…
Single neuron models have a long tradition in computational neuroscience. Detailed biophysical models such as the Hodgkin-Huxley model as well as simplified neuron models such as the class of integrate-and-fire models relate the input…
This paper establishes limit theorems for a class of stochastic hybrid systems (continuous deterministic dynamic coupled with jump Markov processes) in the fluid limit (small jumps at high frequency), thus extending known results for jump…
The interactions between diffusing molecules and membrane-bound receptors drive numerous cellular processes. In this work, we develop a spatial model of molecular interactions with membrane receptors by homogenizing the cell membrane and…
The synaptic connectivity of cortex is plastic, with experience shaping the ongoing interactions between neurons. Theoretical studies of spike timing-dependent plasticity (STDP) have focused on either just pairs of neurons or large-scale…
Neuromorphic computing and spiking neural networks (SNN) mimic the behavior of biological systems and have drawn interest for their potential to perform cognitive tasks with high energy efficiency. However, some factors such as temporal…
We consider a new class of non Markovian processes with a countable number of interacting components. At each time unit, each component can take two values, indicating if it has a spike or not at this precise moment. The system evolves as…
Neuronal network synchronization has received wide interests. Network connection structure is known to play a key role in its synchronization. In the present manuscript, we study the influence of initial membrane potentials together with…
Learning in the brain requires complementary mechanisms: potentiation and activity-dependent homeostatic scaling. We introduce synaptic scaling to a biologically-realistic spiking model of neocortex which can learn changes in oscillatory…
A self-consistent theory is proposed for the general problem of interacting undulating fluid membranes subject to the constraint that they do not interpenetrate. We implement the steric constraint via an exact functional integral…
Starting from a microscopic model for a system of neurons evolving in time which individually follow a stochastic integrate-and-fire type model, we study a mean-field limit of the system. Our model is described by a system of SDEs with…
Neural activity exhibits a vast range of timescales that can be several fold larger than the membrane time constant of individual neurons. Two types of mechanisms have been proposed to explain this conundrum. One possibility is that large…
Spiking Neural Networks (SNNs) have attracted enormous research interest due to temporal information processing capability, low power consumption, and high biological plausibility. However, the formulation of efficient and high-performance…
Developing networks of neural systems can exhibit spontaneous, synchronous activities called neural bursts, which can be important in the organization of functional neural circuits. Before the network matures, the activity level of a burst…
We study a system of particles in the interval $[0,\epsilon^{-1}] \cap \mathbb Z$, $\epsilon^{-1}$ a positive integer. The particles move as symmetric independent random walks (with reflections at the endpoints); simultaneously new…
The dynamics of local cortical networks are irregular, but correlated. Dynamic excitatory--inhibitory balance is a plausible mechanism that generates such irregular activity, but it remains unclear how balance is achieved and maintained in…
We consider a new class of non Markovian processes with a countable number of interacting components, both in discrete and continuous time. Each component is represented by a point process indicating if it has a spike or not at a given…