Related papers: Self-consistent moment dynamics for networks of sp…
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…
Spiking neural network is a type of artificial neural network in which neurons communicate between each other with spikes. Spikes are identical Boolean events characterized by the time of their arrival. A spiking neuron has internal…
The paper deals with non-linear Poisson neuron network models with bounded memory dynamics, that can include both Hebbian learning mechanisms and refractory periods. The state of a network is described by the times elapsed since its neurons…
We study the dynamics of phase synchronization in growing populations of discrete phase oscillatory systems when the division process is coupled to the distribution of oscillator phases. Using mean field theory, linear stability analysis,…
We investigate the behavior of a simple majority dynamics on networks of agents whose interaction topology exhibits a community structure. By leveraging recent advancements in the analysis of dynamics, we prove that, when the states of the…
We analyze networked heterogeneous nonlinear systems, with diffusive coupling and interconnected over a generic static directed graph. Due to the network's hetereogeneity, complete synchronization is impossible, in general, but an emergent…
We study the collective dynamics of a Leaky Integrate and Fire network in which precise relative phase relationship of spikes among neurons are stored, as attractors of the dynamics, and selectively replayed at differentctime scales. Using…
We analyze the dynamics of networks of spiking neural oscillators. First, we present an exact linear stability theory of the synchronous state for networks of arbitrary connectivity. For general neuron rise functions, stability is…
Spikes are the currency in central nervous systems for information transmission and processing. They are also believed to play an essential role in low-power consumption of the biological systems, whose efficiency attracts increasing…
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…
Auto-regulation, a process wherein a protein negatively regulates its own production, is a common motif in gene expression networks. Negative feedback in gene expression plays a critical role in buffering intracellular fluctuations in…
One of the major challenges in neuroscience is to determine how noise that is present at the molecular and cellular levels affects dynamics and information processing at the macroscopic level of synaptically coupled neuronal populations.…
Firing rate fluctuations in neural populations are observed experimentally over multiple time scales, in single neurons, across trials when elicited by stimuli, and across populations. In this work, we examine how firing rate fluctuations…
We describe a simple conductance-based model neuron that includes intra- and extra-cellular ion concentration dynamics and show that this model exhibits periodic bursting. The bursting arises as the fast spiking behavior of the neuron is…
Collective dynamics of spiking networks of neurons has been of central interest to both computation neuroscience and network science. Over the past years a new generation of neural population models based on exact reductions (ER) of spiking…
In order to describe the firing activity of a homogenous assembly of neurons, we consider time elapsed models, which give mathematical descriptions of the probability density of neurons structured by the distribution of times elapsed since…
Idealized networks of integrate-and-fire neurons with impulse-like interactions obey McKean-Vlasov diffusion equations in the mean-field limit. These equations are prone to blowups: for a strong enough interaction coupling, the mean-field…
Learning is based on synaptic plasticity, which affects and is driven by neural activity. Because pre- and postsynaptic spiking activity is shaped by randomness, the synaptic weights follow a stochastic process, requiring a probabilistic…
For the retrieval dynamics of sparsely coded attractor associative memory models with synaptic noise the inclusion of a macroscopic time-dependent threshold is studied. It is shown that if the threshold is chosen appropriately as a function…
Spiking activity of neurons engaged in learning and performing a task show complex spatiotemporal dynamics. While the output of recurrent network models can learn to perform various tasks, the possible range of recurrent dynamics that…