Related papers: Modeling bursting in neuronal networks using facil…
We present a mathematical analysis of a networks with Integrate-and-Fire neurons and adaptive conductances. Taking into account the realistic fact that the spike time is only known within some \textit{finite} precision, we propose a model…
Exploiting the specific structure of neuron conductance-based models, the paper investigates the mathematical modeling of neuronal bursting modulation. The proposed approach combines singularity theory and geometric singular perturbations…
The modular and hierarchical organization of the brain is believed to support the coexistence of segregated (specialization) and integrated (binding) information processes. A relevant question is yet to understand how such architecture…
Currently we routinely develop a complex neuronal network to explain observed but often paradoxical phenomena based upon biological recordings. Here we present a general approach to demonstrate how to mathematically tackle such a complex…
Activity of inhibitory neuron with delayed feedback is considered in the framework of point stochastic processes. The neuron receives excitatory input impulses from a Poisson stream, and inhibitory impulses from the feedback line with a…
The distinct timescales of synaptic plasticity and neural activity dynamics play an important role in the brain's learning and memory systems. Activity-dependent plasticity reshapes neural circuit architecture, determining spontaneous and…
Spontaneous brain activity in the absence of external stimuli is not random but contains complex dynamical structures such as neuronal avalanches with power-law duration and size distributions. These experimental observations have been…
`Bursting', defined as periods of high frequency firing of a neuron separated by periods of quiescence, has been observed in various neuronal systems, both \textit{in vitro} and \textit{in vivo}. It has been associated with a range of…
First return maps of interspike intervals for biological neurons that generate repetitive bursts of impulses can display stereotyped structures (neuronal signatures). Such structures have been linked to the possibility of multicoding and…
Experiments show that spike-triggered stimulation performed with Bidirectional Brain-Computer-Interfaces (BBCI) can artificially strengthen connections between separate neural sites in motor cortex (MC). What are the neuronal mechanisms…
A discrete-time random process is described which can generate bursty sequences of events. A Bernoulli process, where the probability of an event occurring at time $t$ is given by a fixed probability $x$, is modified to include a memory…
Post-Traumatic Stress Disorder (PTSD) is fundamentally a neuroplastic problem traumatic contact events encode over-reactive neural pathways through Hebbian long-term potentiation, producing hair-triggered amygdala-HPA stress cascades that…
The effect of stochasticity, in the form of Gaussian white noise, in a predator-prey model with two distinct time-scales is presented. A supercritical singular Hopf bifurcation yields a Type II excitability in the deterministic model. We…
This paper proposes a framework for the biological learning mechanism as a general learning system. The proposal is as follows. The bursting and tonic modes of firing patterns found in many neuron types in the brain correspond to two…
Collective rhythmic dynamics from neurons is vital for cognitive functions such as memory formation but how neurons self-organize to produce such activity is not well understood. Attractor-based models have been successfully implemented as…
Self-exciting processes of Hawkes type have been used to model various phenomena including earthquakes, neural activities, and views of online videos. Studies of temporal networks have revealed that sequences of social interevent times for…
Prior work on probing neural networks primarily relies on input-space analysis or parameter perturbation, both of which face fundamental limitations in accessing structural information encoded in intermediate representations. We introduce…
The branching process is the minimal model for propagation dynamics, avalanches and criticality, broadly used in neuroscience. A simple extension of it, adding inhibitory nodes, induces a much-richer phenomenology, including, an…
We present an interacting branching model of neural network dynamics, incorporating key biological features such as inhibition with several types of inhibitory interactions. We establish a hierarchy of analytical mean-field approximations…
We introduce a novel model for updating perceptual beliefs about the environment by extending the concept of Allostasis to the control of internal representations. Allostasis is a fundamental regulatory mechanism observed in animal…