Related papers: Astrocytic resource diffusion stabilizes persisten…
The spiking activity of principal cells in mammalian hippocampus encodes an internalized neuronal representation of the ambient space---a cognitive map. Once learned, such a map enables the animal to navigate a given environment for a long…
The density of synaptic receptors in front of presynaptic release sites is stabilized in the presence of scaffold proteins, but the receptors and scaffold molecules have local exchanges with characteristic times shorter than that of the…
Seizure activity is a ubiquitous and pernicious pathophysiology that, in principle, should yield to mathematical treatments of (neuronal) ensemble dynamics - and therefore interventions on stochastic chaos. A seizure can be characterised as…
Biological systems use neural circuits to integrate input information and produce outputs. Synaptic convergence, where multiple neurons converge their inputs onto a single downstream neuron, is common in natural neural circuits. However,…
A neural correlate of parametric working memory is a stimulus specific rise in neuron firing rate that persists long after the stimulus is removed. Network models with local excitation and broad inhibition support persistent neural…
We develop an unconditionally energy-stable tensor-product space-time discretization framework for the solution of a linear kinetic transport equation in one space dimension. The kinetic equation is a simplified model of radiative transfer…
Complex coherent dynamics is present in a wide variety of neural systems. A typical example is the voltage transitions between up and down states observed in cortical areas in the brain. In this work, we study this phenomenon via a…
We use tools of bifurcation theory to characterize dynamics of astrocytic~IP$_3$ and~Ca$^{2+}$ for different~IP$_3$ regimes from a mathematical point of view. We do so following a bottom-up approach, starting from a compact, well-stirred…
We report on our theoretical and numerical results concerning the transport mechanisms in the asteroid belt. We first derive a simple kinetic model of chaotic diffusion and show how it gives rise to some simple correlations (but not laws)…
Gamma-band rhythmic inhibition is a ubiquitous phenomenon in neural circuits yet its computational role still remains elusive. We show that a model of Gamma-band rhythmic inhibition allows networks of coupled cortical circuit motifs to…
We present a general linear dispersion relation which describes the coupled behavior of magnetorotational, photon bubble, and convective instabilities in weakly magnetized, differentially rotating accretion disks. We presume the accretion…
We study the effects of additive noise on traveling pulse solutions in spatially extended neural fields with linear adaptation. Neural fields are evolution equations with an integral term characterizing synaptic interactions between neurons…
We develop a complete stability theory for two-dimensional periodic traveling waves of reaction-diffusion systems. More precisely, we identify a diffusive spectral stability assumption, prove that it implies nonlinear stability and provide…
Stable diffusion models have ushered in a new era of advancements in image generation, currently reigning as the state-of-the-art approach, exhibiting unparalleled performance. The process of diffusion, accompanied by denoising through…
While neuromorphic computing architectures based on Spiking Neural Networks (SNNs) are increasingly gaining interest as a pathway toward bio-plausible machine learning, attention is still focused on computational units like the neuron and…
The lateral diffusion and trapping of neurotransmitter receptors within the postsynaptic membrane of a neuron plays a key role in determining synaptic strength and plasticity. Trapping is mediated by the reversible binding of receptors to…
Persistent activity is postulated to drive neural network plasticity and learning. To investigate its underlying cellular mechanisms, we developed a biophysically tractable model that explains the emergence, sustenance, and eventual…
Working memory (WM) is limited in its temporal length and capacity. Classic conceptions of WM capacity assume the system possesses a finite number of slots, but recent evidence suggests WM may be a continuous resource. Resource models…
We study a stochastic nonlocal PDE, arising in the context of modelling spatially distributed neural activity, which is capable of sustaining stationary and moving spatially-localized ``activity bumps''. This system is known to undergo a…
The stability of synchronous states is analysed in the context of two populations of inhibitory and excitatory neurons, characterized by different pulse-widths. The problem is reduced to that of determining the eigenvalues of a suitable…