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Reversible electropermeabilization, commonly referred to as electroporation, is a transient increase in cell membrane permeability induced by short, high-voltage electric pulses. We present a stochastically perturbed version of a…
Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link…
Since the first recordings made of evoked action potentials it has become apparent that the responses of individual neurons to ongoing physiologically relevant input, are highly variable. This variability is manifested in non-stationary…
A key appeal of the recently proposed Neural Ordinary Differential Equation (ODE) framework is that it seems to provide a continuous-time extension of discrete residual neural networks. As we show herein, though, trained Neural ODE models…
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…
Information processing in the brain crucially depends on encoding properties of single neurons, with particular relevance of the spike-generation mechanism. The latter hinges upon the bifurcation type at the transition point between resting…
In synaptic molecular communication, the activation of postsynaptic receptors by neurotransmitters (NTs) is governed by a stochastic reaction-diffusion process and, hence, inherently random. It is currently not fully understood how this…
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…
Recent experimental and theoretical studies have indicated that the putative criticality of cortical dynamics may corresponds to a synchronization phase transition. The critical dynamics near such a critical point needs further…
We study numerically and analytically first- and second-order phase transitions in neuronal networks stimulated by shot noise (a flow of random spikes bombarding neurons). Using an exactly solvable cortical model of neuronal networks on…
Stochastic regularization of neural networks (e.g. dropout) is a wide-spread technique in deep learning that allows for better generalization. Despite its success, continuous-time models, such as neural ordinary differential equation (ODE),…
The brain produces rhythms in a variety of frequency bands. Some are likely by-products of neuronal processes; others are thought to be top-down. Produced entirely naturally, these rhythms have clearly recognizable beats, but they are very…
Both natural and synthetic chemical systems not only exhibit a range of non-trivial dynamics, but also transition between qualitatively different dynamical behaviours as environmental parameters change. Such transitions are called…
The effects of spike timing precision and dynamical behavior on error correction in spiking neurons were investigated. Stationary discharges -- phase locked, quasiperiodic, or chaotic -- were induced in a simulated neuron by presenting…
We consider evolutionary PDE inclusions of the form \[ -\lambda \dot{u}_\lambda + \Delta u - \mathrm{D} W_0(u) + f \ni \partial \mathcal{R}_1(\dot{u}) \qquad\text{in $(0,T) \times \Omega$,} \] where $\mathcal{R}_1$ is a positively…
The hyperbolic dependence of catalytic rate on substrate concentration is a classical result in enzyme kinetics, quantified by the celebrated Michaelis-Menten equation. The ubiquity of this relation in diverse chemical and biological…
This work continues the analysis of complex dynamics in a class of bidimensional nonlinear hybrid dynamical systems with resets modeling neuronal voltage dynamics with adaptation and spike emission. We show that these models can generically…
In this work we study, analytically and employing Monte Carlo simulations, the influence of the competition between several activity-dependent synaptic processes, such as short-term synaptic facilitation and depression, on the maximum…
In timing-based neural codes, neurons have to emit action potentials at precise moments in time. We use a supervised learning paradigm to derive a synaptic update rule that optimizes via gradient ascent the likelihood of postsynaptic firing…
Rebinding kinetics of molecular ligands plays a critical role in biomachinery, from regulatory networks to protein transcription, and is also a key factor for designing drugs and high-precision biosensors.In this study, we investigate…