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It is well known that bursting activity plays an important role in the processes of transmission of neural signals. In terms of population dynamics, macroscopic bursting can be described using a mean-field approach. Mean field theory…
The result of computational operations performed at the single cell level are coded into sequences of action potentials (APs). In the cerebral cortex, due to its columnar organization, large number of neurons are involved in any individual…
A simple threshold model of neuron firing (with the neuron membrane electrochemical potential governed by the chaotic Rossler attractor) has been analyzed by mapping the generated irregular spiking time-series into telegraph signals. In…
Probabilistic inference offers a principled framework for understanding both behaviour and cortical computation. However, two basic and ubiquitous properties of cortical responses seem difficult to reconcile with probabilistic inference:…
What input signals will lead to synchrony vs. desynchrony in a group of biological oscillators? This question connects with both classical dynamical systems analyses of entrainment and phase locking and with emerging studies of stimulation…
Phenotype transition takes place in many biological processes such as differentiation, and understanding how a cell reprograms its global gene expression profile is a problem of rate theories. A cell phenotype transition accompanies with…
It has been recently shown that the exponential growth rate of a population of bacterial cells starting from a single cell shows transient oscillations due to early synchronized bursts of division. These oscillations are enhanced by cell…
We study rate-induced phase-tipping (RP-tipping) between two stable limit cycles of a birhythmic oscillator. We say that such an oscillator RP-tips when a time variation of an input parameter preserves the bistability of the limit cycles…
A widely accepted view of computations in the brain relies on population coding, where the neural ensemble firing rate is modulated in a stable manner to transmit information and perform various cognitive tasks. At the same time,…
The experimental study of neural networks requires simultaneous measurements of a massive number of neurons, while monitoring properties of the connectivity, synaptic strengths and delays. Current technological barriers make such a mission…
The occurrence of sleep passed through the evolutionary sieve and is widespread in animal species. Sleep is known to be beneficial to cognitive and mnemonic tasks, while chronic sleep deprivation is detrimental. Despite the importance of…
Slow-wave sleep in mammalians is characterized by a change of large-scale cortical activity currently paraphrased as cortical Up/Down states. A recent experiment demonstrated a bistable collective behaviour in ferret slices, with the…
Oscillations are omnipresent in neural population signals, like multi-unit recordings, EEG/MEG, and the local field potential. They have been linked to the population firing rate of neurons, with individual neurons firing in a…
We continue the work of a series of previous studies of a mathematical model that describes the mean-field limit behavior of a homogeneous network of excitatory point spiking neurons. Contrary to other models, here noise is intrinsic to the…
In the light of recent experimental findings that gap junctions are essential for low level intensity detection in the sensory periphery, the Greenberg-Hastings cellular automaton is employed to model the response of a two-dimensional…
We review the description of the lowest-energy nucleon excitation -- the $\Delta$(1232)-resonance. Much of the recent experimental effort has been focused on the precision measurements of the nucleon-to-$\Delta$ transition by means of…
The recent discovery of special human neocortical pyramidal neurons that can individually learn the XOR function highlights the significant performance gap between biological and artificial neurons. The output of these pyramidal neurons…
Neural synchronization is believed to be critical for many brain functions. It frequently exhibits temporal variability, but it is not known if this variability has a specific temporal patterning. This study explores these…
In this work we consider a general non-autonomous hybrid system based on the integrate-and-fire model, widely used as simplified version of neuronal models and other types of excitable systems. Our unique assumption is that the system is…
Cortical oscillations are thought to be involved in many cognitive functions and processes. Several mechanisms have been proposed to regulate oscillations. One prominent but understudied mechanism is gap-junctional coupling. Gap junctions…