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Human cognition emerges from coordinated spiking dynamics in distributed neural circuits, where information is encoded via both firing rates and precise spike timing determined by brain rhythms. Inspired by this notion, we propose a…
We study a system of dynamical units, each of which shows excitable or oscillatory behavior, depending on the choice of parameters. When we couple these units with repressive bonds, we can control the duration of collective oscillations for…
The Jansen-Rit model of a cortical column in the cerebral cortex is widely used to simulate spontaneous brain activity (EEG) and event-related potentials. It couples a pyramidal cell population with two interneuron populations, of which one…
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…
Spontaneous oscillations measured by Local field potentials (LFPs), electroencephalograms and magnetoencephalograms exhibits variety of oscillations spanning frequency band ($1-100$ Hz) in animals and humans. Both instantaneous power and…
We investigated the locking behaviors of coupled limit-cycle oscillators with phase and amplitude dynamics. We focused on how the dynamics are affected by inhomogeneous coupling strength and by angular and radial shifts in the coupling…
The phenomenon of high-order ($p/q$) synchronization, induced by \textit{two different} frequencies in the system, is well-known and studied extensively in forced oscillators including neurons and to a lesser extent in coupled oscillators.…
Winner Take All (WTA) circuits a type of Spiking Neural Networks (SNN) have been suggested as facilitating the brain's ability to process information in a Bayesian manner. Research has shown that WTA circuits are capable of approximating…
The Bayesian view of the brain hypothesizes that the brain constructs a generative model of the world, and uses it to make inferences via Bayes' rule. Although many types of approximate inference schemes have been proposed for hierarchical…
This paper considers the phenomenon of distinct regional frequencies recently observed in some power systems. First, a reduced-order mathematical model describing this behaviour is developed. Then, techniques to solve the model are…
Recurrent neural networks (RNNs) are machine learning models widely used for learning temporal relationships. Current state-of-the-art RNNs use integrating or spiking neurons -- two classes of computing units whose outputs depend directly…
We study the stable spatiotemporal patterns that arise in a 3D network of neuron oscillators, whose dynamics is described by the Leaky Integrate-and-Fire (LIF) model. More specifically, we investigate the form of the chimera states induced…
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…
Cells sense their surrounding by employing intracellular signaling pathways that transmit hormonal signals from the cell membrane to the nucleus. TGF-$\beta$/SMAD signaling encodes various cell fates, controls tissue homeostasis and is…
NF-{\kappa}B, one of key regulators of inflammation, apoptosis, and differentiation, was found to have noisy oscillatory shuttling between the nucleus and the cytoplasm in single cells when cells are stimulated by cytokine TNF{\alpha}. We…
The organization of higher-order interactions plays a central role in shaping collective dynamics, yet a general structural principle governing contagion on hypergraphs remains lacking. Here we introduce a nesting coefficient that…
Hippocampal neurons exhibit precise phase locking to network oscillations, but the computational principle governing this temporal precision is still unclear. Neural information is conveyed jointly by firing rates and spike timing, but…
Recurrent networks of dynamic elements frequently exhibit emergent collective oscillations, which can display substantial regularity even when the individual elements are considerably noisy. How noise-induced dynamics at the local level…
Cells continuously sense their surroundings to detect modifications and generate responses. Very often changes in extracellular concentrations initiate signaling cascades that eventually result in changes in gene expression. Increasing…
Recurrent neural networks (RNNs) are powerful dynamical models, widely used in machine learning (ML) and neuroscience. Prior theoretical work has focused on RNNs with additive interactions. However, gating - i.e. multiplicative -…