Related papers: 2$\theta$-burster for rhythm-generating circuits

We study a simple map as a minimal model of excitable cells. The map has two fast variables which mimic the behavior of class I neurons, undergoing a sub-critical Hopf bifurcation. Adding a third slow variable allows the system to present…

It has been conjectured that the mass spectrum of the O(3) non-linear sigma model with a theta term in 2 dimensions may possess an excited state, which decays when theta is lowered from pi below a critical value. Since the direct numerical…

We consider SGD-type optimization on infinite-dimensional quadratic problems with power law spectral conditions. It is well-known that on such problems deterministic GD has loss convergence rates $L_t=O(t^{-\zeta})$, which can be improved…

Signaling networks are designed to sense an environmental stimulus and adapt to it. We propose and study a minimal model of signaling network that can sense and respond to external stimuli of varying strength in an adaptive manner. The…

This paper proposes a methodology to extract a low-dimensional integrate-and-fire model from an arbitrarily detailed single-compartment biophysical model. The method aims at relating the modulation of maximal conductance parameters in the…

This paper proposes to model the intracellular signalling networks using a fusion of behaviour-based systems and the blackboard architecture. In virtue of this fusion, the model developed by us, which has been named Cellulat, allows to take…

We report a detailed analysis on the emergence of bursting in a recently developed neural mass model that takes short-term synaptic plasticity into account. The one being used here is particularly important, as it represents an exact…

Brain dynamics can exhibit narrow-band nonlinear oscillations and multistability. For a subset of disorders of consciousness and motor control, we hypothesize that some symptoms originate from the inability to spontaneously transition from…

The activity generated by an ensemble of neurons is affected by various noise sources. It is a well-recognised challenge to understand the effects of noise on the stability of such networks. We demonstrate that the patterns of activity…

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…

Neural oscillations are electrical activities of the brain measurable at different frequencies. This paper studies the interaction between the fast and slow processes in the brain. We recorded signals intracranially from the simple Wistar…

We present a phenomenological reduced-order model to capture the transition to thermoacoustic instability in turbulent combustors. The model is based on the framework of synchronization and considers the acoustic field and the unsteady heat…

Unlike isolated beta-cells, which usually produce continuous spikes or fast and irregular bursts, electrically coupled beta-cells are apt to exhibit robust bursting action potentials. We consider the noise induced by thermal fluctuations as…

For a networked control system, we consider the problem of encoder and controller design. We study a discrete-time linear plant with a finite horizon performance cost, comprising of a quadratic function of the states and controls, and an…

We present three dynamic error feedback controllers for robust output regulation of regular linear systems. These controllers are (i) a minimal order robust controller for exponentially stable systems (ii) an observer-based robust…

Models of cortical neuronal circuits commonly depend on inhibitory feedback to control gain, provide signal normalization, and to selectively amplify signals using winner-take-all (WTA) dynamics. Such models generally assume that excitatory…

Ternary logic system is the most promising and pursued alternate to the prevailing binary logic systems due to the energy efficiency of circuits following reduced circuit complexity and chip area. In this paper, we have proposed a ternary…

While ordinary differential equations (ODEs) form the conceptual framework for modelling many cellular processes, specific situations demand stochastic models to capture the influence of noise. The most common formulation of stochastic…

When a founder cell and its progeny divide with incomplete cytokinesis, a network forms in which each intercellular bridge corresponds to a past mitotic event. Networks built in this manner are required for gamete production in many…

Bursts of images exhibit significant self-similarity across both time and space. This motivates a representation of the kernels as linear combinations of a small set of basis elements. To this end, we introduce a novel basis prediction…