Related papers: Observing hidden neuronal states in experiments

We analyze pattern formation on a network of cells where each cell inhibits its neighbors through cell-to-cell contact signaling. The network is modeled as an interconnection of identical dynamical subsystems each of which represents the…

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…

We disclose the generality of the intrinsic mechanisms underlying multistability in reciprocally inhibitory 3-cell circuits composed of simplified, low-dimensional models of oscillatory neurons, as opposed to those of a detailed Hodgkin-…

We show that it is possible to learn protocols that effect fast and efficient state-to-state transformations in simulation models of active particles. By encoding the protocol in the form of a neural network we use evolutionary methods to…

We give a constructive method for realizing an arbitrary directed graph (with no one-cycles) as a heteroclinic or an excitable dynamic network in the phase space of a system of coupled cells of two types. In each case, the system is…

Many natural and man-made network systems need to maintain certain patterns, such as working at equilibria or limit cycles, to function properly. Thus, the ability to stabilize such patterns is crucial. Most of the existing studies on…

The time elapsed model describes the firing activity of an homogeneous assembly of neurons thanks to the distribution of times elapsed since the last discharge. It gives a mathematical description of the probability density of neurons…

We study the steady state of driven elastic strings in disordered media below the depinning threshold. In the low-temperature limit, for a fixed sample, the steady state is dominated by a single configuration, which we determine exactly…

Dynamical balance of excitation and inhibition is usually invoked to explain the irregular low firing activity observed in the cortex. We propose a robust nonlinear balancing mechanism for a random network of spiking neurons, which works…

Cortical neurons emit seemingly erratic trains of action potentials or "spikes," and neural network dynamics emerge from the coordinated spiking activity within neural circuits. These rich dynamics manifest themselves in a variety of…

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 present an example of the practical implementation of a protocol for experimental bifurcation detection based on on-line identification and feedback control ideas. The idea is to couple the experiment with an on-line computer-assisted…

Experimental continuation encompasses a set of methods that combine control and continuation to obtain the full bifurcation diagram of a nonlinear system experimentally, including responses that would be unstable in the system without…

The neural dynamics of the nematode C. elegans are experimentally low-dimensional and correspond to discrete behavioral states, where previous modeling work has found neural proxies for some of these states. Experimental results further…

We implement a computer-assisted approach that, under appropriate conditions, allows the bifurcation analysis of the coarse dynamic behavior of microscopic simulators without requiring the explicit derivation of closed macroscopic equations…

We perform one and two-parameter numerical bifurcation analysis of a mechanotransduction model approximating the dynamics of mesenchymal stem cell differentiation into neurons, adipocytes, myocytes and osteoblasts. For our analysis, we use…

Analytical equations were found for interdigitated electrodes, which considered reversible electrode reactions and pure diffusion within confined spaces. A conformal transformation, obtained by the use of Jacobian elliptic functions, was…

The elapsed-time model describes the behavior of interconnected neurons through the time since their last spike. It is an age-structured non-linear equation in which age corresponds to the elapsed time since the last discharge, and models…

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…

Simultaneous recordings from many neurons hide important information and the connections characterizing the network remain generally undiscovered despite the progresses of statistical and machine learning techniques. Discerning the presence…