Propofol anesthesia destabilizes neural dynamics across cortex.

Every day, hundreds of thousands of people undergo general anesthesia. One hypothesis is that anesthesia disrupts dynamic stability-the ability of the brain to balance excitability with the need to be stable and controllable. To test this hypothesis, we developed a method for quantifying changes in population-level dynamic stability in complex systems: delayed linear analysis for stability estimation (DeLASE).

Winning the Lottery With Neural Connectivity Constraints: Faster Learning Across Cognitive Tasks With Spatially Constrained Sparse RNNs.

Recurrent neural networks (RNNs) are often used to model circuits in the brain and can solve a variety of difficult computational problems requiring memory, error correction, or selection (Hopfield, 1982; Maass et al., 2002; Maass, 2011). However, fully connected RNNs contrast structurally with their biological counterparts, which are extremely sparse (about 0.

Network inference from short, noisy, low time-resolution, partial measurements: Application to neuronal calcium dynamics.

Network link inference from measured time series data of the behavior of dynamically interacting network nodes is an important problem with wide-ranging applications, e.g., estimating synaptic connectivity among neurons from measurements of their calcium fluorescence.

Complexity reduction ansatz for systems of interacting orientable agents: Beyond the Kuramoto model.

Previous results have shown that a large class of complex systems consisting of many interacting heterogeneous phase oscillators exhibit an attracting invariant manifold. This result has enabled reduced analytic system descriptions from which all the long term dynamics of these systems can be calculated. Although very useful, these previous results are limited by the restriction that the individual interacting system components have one-dimensional dynamics, with states described by a single, scalar, angle-like variable (e.

Observing microscopic transitions from macroscopic bursts: Instability-mediated resetting in the incoherent regime of the D-dimensional generalized Kuramoto model.

This paper considers a recently introduced D-dimensional generalized Kuramoto model for many (N≫1) interacting agents, in which the agent states are D-dimensional unit vectors. It was previously shown that, for even (but not odd) D, similar to the original Kuramoto model (D=2), there exists a continuous dynamical phase transition from incoherence to coherence of the time asymptotic attracting state (time t→∞) as the coupling parameter K increases through a critical value which we denote K >0. We consider this transition from the point of view of the stability of an incoherent state, where an incoherent state is defined as one for which the N→∞ distribution function is time-independent and the macroscopic order parameter is zero.

Hybrid forecasting of chaotic processes: Using machine learning in conjunction with a knowledge-based model.

A model-based approach to forecasting chaotic dynamical systems utilizes knowledge of the mechanistic processes governing the dynamics to build an approximate mathematical model of the system. In contrast, machine learning techniques have demonstrated promising results for forecasting chaotic systems purely from past time series measurements of system state variables (training data), without prior knowledge of the system dynamics. The motivation for this paper is the potential of machine learning for filling in the gaps in our underlying mechanistic knowledge that cause widely-used knowledge-based models to be inaccurate.

Modeling the network dynamics of pulse-coupled neurons.

We derive a mean-field approximation for the macroscopic dynamics of large networks of pulse-coupled theta neurons in order to study the effects of different network degree distributions and degree correlations (assortativity). Using the ansatz of Ott and Antonsen [Chaos 18, 037113 (2008)], we obtain a reduced system of ordinary differential equations describing the mean-field dynamics, with significantly lower dimensionality compared with the complete set of dynamical equations for the system. We find that, for sufficiently large networks and degrees, the dynamical behavior of the reduced system agrees well with that of the full network.