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A neural network model that exhibits stochastic population bursting is studied by simulation. First return maps of inter-burst intervals exhibit recurrent unstable periodic orbit (UPO)-like trajectories similar to those found in experiments on hippocampal slices. Applications of various control methods and surrogate analysis for UPO-detection also yield results similar to those of experiments. Our results question the interpretation of the experimental data as evidence for deterministic chaos and suggest caution in the use of UPO-based methods for detecting determinism in time-series data.
For general dissipative dynamical systems we study what fraction of solutions exhibit chaotic behavior depending on the dimensionality $d$ of the phase space. We find that a system of $d$ globally coupled ODEs with quadratic and cubic non-linearities
We develop a spacetime neural network method with second order optimization for solving quantum dynamics from the high dimensional Schr{o}dinger equation. In contrast to the standard iterative first order optimization and the time-dependent variation
We discuss, in this paper, the dynamical properties of extremely diluted, non-monotonic neural networks. Assuming parallel updating and the Hebb prescription for the synaptic connections, a flow equation for the macroscopic overlap is derived. A rich
In this work, we characterize the performance of a deep convolutional neural network designed to detect and quantify chemical elements in experimental X-ray photoelectron spectroscopy data. Given the lack of a reliable database in literature, in orde
Domain walls, optimal droplets and disorder chaos at zero temperature are studied numerically for the solid-on-solid model on a random substrate. It is shown that the ensemble of random curves represented by the domain walls obeys Schramms left passa