10,352 research outputs found
Measurement of Anomalous Diffusion Using Recurrent Neural Networks
Anomalous diffusion occurs in many physical and biological phenomena, when
the growth of the mean squared displacement (MSD) with time has an exponent
different from one. We show that recurrent neural networks (RNN) can
efficiently characterize anomalous diffusion by determining the exponent from a
single short trajectory, outperforming the standard estimation based on the MSD
when the available data points are limited, as is often the case in
experiments. Furthermore, the RNN can handle more complex tasks where there are
no standard approaches, such as determining the anomalous diffusion exponent
from a trajectory sampled at irregular times, and estimating the switching time
and anomalous diffusion exponents of an intermittent system that switches
between different kinds of anomalous diffusion. We validate our method on
experimental data obtained from sub-diffusive colloids trapped in speckle light
fields and super-diffusive microswimmers.Comment: 6 pages, 4 figures. Supplemental material available as separate file
in the Ancillary Files sectio
Transient spatiotemporal chaos in a diffusively and synaptically coupled Morris-Lecar neuronal network
Thesis (M.S.) University of Alaska Fairbanks, 2014Transient spatiotemporal chaos was reported in models for chemical reactions and in experiments for turbulence in shear flow. This study shows that transient spatiotemporal chaos also exists in a diffusively coupled Morris-Lecar (ML) neuronal network, with a collapse to either a global rest state or to a state of pulse propagation. Adding synaptic coupling to this network reduces the average lifetime of spatiotemporal chaos for small to intermediate coupling strengths and almost all numbers of synapses. For large coupling strengths, close to the threshold of excitation, the average lifetime increases beyond the value for only diffusive coupling, and the collapse to the rest state dominates over the collapse to a traveling pulse state. The regime of spatiotemporal chaos is characterized by a slightly increasing Lyapunov exponent and degree of phase coherence as the number of synaptic links increases. In contrast to the diffusive network, the pulse solution must not be asymptotic in the presence of synapses. The fact that chaos could be transient in higher dimensional systems, such as the one being explored in this study, point to its presence in every day life. Transient spatiotemporal chaos in a network of coupled neurons and the associated chaotic saddle provide a possibility for switching between metastable states observed in information processing and brain function. Such transient dynamics have been observed experimentally by Mazor, when stimulating projection neurons in the locust antennal lobe with different odors
Synchronizations in small-world networks of spiking neurons: Diffusive versus sigmoid couplings
By using a semi-analytical dynamical mean-field approximation previously
proposed by the author [H. Hasegawa, Phys. Rev. E, {\bf 70}, 066107 (2004)], we
have studied the synchronization of stochastic, small-world (SW) networks of
FitzHugh-Nagumo neurons with diffusive couplings. The difference and similarity
between results for {\it diffusive} and {\it sigmoid} couplings have been
discussed. It has been shown that with introducing the weak heterogeneity to
regular networks, the synchronization may be slightly increased for diffusive
couplings, while it is decreased for sigmoid couplings. This increase in the
synchronization for diffusive couplings is shown to be due to their local,
negative feedback contributions, but not due to the shorten average distance in
SW networks. Synchronization of SW networks depends not only on their structure
but also on the type of couplings.Comment: 17 pages, 8 figures, accepted in Phys. Rev. E with some change
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