Martin Kassabov, Steven H. Strogatz, Alex Townsend
Consider n identical Kuramoto oscillators on a random graph. Specifically, consider \ER random graphs in which any two oscillators are bidirectionally coupled with unit strength, independently and at random, with probability 0≤p≤1. We say that a network is globally synchronizing if the oscillators converge to the all-in-phase synchronous state for almost all initial conditions. Is there a critical threshold for p above which global synchrony is extremely likely but below which it is extremely rare? It is suspected that a critical threshold exists and is close to the so-called connectivity threshold, namely, p∼log(n)/n for n≫1. Ling, Xu, and Bandeira made the first progress toward proving a result in this direction: they showed that if p≫log(n)/n1/3, then \ER networks of Kuramoto oscillators are globally synchronizing with high probability as n→∞. Here we improve that result by showing that p≫log2(n)/n suffices. Our estimates are explicit: for example, we can say that there is more than a 99.9996% chance that a random network with n=106 and p>0.01117 is globally synchronizing.

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İlker Türker, Serkan Aksu

Applied Acoustics
Volume 191, 30 March 2022, 108660

We propose a novel time-graph representation method for sounds and time series.
Quantized amplitude levels serve as nodes, while neighborhood of these nodes in time domain define connections.
Applying various undersampling rates, a multilayer graph representation is achieved, further composed as RGB images.
Flattened graph representations from each time frame are tiled to compose a time-graph representation.
The proposed representation improves classification accuracy when used in combination with mel-spectrograms.

Read the full article at: www.sciencedirect.com