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Sorry, am I missing something? "Topology" here just seems to mean connectivity, and I can't even tell why they have a notion of 3x3 connectivity-matrix structure. A whole lot of this seems under-explained.

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qazwsxedchac 2 days ago | parent | next [-]

There's an earlier paper [0] involving the same authors which explains this a bit better.

AIUI, they use the 3x3 neighbourhoods to capture local directional and curvature (i.e. gradient) information in the distance matrix. They then apply two heuristics (reduction to an 8-bit binary number and binning into sextiles) to reduce the floating point gradient information to coarse integers to aid pattern recognition.

The more recent paper adds another heuristic (empirically chosen similarity threshold) to aid finding starting points of recurring patterns.

[0] https://doi.org/10.1038/s41531-021-00240-4 , Equation (5) onwards.

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ano-ther a day ago | parent [-]

Thanks. What I don’t understand is how searching for previous patterns that are similar helps in predicting timelines that are chaotic (it seems to be quite good at that).

	▲	qazwsxedchac a day ago \| parent [-]
		It only helps because the chaotic system under consideration has periodic components. The attractor shown in figure 1e has such periodic components, and identifying these does help, but only with very near term forecasting. When the accumulated forecast error crosses a threshold, it suddenly causes a large phase error, best seen from about point 75 onwards in the x and y components. From that point onwards the forecast is useless.

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keithalewis 2 days ago | parent | prev [-]

You are missing what is missing. Their source code does not fill in the missing pieces.