Subsampling scaling

Abstract

In real-world applications, observations are often constrained to a small fraction of a system. Such spatial subsampling can be caused by the inaccessibility or the sheer size of the system, and cannot be overcome by longer sampling. Spatial subsampling can strongly bias inferences about a system's aggregated properties. To overcome the bias, we derive analytically a subsampling scaling framework that is applicable to different observables, including distributions of neuronal avalanches, of number of people infected during an epidemic outbreak, and of node degrees. We demonstrate how to infer the correct distributions of the underlying full system, how to apply it to distinguish critical from subcritical systems, and how to disentangle subsampling and finite size effects. Lastly, we apply subsampling scaling to neuronal avalanche models and to recordings from developing neural networks. We show that only mature, but not young networks follow power-law scaling, indicating self-organization to criticality during development.

Characteristic Earthquake Magnitude Frequency Distributions on Faults Calculated From Consensus Data in California

“…The participation magnitude‐frequency distribution at points is most applicable to hazard calculations and is expected to be characteristic with a balance toward higher magnitudes because more large events that nucleate far away on different faults can spread onto a specific fault or fault section than can smaller ones. This is an example of spatial subsampling, something known to affect exponential distribution shapes (e.g., Priesemann et al, ; Levina & Priesemann, ). We demonstrate this effect by constructing a synthetic earthquake catalog for a single fault surface that is constrained to have Gutenberg‐Richter nucleation magnitude frequency.…”

Quantifying Information Modification in Developing Neural Networks via Partial Information Decomposition

“…found that functional projections grew rapidly during the first week in vitro in dense cultures, reaching across the entire array within 15 days ( Figure 9)"); while, in a last stage, (iv) connectivity often leads to activity pattern where all neurons become simultaneously active in large, culture spanning bursts of activity. This can, for example, be seen for data used here in the development of large, system spanning neural avalanches with maturation of the culture (see Figure 4 in [33] and Figure 13 in the corresponding preprint [34]; for the definition of neural avalanches as used here, see [35]). The number of such system spanning avalanches was [0, 0, 7, 50, 73] for the five recording weeks.…”

Scale invariance in natural and artificial collective systems: a review

“…The work on subsample scaling is an active domain of interest, e.g. a novel methodology was presented by Levina & Priesemann in early 2017 [91].…”