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1. Heavy-tailed distributions, correlations, kurtosis and Taylor’s Law of fluctuation scaling

   https://doi.org/10.1098/rspa.2020.0610  

   Cohen, Joel E.; Davis, Richard A.; Samorodnitsky, Gennady (December 2020, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences)

   null (Ed.)

   Pillai & Meng (Pillai & Meng 2016 Ann. Stat. 44 , 2089–2097; p. 2091) speculated that ‘the dependence among [random variables, rvs] can be overwhelmed by the heaviness of their marginal tails ·· ·’. We give examples of statistical models that support this speculation. While under natural conditions the sample correlation of regularly varying (RV) rvs converges to a generally random limit, this limit is zero when the rvs are the reciprocals of powers greater than one of arbitrarily (but imperfectly) positively or negatively correlated normals. Surprisingly, the sample correlation of these RV rvs multiplied by the sample size has a limiting distribution on the negative half-line. We show that the asymptotic scaling of Taylor’s Law (a power-law variance function) for RV rvs is, up to a constant, the same for independent and identically distributed observations as for reciprocals of powers greater than one of arbitrarily (but imperfectly) positively correlated normals, whether those powers are the same or different. The correlations and heterogeneity do not affect the asymptotic scaling. We analyse the sample kurtosis of heavy-tailed data similarly. We show that the least-squares estimator of the slope in a linear model with heavy-tailed predictor and noise unexpectedly converges much faster than when they have finite variances. 

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2. North American Blackout Time Series Statistics and Implications for Blackout Risk

   https://doi.org/10.1109/TPWRS.2015.2510627  

   Carreras, Benjamin A; Newman, David E; Dobson, Ian (November 2016, IEEE Transactions on Power Systems)

   We use North American Electric Reliability Corporation historical data to give improved estimates of distributions of blackout size, time correlations, and waiting times for the Eastern and Western interconnections of the North American grid. We then explain and estimate the implications of the power law region (heavy tails) in the empirical distribution of blackout size in the historical data for the Western interconnection. Annual mean blackout size has high variability and the risk of large blackouts exceeds the risk of medium size blackouts. Ways to communicate blackout risk are discussed. 

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3. Power-law behavior of transcription factor dynamics at the single-molecule level implies a continuum affinity model

   https://doi.org/10.1093/nar/gkab072  

   Garcia, David A; Fettweis, Gregory; Presman, Diego M; Paakinaho, Ville; Jarzynski, Christopher; Upadhyaya, Arpita; Hager, Gordon L (February 2021, Nucleic Acids Research)

   null (Ed.)

   Abstract Single-molecule tracking (SMT) allows the study of transcription factor (TF) dynamics in the nucleus, giving important information regarding the diffusion and binding behavior of these proteins in the nuclear environment. Dwell time distributions obtained by SMT for most TFs appear to follow bi-exponential behavior. This has been ascribed to two discrete populations of TFs—one non-specifically bound to chromatin and another specifically bound to target sites, as implied by decades of biochemical studies. However, emerging studies suggest alternate models for dwell-time distributions, indicating the existence of more than two populations of TFs (multi-exponential distribution), or even the absence of discrete states altogether (power-law distribution). Here, we present an analytical pipeline to evaluate which model best explains SMT data. We find that a broad spectrum of TFs (including glucocorticoid receptor, oestrogen receptor, FOXA1, CTCF) follow a power-law distribution of dwell-times, blurring the temporal line between non-specific and specific binding, suggesting that productive binding may involve longer binding events than previously believed. From these observations, we propose a continuum of affinities model to explain TF dynamics, that is consistent with complex interactions of TFs with multiple nuclear domains as well as binding and searching on the chromatin template. 

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4. Autocorrelation properties of temporal networks governed by dynamic node variables

   https://doi.org/10.1103/PhysRevResearch.7.013083  

   Hartle, Harrison; Masuda, Naoki (January 2025, Physical Review Research)

   We study synthetic temporal networks whose evolution is determined by stochastically evolving node variables—synthetic analogues of, e.g., temporal proximity networks of mobile agents. We quantify the long-timescale correlations of these evolving networks by an autocorrelative measure of network-structural memory. Several distinct patterns of autocorrelation arise, including power-law decay and exponential decay, depending on the choice of node-variable dynamics and connection probability function. Our methods are also applicable in wider contexts; our temporal network models are tractable mathematically and in simulation, and our long-term memory quantification is analytically tractable and straightforwardly computable from temporal network data. Published by the American Physical Society2025 

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5. A Search for Cosmic Ray Bursts at 0.1 PeV with a Small Air Shower Array

   https://doi.org/10.3390/sym14030501  

   Clay, Roger; Singh, Jassimar; Homola, Piotr; Bar, Olaf; Beznosko, Dmitry; Bhatt, Apoorva; Bhatta, Gopal; Bibrzycki, Łukasz; Budnev, Nikolay; Alvarez-Castillo, David E.; et al (March 2022, Symmetry)

   The Cosmic Ray Extremely Distributed Observatory (CREDO) pursues a global research strategy dedicated to the search for correlated cosmic rays, so-called Cosmic Ray Ensembles (CRE). Its general approach to CRE detection does not involve any a priori considerations, and its search strategy encompasses both spatial and temporal correlations, on different scales. Here we search for time clustering of the cosmic ray events collected with a small sea-level extensive air shower array at the University of Adelaide. The array consists of seven one-square-metre scintillators enclosing an area of 10 m × 19 m. It has a threshold energy ~0.1 PeV, and records cosmic ray showers at a rate of ~6 mHz. We have examined event arrival times over a period of over 2.5 years in two equipment configurations (without and with GPS timing), recording ~300 k events and ~100 k events. We determined the event time spacing distributions between individual events and the distributions of time periods which contained specific numbers of multiple events. We find that the overall time distributions are as expected for random events. The distribution which was chosen a priori for particular study was for time periods covering five events (four spacings). Overall, these distributions fit closely with expectation, but there are two outliers of short burst periods in data for each configuration. One of these outliers contains eight events within 48 s. The physical characteristics of the array will be discussed together with the analysis procedure, including a comparison between the observed time distributions and expectation based on randomly arriving events. 

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