Large-Scale, Wavelet-Based Analysis of Lysosomal Trajectories and Co-Movements of Lysosomes with Nanoparticle Cargos

Lysosomes—that is, acidic organelles known for degradation/recycling—move through the cytoplasm alternating between bursts of active transport and short, diffusive motions or even pauses. While their mobility is essential for lysosomes’ fusogenic and non-fusogenic interactions with target organelles, their movements have not been characterized in adequate detail. Here, large-scale statistical analysis of lysosomal movement trajectories reveals that lysosome trajectories in all examined cell types—both cancer and noncancerous ones—are superdiffusive and characterized by heavy-tailed distributions of run and flight lengths. Consideration of Akaike weights for various potential models (lognormal, power law, truncated power law, stretched exponential, and exponential) indicates that the experimental data are best described by the lognormal distribution, which, in turn, can be related to one of the space-search strategies particularly effective when “thorough” search needs to balance search for rare target(s) (organelles). In addition, automated, wavelet-based analysis allows for co-tracking the motions of lysosomes and the cargos they carry—particularly the nanoparticle aggregates known to cause selective lysosome disruption in cancerous cells. The methods we describe here could help study nanoparticle assemblies, viruses, and other objects transported inside various vesicle types, as well as coordinated movements of organelles/particles in the cytoplasm. Custom-written code that includes integrated workflow for our analyses is made available for academic use.

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From the central limit theorem to heavy-tailed distributions

Journal of Applied Probability ◽

10.1239/jap/1059060906 ◽

2003 ◽

Vol 40 (3) ◽

pp. 803-806 ◽

Cited By ~ 4

Author(s):

Jinwen Chen

Keyword(s):

Central Limit Theorem ◽

Limit Theorem ◽

Central Limit ◽

Power Law ◽

Power Law Distribution ◽

The Central Limit Theorem ◽

Heavy Tailed Distributions ◽

Heavy Tailed ◽

Random Indices ◽

Power Law Distributions

It has been observed that in many practical situations randomly stopped products of random variables have power law distributions. In this note we show that, in order for such a product to have a power law distribution, the only random indices are the exponentially distributed ones. We also consider a more general problem, which is closely related to problems concerning transformation from the central limit theorem to heavy-tailed distributions.

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POWER LAWS AND OTHER HEAVY-TAILED DISTRIBUTIONS IN LINGUISTIC TYPOLOGY

Advances in Complex Systems ◽

10.1142/s0219525911500196 ◽

2012 ◽

Vol 15 (03n04) ◽

pp. 1150019 ◽

Cited By ~ 4

Author(s):

GERHARD JÄGER

Keyword(s):

Large Scale ◽

Similarity Judgment ◽

Power Laws ◽

Data Bases ◽

Statistical Validation ◽

Quantitative Distribution ◽

Heavy Tailed Distributions ◽

The World ◽

Heavy Tailed ◽

Project Data

The paper investigates the quantitative distribution of language types across languages of the world. The studies are based on three large-scale typological data bases: The World Color Survey, the Automated Similarity Judgment Project data base, and the World Atlas of Language Structures. The main finding is that a surprisingly large and varied collection of linguistic typologies show power law behavior. The bulk of the paper deals with the statistical validation of these findings.

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Heavy-tailed distributions for building stock data

Environment and Planning B Urban Analytics and City Science ◽

10.1177/2399808318794499 ◽

2018 ◽

Vol 46 (7) ◽

pp. 1281-1296 ◽

Cited By ~ 1

Author(s):

Patrick Erik Bradley ◽

Martin Behnisch

Keyword(s):

Power Law ◽

Building Stock ◽

Underlying Distribution ◽

Large Cities ◽

Statistical Framework ◽

Heavy Tailed Distributions ◽

Heavy Tailed Distribution ◽

Event Histories ◽

Heavy Tailed ◽

Log Normal

The question of inferring the owner of a set of building stocks (e.g. from which country the buildings are taken) from building-related quantities like number of buildings or types of building event histories necessitates the knowledge of their distributions in order to compare them. If the distribution function is a power law, then a version of the 80/20 rule can be applied to describe the variable. This distribution is an example of a heavy-tailed distribution; another example is the log-normal distribution. Heavy-tailed distributions have the property that studying the effects of the few large values already yields most of the overall effect of the whole quantity. For example, if reducing the CO2 emissions of the buildings of a country is the issue, then in case of a heavy-tailed distribution, only the effects of the relatively few large cities need to be considered. It is shown that the number of buildings in German municipalities or counties or the number of building-related event histories of a certain vanished building stock follow a heavy-tailed distribution and give evidence for the type of underlying distribution. The methodology used is a recent statistical framework for discerning power law and other heavy-tailed distributions in empirical data.

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An analysis of power law distributions and tipping points during the global financial crisis

Annals of Actuarial Science ◽

10.1017/s1748499518000088 ◽

2018 ◽

Vol 13 (1) ◽

pp. 80-91 ◽

Cited By ~ 1

Author(s):

Yifei Li ◽

Lei Shi ◽

Neil Allan ◽

John Evans

Keyword(s):

Financial Crisis ◽

Power Law ◽

Global Financial Crisis ◽

Operational Risk ◽

Tipping Point ◽

Power Law Distribution ◽

Heavy Tailed Distributions ◽

Heavy Tailed ◽

The Global Financial Crisis ◽

Power Law Distributions

AbstractHeavy-tailed distributions have been observed for various financial risks and papers have observed that these heavy-tailed distributions are power law distributions. The breakdown of a power law distribution is also seen as an indicator of a tipping point being reached and a system then moves from stability through instability to a new equilibrium. In this paper, we analyse the distribution of operational risk losses in US banks, credit defaults in US corporates and market risk events in the US during the global financial crisis (GFC). We conclude that market risk and credit risk do not follow a power law distribution, and even though operational risk follows a power law distribution, there is a better distribution fit for operational risk. We also conclude that whilst there is evidence that credit defaults and market risks did reach a tipping point, operational risk losses did not. We conclude that the government intervention in the banking system during the GFC was a possible cause of banks avoiding a tipping point.

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Cascade events in geographical space

International Journal of Modern Physics C ◽

10.1142/s0129183122500504 ◽

2021 ◽

Author(s):

Dylan Marcus T. Ordoñez ◽

Rene C. Batac

Keyword(s):

Discrete Model ◽

Large Scale ◽

Power Laws ◽

The Other ◽

Built Environments ◽

Voronoi Cells ◽

Heavy Tailed Distributions ◽

Geographic Datasets ◽

Heavy Tailed ◽

Geographical Space

In this paper, we present a simple discrete model of cascade behavior in an actual geographical space with built environments. By simultaneously triggering and relaxing random locations in a network of Voronoi cells interacting via the gravity model, we observe nontrivial statistics with heavy-tailed distributions of cells and actual area extents involved in the cascade. The distributions of these affected areas follow unimodal statistics, unlike the other externally-driven models operating over uniform neighborhoods that exhibit power-laws. Majority of the cascades are limited within the immediate neighborhoods of adjacent Voronoi cells, even for sufficiently large triggering magnitudes. The results are viewed from the perspective of inhomogeneous driving in sandpile-based models, and benchmarked with distributions obtained in other geographic datasets. The method offers a complexity perspective into the generation of large-scale events in physical and intangible flows, and explains their origins from cascaded accumulations of slow, random, and intermittent processes.

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Heavy-Tailed Distributions Generated by Randomly Sampled Gaussian, Exponential and Power-Law Functions

Applied Mathematics ◽

10.4236/am.2014.513198 ◽

2014 ◽

Vol 05 (13) ◽

pp. 2050-2056

Author(s):

Frederic von Wegner

Keyword(s):

Power Law ◽

Heavy Tailed Distributions ◽

Heavy Tailed

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

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2020.0610 ◽

2020 ◽

Vol 476 (2244) ◽

pp. 20200610

Author(s):

Joel E. Cohen ◽

Richard A. Davis ◽

Gennady Samorodnitsky

Keyword(s):

Power Law ◽

Statistical Models ◽

Natural Conditions ◽

Heavy Tailed Distributions ◽

Sample Correlation ◽

Taylor’S Law ◽

Heavy Tailed ◽

Fluctuation Scaling ◽

Random Limit ◽

Asymptotic Scaling

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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