Size distribution of function-based human gene sets and the split–merge model

Li, Wentian; Fontanelli, Oscar; Miramóntes, Pedro

doi:10.1098/rsos.160275

Cited by 8 publications

(3 citation statements)

References 95 publications

(124 reference statements)

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“…Since the introduction of the two-parameter Discrete Generalized Beta Distribution (DGBD) (or Beta-like Rank Function or Cocho Rank Function) [1,2], a wide range of real-life data have been successfully fitted by this function [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25]. Two questions naturally arise: first, what's the corresponding probability density function (pdf) of the DGBD?…”

Section: Introductionmentioning

confidence: 99%

Beta Rank Function: A Smooth Double-Pareto-Like Distribution

Fontanelli

Miramóntes

Mansilla

et al. 2019

Preprint

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The Beta Rank Function (BRF), x(u) = A(1 − u) b /u a , where u ∈ (0, 1] is the normalized and continuous rank of an observation x, has wide applications in fitting real-world data from social science to biological phenomena. The probability density function (pdf) converted from the BRF, f X (x), does not usually have an analytic expression except for specific parameter values. We show however that it is approximately a unimodal skewed and asymmetric two-sided power law/double Pareto/log-Laplacian distribution. The pdf of the BRF has very simple properties when the independent variable is log-transformed: f Z=log(X) (z) .

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Section: Introductionmentioning

confidence: 99%

Beta Rank Function: A Smooth Double-Pareto-Like Distribution

Fontanelli

Miramóntes

Mansilla

et al. 2019

Preprint

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“…[34–36]) which have parameters that influence which sizes of modules they can detect (as discussed, for example, in [37]). Finally, as discussed in [38], knowing the module size distribution can improve the null models used for gene set enrichment analyses. We believe these advantages to hold also in the particular case of modules being studied in their capacity as building blocks.…”

Section: Introductionmentioning

confidence: 99%

Reusable building blocks in biological systems

Mireles

Conrad

2018

J. R. Soc. Interface.

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One of the most widely recognized features of biological systems is their modularity. The modules that constitute biological systems are said to be redeployed and combined across several conditions, thus acting as building blocks. In this work, we analyse to what extent are these building blocks reusable as compared with those found in randomized versions of a system. We develop a notion of decompositions of systems into phenotypic building blocks, which allows them to overlap while maximizing the number of times a building block is reused across several conditions. Different biological systems present building blocks whose reusability ranges from single use (e.g. condition specific) to constitutive, although their average reusability is not always higher than random equivalents of the system. These decompositions reveal a distinct distribution of building block sizes in real biological systems. This distribution stems, in part, from the peculiar usage pattern of the elements of biological systems, and constitutes a new angle to study the evolution of modularity.

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“…To model the formation of SAUs, we implement a version of the split–merge process , a computational mechanism in which administrative units are created and destroyed by joining and dividing them, thereby emulating the role of governments delineating internal boundaries. This process was originally proposed in [ 45 ].…”

Section: Introductionmentioning

confidence: 99%

Population patterns in World’s administrative units

et al. 2017

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Whereas there has been an extended discussion concerning city population distribution, little has been said about that of administrative divisions. In this work, we investigate the population distribution of second-level administrative units of 150 countries and territories and propose the discrete generalized beta distribution (DGBD) rank-size function to describe the data. After testing the balance between the goodness of fit and number of parameters of this function compared with a power law, which is the most common model for city population, the DGBD is a good statistical model for 96% of our datasets and preferred over a power law in almost every case. Moreover, the DGBD is preferred over a power law for fitting country population data, which can be seen as the zeroth-level administrative unit. We present a computational toy model to simulate the formation of administrative divisions in one dimension and give numerical evidence that the DGBD arises from a particular case of this model. This model, along with the fitting of the DGBD, proves adequate in reproducing and describing local unit evolution and its effect on the population distribution.

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Size distribution of function-based human gene sets and the split–merge model

Cited by 8 publications

References 95 publications

Beta Rank Function: A Smooth Double-Pareto-Like Distribution

Beta Rank Function: A Smooth Double-Pareto-Like Distribution

Reusable building blocks in biological systems

Population patterns in World’s administrative units

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