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

2016 ◽  
Vol 3 (8) ◽  
pp. 160275 ◽  
Author(s):  
Wentian Li ◽  
Oscar Fontanelli ◽  
Pedro Miramontes
Keyword(s):  
Size Distribution ◽  
Power Law ◽  
Common Property ◽  
Target Genes ◽  
Human Gene ◽  
Beta Function ◽  
Gene Families ◽  
Rank Function ◽  
Power Law Distribution ◽  
Gene Sets

The sizes of paralogues—gene families produced by ancestral duplication—are known to follow a power-law distribution. We examine the size distribution of gene sets or gene families where genes are grouped by a similar function or share a common property. The size distribution of Human Gene Nomenclature Committee (HGNC) gene sets deviate from the power-law, and can be fitted much better by a beta rank function. We propose a simple mechanism to break a power-law size distribution by a combination of splitting and merging operations. The largest gene sets are split into two to account for the subfunctional categories, and a small proportion of other gene sets are merged into larger sets as new common themes might be realized. These operations are not uncommon for a curator of gene sets. A simulation shows that iteration of these operations changes the size distribution of Ensembl paralogues and could lead to a distribution fitted by a rank beta function. We further illustrate application of beta rank function by the example of distribution of transcription factors and drug target genes among HGNC gene families.

Priority Weighted Fitness Model in Networks

2012 ◽  
Vol 229-231 ◽  
pp. 1854-1857
Author(s):  
Xin Yi Chen
Keyword(s):  
World Wide Web ◽  
Power Law ◽  
Common Property ◽  
World Wide ◽  
Genetic Networks ◽  
Power Law Distribution ◽  
Large Networks ◽  
Scale Free ◽  
The World ◽  
Complex Topology

Systems as diverse as genetic networks or the World Wide Web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a power-law distribution. This feature was found to be a consequence of three generic mechanisms: (i) networks expand continuously by the addition of new vertices, (ii) new vertex with priority selected different edges of weighted selected that connected to different vertices in the system, and (iii) by the fitness probability that a new vertices attach preferentially to sites that are already well connected. A model based on these ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena. Experiment results show that the model is more close to the actual Internet network.

Power Law Distributions and the Size Distribution of Strikes

2017 ◽  
Vol 48 (3) ◽  
pp. 561-587 ◽  
Author(s):  
Michele Campolieti
Keyword(s):  
Size Distribution ◽  
Power Law ◽  
Model Fit ◽  
Power Law Distribution ◽  
Policy Perspective ◽  
Methodological Research ◽  
Canadian Data ◽  
Alternative Measures ◽  
Power Law Distributions ◽  
Research And Policy

Using Canadian data from 1976 to 2014, I study the size distribution of strikes with three alternative measures of strike size: the number of workers on strike, strike duration in calendar days, and the number of person calendar days lost to a strike. I use a maximum likelihood framework that provides a way to estimate distributions, evaluate model fit, and also test against alternative distributions. I consider a few theories that can create power law distributions in strike size, such as the joint costs model that posits strike size is inversely proportional to dispute costs. I find that the power law distribution fits the data for the number of lost person calendar days relatively well and is also more appropriate than the lognormal distribution. I also discuss the implications of my findings from a methodological, research, and policy perspective.

scholarly journals Size distribution of particles in Saturn’s rings from aggregation and fragmentation

2015 ◽  
Vol 112 (31) ◽  
pp. 9536-9541 ◽  
Author(s):  
Nikolai Brilliantov ◽  
P. L. Krapivsky ◽  
Anna Bodrova ◽  
Frank Spahn ◽  
Hisao Hayakawa ◽  
...  
Keyword(s):  
Size Distribution ◽  
Power Law ◽  
Momentum Conservation ◽  
Power Law Distribution ◽  
Water Ice ◽  
Flat Disk ◽  
Cutoff Radius ◽  
Saturn’S Rings ◽  
Saturn's Rings ◽  
Interparticle Collisions

Saturn’s rings consist of a huge number of water ice particles, with a tiny addition of rocky material. They form a flat disk, as the result of an interplay of angular momentum conservation and the steady loss of energy in dissipative interparticle collisions. For particles in the size range from a few centimeters to a few meters, a power-law distribution of radii, ∼r−q with q≈3, has been inferred; for larger sizes, the distribution has a steep cutoff. It has been suggested that this size distribution may arise from a balance between aggregation and fragmentation of ring particles, yet neither the power-law dependence nor the upper size cutoff have been established on theoretical grounds. Here we propose a model for the particle size distribution that quantitatively explains the observations. In accordance with data, our model predicts the exponent q to be constrained to the interval 2.75≤q≤3.5. Also an exponential cutoff for larger particle sizes establishes naturally with the cutoff radius being set by the relative frequency of aggregating and disruptive collisions. This cutoff is much smaller than the typical scale of microstructures seen in Saturn’s rings.

The Size Distribution of Particles Released by Garments During Helmke Drum Tests

2001 ◽  
Vol 44 (4) ◽  
pp. 24-27 ◽  
Author(s):  
David Ensor ◽  
Jenni Elion ◽  
Jan Eudy
Keyword(s):  
Particle Size ◽  
Size Distribution ◽  
Power Law ◽  
High Performance ◽  
Fine Particles ◽  
Particle Diameter ◽  
Test Method ◽  
Power Law Distribution ◽  
Controlled Environments ◽  
Size Distribution Of Particles

The Helmke Drum test method to measure particles shed from garments was developed twenty years ago. It consists of a tumbling drum containing the garment under test. A probe connected to an optical particle counter is used to transport the sample from the drum. Dilution air is drawn into the drum from the surrounding cleanroom. The optical particle counters at the time of development were limited in resolution to 0.5 μm diameter. This particle size requirement is still in the current version of IEST-RP-CC003.2, Garment Systems Considerations for Cleanrooms and Other Controlled Environments. A question was raised in the current IEST Contamination Control Working Group 003, "Garment System Considerations for Cleanrooms and Other Controlled Environments," as to whether the method could be extended to smaller particle diameters. The method would benefit by including measurements of smaller particle diameters for two reasons: the higher particle counts expected for sub-0.5 μm particles might improve the statistics of the method; and there is a growing need to consider contamination by ultra-fine particles during the manufacture of high performance products. We hypothesized that the size distribution of particles released by garments follows a power law similar to that for cleanroom classes. The form of the power law distribution is N(d) = Ad(-B), where N(d) is the cumulative concentration greater to or equal to d, d is the particle diameter, and A and B are statistically determined coefficients. The size distributions from a number of Helmke Drum tests were analyzed and were found to be highly correlated to the power law equation. However, the slopes appeared to vary depending on the type of garment tested. These results support including guidance with respect to particle size in the Helmke Drum test section in the upcoming revision of IEST-RP-CC003.2.

BUSINESS CYCLE FLUCTUATIONS AND FIRMS' SIZE DISTRIBUTION DYNAMICS

2004 ◽  
Vol 07 (02) ◽  
pp. 223-240 ◽  
Author(s):  
DOMENICO DELLI GATTI ◽  
CORRADO DI GUILMI ◽  
EDOARDO GAFFEO ◽  
GIANFRANCO GIULIONI ◽  
MAURO GALLEGATI ◽  
...  
Keyword(s):  
Size Distribution ◽  
Power Law ◽  
Power Law Distribution ◽  
Distribution Dynamics ◽  
Size Change ◽  
Empirical Distributions ◽  
Straight Line ◽  
Distribution Shifts ◽  
Time Invariant ◽  
Power Law Distributions

Power law behavior is an emerging property of many economic models. In this paper we emphasize the fact that power law distributions are persistent but not time invariant. In fact, the scale and shape of the firms' size distribution fluctuate over time. In particular, on a log–log space, both the intercept and the slope of the power law distribution of firms' size change over the cycle: during expansions (recessions) the straight line representing the distribution shifts up and becomes less steep (steeper). We show that the empirical distributions generated by simulations of the model presented in Ref. 11 mimic real empirical distributions remarkably well.

POWER-LAW DISTRIBUTION OF RIVER BASIN SIZES

Fractals ◽  
1993 ◽  
Vol 01 (03) ◽  
pp. 521-528 ◽  
Author(s):  
HIDEKI TAKAYASU
Keyword(s):  
Size Distribution ◽  
River Basin ◽  
Power Law ◽  
Point Of View ◽  
The Self ◽  
General Point ◽  
Size Distributions ◽  
Power Law Distribution ◽  
River Models ◽  
River Pattern

River models are reviewed with emphasis on the power-law nature of basin size distributions. From a general point of view, the whole river pattern on a surface can be regarded as a kind of tiling by random self-affine branches. Applying the idea of stable distributions, we show that the self-affinity and tiling condition naturally derive the power-law basin size distribution.

Spatial Distribution of Tourism Activities: A Polya Urn Process Model of Rank-Size Distribution

2019 ◽  
Vol 59 (2) ◽  
pp. 231-246 ◽  
Author(s):  
Pong Lung Lau ◽  
Tay T. R. Koo ◽  
Cheng-Lung Wu
Keyword(s):  
Size Distribution ◽  
Power Law ◽  
Process Model ◽  
Word Of Mouth ◽  
Preferential Attachment ◽  
Power Law Distribution ◽  
Habit Persistence ◽  
Pólya Urn ◽  
Polya Urn ◽  
Attachment Process

The power law is considered one of the most enduring regularities in human geography. This article aims to develop an understanding of the circumstances that may result in the power law distribution in the geography of tourism activities. The finite Polya urn process is adopted as a device to model the preferential attachment process in the flow of tourists. The model generates a rank-size distribution of tourism regions along with intuitively appealing parameters. Empirically examined using two independent sets of Australian inbound and outbound tourism data, results show that the rank-size distribution emerging from the finite Polya urn process is a superior fit to the conventional power law curve. This rank-size distribution (termed the Polya urn process model of visitor distribution) is compatible with tourist behaviors such as habit persistence and word-of-mouth effects, and can be adopted by tourism modelers to predict and efficiently summarize the spatiality of tourism.

A comparison of two alternative approaches to modelling the sea ice floe size distribution.

2020 ◽  
Author(s):  
Adam Bateson ◽  
Daniel Feltham ◽  
David Schröder ◽  
Lucia Hosekova ◽  
Jeff Ridley ◽  
...  
Keyword(s):  
Sea Ice ◽  
Size Distribution ◽  
Power Law ◽  
Spatial Scales ◽  
Thickness Distribution ◽  
Power Law Distribution ◽  
Momentum Exchange ◽  
Alternative Approaches ◽  
The Impact ◽  
Large Response

<p>Sea ice exists as individual units of ice called floes. These floes can vary by orders of magnitude in diameter over small spatial scales. They are better described by a floe size distribution (FSD) rather than by a single diameter. Observations of the FSD are frequently fitted to a power law with a negative exponent. Floe size can influence several sea ice processes including the lateral melt rate, momentum exchange between the sea ice, ocean and atmosphere, and sea ice rheology. There have been several recent efforts to develop a model of the floe size distribution to include within sea ice models to improve the representation of floe size beyond a fixed single value. Some of these involve significant approximations about the shape and variability of the distribution whereas others adopt a more prognostic approach that does not restrict the shape of the distribution.</p><p>In this study we compare the impacts of two alternative approaches to modelling the FSD within the CICE sea ice model. The first assumes floes follow a power law distribution with a constant exponent. Parameterisations of processes thought to influence the floe size distribution are expressed in terms of a variable FSD tracer. The second uses a prognostic floe size-thickness distribution. The sea ice area in individual floe size categories evolves independently such that the shape of distribution is an emergent behaviour rather than imposed. Here we compare the impact of the two modelling approaches on the thermodynamic evolution of the sea ice. We show that both predict an increase in lateral melt with a compensating reduction in basal melt. We find that the magnitude of this change is highly dependent on the form of the distribution for the smallest floes. We also explore the impact of both FSD models on the momentum exchange of the sea ice and find a large response in the spatial distribution of sea ice volume. Finally, we will discuss whether the results from the prognostic FSD model support the assumptions required to construct the power law derived FSD model.</p>

Gibrat's Law for (All) Cities: Comment

2009 ◽  
Vol 99 (4) ◽  
pp. 1672-1675 ◽  
Author(s):  
Moshe Levy
Keyword(s):  
Income Distribution ◽  
Size Distribution ◽  
Power Law ◽  
Empirical Distribution ◽  
Wealth Distribution ◽  
City Size ◽  
Power Law Distribution ◽  
Gibrat’S Law ◽  
Gibrat's Law ◽  
City Size Distribution

Jan Eeckhout (2004) reports that the empirical city size distribution is lognormal, consistent with Gibrat's Law. We show that for the top 0.6 percent of the largest cities, the empirical distribution is dramatically different from the lognormal, and follows a power law. This top part is extremely important as it accounts for more than 23 percent of the population. The empirical hybrid lognormal-power-law distribution revealed may be characteristic of other key distributions, such as the wealth distribution and the income distribution. This distribution is not consistent with a simple Gibrat proportionate effect process, and its origin presents a puzzle yet to be answered. (JEL R11, R12, R23)

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