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.

DISTRIBUTION OF VOTES AND A MODEL OF POLITICAL OPINION FORMATION FOR MAJORITY ELECTIONS

2012 ◽  
Vol 16 ◽  
pp. 1-12 ◽  
Author(s):  
DODE PRENGA ◽  
MARGARITA IFTI
Keyword(s):  
Power Law ◽  
Gaussian Distribution ◽  
Similar Pattern ◽  
Word Of Mouth ◽  
Preferential Attachment ◽  
The Other ◽  
Opinion Formation ◽  
Power Law Distribution ◽  
Parliamentary Elections ◽  
Data Points

We study the behavior of the number of votes cast for different electoral subjects in majority elections, and in particular, the Albanian elections of the last 10 years, as well as the British, Russian, and Canadian elections. We report the frequency of obtaining a certain percentage (fraction) of votes versus this fraction for the parliamentary elections. In the distribution of votes cast in majority elections we identify two regimes. In the low percentiles we see a power law distribution, with exponent about -1.7. In the power law regime we find over 80% of the data points, while they relate to 20% of the votes cast. Votes of the small electoral subjects are found in this regime. The other regime includes percentiles above 20%, and has Gaussian distribution. It corresponds to large electoral subjects. A similar pattern is observed in other first past the post (FPP) elections, such as British and Canadian, but here the Gaussian is reduced to an exponential. Finally we show that this distribution can not be reproduced by a modified "word of mouth" model of opinion formation. This behavior can be reproduced by a model that comprises different number of zealots, as well as different campaign strengths for different electoral subjects, in presence of preferential attachment of voters to candidates.

scholarly journals Subgraphs in preferential attachment models

2019 ◽  
Vol 51 (03) ◽  
pp. 898-926
Author(s):  
Alessandro Garavaglia ◽  
Clara Stegehuis
Keyword(s):  
Power Law ◽  
Optimization Problem ◽  
Preferential Attachment ◽  
Urn Model ◽  
Expected Number ◽  
Pólya Urn ◽  
Polya Urn ◽  
Pólya Urn Model ◽  
Attachment Model ◽  
Law Degree

AbstractWe consider subgraph counts in general preferential attachment models with power-law degree exponent $\tau > 2$ . For all subgraphs H, we find the scaling of the expected number of subgraphs as a power of the number of vertices. We prove our results on the expected number of subgraphs by defining an optimization problem that finds the optimal subgraph structure in terms of the indices of the vertices that together span it and by using the representation of the preferential attachment model as a Pólya urn model.

scholarly journals The structure of co-publications multilayer network

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Ghislain Romaric Meleu ◽  
Paulin Yonta Melatagia
Keyword(s):  
Power Law ◽  
Degree Distribution ◽  
Preferential Attachment ◽  
Small World ◽  
Generation Model ◽  
Small World Network ◽  
Power Law Distribution ◽  
Multilayer Networks ◽  
Multilayer Network ◽  
Scientific Papers

AbstractUsing the headers of scientific papers, we have built multilayer networks of entities involved in research namely: authors, laboratories, and institutions. We have analyzed some properties of such networks built from data extracted from the HAL archives and found that the network at each layer is a small-world network with power law distribution. In order to simulate such co-publication network, we propose a multilayer network generation model based on the formation of cliques at each layer and the affiliation of each new node to the higher layers. The clique is built from new and existing nodes selected using preferential attachment. We also show that, the degree distribution of generated layers follows a power law. From the simulations of our model, we show that the generated multilayer networks reproduce the studied properties of co-publication networks.

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.

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.

scholarly journals Formation of Chinese venture capital syndication network

2020 ◽  
Vol 72 (1) ◽  
pp. 49-64 ◽  
Author(s):  
Makoto Nirei ◽  
Toshiaki Shoji ◽  
Fei Yu
Keyword(s):  
Venture Capital ◽  
Power Law ◽  
Degree Distribution ◽  
Preferential Attachment ◽  
Statistical Properties ◽  
Power Law Distribution

AbstractUsing a dataset that recorded a large number of investment transactions in China from 1991 to 2018, we examine the statistical properties of the Chinese venture capital (VC) syndication network. Our main findings are as follows. First, the number of investment transactions sharply increased after 2014. Second, more than half of the VC firms are located in Beijing, Shanghai, and Shenzhen. Third, the degree distribution becomes roughly straight on a log–log plot. Fourth, the hypothesis that the degree distribution follows a power-law distribution is not rejected for 2015 and 2016. Fifth, better connected VC firms increase their connectivity faster, which suggests the existence of preferential attachment.

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