Universality of rank-ordering distributions in the arts and sciences.
Searching for generic behaviors has been one of the driving forces leading to a deep understanding and classification of diverse phenomena. Usually a starting point is the development of a phenomenology based on observations. Such is the case for power law distributions encountered in a wealth of si...
| Main Authors: | , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Public Library of Science (PLoS)
2009-01-01
|
| Series: | PLoS ONE |
| Online Access: | http://europepmc.org/articles/PMC2652070?pdf=render |
| _version_ | 1811268575061606400 |
|---|---|
| author | Gustavo Martínez-Mekler Roberto Alvarez Martínez Manuel Beltrán del Río Ricardo Mansilla Pedro Miramontes Germinal Cocho |
| author_facet | Gustavo Martínez-Mekler Roberto Alvarez Martínez Manuel Beltrán del Río Ricardo Mansilla Pedro Miramontes Germinal Cocho |
| author_sort | Gustavo Martínez-Mekler |
| collection | DOAJ |
| description | Searching for generic behaviors has been one of the driving forces leading to a deep understanding and classification of diverse phenomena. Usually a starting point is the development of a phenomenology based on observations. Such is the case for power law distributions encountered in a wealth of situations coming from physics, geophysics, biology, lexicography as well as social and financial networks. This finding is however restricted to a range of values outside of which finite size corrections are often invoked. Here we uncover a universal behavior of the way in which elements of a system are distributed according to their rank with respect to a given property, valid for the full range of values, regardless of whether or not a power law has previously been suggested. We propose a two parameter functional form for these rank-ordered distributions that gives excellent fits to an impressive amount of very diverse phenomena, coming from the arts, social and natural sciences. It is a discrete version of a generalized beta distribution, given by f(r) = A(N+1-r)(b)/r(a), where r is the rank, N its maximum value, A the normalization constant and (a, b) two fitting exponents. Prompted by our genetic sequence observations we present a growth probabilistic model incorporating mutation-duplication features that generates data complying with this distribution. The competition between permanence and change appears to be a relevant, though not necessary feature. Additionally, our observations mainly of social phenomena suggest that a multifactorial quality resulting from the convergence of several heterogeneous underlying processes is an important feature. We also explore the significance of the distribution parameters and their classifying potential. The ubiquity of our findings suggests that there must be a fundamental underlying explanation, most probably of a statistical nature, such as an appropriate central limit theorem formulation. |
| first_indexed | 2024-04-12T21:24:16Z |
| format | Article |
| id | doaj.art-0cab7601b4be491c82dbec55320c1d7b |
| institution | Directory Open Access Journal |
| issn | 1932-6203 |
| language | English |
| last_indexed | 2024-04-12T21:24:16Z |
| publishDate | 2009-01-01 |
| publisher | Public Library of Science (PLoS) |
| record_format | Article |
| series | PLoS ONE |
| spelling | doaj.art-0cab7601b4be491c82dbec55320c1d7b2022-12-22T03:16:12ZengPublic Library of Science (PLoS)PLoS ONE1932-62032009-01-0143e479110.1371/journal.pone.0004791Universality of rank-ordering distributions in the arts and sciences.Gustavo Martínez-MeklerRoberto Alvarez MartínezManuel Beltrán del RíoRicardo MansillaPedro MiramontesGerminal CochoSearching for generic behaviors has been one of the driving forces leading to a deep understanding and classification of diverse phenomena. Usually a starting point is the development of a phenomenology based on observations. Such is the case for power law distributions encountered in a wealth of situations coming from physics, geophysics, biology, lexicography as well as social and financial networks. This finding is however restricted to a range of values outside of which finite size corrections are often invoked. Here we uncover a universal behavior of the way in which elements of a system are distributed according to their rank with respect to a given property, valid for the full range of values, regardless of whether or not a power law has previously been suggested. We propose a two parameter functional form for these rank-ordered distributions that gives excellent fits to an impressive amount of very diverse phenomena, coming from the arts, social and natural sciences. It is a discrete version of a generalized beta distribution, given by f(r) = A(N+1-r)(b)/r(a), where r is the rank, N its maximum value, A the normalization constant and (a, b) two fitting exponents. Prompted by our genetic sequence observations we present a growth probabilistic model incorporating mutation-duplication features that generates data complying with this distribution. The competition between permanence and change appears to be a relevant, though not necessary feature. Additionally, our observations mainly of social phenomena suggest that a multifactorial quality resulting from the convergence of several heterogeneous underlying processes is an important feature. We also explore the significance of the distribution parameters and their classifying potential. The ubiquity of our findings suggests that there must be a fundamental underlying explanation, most probably of a statistical nature, such as an appropriate central limit theorem formulation.http://europepmc.org/articles/PMC2652070?pdf=render |
| spellingShingle | Gustavo Martínez-Mekler Roberto Alvarez Martínez Manuel Beltrán del Río Ricardo Mansilla Pedro Miramontes Germinal Cocho Universality of rank-ordering distributions in the arts and sciences. PLoS ONE |
| title | Universality of rank-ordering distributions in the arts and sciences. |
| title_full | Universality of rank-ordering distributions in the arts and sciences. |
| title_fullStr | Universality of rank-ordering distributions in the arts and sciences. |
| title_full_unstemmed | Universality of rank-ordering distributions in the arts and sciences. |
| title_short | Universality of rank-ordering distributions in the arts and sciences. |
| title_sort | universality of rank ordering distributions in the arts and sciences |
| url | http://europepmc.org/articles/PMC2652070?pdf=render |
| work_keys_str_mv | AT gustavomartinezmekler universalityofrankorderingdistributionsintheartsandsciences AT robertoalvarezmartinez universalityofrankorderingdistributionsintheartsandsciences AT manuelbeltrandelrio universalityofrankorderingdistributionsintheartsandsciences AT ricardomansilla universalityofrankorderingdistributionsintheartsandsciences AT pedromiramontes universalityofrankorderingdistributionsintheartsandsciences AT germinalcocho universalityofrankorderingdistributionsintheartsandsciences |