Generalized Nonlinear Yule Models

J 2016

Generalized Nonlinear Yule Models

LÁNSKÝ, Petr, Federico POLITO and Laura SACERDOTE

Basic information

Original name

Generalized Nonlinear Yule Models

Name in Czech

Zobecnene nelinearni Yulovy modely

Authors

LÁNSKÝ, Petr (203 Czech Republic, guarantor, belonging to the institution), Federico POLITO (380 Italy) and Laura SACERDOTE (380 Italy)

Edition

JOURNAL OF STATISTICAL PHYSICS, 2016, 0022-4715

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

United States of America

Confidentiality degree

není předmětem státního či obchodního tajemství

Impact factor

Impact factor: 1.349

RIV identification code

RIV/00216224:14310/16:00088377

Organization unit

Faculty of Science

DOI

http://dx.doi.org/10.1007/s10955-016-1630-9

UT WoS

000386681800008

Keywords in English

FRACTIONAL POISSON-PROCESS; ORDER STATISTIC PROPERTY; POINT-PROCESSES; GROWING NETWORKS; BIRTH PROCESSES

Abstract

V originále

With the aim of considering models related to random graphs growth exhibiting persistent memory, we propose a fractional nonlinear modification of the classical Yule model often studied in the context of macroevolution. Here the model is analyzed and interpreted in the framework of the development of networks such as the World Wide Web. Nonlinearity is introduced by replacing the linear birth process governing the growth of the in-links of each specific webpage with a fractional nonlinear birth process with completely general birth rates. Among the main results we derive the explicit distribution of the number of in-links of a webpage chosen uniformly at random recognizing the contribution to the asymptotics and the finite time correction. The mean value of the latter distribution is also calculated explicitly in the most general case. Furthermore, in order to show the usefulness of our results, we particularize them in the case of specific birth rates giving rise to a saturating behaviour, a property that is often observed in nature. The further specialization to the non-fractional case allows us to extend the Yule model accounting for a nonlinear growth.

Links

GA15-06991S, research and development project

Name: Analýza funkcionálních dat a související témata

Investor: Czech Science Foundation

Citovat

LÁNSKÝ, Petr, Federico POLITO and Laura SACERDOTE. Generalized Nonlinear Yule Models. JOURNAL OF STATISTICAL PHYSICS. 2016, vol. 165, No 3, p. 661-679. ISSN 0022-4715. Available from: https://dx.doi.org/10.1007/s10955-016-1630-9.

@article{1361781,
   author = {Lánský, Petr and Polito, Federico and Sacerdote, Laura},
   article_number = {3},
   doi = {http://dx.doi.org/10.1007/s10955-016-1630-9},
   keywords = {FRACTIONAL POISSON-PROCESS; ORDER STATISTIC PROPERTY; POINT-PROCESSES; GROWING NETWORKS; BIRTH PROCESSES},
   language = {eng},
   issn = {0022-4715},
   journal = {JOURNAL OF STATISTICAL PHYSICS},
   title = {Generalized Nonlinear Yule Models},
   volume = {165},
   year = {2016}
}

TY  - JOUR
ID  - 1361781
AU  - Lánský, Petr - Polito, Federico - Sacerdote, Laura
PY  - 2016
TI  - Generalized Nonlinear Yule Models
JF  - JOURNAL OF STATISTICAL PHYSICS
VL  - 165
IS  - 3
SP  - 661-679
EP  - 661-679
SN  - 00224715
KW  - FRACTIONAL POISSON-PROCESS
KW  - ORDER STATISTIC PROPERTY
KW  - POINT-PROCESSES
KW  - GROWING NETWORKS
KW  - BIRTH PROCESSES
N2  - With the aim of considering models related to random graphs growth exhibiting persistent memory, we propose a fractional nonlinear modification of the classical Yule model often studied in the context of macroevolution. Here the model is analyzed and interpreted in the framework of the development of networks such as the World Wide Web. Nonlinearity is introduced by replacing the linear birth process governing the growth of the in-links of each specific webpage with a fractional nonlinear birth process with completely general birth rates. Among the main results we derive the explicit distribution of the number of in-links of a webpage chosen uniformly at random recognizing the contribution to the asymptotics and the finite time correction. The mean value of the latter distribution is also calculated explicitly in the most general case. Furthermore, in order to show the usefulness of our results, we particularize them in the case of specific birth rates giving rise to a saturating behaviour, a property that is often observed in nature. The further specialization to the non-fractional case allows us to extend the Yule model accounting for a nonlinear growth.
ER  -

LÁNSKÝ, Petr, Federico POLITO and Laura SACERDOTE. Generalized Nonlinear Yule Models. \textit{JOURNAL OF STATISTICAL PHYSICS}. 2016, vol.~165, No~3, p.~661-679. ISSN~0022-4715. Available from: https://dx.doi.org/10.1007/s10955-016-1630-9.

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