Replica methods for loopy sparse random graphs

A. C C Coolen

doi:10.1088/1742-6596/699/1/012022

Replica methods for loopy sparse random graphs

A. C C Coolen^*

^*Corresponding author for this work

Research output: Contribution to journal › Conference paper › peer-review

11 Citations (Scopus)

150 Downloads (Pure)

Abstract

I report on the development of a novel statistical mechanical formalism for the analysis of random graphs with many short loops, and processes on such graphs. The graphs are defined via maximum entropy ensembles, in which both the degrees (via hard constraints) and the adjacency matrix spectrum (via a soft constraint) are prescribed. The sum over graphs can be done analytically, using a replica formalism with complex replica dimensions. All known results for tree-like graphs are recovered in a suitable limit. For loopy graphs, the emerging theory has an appealing and intuitive structure, suggests how message passing algorithms should be adapted, and what is the structure of theories describing spin systems on loopy architectures. However, the formalism is still largely untested, and may require further adjustment and refinement.

Original language	English
Article number	012022
Number of pages	11
Journal	Journal of Physics: Conference Series
Volume	699
Issue number	1
DOIs	https://doi.org/10.1088/1742-6596/699/1/012022
Publication status	Published - 6 Apr 2016

Access to Document

10.1088/1742-6596/699/1/012022Licence: CC BY

Replica methods for loopy_COOLEN_Firstonline6April2016_GOLD VoRFinal published version, 875 KBLicence: CC BY

Cite this

@article{f1f9c7d066cd48c0adbde260426a2329,

title = "Replica methods for loopy sparse random graphs",

abstract = "I report on the development of a novel statistical mechanical formalism for the analysis of random graphs with many short loops, and processes on such graphs. The graphs are defined via maximum entropy ensembles, in which both the degrees (via hard constraints) and the adjacency matrix spectrum (via a soft constraint) are prescribed. The sum over graphs can be done analytically, using a replica formalism with complex replica dimensions. All known results for tree-like graphs are recovered in a suitable limit. For loopy graphs, the emerging theory has an appealing and intuitive structure, suggests how message passing algorithms should be adapted, and what is the structure of theories describing spin systems on loopy architectures. However, the formalism is still largely untested, and may require further adjustment and refinement.",

author = "Coolen, {A. C C}",

year = "2016",

month = apr,

day = "6",

doi = "10.1088/1742-6596/699/1/012022",

language = "English",

volume = "699",

journal = "Journal of Physics: Conference Series",

issn = "1742-6588",

publisher = "IOP Publishing",

number = "1",

}

TY - JOUR

T1 - Replica methods for loopy sparse random graphs

AU - Coolen, A. C C

PY - 2016/4/6

Y1 - 2016/4/6

N2 - I report on the development of a novel statistical mechanical formalism for the analysis of random graphs with many short loops, and processes on such graphs. The graphs are defined via maximum entropy ensembles, in which both the degrees (via hard constraints) and the adjacency matrix spectrum (via a soft constraint) are prescribed. The sum over graphs can be done analytically, using a replica formalism with complex replica dimensions. All known results for tree-like graphs are recovered in a suitable limit. For loopy graphs, the emerging theory has an appealing and intuitive structure, suggests how message passing algorithms should be adapted, and what is the structure of theories describing spin systems on loopy architectures. However, the formalism is still largely untested, and may require further adjustment and refinement.

AB - I report on the development of a novel statistical mechanical formalism for the analysis of random graphs with many short loops, and processes on such graphs. The graphs are defined via maximum entropy ensembles, in which both the degrees (via hard constraints) and the adjacency matrix spectrum (via a soft constraint) are prescribed. The sum over graphs can be done analytically, using a replica formalism with complex replica dimensions. All known results for tree-like graphs are recovered in a suitable limit. For loopy graphs, the emerging theory has an appealing and intuitive structure, suggests how message passing algorithms should be adapted, and what is the structure of theories describing spin systems on loopy architectures. However, the formalism is still largely untested, and may require further adjustment and refinement.

UR - http://www.scopus.com/inward/record.url?scp=84964849749&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/699/1/012022

DO - 10.1088/1742-6596/699/1/012022

M3 - Conference paper

AN - SCOPUS:84964849749

SN - 1742-6588

VL - 699

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

IS - 1

M1 - 012022

ER -

Replica methods for loopy sparse random graphs

Abstract

Access to Document

Other files and links

Fingerprint

Cite this