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Scale-freeness for networks as a degenerate ground state: A Hamiltonian formulation
Umeå University, Faculty of Science and Technology, Physics. (Center for Models for Life - 2100 Copenhagen, Denmark)
Umeå University, Faculty of Science and Technology, Physics. (Center for Models for Life - 2100 Copenhagen, Denmark)
Department of Physics, BK21 Physics Research Division, and Institute of Basic Science, Sungkyunkwan University - Suwon 440-746, Korea.
2007 (English)In: Europhysics letters, ISSN 0295-5075, E-ISSN 1286-4854, Vol. 78, no 2, 28004-1-28004-5 p.Article in journal (Other (popular science, discussion, etc.)) Published
Abstract [en]

The origin of scale-free degree distributions in the context of networks is addressed through an analogous non-network model in which the node degree corresponds to the number of balls in a box and the rewiring of links to balls moving between the boxes. A statistical mechanical formulation is presented and the corresponding Hamiltonian is derived. The energy, the entropy, as well as the degree distribution and its fluctuations are investigated at various temperatures. The scale-free distribution is shown to correspond to the degenerate ground state, which has small fluctuations in the degree distribution and yet a large entropy. We suggest an implication of our results from the viewpoint of the stability in evolution of networks.

Place, publisher, year, edition, pages
2007. Vol. 78, no 2, 28004-1-28004-5 p.
Keyword [en]
Complex systems, Networks
National Category
Condensed Matter Physics
Identifiers
URN: urn:nbn:se:umu:diva-6513DOI: 10.1209/0295-5075/78/28004OAI: oai:DiVA.org:umu-6513DiVA: diva2:146182
Available from: 2007-12-13 Created: 2007-12-13 Last updated: 2017-12-14Bibliographically approved
In thesis
1. Structures in complex systems: Playing dice with networks and books
Open this publication in new window or tab >>Structures in complex systems: Playing dice with networks and books
2009 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Complex systems are neither perfectly regular nor completely random. They consist of a multitude of players who, in many cases, playtogether in a way that makes their combined strength greater than the sum of their individual achievements. It is often very effective to represent these systems as networks where the actual connections between the players take on a crucial role.Networks exist all around us and are an important part of our world, from the protein machinery inside our cells to social interactions and man-madecommunication systems. Many of these systems have developed over a long period of time and are constantly undergoing changes driven by complicated microscopic events. These events are often too complicated for us to accurately resolve, making the world seem random and unpredictable. There are however ways of using this unpredictability in our favor by replacing the true events by much simpler stochastic rules giving effectively the same outcome. This allows us to capture the macroscopic behavior of the system, to extract important information about the dynamics of the system and learn about the reason for what we observe. Statistical mechanics gives the tools to deal with such large systems driven by underlying random processes under various external constraints, much like how intracellular networks are driven by random mutations under the constraint of natural selection.This similarity makes it interesting to combine the two and to apply some of the tools provided by statistical mechanics on biological systems.In this thesis, several null models are presented, with this view point in mind, to capture and explain different types of structural properties of real biological networks.

The most recent major transition in evolution is the development of language, both spoken and written. This thesis also brings up the subject of quantitative linguistics from the eyes of a physicist, here called linguaphysics. Also in this case the data is analyzed with an assumption of an underlying randomness. It is shown that some statistical properties of books, previously thought to be universal, turn out to exhibit author specific size dependencies. A meta book theory is put forward which explains this dependency by describing the writing of a text as pulling a section out of a huge, individual, abstract mother book.

Abstract [sv]

Komplexa system är varken perfekt ordnade eller helt slumpmässiga. De består av en mängd aktörer, som i många fall agerar tillsammans på ett sådant sätt att deras kombinerade styrka är större än deras individuella prestationer. Det är ofta effektivt att representera dessa system som nätverk där de faktiska kopplingarna mellan aktörerna spelar en avgörande roll. Nätverk finns överallt omkring oss och är en viktig del av vår värld , från proteinmaskineriet inne i våra celler till sociala samspel och människotillverkade kommunikationssystem.Många av dessa system har utvecklats under lång tid och genomgår hela tiden förändringar som drivs på av komplicerade småskaliga händelser.Dessa händelser är ofta för komplicerade för oss att noggrant kunna analysera, vilket får vår värld att verka slumpmässig och oförutsägbar. Det finns dock sätt att använda denna oförutsägbarhet till vår fördel genom att byta ut de verkliga händelserna mot mycket enklare regler baserade på sannolikheter, som ger effektivt sett samma utfall. Detta tillåter oss att fånga systemets övergripande uppförande, att utvinna viktig information om systemets dynamik och att få kunskap om anledningen till vad vi observerar. Statistisk mekanik hanterar stora system pådrivna av sådana underliggande slumpmässiga processer under olika restriktioner, på liknande sätt som nätverk inne i celler drivs av slumpmässiga mutationer under restriktionerna från naturligt urval. Denna likhet gör det intressant att kombinera de två och att applicera de verktyg som ges av statistisk mekanik på biologiska system. I denna avhandling presenteras flera nollmodeller som, baserat på detta synsätt, fångar och förklarar olika typer av strukturella egenskaper hos verkliga biologiska nätverk.

Den senaste stora evolutionära övergången är utvecklandet av språk, både talat och skrivet. Denna avhandling tar också upp ämnet om kvantitativ linguistik genom en fysikers ögon, här kallat linguafysik. även i detta fall så analyseras data med ett antagande om en underliggande slumpmässighet. Det demonstreras att vissa statistiska egenskaper av böcker, som man tidigare trott vara universella, egentligen beror på bokens längd och på författaren. En metaboksteori ställs fram vilken förklarar detta beroende genom att beskriva författandet av en text som att rycka ut en sektion ur en stor, individuell, abstrakt moderbok.

Place, publisher, year, edition, pages
Umeå: Umeå University, Department of physics, 2009. 63 p.
Keyword
Complex systems, networks, statistical physics, biological networks, quantitative linguistics, word frequencies.
National Category
Physical Sciences
Identifiers
urn:nbn:se:umu:diva-27694 (URN)978-91-7264-910-1 (ISBN)
Public defence
2009-12-17, N360, Naturvetarhuset, Umeå universitet, 901 87, Umeå, Umeå, 13:00 (English)
Opponent
Supervisors
Available from: 2009-11-20 Created: 2009-11-16 Last updated: 2010-11-01Bibliographically approved

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