Investigating Mesoscale Structures of Networks via Transport Properties

download Investigating Mesoscale Structures of Networks via Transport Properties

of 178

  • date post

    15-Jul-2015
  • Category

    Science

  • view

    215
  • download

    3

Embed Size (px)

Transcript of Investigating Mesoscale Structures of Networks via Transport Properties

  • Investigating Mesoscale Structures of Networks via Transport Properties

    seminar at National Institute for Mathematical Sciences (NIMS), December 10, 2014.

    SHL and P. Holme, Pathlength scaling in graphs with incomplete navigational information, Physica A 390, 3996 (2011); Exploring Maps with Greedy Navigators, Phys. Rev. Lett. 108, 128701 (2012). SHL, M. Cucuringu, and M. A. Porter, Density-based and transport-based core-periphery structures in networks, Phys. Rev. E 89, 032810 (2014); SHL, M. D. Fricker, and M. A. Porter, Mesoscale Analyses of Fungal Networks, e-print arXiv:1406.5855; M. Cucuringu, M. P. Rombach, SHL, and M. A. Porter, Detection of Core-Periphery Structure in Networks Using Spectral Methods and Geodesic Paths, e-print arXiv:1410.6572; SHL, D. Kim, and H. Jeong, Is Nestedness in Networks Generalized Core-Periphery Structures?, in preparation. SHL, M. Farazmand, G. Haller, and M. A. Porter, Finding Lagrangian Coherent Structures Using Community Detection, in preparation.

    Sang Hoon Lee Department of Energy Science, Sungkyunkwan University

    http://sites.google.com/site/lshlj82

  • statistical physics: micro interactions macro

    regular/random networks (interactions)

    magnet gas

    microscale structure

    macroscale properties

    microscale structure

    macroscale properties

  • irregular, or complex (partially random) networks

    How about this? Something new but ubiquitous topology

    ref) M. E. J. Newman, Phys. Rev. E 74, 036104 (2006).

    Albert

    Albert

    Nakarado

    Barabasi

    Jeong

    Aleksiejuk

    Holyst

    Stauffer

    Allaria

    Arecchi

    DigarboMeucci

    Almaas

    Kovacs

    Vicsek

    Oltvai

    Krapivsky

    Redner

    Kulkarni

    StroudAmaral

    Scala BarthelemyStanley

    Meyers

    Newman

    Martin

    Schrag

    Antal

    Arenas

    Cabrales

    DiazGuilera

    Guimera

    VegaRedondo

    DanonGleiser

    Baiesi

    Paczuski

    BakSneppen

    Banavar

    Maritan

    Rinaldo

    Bianconi

    Ravasz

    NedaSchubert

    Barahona

    Pecora

    Barrat

    PastorSatorras

    Vespignani

    Weigt

    Gondran

    Guichard

    Battiston

    Catanzaro

    BenNaim

    Frauenfelder

    Toroczkai

    Berlow

    BernardesCosta

    Araujo

    Kertesz

    Capocci

    Boccaletti

    Bragard

    Mancini

    Kurths

    Valladares

    Osipov

    Zhou

    Pelaez

    Maza

    Boguna

    Bonanno

    Lillo

    Mantegna

    Mendoza

    Hentschel

    Broder

    Kumar

    Maghoul

    Raghavan

    Rajagopalan

    StataTomkins

    Wiener

    Bucolo

    Fortuna

    Larosa

    Buhl

    Gautrais

    Sole

    KuntzValverde

    DeNeubourg

    Theraulaz

    CaldarelliDeLosRios

    Munoz

    Coccetti

    CallawayHopcrof t

    KleinbergStrogatz

    Watts

    Camacho

    Servedio

    Colaiori

    Caruso

    Latora

    Rapisarda

    Tadic

    CastellanoVilone

    ChatePikovsky

    Rudzick

    ChavezHwang

    Amann

    ClausetMoore

    CohenBenAvraham

    Havlin

    Erez

    Cosenza

    Crucitt i

    Frasca

    Stagni

    Usai

    MarchioriPorta

    DaFontouraCosta

    DiAmbra

    DeArcangelis

    Herrmann

    DeFraysseix

    DeLucia

    Bottaccio

    Montuori

    Pietronero

    DeMenezes

    Moukarzel

    Penna

    DeMoura

    Motter

    Grebogi

    Dezso

    Dobr in

    Beg

    Dodds

    Muhamad

    RothmanSabel

    Donetti

    Dorogovtsev

    Goltsev

    Mendes

    Samukhin

    Dunne

    Williams Martinez

    Echenique

    GomezGardenes

    Moreno

    Vazquez

    Ergun

    Rodgers

    Eriksen

    SimonsenMaslov

    Farkas

    Derenyi

    FerreriCancho

    JanssenKohlerFink

    Johnson

    Carroll

    Flake

    Lawrence

    Giles

    Coetzee

    Spata

    Fortunato

    Fronczak

    Fronczak

    Jedynak

    Sienkiewicz

    GarlaschelliCastri

    Loffredo

    Gastner

    Girvan

    Goh

    Ghim

    Kahng

    Kim

    Lee

    Oh

    Floria

    Gonzales

    Sousa

    Gorman

    Gregoire

    GrossKujala

    Hamalainen

    Timmermann

    Schnitzler

    Salmelin

    Guardiola

    Llas

    Perez

    Giralt

    Mossa

    Turtschi

    Hari Ilmoniemi

    Knuutila

    Lounasmaa

    Heagy

    Herrmann

    Provero

    Hong

    Roux

    Holme

    EdlingLiljeros

    Ghoshal

    Huss

    Kim

    YoonHan

    TrusinaMinnhagen

    Holter

    Mitra

    Cieplak

    Fedroff

    Hong

    Choi

    Park

    LopezRuiz

    Mason

    Tombor

    Jin

    Jung

    Kim

    Park

    Kalapala

    Sanwalani

    Chung

    Kim

    Kinney

    Kumar

    Leyvraz

    SivakumarUpfal

    Lahtinen

    Kaski

    Leone

    Zecchina

    Aberg

    Liu

    Lai

    Hoppensteadt

    Ye

    Lusseau

    Macdonald

    Rigon

    Giacometti

    RodrigueziTurbe

    Marodi

    Dovidio

    Marro

    Dickman

    Zaliznyak

    Matthews

    Mirollo

    Vallone

    Montoya

    Moreira

    AndradeGomez

    Pacheco

    Nekovee

    VazquezPrada

    Dasgupta

    Nishikawa

    Forrest

    Balthrop

    Leicht

    Rho

    Onnela

    Chakraborti

    Kanto

    Jarisaramaki

    RosenblumBassler

    Corral

    Park

    Rubi

    Smith

    Pennock

    Glover

    Petermannn

    Pluchino

    PodaniSzathmary

    PorterMucha

    Warmbrand

    RadicchiCecconi

    Loreto

    Parisi

    Ramasco

    Somera

    Mongru

    DarbyDowman

    Rosvall

    Rozenfeld

    Schafer

    Abel

    Schwartz

    Shefi

    Golding

    Segev

    BenJacob

    Ayali

    Soffer

    Kepler

    Salazarciudad

    Garciafernandez

    Song

    Makse

    AharonyAdlerMeyerOrtmanns

    Szabo Alava

    Thurner

    TassWeule

    Volkmann

    Freund

    Tieri

    Valensin

    Castellani

    Remondini

    Franceschi

    Kozma

    Hengartner

    Korniss

    Torres

    Garrido

    Cancho

    Vannucchi

    Flammini

    Vazquez

    Czirok

    Cohen

    Shochet

    Vragovic

    Louis

    Wuchty

    Yeung

    Yook

    Tu

    Yusong

    Lingjiang

    Muren

    Zaks

    Park

    Collaborations Between Network Scientists

    This figure shows a network of collaborationsbetween scientists working on networks. Itwas compiled from the bibliographies of tworeview articles, by M. Newman (SIAM Review2003) and by S. Boccaletti et al. (Physics Re-ports 2006). Vertices represent scientists whosenames appear as authors of papers in those bib-liographies and an edge joins any two whosenames appear on the samepaper. A small num-ber of other references were added by handto bring the network up to date. This figureshows the largest component of the resultingnetwork, which contains 379 individuals. Sizesof vertices are proportional to their so-calledcommunity centrality. Colors represent ver-tex degrees with redder vertices having higherdegree.

    a snapshot of network of network scientists

  • They are everywhere, indeed.

    the Internet biochemical network

    brain

    ad infinitum

  • The most complicated system in the universe known to itself

    microscale structure: neuron

    macroscopic structure: brain or cognition

  • Volume 12, Number 6, 2006 THE NEUROSCIENTIST 521

    with its growth by creation of new nodes, which preferen-tially form connections to existing hubs. One fMRI studyhas reported a power law degree distribution for a func-tional network of activated voxels (Eguluz and others2005). But the degree distribution of whole-brain fMRInetworks of cortical regions has also been described asan exponentially truncated power law (Achard and oth-ers 2006), meaning broadly that the probability of veryhighly connected hubs is less in the brain than in the

    WWW, but there is more probability of a hub in thebrain than in a random graph. The hubs of this networkwere predominantly regions of the heteromodal and uni-modal association cortex.

    Truncated power law degree distributions are wide-spread in complex systems that are physically embeddedor constrained, such as transport or infrastructural net-works, and in systems in which nodes have a finite life span,such as the social network of collaborating Hollywood

    Fig. 6. Small-world functional brain networks (Achard and others 2006). Anatomical map of a small-world human brainfunctional network created by thresholding the scale 4 wavelet correlation matrix representing functional connectivity inthe frequency interval 0.03 to 0.06 Hz. A, Four hundred five undirected edges, ~10% of the 4005 possible interregionalconnections, are shown in a sagittal view of the right side of the brain. Nodes are located according to the y and z coor-dinates of the regional centroids in Talairach space. Edges representing connections between nodes separated by aEuclidean distance 7.5 cm are blue. B, Degree distribution of a small-world brain functional network. Plot of the log of the cumulative prob-ability of degree, log(P(ki)), versus log of degree, log(ki). The plus sign indicates observed data, the solid line is the best-fitting exponentially truncated power law, the dotted line is an exponential, and the dashed line is a power law. C, Resilience of the human brain functional network (right column) compared with random (left column) and scale-free(middle column) networks. Size of the largest connected cluster in the network (scaled to maximum; y axis) versus theproportion of tota