lunduniversity.lu.se

Forskar­utbildnings­kurser

Faculty of Engineering | Lund University

Detaljer för kursplan för kurs FRTN30F giltig från och med Spring 2017

Utskriftsvänlig visning

Allmänt
  • English
  • Varje vårtermin
Syfte
  • The course provides an introduction to and some analysis of the main mathematical models used to describe large networks and dynamical processes that evolve on networks. Motivation and applications will be drawn from social, economic, natural, and infrastructure networks, as well as networked decision systems such as sensor networks.
Innehåll
  • Basic graph theory: connectivity, degree distributions, trees, adjacency matrices, spectrum.
    Random graphs: Erdos-Renyi, configuration model, preferential attachment, small-world, branching process approximations
    Flows and games on graphs: max-flow, min-cut, optimal transport, Wardrop equilibria, evolutionary dynamics.
    Random walks on graphs: invariant distributions, hitting times, mixing times.
    Dynamical systems on graphs: distributed averaging, interacting particle systems, epidemics, opinion dynamics. Mean-field and branching process approximations.
Kunskap och förståelse
  • För godkänd kurs skall doktoranden
  • know the basic principles of graph theory and apply them to model real-world networks
    have insight in the basic differences between different models of random graphs
    be familiar with the properties of random walks on graphs
    be able to analyze simple dynamical systems over networks
    understand emerging phenomena in large-scale networks
    be able to give an overview of modern directions in network science
Färdighet och förmåga
  • För godkänd kurs skall doktoranden
  • be able to analyze properties of (random) graphs both quantitatively and qualitatively
    be able to handle basic analytical computations for random walks
    be able to analyze simple dynamical systems over networks and to relate their behavior to the network structure
    be able to use computer tools for simulation and analysis of networks
Värderingsförmåga och förhållningssätt
  • För godkänd kurs skall doktoranden
  • be able to understand relations and limitations when simple models are used to describe complex networks
    be able to evaluate dominating emerging phenomena in network dynamics
Undervisningsformer
  • Föreläsningar
  • Laborationer
  • övningar
Examinationsformer
  • Skriftlig tentamen
  • Inlämningsuppgifter
  • Skriftlig examen, fyra godkända inlämningsuppgifter.
  • Underkänd, godkänd
Förkunskapskrav
Förutsatta förkunskaper
  • FRT010 Automatic Control, Basic Course
Urvalskriterier
Litteratur
  •  
  • D. Easley & J. Kleinberg: Networks, crowds and markets, reasoning about a highly connected world. Cambridge University Press, 2010, ISBN: 978-0-521-19533-1. Supplement to lecturer's notes.
    R. Van Der Hofstad: Random Graphs and Complex Networks. Supplement to lecturer's notes. Tillgänglig online via http://www.win.tue.nl/~rhofstad/.
    D. Levin, Y. Peres, E. Wilmer: Markov chains and mixing times. American Mathematical Society, 2009, ISBN: 978-0-8218-4739-8. Supplement to lecturer's notes.
Övrig information
Kurskod
  • FRTN30F
Administrativ information
  •  -10-27
  • Professor Thomas Johansson

Alla publicerade kurstillfällen för kursplanen

1 kurstillfälle.

Startdatum Slutdatum Publicerad
2017‑03‑20 2017‑06‑01 2016‑10‑31

Utskriftsvänlig visning