Network Dynamics
Nätverksdynamik

FRTN30F, 7.5 högskolepoäng

Gäller från och med: Spring 2017
Beslutad av: Professor Thomas Johansson
Datum för fastställande: 2016-10-27

Allmänna uppgifter

Avdelning: Automatic Control
Kurstyp: Gemensam kurs, avancerad nivå och forskarnivå
Kursen ges även på avancerad nivå med kurskod: FRTN30
Undervisningsspråk: English

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.

Mål

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

Kursinnehåll

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.

Kurslitteratur

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.

Kursens undervisningsformer

Undervisningsformer: Föreläsningar, laborationer, övningar

Kursens examination

Examinationsformer: Skriftlig tentamen, inlämningsuppgifter. Skriftlig examen, fyra godkända inlämningsuppgifter.
Betygsskala: Underkänd, godkänd
Examinator: Senior lecturer Giacomo Como

Antagningsuppgifter

Förutsatta förkunskaper: FRT010 Automatic Control, Basic Course

Kurstillfällesinformation

Startdatum: 2017-03-20
Slutdatum: 2017-06-01
Kursfart: Full time

Anmälningsinformation

Contact Giacomo Como, giacomo.como@control.lth.se

Kontaktinformation och övrigt

Kursansvarig: Giacomo Como <giacomo.como@control.lth.se>