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Third-Cycle Courses

Faculty of Engineering | Lund University

Details for the Course Syllabus for Course FRTN30F valid from Spring 2017

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General
  • English
  • Every spring semester
Aim
  • 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.
Contents
  • 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.
Knowledge and Understanding
  • For a passing grade the doctoral student must
  • 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
Competences and Skills
  • For a passing grade the doctoral student must
  • 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
Judgement and Approach
  • For a passing grade the doctoral student must
  • 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
Types of Instruction
  • Lectures
  • Laboratory exercises
  • Exercises
Examination Formats
  • Written exam
  • Written assignments
  • Skriftlig examen, fyra godkända inlämningsuppgifter.
  • Failed, pass
Admission Requirements
Assumed Prior Knowledge
  • FRT010 Automatic Control, Basic Course
Selection Criteria
Literature
  •  
  • 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.
Further Information
Course code
  • FRTN30F
Administrative Information
  • 2016-10-27
  • Professor Thomas Johansson

All Published Course Occasions for the Course Syllabus

1 course occasion.

Start Date End Date Published
2017‑03‑20 2017‑06‑01 2016‑10‑31

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