Complexity and Networks

Faculteit Science and Engineering
Jaar 2019/20
Vakcode WMMA16000
Vaknaam Complexity and Networks
Niveau(s) master
Voertaal Engels
Periode semester I a
ECTS 5
Rooster rooster.rug.nl

Uitgebreide vaknaam Complexity and Networks
Leerdoelen Part 1:
- The student can apply the mean-field theory
- The student can describe how different network topologies affect the onset of synchronization
- The student can explain the relation between the master stability function and linear stability

Part 2:
- The student is able to bound controllable space by using graph partitions
- The student is able to verify whether a given set of nodes is a zero forcing set
- The student is able to apply the theory to specific classes of graphs in order to select leaders rendering the system controllable

Part 3:
- The student is able to mathematically describe random graphs in terms of properties like connected components, average degree and diameter
- The student is familiar with major examples like the Erdös-Renyi graph, the configuration model and the preferential attachment graph
- The student is able to follow the proof of phase transition for connectivity in the Erdös-Renyi graph

Part 4:
- The student can mathematically distinguish rigid and flexible structures
- The student can construct rigid and globally rigid frameworks in 2D
- The student is able to apply basic aspects of rigidity graph theory in sensor network localization and robotic formation control
Omschrijving
Uren per week
Toetsvorm Opdracht (AST)
(Each of the four parts will be assessed individually by homework exercises. The final grade is the average of the four grades if the grade of each homework is 4 or higher otherwise the final grade is minimum of the homework grades. The homeworks will be set at the beginning of the second week of each part (still covering subjects from that week) and should be handed in two weeks later. The homework will be marked and returned asap. At the end of the course there will be a feedback meeting with all lecturers present where the student can ask questions about and get feedback on their homeworks.)
Vaksoort master
Coördinator prof. dr. D. Rodrigues Valesin
Docent(en) prof. dr. M.K. Camlibel , A.V. Kiselev ,prof. dr. D. Rodrigues Valesin
Entreevoorwaarden The course assumes prior knowledge in:
- Real and complex analysis
- Probability theory
- Linear algebra (vector spaces, invariant subspaces, quotient spaces, eigenvalues, eigenvectors)
- Fourier series
- Dynamical systems (equilibria, linear stability)
- Systems theory (state and controllability)
- Programming skills
Opmerkingen Literature:

Part 1:
References:
- Introduction to Modern Dynamics: Chaos, Networks, Space and Time. D. D. Nolte, Oxford University Press, 2015.
- Synchronization in Complex Networks. A. Arenas, A. Díaz-Guilera, J. Kurths, Y. Moreno, C. Zhou, Physics Reports, vol. 469, pp. 93-153, 2008.

Part 3:
Main reference:
- Van Der Hofstad, Remco. "Random graphs and complex networks." Available on http://www.win.tue.nl/rhofstad/NotesRGCN.pdf (2009).
Additional reference:
- Durrett, Richard. Random graph dynamics. Vol. 200, no. 7. Cambridge: Cambridge university press, 2007.

Part 4:
Reference:
- Notes on Rigidity Theory, James Cruickshank
Opgenomen in
Opleiding Jaar Periode Type
MSc Applied Mathematics: Computational Mathematics  ( MSc Applied Mathematics: Computational Mathematics ) - semester I a verplicht
MSc Applied Mathematics: Systems and Control  (MSc Applied Mathematics: Systems and Control) - semester I a verplicht
MSc Courses for Exchange Students: Mathematics 19-20 - semester I a
MSc Mathematics and Physics (double degree)  (Mathematics and Complex Dynamical Systems (45 ects)) - semester I a verplicht
MSc Mathematics: Mathematics and Complex Dynamical Systems - semester I a verplicht
MSc Mathematics: Science, Business and Policy  (MSc Mathematics: Science, Business and Policy) - semester I a verplicht
MSc Mathematics: Statistics and Big Data  (MSc Mathematics: Statistics and Big Data) - semester I a verplicht