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 meanfield 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 ErdösRenyi graph, the configuration model and the preferential attachment graph  The student is able to follow the proof of phase transition for connectivity in the ErdösRenyi 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 ,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. DíazGuilera, J. Kurths, Y. Moreno, C. Zhou, Physics Reports, vol. 469, pp. 93153, 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 
