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| Date | title | short info | sources |
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| 1 |
29.11 |
Diffusion Driven Pattern Formation
(Marius)
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This paper studies an example of meta-foodwebs, networks of interacting species that are interacting by diffusion. Breakdown of the stability of the homogeneous state leads to pattern formation.
Understand and present the results of the paper.
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Master stability functions reveal diffusion-driven pattern formation in networks
Andreas Brechtel, Philipp Gramlich, Daniel Ritterskamp, Barbara Drossel, and Thilo Gross
Phys. Rev. E 97, 032307
Paper
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| 2 |
13.12. |
Phase reduction method for oscillator networks
(Raphael)
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This paper shows how arbitrary limit cycle oscillators, coupled on a network, can be reduced to a canonical phase description, amenable to unified study.
Understand and present the paper, sections 1, 2, 3, and 5.1.
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https://arxiv.org/abs/1704.03293 |
| 3 |
10.1 |
Sampling-based stability
(Seb.+Lisa)
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In order to investigate the non-linear behaviour of complicated network ensembles, it is often useful to study probabilistic properties of the deterministic systems by sampling.
Understand the paper, implement such a sampling algorithm, and present the results.
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https://doi.org/10.1038/nphys2516
(contact me for a copy if you don't have access)
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| 4 |
17.1. |
Path lengths in small-world networks
(Annabelle)
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Using a mean-field approach, Newmann, Moore and Watts calculated the distribution of path lengths in Watts-Strogatz Small world networks.
Understand and present the results of the paper.
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https://arxiv.org/abs/cond-mat/9909165
Alternative https://arxiv.org/abs/1112.1728
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| 5 |
24.1. |
Network resilience and percolation theory
(Reyk+Anna)
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The paper studies scale free networks and derives a result for the critical fraction of nodes that need to fail before the network disconnects, this is analogous to percolation theory.
Understand and present the results of the paper.
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https://arxiv.org/abs/cond-mat/0007048 |
| 6 |
31.1. |
Protein folding models |
Using a mean field approach, the paper calculates the diameter of a geometric
networks model built to resemble protein folding functional networks.
Understand and present the results of the paper.
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https://arxiv.org/abs/1607.01435 |
| 7 |
7.2. |
Mean-field small-world spectra
(Konstantin)
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Understand the mean-field Laplacian matrix in the paper and present the results of the paper.
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Grabow, 2012.
https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.108.218701 |
| 8 |
7.2. |
Percolation phase transition
(Johannes)
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Coalition formation in complex networks - opinion spreading.
Understand and present the results of the paper.
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https://arxiv.org/pdf/physics/0603023.pdf |
| 9 |
14.2. |
Random Matrix Theory
(Team PC)
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Random Matrix Theory is the theory of ensembles of matrices and their statistical observables. The classical results concern the distribution of eigenvalues of such ensembles.
This project is to give an introduction to RMT and derive the semicircle law.
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https://en.wikipedia.org/wiki/Random_matrix
https://en.wikipedia.org/wiki/Wigner_semicircle_distribution
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