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- Carsten Grabow, Stefan Grosskinsky, Marc Timme
- Physical review letters
- 2012

Collective dynamics on small-world networks emerge in a broad range of systems with their spectra characterizing fundamental asymptotic features. Here we derive analytic mean-field predictions for the spectra of small-world models that systematically interpolate between regular and random topologies by varying their randomness. These theoretical predictions… (More)

- Frank Hellmann, Paul Schultz, Carsten Grabow, Jobst Heitzig, Jürgen Kurths
- Scientific reports
- 2016

The notion of a part of phase space containing desired (or allowed) states of a dynamical system is important in a wide range of complex systems research. It has been called the safe operating space, the viability kernel or the sunny region. In this paper we define the notion of survivability: Given a random initial condition, what is the likelihood that… (More)

- Martin Wolf, Alexander D. Popov, +27 authors Sebastian Uhlmann
- 2006

In this thesis, we report on different aspects of integrability in supersymmetric gauge theories. Our main tool of investigation is supertwistor geometry. In the first chapter, we briefly review the basics of twistor geometry. Afterwards, we discuss self-dual super Yang-Mills (SYM) theory and some of its relatives. In particular, a detailed twistor… (More)

- Carsten Grabow, Stefan Grosskinsky, Marc Timme
- ArXiv
- 2011

Synchrony is one of the most common dynamical states emerging on networks. The speed of convergence towards synchrony provides a fundamental collective time scale for synchronizing systems. Here we study the asymptotic synchronization times for directed networks with topologies ranging from completely ordered, grid-like, to completely disordered, random,… (More)

- Michael Flohr, Carsten Grabow, Michael Koehn
- 2007

We present fermionic quasi-particle sum representations consisting of a single fundamental fermionic form for all characters of the logarithmic conformal field theory models with central charge cp,1, p ≥ 2, and suggest a physical interpretation. We also show that it is possible to correctly extract dilogarithm identities.

- Carsten Grabow, Stefan Grosskinsky, Jürgen Kurths, Marc Timme
- Physical review. E, Statistical, nonlinear, and…
- 2015

Complex networks exhibit a wide range of collective dynamic phenomena, including synchronization, diffusion, relaxation, and coordination processes. Their asymptotic dynamics is generically characterized by the local Jacobian, graph Laplacian, or a similar linear operator. The structure of networks with regular, small-world, and random connectivities are… (More)

Based on our article [FGK07], published in Nuclear Physics B, fermionic quasiparticle sum representations consisting of only one single fundamental fermionic form are presented for all characters of the logarithmic conformal field theory models with central charge cp,1, p ≥ 2. These new representations are embedded in the surrounding field of Nahm’s… (More)

- Carsten Grabow, Stefan Grosskinsky, Marc Timme
- ArXiv
- 2011

Collective dynamics on small-world networks emerge in a broad range of systems with their spectra characterizing fundamental asymptotic features. Here we derive analytic mean field predictions for the spectra of small-world models that systematically interpolate between regular and random topologies by varying their randomness. These theoretical predictions… (More)

- Alexander D. Popov, Holger Frahm, +10 authors Marco Krohn
- 2006

In this thesis, we report on different aspects of integrability in supersymmetric gauge theories. Our main tool of investigation is supertwistor geometry. In the first chapter, we briefly review the basics of twistor geometry. Afterwards, we discuss self-dual super Yang-Mills (SYM) theory and some of its relatives. In particular, a detailed twistor… (More)

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