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Abstract:

In large and complex systems, failures can have dramatic consequences, such as black-outs, pandemics or the loss of entire classes of an ecosystem. Nevertheless, it is a centuries-old intuition that by using networks to capture the core of the complexity of such systems, one might understand in which part of a system a phenomenon originates.

I investigate this intuition using spectral methods to decouple the dynamics of complex systems near stationary states into independent dynamical modes. In this description, phenomena are tied to a specific part of a system through localized eigenvectors which have large amplitudes only on a few nodes of the system’s network. Studying the occurrence of localized eigenvectors, I find that such localization occurs exactly for a few small network structures, and approximately for the dynamical modes associated with the most prominent failures in complex systems.

My findings confirm that understanding the functioning of complex systems generally requires to treat them as complex entities, rather than collections of interwoven small parts. Exceptions to this are only few structures carrying exact localization, whose functioning is tied to the meso-scale, between the size of individual elements and the size of the global network. However, while understanding the functioning of a complex system is hampered by the necessary global analysis, the prominent failures, due to their localization, allow an understanding on a manageable local scale.

Intriguingly, food webs might exploit this localization of failures to stabilize by causing the break-off of small problematic parts, whereas typical attempts to optimize technological systems for stability lead to delocalization and large-scale failures. Thus, this thesis provides insights into the interplay of complexity and localization, which is paramount to ascertain the functioning of the ever-growing networks on which we humans depend.

Find a copy of my dissertation on QUCOSA .

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  • Using Analytics for smart Enterprise Asset Management
    E. Toensing, H. Aufderheide
  • DevOps with Python (Talk).
    H. Aufderheide
    TNG BigTech Day 2017, Munich
  • Data Driven Monitoring of Rolling Stock Components
    F Ferroni, M. Klimmek, H. Aufderheide, J. Laia, D.Klingebiel, M. Davidich
    Proceedings of SAI Intelligent Systems Conference 2016
  • Large networks have small problems (Talk).
    H. Aufderheide, T. Gross
    DPG Conference 2014, Dresden
  • Predicting responses in complex interaction networks (Talk).
    H. Aufderheide, L. Rudolf, T. Gross, K. D. Lafferty
    Dynamics Days Berlin-Brandenburg 2013, Berlin
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  • Meso-scale symmetries explain the dynamical equivalence of food webs (Poster).
    H. Aufderheide, L. Rudolf, T. Gross
    SIAM Conference for Dynamical Systems 2013, Snowbird, Utah
  • Meso-scale symmetries explain dynamical equivalence of food webs (Talk).
    H. Aufderheide, L. Rudolf, T. Gross
    DPG Conference 2012, Berlin
  • Symmetries in Complex Networks (Poster).
    H. Aufderheide, L. Rudolf, T. Gross
    DPG Conference 2011, Dresden
  • Hard-Core Boson Quench Dynamics (Poster).
    H. Aufderheide, D. Karevski
    MECO Conference 2010, Pont-a-Mousson
  • Large networks have small problems
    H. Aufderheide, T. Gross
    in preparation (write me to obtain a preprint)
  • Predicting community responses in the face of imperfect knowledge and network complexity
    H. Aufderheide, L. Rudolf, T. Gross, K. D. Lafferty
  • Meso-scale symmetries explain the dynamical equivalence of food webs Featured in "NJP Highlights of 2012"
    H. Aufderheide, L. Rudolf, T. Gross
  • Entangling many-body bound states with propagative modes in Bose-Hubbard systems
    M. Collura, H. Aufderheide, G. Roux, D. Karevski
I have filed around 20 patent applications for rail analytics, typically using advanced analytics to tackle engineering problems. Take a look at the granted ones on google patents.