I have begun to plant thee and will labor To make thee full of growing.

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 .

• Ebook: How Railway IT Systems are Moving to AWS Cloud Computing
  Read it here
• Blog: Architecting for Resilience in the cloud for critical railway systems
  Read it here
• Blog: Running your own server for Jamulus, an open source solution to jam with other musicians online
  Read it here
• Blog: Scale your Nextcloud with Storage on Amazon Simple Storage Service (Amazon S3)
  Read it here
• Blog: Advanced Nextcloud Workflows with Amazon Simple Storage Service (Amazon S3)
  Read it here

• Using Analytics for smart Enterprise Asset Management
  E. Toensing, H. Aufderheide
  Rail Asset Management APAC 2019
• 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

• 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
  Proc. R. Soc. B 280 (2013) or ArXiv Preprint
• Meso-scale symmetries explain the dynamical equivalence of food webs Featured in "NJP Highlights of 2012"
  H. Aufderheide, L. Rudolf, T. Gross
  New J. Phys. 14 (2012) 105014 or ArXiv Preprint
• Entangling many-body bound states with propagative modes in Bose-Hubbard systems
  M. Collura, H. Aufderheide, G. Roux, D. Karevski
  Phys. Rev. A 86 (2012) 013615 or ArXiv Preprint

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.