@phdthesis{Hock2014,
  author    = {Hock, David Rog{\´e}r},
  title     = {Analysis and Optimization of Resilient Routing in Core Communication Networks},
  issn      = {1432-8801},
  doi       = {10.25972/OPUS-10168},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-101681},
  school      = {Universit{\"a}t W{\"u}rzburg},
  pages     = {175},
  year      = {2014},
  abstract  = {Routing is one of the most important issues in any communication network. It defines on which path packets are transmitted from the source of a connection to the destination. It allows to control the distribution of flows between different locations in the network and thereby is a means to influence the load distribution or to reach certain constraints imposed by particular applications. As failures in communication networks appear regularly and cannot be completely avoided, routing is required to be resilient against such outages, i.e., routing still has to be able to forward packets on backup paths even if primary paths are not working any more. Throughout the years, various routing technologies have been introduced that are very different in their control structure, in their way of working, and in their ability to handle certain failure cases. Each of the different routing approaches opens up their own specific questions regarding configuration, optimization, and inclusion of resilience issues. This monograph investigates, with the example of three particular routing technologies, some concrete issues regarding the analysis and optimization of resilience. It thereby contributes to a better general, technology-independent understanding of these approaches and of their diverse potential for the use in future network architectures. The first considered routing type, is decentralized intra-domain routing based on administrative IP link costs and the shortest path principle. Typical examples are common today's intra-domain routing protocols OSPF and IS-IS. This type of routing includes automatic restoration abilities in case of failures what makes it in general very robust even in the case of severe network outages including several failed components. Furthermore, special IP-Fast Reroute mechanisms allow for a faster reaction on outages. For routing based on link costs, traffic engineering, e.g. the optimization of the maximum relative link load in the network, can be done indirectly by changing the administrative link costs to adequate values. The second considered routing type, MPLS-based routing, is based on the a priori configuration of primary and backup paths, so-called Label Switched Paths. The routing layout of MPLS paths offers more freedom compared to IP-based routing as it is not restricted by any shortest path constraints but any paths can be setup. However, this in general involves a higher configuration effort. Finally, in the third considered routing type, typically centralized routing using a Software Defined Networking (SDN) architecture, simple switches only forward packets according to routing decisions made by centralized controller units. SDN-based routing layouts offer the same freedom as for explicit paths configured using MPLS. In case of a failure, new rules can be setup by the controllers to continue the routing in the reduced topology. However, new resilience issues arise caused by the centralized architecture. If controllers are not reachable anymore, the forwarding rules in the single nodes cannot be adapted anymore. This might render a rerouting in case of connection problems in severe failure scenarios infeasible.},
  subject      = {Leistungsbewertung},
  language  = {en}
}
@phdthesis{Zeeb2013,
  author    = {Zeeb, Steffen},
  title     = {Chaos Synchronization in Time-Delayed Coupled Networks},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-78966},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2013},
  abstract  = {Die vorliegende Arbeit befasst sich mit der Untersuchung verschiedener Aspekte der Chaos Synchronisation von Netzwerken mit zeitverz{\"o}gerten Kopplungen. Ein Netzwerk aus identischen chaotischen Einheiten kann vollst{\"a}ndig und isochron synchronisieren, auch wenn der Signalaustausch einer starken Zeitverz{\"o}gerung unterliegt. Im ersten Teil der Arbeit werden Systeme mit mehreren Zeitverz{\"o}gerungen betrachtet. Dabei erstrecken sich die verschiedenen Zeitverz{\"o}gerungen jeweils {\"u}ber einen weiten Bereich an Gr{\"o}ßenordnungen. Es wird gezeigt, dass diese Zeitverz{\"o}gerungen im Lyapunov Spektrum des Systems auftreten; verschiedene Teile des Spektrums skalieren jeweils mit einer der Zeitverz{\"o}gerungen. Anhand des Skalierungsverhaltens des maximalen Lyapunov Exponenten k{\"o}nnen verschiedene Arten von Chaos definiert werden. Diese bestimmen die Synchronisationseigenschaften eines Netzwerkes und werden insbesondere wichtig bei hierarchischen Netzwerken, d.h. bei Netzwerken bestehend aus Unternetzwerken, bei welchen Signale innerhalb des Unternetzwerkes auf einer anderen Zeitskala ausgetauscht werden als zwischen verschiedenen Unternetzwerken. F{\"u}r ein solches System kann sowohl vollst{\"a}ndige als auch Unternetzwerksynchronisation auftreten. Skaliert der maximale Lyapunov Exponent mit der k{\"u}rzeren Zeitverz{\"o}gerung des Unternetzwerkes dann k{\"o}nnen nur die Elemente des Unternetzwerkes synchronisieren. Skaliert der maximale Lyapunov Exponent allerdings mit der l{\"a}ngeren Zeitverz{\"o}gerung kann das komplette Netzwerk vollst{\"a}ndig synchronisieren. Dies wird analytisch f{\"u}r die Bernoulli Abbildung und numerisch f{\"u}r die Zelt Abbildung gezeigt. Der zweite Teil befasst sich mit der Attraktordimension und ihrer {\"A}nderung am {\"U}bergang zur vollst{\"a}ndiger Chaos Synchronisation. Aus dem Lyapunov Spektrum des Systems wird die Kaplan-Yorke Dimension berechnet und es wird gezeigt, dass diese am Synchronisations{\"u}bergang aus physikalischen Gr{\"u}nden einen Sprung haben muss. Aus der Zeitreihe der Dynamik des Systems wird die Korrelationsdimension bestimmt und anschließend mit der Kaplan-Yorke Dimension verglichen. F{\"u}r Bernoulli Systeme finden wir in der Tat eine Diskontinuit{\"a}t in der Korrelationsdimension. Die St{\"a}rke des Sprungs der Kaplan-Yorke Dimension wird f{\"u}r ein Netzwerk aus Bernoulli Einheiten als Funktion der Netzwerkgr{\"o}ße berechnet. Desweiteren wird das Skalierungsverhalten der Kaplan-Yorke Dimension sowie der Kolmogoroventropie in Abh{\"a}ngigkeit der Systemgr{\"o}ße und der Zeitverz{\"o}gerung untersucht. Zu guter Letzt wird eine Verstimmung der Einheiten, d.h., ein "parameter mismatch", eingef{\"u}hrt und analysiert wie diese das Verhalten der Attraktordimension {\"a}ndert. Im dritten und letzten Teil wird die lineare Antwort eines synchronisierten chaotischen Systems auf eine kleine externe St{\"o}rung untersucht. Diese St{\"o}rung bewirkt eine Abweichung der Einheiten vom perfekt synchronisierten Zustand. Die Verteilung der Abst{\"a}nde zwischen zwei Einheiten dient als Maß f{\"u}r die lineare Antwort des Systems. Diese Verteilung sowie ihre Momente werden numerisch und f{\"u}r Spezialf{\"a}lle auch analytisch berechnet. Wir finden, dass im synchronisierten Zustand, in Abh{\"a}ngigkeit der Parameter des Systems, Verteilungen auftreten k{\"o}nnen die einem Potenzgesetz gehorchen und dessen Momente divergieren. Als weiteres Maß f{\"u}r die lineare Antwort wird die Bit Error Rate einer {\"u}bermittelten bin{\"a}ren Nachricht verwendet. The Bit Error Rate ist durch ein Integral {\"u}ber die Verteilung der Abst{\"a}nde gegeben. In dieser Arbeit wird sie vorwiegend numerisch untersucht und wir finden ein komplexes, nicht monotones Verhalten als Funktion der Kopplungsst{\"a}rke. F{\"u}r Spezialf{\"a}lle weist die Bit Error Rate eine "devil's staircase" auf, welche mit einer fraktalen Struktur in der Verteilung der Abst{\"a}nde verkn{\"u}pft ist. Die lineare Antwort des Systems auf eine harmonische St{\"o}rung wird ebenfalls untersucht. Es treten Resonanzen auf, welche in Abh{\"a}ngigkeit von der Zeitverz{\"o}gerung unterdr{\"u}ckt oder verst{\"a}rkt werden. Eine bi-direktional gekoppelte Kette aus drei Einheiten kann eine St{\"o}rung vollst{\"a}ndig heraus filtern, so dass die Bit Error Rate und auch das zweite Moment verschwinden.},
  subject      = {Chaostheorie},
  language  = {en}
}
@phdthesis{Heiligenthal2012,
  author    = {Heiligenthal, Sven},
  title     = {Strong and Weak Chaos in Networks of Semiconductor Lasers with Time-Delayed Couplings},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-77958},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2012},
  abstract  = {This thesis deals with the chaotic dynamics of nonlinear networks consisting of semiconductor lasers which have time-delayed self-feedbacks or mutual couplings. These semiconductor lasers are simulated numerically by the Lang-Kobayashi equations. The central issue is how the chaoticity of the lasers, measured by the maximal Lyapunov exponent, changes when the delay time is changed. It is analysed how this change of chaoticity with increasing delay time depends on the reflectivity of the mirror for the self-feedback or the strength of the mutal coupling, respectively. The consequences of the different types of chaos for the effect of chaos synchronization of mutually coupled semiconductor lasers are deduced and discussed. At the beginning of this thesis, the master stability formalism for the stability analysis of nonlinear networks with delay is explained. After the description of the Lang-Kobayashi equations and their linearizations as a model for the numerical simulation of semiconductor lasers with time-delayed couplings, the artificial sub-Lyapunov exponent \$\lambda_{0}\$ is introduced. It is explained how the sign of the sub-Lyapunov exponent can be determined by experiments. The notions of "strong chaos" and "weak chaos" are introduced and distinguished by their different scaling properties of the maximal Lyapunov exponent with the delay time. The sign of the sub-Lyapunov exponent \$\lambda_{0}\$ is shown to determine the occurence of strong or weak chaos. The transition sequence "weak to strong chaos and back to weak chaos" upon monotonically increasing the coupling strength \$\sigma\$ of a single laser's self-feedback is shown for numerical calculations of the Lang-Kobayashi equations. At the transition between strong and weak chaos, the sub-Lyapunov exponent vanishes, \$\lambda_{0}=0\$, resulting in a special scaling behaviour of the maximal Lyapunov exponent with the delay time. Transitions between strong and weak chaos by changing \$\sigma\$ can also be found for the R{\"o}ssler and Lorenz dynamics. The connection between the sub-Lyapunov exponent and the time-dependent eigenvalues of the Jacobian for the internal laser dynamics is analysed. Counterintuitively, the difference between strong and weak chaos is not directly visible from the trajectory although the difference of the trajectories induces the transitions between the two types of chaos. In addition, it is shown that a linear measure like the auto-correlation function cannot unambiguously reveal the difference between strong and weak chaos either. Although the auto-correlations after one delay time are significantly higher for weak chaos than for strong chaos, it is not possible to detect a qualitative difference. If two time-scale separated self-feedbacks are present, the shorter feedback has to be taken into account for the definition of a new sub-Lyapunov exponent \$\lambda_{0,s}\$, which in this case determines the occurence of strong or weak chaos. If the two self-feedbacks have comparable delay times, the sub-Lyapunov exponent \$\lambda_{0}\$ remains the criterion for strong or weak chaos. It is shown that the sub-Lyapunov exponent scales with the square root of the effective pump current \$\sqrt{p-1}\$, both in its magnitude and in the position of the critical coupling strengths. For networks with several distinct sub-Lyapunov exponents, it is shown that the maximal sub-Lyapunov exponent of the network determines whether the network's maximal Lyapunov exponent scales strongly or weakly with increasing delay time. As a consequence, complete synchronization of a network is excluded for arbitrary networks which contain at least one strongly chaotic laser. Furthermore, it is demonstrated that the sub-Lyapunov exponent of a driven laser depends on the number of the incoherently superimposed inputs from unsynchronized input lasers. For networks of delay-coupled lasers operating in weak chaos, the condition \$|\gamma_{2}|<\mathrm{e}^{-\lambda_{\mathrm{m}}\,\tau}\$ for stable chaos synchronization is deduced using the master stability formalism. Hence, synchronization of any network depends only on the properties of a single laser with self-feedback and the eigenvalue gap of the coupling matrix. The characteristics of the master stability function for the Lang-Kobayashi dynamics is described, and consequently, the master stability function is refined to allow for precise practical prediction of synchronization. The prediction of synchronization with the master stability function is demonstrated for bidirectional and unidirectional networks. Furthermore, the master stability function is extended for two distinct delay times. Finally, symmetries and resonances for certain values of the ratio of the delay times are shown for the master stability function of the Lang-Kobyashi equations.},
  subject      = {Halbleiterlaser},
  language  = {en}
}
@article{ReichardtAlaminoSaad2011,
  author    = {Reichardt, Joerg and Alamino, Roberto and Saad, David},
  title     = {The interplay between microscopic and mesoscopic structures in complex networks},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-68993},
  year      = {2011},
  abstract  = {Understanding a complex network's structure holds the key to understanding its function. The physics community has contributed a multitude of methods and analyses to this cross-disciplinary endeavor. Structural features exist on both the microscopic level, resulting from differences between single node properties, and the mesoscopic level resulting from properties shared by groups of nodes. Disentangling the determinants of network structure on these different scales has remained a major, and so far unsolved, challenge. Here we show how multiscale generative probabilistic exponential random graph models combined with efficient, distributive message-passing inference techniques can be used to achieve this separation of scales, leading to improved detection accuracy of latent classes as demonstrated on benchmark problems. It sheds new light on the statistical significance of motif-distributions in neural networks and improves the link-prediction accuracy as exemplified for gene-disease associations in the highly consequential Online Mendelian Inheritance in Man database.},
  subject      = {Netzwerk},
  language  = {en}
}
@article{PinkertSchultzReichardt2010,
  author    = {Pinkert, Stefan and Schultz, Joerg and Reichardt, Joerg},
  title     = {Protein Interaction Networks-More Than Mere Modules},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-68426},
  year      = {2010},
  abstract  = {It is widely believed that the modular organization of cellular function is reflected in a modular structure of molecular networks. A common view is that a ''module'' in a network is a cohesively linked group of nodes, densely connected internally and sparsely interacting with the rest of the network. Many algorithms try to identify functional modules in protein-interaction networks (PIN) by searching for such cohesive groups of proteins. Here, we present an alternative approach independent of any prior definition of what actually constitutes a ''module''. In a self-consistent manner, proteins are grouped into ''functional roles'' if they interact in similar ways with other proteins according to their functional roles. Such grouping may well result in cohesive modules again, but only if the network structure actually supports this. We applied our method to the PIN from the Human Protein Reference Database (HPRD) and found that a representation of the network in terms of cohesive modules, at least on a global scale, does not optimally represent the network's structure because it focuses on finding independent groups of proteins. In contrast, a decomposition into functional roles is able to depict the structure much better as it also takes into account the interdependencies between roles and even allows groupings based on the absence of interactions between proteins in the same functional role. This, for example, is the case for transmembrane proteins, which could never be recognized as a cohesive group of nodes in a PIN. When mapping experimental methods onto the groups, we identified profound differences in the coverage suggesting that our method is able to capture experimental bias in the data, too. For example yeast-two-hybrid data were highly overrepresented in one particular group. Thus, there is more structure in protein-interaction networks than cohesive modules alone and we believe this finding can significantly improve automated function prediction algorithms.},
  subject      = {Netzwerk},
  language  = {en}
}
@phdthesis{Menth2004,
  author    = {Menth, Michael},
  title     = {Efficient admission control and routing for resilient communication networks},
  doi       = {10.25972/OPUS-846},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-9949},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2004},
  abstract  = {This work is subdivided into two main areas: resilient admission control and resilient routing. The work gives an overview of the state of the art of quality of service mechanisms in communication networks and proposes a categorization of admission control (AC) methods. These approaches are investigated regarding performance, more precisely, regarding the potential resource utilization by dimensioning the capacity for a network with a given topology, traffic matrix, and a required flow blocking probability. In case of a failure, the affected traffic is rerouted over backup paths which increases the traffic rate on the respective links. To guarantee the effectiveness of admission control also in failure scenarios, the increased traffic rate must be taken into account for capacity dimensioning and leads to resilient AC. Capacity dimensioning is not feasible for existing networks with already given link capacities. For the application of resilient NAC in this case, the size of distributed AC budgets must be adapted according to the traffic matrix in such a way that the maximum blocking probability for all flows is minimized and that the capacity of all links is not exceeded by the admissible traffic rate in any failure scenario. Several algorithms for the solution of that problem are presented and compared regarding their efficiency and fairness. A prototype for resilient AC was implemented in the laboratories of Siemens AG in Munich within the scope of the project KING. Resilience requires additional capacity on the backup paths for failure scenarios. The amount of this backup capacity depends on the routing and can be minimized by routing optimization. New protection switching mechanisms are presented that deviate the traffic quickly around outage locations. They are simple and can be implemented, e.g, by MPLS technology. The Self-Protecting Multi-Path (SPM) is a multi-path consisting of disjoint partial paths. The traffic is distributed over all faultless partial paths according to an optimized load balancing function both in the working case and in failure scenarios. Performance studies show that the network topology and the traffic matrix also influence the amount of required backup capacity significantly. The example of the COST-239 network illustrates that conventional shortest path routing may need 50\% more capacity than the optimized SPM if all single link and node failures are protected.},
  subject      = {Kommunikation},
  language  = {en}
}