Applied Mathematics

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https://hdl.handle.net/2440/8

Applied Mathematics at the University of Adelaide is one of the leading groups in teaching and research in Australia. Members conduct internationally recognized research into a wide range of Applied Mathematics. The research within Applied Mathematics can be loosely grouped into the following areas.

  • Biomedical Engineering
  • Fluid Dynamics
  • Optimisation
  • Stochastic Modelling
  • Teletraffic Research

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Browsing Applied Mathematics by Author "Alderson, D."

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    The "robust yet fragile" nature of the Internet
    (Natl Acad Sciences, 2005) Doyle, J.; Alderson, D.; Li, L.; Low, S.; Roughan, M.; Shalunov, S.; Tanaka, R.; Willinger, W.
    The search for unifying properties of complex networks is popular, challenging, and important. For modeling approaches that focus on robustness and fragility as unifying concepts, the Internet is an especially attractive case study, mainly because its applications are ubiquitous and pervasive, and widely available expositions exist at every level of detail. Nevertheless, alternative approaches to modeling the Internet often make extremely different assumptions and derive opposite conclusions about fundamental properties of one and the same system. Fortunately, a detailed understanding of Internet technology combined with a unique ability to measure the network means that these differences can be understood thoroughly and resolved unambiguously. This article aims to make recent results of this process accessible beyond Internet specialists to the broader scientific community and to clarify several sources of basic methodological differences that are relevant beyond either the Internet or the two specific approaches focused on here (i.e., scale-free networks and highly optimized tolerance networks).
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    The many facets of Internet topology and traffic
    (American Institute of Mathematical Sciences, 2006) Alderson, D.; Chang, H.; Roughan, M.; Uhlig, S.; Willinger, W.
    The Internet’s layered architecture and organizational structure give rise to a number of different topologies, with the lower layers defining more physical and the higher layers more virtual/logical types of connectivity structures. These structures are very dif-ferent, and successful Internet topology modeling requires annotating the nodes and edges of the corresponding graphs with information that reflects their network-intrinsic meaning. These structures also give rise to different representations of the traffic that traverses the heterogeneous Internet, and a traffic matrix is a compact and succinct description of the traffic exchanges between the nodes in a given connectivity structure. In this paper, we summarize recent advances in Internet research related to (i) inferring and modeling the router-level topologies of individual service providers (i.e., the physical connectivity structure of an ISP, where nodes are routers/switches and links represent physical connections), (ii) estimating the intra-AS traffic matrix when the AS’s router-level topology and routing configuration are known, (iii) inferring and modeling the Internet’s AS-level topology, and (iv) estimating the inter-AS traffic matrix. We will also discuss recent work on Internet connectivity structures that arise at the higher layers in the TCP/IP protocol stack and are more virtual and dynamic; e.g., overlay networks like the WWW graph, where nodes are web pages and edges represent existing hyperlinks, or P2P networks like Gnutella, where nodes represent peers and two peers are connected if they have an active network connection.