We formulate the Nahm transform in the context of parabolic Higgs bundles on P 1 and extend its scope in completely algebraic terms. This transform requires parabolic Higgs bundles to satisfy an admissibility condition and allows Higgs fields to have poles of arbitrary order and arbitrary behavior. Our methods are constructive in nature and examples are provided. The extended Nahm transform is established as an algebraic duality between moduli spaces of parabolic Higgs bundles. The guiding principle behind the construction is to investigate the behavior of spectral data near the poles of Higgs fields. 14H60; 14E05, 14J26

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The efficient dimensioning of cellular wireless access networks depends highly on the accuracy of the underlying mathematical models of user distribution and traffic estimations. Mobility prediction also considered as an effective method contributing to the accuracy of IP multicast based multimedia transmissions, and ad hoc routing algorithms. In this paper we focus on the tradeoff between the accuracy and the complexity of the mathematical models used to describe user movements in the network. We propose mobility model extension, in order to utilize user's movement history thus providing more accurate results than other widely used models in the literature. The new models are applicable in real-life scenarios, because these rely on additional information effectively available in cellular networks (e.g. handover history), too. The complexity of the proposed models is analyzed, and the accuracy is justified by means of simulation.