(µ, ν) of the singular fibre of Seif i (X) over a point x ∈ int X satisfies µ ≤ 2π/L(Σ x ). collapsing three-manifolds 3 It should be noted that the Euler characteristic of X and the number of singular fibres of M i in Theorems 0.2 and 0.3 are estimated by a constant depending only on the upper

compatible strains in panmictic host populations does not act directly on CI intensity but favors higher "effective fecundity," the number of infected progeny an infected female produces. We analyze the consequences of host population subdivision using deterministic and stochastic models

We are surrounded by electronic devices that take advantage of wireless technologies, from our computer mice, which require little amounts of information, to our cellphones, which demand increasingly higher data rates. Until today, the coexistence of such a variety of services has been guaranteed by a fixed assignment of spectrum resources by regulatory agencies. This has resulted into a blind alley, as current wireless spectrum has become an expensive and a scarce resource. However, recent measurements in dense areas paint a very different picture: there is an actual underutilization of the spectrum by legacy sys-tems. Cognitive radio exhibits a tremendous promise for increasing the spectral efficiency for future wireless systems. Ideally, new secondary users would have a perfect panorama of the spectrum usage, and would opportunistically communicate over the available re-sources without degrading the primary systems. Yet in practice, monitoring the spectrum resources, detecting available resources for opportunistic communication, and transmit-ting over the resources are hard tasks. This thesis addresses the tasks of monitoring, de-