Biomedical subjects
Publications and source records attributed to Michael Baake.
Discrete tomography is a well-established method to investigate finite point sets, in particular finite subsets of periodic systems. Here, we start to develop an efficient approach for the treatment of finite subsets of mathematical quasicrystals. To this end, the class of cyclotomic model sets is introduced, and the corresponding consistency, reconstruction and uniqueness problems of the discrete tomography of these sets are discussed.
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The impulse response function (IRF) of a localized bolus in cerebral blood flow codes important information on the tissue type. It is indirectly accessible both from MR and CT imaging methods, at least in principle. In practice, however, noise and limited signal resolution render standard deconvolution techniques almost useless. Parametric signal descriptions look more promising, and it is the aim of this contribution to develop some improvements along this line.
Recent work on mutation-selection models has revealed that, under specific assumptions on the fitness function and the mutation rates, asymptotic estimates for the leading eigenvalue of the mutation-reproduction matrix may be obtained through a low-dimensional maximum principle in the limit N-->infinity (where N, or N(d) with d> or =1, is proportional to the number of types). In order to extend this variational principle to a larger class of models, we consider here a family of reversible matrices of asymptotic dimension N(d) and identify conditions under which the high-dimensional Rayleigh-Ritz variational problem may be reduced to a low-dimensional one that yields the leading eigenvalue up to an error term of order 1/N. For a large class of mutation-selection models, this implies estimates for the mean fitness, as well as a concentration result for the ancestral distribution of types.
We analyze a class of models for unequal crossover (UC) of sequences containing sections with repeated units that may differ in length. In these, the probability of an 'imperfect' alignment, in which the shorter sequence has d units without a partner in the longer one, scales like qd as compared to 'perfect' alignments where all these copies are paired. The class is parameterized by this penalty factor q. An effectively infinite population size and thus deterministic dynamics is assumed. For the extreme cases q = 0 and q = 1, and any initial distribution whose moments satisfy certain conditions, we prove the convergence to one of the known fixed points, uniquely determined by the mean copy number, in both discrete and continuous time. For the intermediate parameter values, the existence of fixed points is shown.