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The lack of a formal link between neural network structure and its emergent function has hampered our understanding of how the brain processes information. We have now come closer to describing such a link by taking the direction of synaptic transmission i ...
We consider a natural subclass of harmonic maps from a surface into G/T, namely cyclic primitive maps. Here G is any simple real Lie group (not necessarily compact), T is a Cartan subgroup and both are chosen so that there is a Coxeter automorphism on G(C) ...
Elsevier2017
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We consider a class of continuous-time branching processes called Markovian binary trees (MBTs), in which the individuals lifetime and reproduction epochs are modelled using a transient Markovian arrival process (TMAP). We develop methods for estimating th ...
Persistent homology, while ostensibly measuring changes in topology, captures multiscale geometrical information. It is a natural tool for the analysis of point patterns. In this paper we explore the statistical power of the persistent homology rank functi ...