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We introduce the concept of the fundamental group of a topological space and demonstrate its utility in classifying spaces by computing several examples. We also use the techniques developed in the paper to prove the Brouwer Fixed Point Theorem for the disk. We assume a knowledge of the basic elements of group theory and point-set topology.
We present two different types of models, deterministic compartmental (based on ordinary differential equations) and stochastic network (based on random graphs), used in the field of populationlevel HIV transmission modeling, and use them to investigate the impact of circular migration (periodic migrations between urban and rural segments of a larger… (More)
Marine Protected Areas (MPAs), marine areas in which human activities are restricted, are implemented worldwide to protect the marine environment. However, with a large proportion of these MPAs being no more than paper parks, it is important to be able to evaluate MPA success, determined by improvements to biophysical, socio-economic and governance… (More)