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We want to discuss various applications of modular forms in topology. The starting point is elliptic genus and its generalizations. The main techniques are the Atiyah-Singer index theorem, the Atiyah-Bott-Segal-Singer Lefschetz fixed point formula, Kac-Moody Lie algebras, modular forms and theta-functions. Just as the representations theory of classical Lie(More)
— Although a number of multi-objective evolutionary algorithms (MOEAs) have been proposed over the last two decades, very few studies have utilized MOEAs for game agent synthesis. Recently, we have suggested a co-evolutionary implementation using the Pareto Evolutionary Programming (PEP) algorithm. This paper describes a series of experiments using PEP for(More)
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