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Singular vectors for the WN algebras and the BRST cohomology for relaxed highestweight Lk(sl(2)) modules
(2019)This thesis presents the computation of singular vectors of the W_n algebras and the BRST cohomology of modules of the simple vertex operator algebra L_k(sl2) associated to the affine Lie algebra of sl2 in the relaxed ... 
Missing data analysis, combinatorial model selection and structure learning
(2019)This thesis examines three problems in statistics: the missing data problem in the context of extracting trends from time series data, the combinatorial model selection problem in regression analysis, and the structure ... 
Exact solutions in multispecies exclusion processes
(2019)The exclusion process has been the default model for the transportation phenomenon. One fundamental issue is to compute the exact formulae analytically. Such formulae enable us to obtain the limiting distribution through ...