I prove a formula expressing the descendent genus g Gromov-Witten invariants of a projective variety X in terms of genus 0 invariants of its symmetric product stack S(X). When X is a point, the latter are structure constants of the symmetric group, and we obtain a new way of calculating the Gromov-Witten invariants of a point.

Quot schemes of quotients a trivial bundle arbitrary rank on nonsingular projective surface X carry perfect obstruction theories and virtual fundamental classes whenever the quotient sheaf has at most 1-dimensional support. The associated generating series Euler characteristics was conjectured to be rational function in Oprea Pandharipande (in, Geom Topol. http://arxiv.org/abs/1903.08787 ) whe...

This paper presents a class of hierarchical fuzzy system applied to a cigar classification system. The weight, texture and chromatic characteristics are used to classify multiple cigars using a previous classification based on heuristic knowledge. In the adaptive part, a gradient descendent and error backpropagation method is applied for adjusting the parameters. A detailed description of the a...

Combinatory Categorial Grammar is a lexicalised formalism which is mildly context-sensitive. Recently Set Combinatory Categorial Grammar, a direct descendent of Combinatory Categorial Grammar was proposed to treat local scrambling adequately. In this paper, we briefly sketch Set Combinatory Categorial Grammar analyses of various Korean syntactic phenomena including coordination, extraction and ...

The inclusion of some paraphyletic groups in a temporally and taxonomically comprehensive phylogenetic classification is inevitable because cladistic methodology is incapable of excluding the possibility that a structurally (i.e., based on the branching pattern of a given cladogram) monophyletic group contains the ancestor of another group, i.e., that it is historically paraphyletic. Paracladis...

The conjectural equivalence of curve counting on Calabi-Yau 3-folds via stable maps and stable pairs is discussed. By considering Calabi-Yau 3-folds with K3 fibrations, the correspondence naturally connects curve and sheaf counting on K3 surfaces. New results and conjectures (with D. Maulik) about descendent integration on K3 surfaces are announced. The recent proof of the Yau-Zaslow conjecture...