Chern classes of reductive groups and an adjunction formula

In this paper, I construct noncompact analogs of the Chern classes of equivariant vector bundles over complex reductive groups. For the tangent bundle, these Chern classes yield an adjunction formula for the Euler characteristic of complete intersections in reductive groups. In the case where the complete intersection is a curve, this formula gives an explicit answer for the Euler characteristic and the genus of the curve.Comment: LATeX, 26 pages; added references, corrected typo

Gelfand-Zetlin polytopes and flag varieties

I construct a correspondence between the Schubert cycles on the variety of complete flags in C^n and some faces of the Gelfand-Zetlin polytope associated with the irreducible representation of SL_n(C) with a strictly dominant highest weight. The construction is based on a geometric presentation of Schubert cells by Bernstein-Gelfand-Gelfand using Demazure modules. The correspondence between the Schubert cycles and faces is then used to interpret the classical Chevalley formula in Schubert calculus in terms of the Gelfand-Zetlin polytopes. The whole picture resembles the picture for toric varieties and their polytopes.Comment: 16 pages, 2 figure

Schubert calculus for algebraic cobordism

We establish a Schubert calculus for Bott-Samelson resolutions in the algebraic cobordism ring of a complete flag variety G/B.Comment: 27 pages, Appendix added, slightly abridged version to appear in Crell

The Effect of Negators, Modals, and Degree Adverbs on Sentiment Composition

Negators, modals, and degree adverbs can significantly affect the sentiment of the words they modify. Often, their impact is modeled with simple heuristics; although, recent work has shown that such heuristics do not capture the true sentiment of multi-word phrases. We created a dataset of phrases that include various negators, modals, and degree adverbs, as well as their combinations. Both the phrases and their constituent content words were annotated with real-valued scores of sentiment association. Using phrasal terms in the created dataset, we analyze the impact of individual modifiers and the average effect of the groups of modifiers on overall sentiment. We find that the effect of modifiers varies substantially among the members of the same group. Furthermore, each individual modifier can affect sentiment words in different ways. Therefore, solutions based on statistical learning seem more promising than fixed hand-crafted rules on the task of automatic sentiment prediction.Comment: In Proceedings of the 7th Workshop on Computational Approaches to Subjectivity, Sentiment and Social Media Analysis (WASSA), San Diego, California, 201