Chern classes of Schubert cells and varieties

We give explicit formulas for the Chern-Schwartz-MacPherson classes of all Schubert varieties in the Grassmannian of $d$-planes in a vector space, and conjecture that these classes are effective. We prove this is the case for (very) small values of $d$.Comment: 31 pages, several figure

Equivariant quantum cohomology of homogeneous spaces

We prove a Chevalley formula for the equivariant quantum multiplication of two Schubert classes in the homogeneous variety X=G/P. As in the case when X is a Grassmannian, studied by the author in a previous paper, this formula implies an effective algorithm to compute the structure constants of the equivariant quantum cohomology algebra of X.Comment: 21 page

Discovering and managing creativity in product development

Creativity is a result of brain activity which differentiates individuals from each other and could ensure an important competitive advantage for a person or for a company. For very innovative branches - like soft ware industry, computer industry, or for automotive industry - creativity is the key of business success. The students should learn that every person can develop basic creative activities, but professional creativity should be trained and it could be enhanced over the level of employees' natural possibilities. They should learn that neurological research still does not offer a scientific basis for understanding creativity but thousand years of creative behavior observations offer some guidelines and procedures which could be used successfully in product development.creativity, managing creativity, product development

Factors Influencing the Surprising Instability of Word Embeddings

Despite the recent popularity of word embedding methods, there is only a small body of work exploring the limitations of these representations. In this paper, we consider one aspect of embedding spaces, namely their stability. We show that even relatively high frequency words (100-200 occurrences) are often unstable. We provide empirical evidence for how various factors contribute to the stability of word embeddings, and we analyze the effects of stability on downstream tasks.Comment: NAACL HLT 201