Product (mathematics)

About: Product (mathematics) is a research topic. Over the lifetime, 44382 publications have been published within this topic receiving 377809 citations.

Red Opal: product-feature scoring from reviews

Abstract: Online shoppers are generally highly task-driven: they have a certain goal in mind, and they are looking for a product with features that are consistent with that goal. Unfortunately, finding a product with specific features is extremely time-consuming using the search functionality provided by existing web sites.In this paper, we present a new search system called Red Opal that enables users to locate products rapidly based on features. Our fully automatic system examines prior customer reviews, identifies product features, and scores each product on each feature. Red Opal uses these scores to determine which products to show when a user specifies a desired product feature. We evaluate our system on four dimensions: precision of feature extraction, efficiency of feature extraction, precision of product scores, and estimated time savings to customers. On each dimension, Red Opal performs better than a comparison system.

Puzzles and (equivariant) cohomology of Grassmannians

Abstract: The product of two Schubert cohomology classes on a Grassmannian ${\rm Gr}_k (\mathbb{c}^n)$ has long been known to be a positive combination of other Schubert classes, and many manifestly positive formulae are now available for computing such a product (eg, the Littlewood-Richardson rule or the more symmetric puzzle rule from A Knutson, T Tao, and C Woodward [KTW]) Recently, W~Graham showed in [G], nonconstructively, that a similar positivity statement holds for {\em $T$-equivariant} cohomology (where the coefficients are polynomials) We give the first manifestly positive formula for these coefficients in terms of puzzles using an ``equivariant puzzle piece'' The proof of the formula is mostly combinatorial but requires no prior combinatorics and only a modicum of equivariant cohomology (which we include) As a by-product the argument gives a new proof of the puzzle (or Littlewood-Richardson) rule in the ordinary-cohomology case, but this proof requires the equivariant generalization in an essential way, as it inducts backwards from the ``most equivariant'' case This formula is closely related to the one in A Molev and B Sagan [MS] for multiplying factorial Schur functions in three sets of variables, although their rule does not give a positive formula in the sense of [G] We include a cohomological interpretation of their problem and a puzzle formulation for it

Yield model for productivity optimization of VLSI memory chips with redundancy and partially good product

Abstract: A model with mixed Poisson statistics has been developed for calculating the yield for memory chips with redundant lines and for partially good product. The mixing process requires two parameters which are readily obtained from product data. The product is described in the model by critical areas which depend on the circuit's sensitivity to defects, and they can be determined in a systematic way. The process is represented in the model by defect densities and gross yield losses. These are measured with defect monitors independently of product type. This paper shows how the yield for any product can be calculated given the critical areas, defect density, and mixing parameter. Future yields are forecast by using expected improvements in defect densities. Examples show good agreement between actual and calculated yields.