Expansion and Reduction

Taylor Expansion, β-Reduction and Normalization

We introduce a notion of reduction on resource vectors, i.e. infinite linear combinations of resource λ-terms. The latter form the multilinear fragment of the differential λ-calculus introduced by Ehrhard and Regnier, and resource vectors are the target of the Taylor expansion of λ-terms. We show that the reduction of resource vectors contains the image, through Taylor expansion, of β-reduction...

Series expansion for functional sufficient dimension reduction

Functional data are infinite-dimensional statistical objects which pose significant challenges to both theorists and practitioners. Both parametric and nonparametric regressions have received attention in the functional data analysis literature. However, the former imposes stringent constraints while the latter suffers from logarithmic convergence rates. In this article, we consider two popular...

Nonlinear model reduction using multiple expansion bases

Nonlinear model reduction is a critical component in the design process of control strategies for complex flows in the nonlinear regime. A Galerkin projection based on POD-modes is developed in this study that takes advantage of multiple bases for particular components of the governing equations. These bases are then linked by the Discrete Empirical Interpolation Method (DEIM) to ultimately arr...

The Epsilon Expansion via Hypergeometric Functions and Differential Reduction

Query Expansion/Reduction and its Impact on Retrieval Effectiveness

Query expansion should help improve information retrieval effectiveness. Reported studies [1-5] using the TREC data generally support this position, though earlier studies [6-8] using smaller test databases did not obtain any conclusive results. Three important research questions remain open. First, assuming that a thesaurus will be used, should a general or data specific thesaurus be used in q...