We present a finite set theory implementation for ACL2. Our library represents sets as fully ordered lists, and provides efficient implementations of the typical set theory operations such as insertion, deletion, union, intersection, difference, cardinality, and sorting lists to create sets. It also includes facilities for quantifying predicates over sets, filtering sets by some criteria, and t...

In this work, we propose an adaptive set-membership constant modulus (SMCM) algorithm with a generalized sidelobe canceler (GSC) structure for blind beamforming. We develop a stochastic gradient (SG) type algorithm based on the concept of SM filtering for adaptive implementation. The filter weights are updated only if the constraint cannot be satisfied. In addition, we also propose an extension...

In this article, a recursive set-membership filtering algorithm for discrete-time nonlinear dynamical systems subject to unknown but bounded process and measurement noises is proposed. The dynamics are represented in pseudolinear form using the state-dependent coefficient (SDC) parameterization. Matrix Taylor expansions utilized expand matrices about state estimates. Upper bounds on norms of re...

This paper presents a novel filtering framework capable of processing cDNA microarray images. The proposed two-component adaptive vector filters integrate well-known concepts from the areas of fuzzy set theory, nonlinear filtering, multidimensional scaling and robust order-statistics. By appropriately setting the weighting coefficients in a generalized framework, the method is capable of removi...

Memory-based collaborative filtering is the most popular approach to build recommender systems. Despite its success in many applications, it still suffers from several major limitations, including data sparsity. Sparse data affect the quality of the user similarity measurement and consequently the quality of the recommender system. In this paper, we propose a novel user similarity measure based...

The skeleton of an object is defined as the set of quench points formed during Blum’s grassfire transformation. Due to high sensitivity of quench points with small changes in the object boundary and the membership function (for fuzzy objects), often, a large number of redundant quench points is formed. Many of these quench points are caused by peripheral protrusions and dents and do not associa...