In 2003, Araujo and Jarosz showed that every bijective linear map θ : A → B between unital standard operator algebras preserving zero products in two ways is a scalar multiple of an inner automorphism. Later in 2007, Zhao and Hou showed that similar results hold if both A,B are unital standard algebras on Hilbert spaces and θ preserves range or domain orthogonality. In particular, such maps are...

A secure scalar product protocol is a type of specific SMC problem, and has found various applications in many areas such as privacy-preserving data mining, privacy-preserving cooperative statistical analysis, and privacy-preserving geometry computation. In this paper, we firstly extend to a solution of homomorphic-encryption based secure scalar product protocol such that it enables the scheme ...

Privacy-preserving data mining seeks to empower conventional data mining techniques with the desirable property of preserving data privacy during the mining process. Given existing approaches on privacy-preserving decision tree induction for horizontally and vertically partitioned data involving multiple parties, we extend current work to multiple parties holding arbitrarily partitioned data. A...

Almost every, essentially: Given a Lebesgue measure space (X,B, μ), a property P (x) predicated of elements of X is said to hold for almost every x ∈ X, if the set X \ {x : P (x) holds} has zero measure. Two sets A,B ∈ B are essentially disjoint if μ(A ∩B) = 0. Conservative system: Is an infinite measure preserving system such that for no set A ∈ B with positive measure are A,T−1A,T−2A, . . . p...

Traditionally, recommender systems present recommendations in ranked lists to the user. In contentand knowledge-based recommender systems, these lists are often sorted on some notion of similarity with a query, ideal product specification, or sample product. However, a lot of information is lost in this way, since two products with the same similarity to a query can differ from this query on a ...

The quadratizations of a (homogeneous nonquadratic) nonlinear polynomial system of ODEs introduced by Myung and Sagle in [17] is considered. The 1-1 correspondence between homogeneous quadratic systems of ODEs and nonassociative algebras is used to prove a special structure of the algebra corresponding to a general homogeneous quadratic systems being a quadratization. Every homogeneous solution...

Let F = (E, p, B;Y ) be a fiber bundle where E, B and Y are connected finite polyhedra. Let f : E → E be a fiber-preserving map and A ⊆ E a closed, locally contractible subset. We present necessary and sufficient conditions for A and its subsets to be the fixed point sets of maps fiber-homotopic to f . The necessary conditions correspond to those introduced by Schirmer in 1990 but, in the fiber...

The integration of spatial context in the classification of hyperspectral images is known to be an effective way in improving classification accuracy. In this paper, a novel spectralspatial classification framework based on edge-preserving filtering is proposed. The proposed framework consists of the following three steps. First, the hyper-spectral image is classified using a pixel-wise classif...

Product lines evolve out of existing products. In order to evaluate the potential of creating a product line from existing products it is necessary to ‘mine’ their architectures and analyze the commonalities and variabilities across those architectures. To manage the evaluation process in a disciplined way this paper introduces the MAP (Mining Architectures for Product lines) method. MAP outlin...