Privacy-preserving classification is the task of learning or training a classifier on the union of privately distributed datasets without sharing the datasets. The emphasis of existing studies in privacy-preserving classification has primarily been put on the design of privacy-preserving versions of particular data mining algorithms, However, in classification problems, preprocessing and postpr...

Let $mathcal {A} $ and $mathcal {B} $ be C$^*$-algebras. Assume that $mathcal {A}$ is of real rank zero and unital with unit $I$ and $k>0$ is a real number. It is shown that if $Phi:mathcal{A} tomathcal{B}$ is an additive map preserving $|cdot|^k$ for all normal elements; that is, $Phi(|A|^k)=|Phi(A)|^k $ for all normal elements $Ainmathcal A$, $Phi(I)$ is a projection, and there exists a posit...

Let $G$ be a finite simple graph whose vertices and edges are weighted by two functions. In this paper we shall define and calculate entropy of a dynamical system on weights of the graph $G$, by using the weights of vertices and edges of $G$. We examine the conditions under which entropy of the dynamical system is zero, possitive or $+infty$. At the end it is shown that, for $rin [0,+infty]$, t...

In this note, we present a method for flattening anatomical surfaces such as branched vessels and intestinal tracts in an areapreserving way. This method is based on the theory of optimal mass transport and conformal mapping of surfaces. The flattened representations differ minimally from conformality in a certain precise sense. Potential applications include the detection and visualization of ...

We calculate the Riemann curvature tensor and sectional curvature for the Lie group of volume-preserving diffeomorphisms of the Klein bottle and projective plane. In particular, we investigate the sign of the sectional curvature, and find a possible disagreement with a theorem of Lukatskii. We suggest an amendment to this theorem.

This paper presents a new formalization of a unificationor join-preserving encoding of partially ordered sets that more essentially captures what it means for an encoding to preserve joins, generalizing the standard definition in AI research. It then shows that every statically typable ontology in the logic of typed feature structures can be encoded in a data structure of fixed size without the...