We present two explicit combinatorial constructions of finitely summable reduced “Gamma”-elements $\gamma\_r\in KK(C^\*\_r(\Gamma),\mathbb{C})$ for any word-hyperbolic group $(\Gamma,S)$ and obtain summability bounds them in terms the cardinality generating set $S\subset\Gamma$ hyperbolicity constant associated Cayley graph.

The original aim of this paper is to construct a graph associated to a vector space. By inspiration of the classical definition for the Cayley graph related to a group we define Cayley graph of a vector space. The vector space Cayley graph ${rm Cay(mathcal{V},S)}$ is a graph with the vertex set the whole vectors of the vector space $mathcal{V}$ and two vectors $v_1,v_2$ join by an edge whenever...

AbstractAnomaly detection can be conceived either through generative modelling of regular training data or by discriminating with respect to negative data. These two approaches exhibit different failure modes. Consequently, hybrid algorithms present an attractive research goal. Unfortunately, dense anomaly requires translational equivariance and very large input resolutions. requirements disqua...

One of the challenges in pattern recognition is open set recognition. Compared with closed recognition, needs to reduce not only empirical risk, but also space and reduction these two risks corresponds classifying known classes identifying unknown respectively. How risk key This paper explores origin by analyzing distribution features. On this basis, spatial location constraint prototype loss f...