A GROUP-EMBEDDABLE NON-AUTOMATIC SEMIGROUP WHOSE UNIVERSAL GROUP IS AUTOMATIC

A group-embeddable non-automatic semigroup whose universal group is automatic

The concept of an automatic structure has been generalized from groups [ECH+] to semigroups [CRRT]. Several authors [CRR, Hof, Kam] have asked the following question: Let S be a finitely generated semigroup embeddable in a group and let G be its universal group [CP, Chapter ]. If G is automatic, must S be automatic? Examples in favour of this implication include: free groups and s...

Characterization and axiomatization of all semigroups whose square is group

In this paper we give a characterization for all semigroups whose square is a group. Moreover, we axiomatize such semigroups and study some relations between the class of these semigroups and Grouplikes,introduced by the author. Also, we observe that this paper characterizes and axiomatizes a class of Homogroups (semigroups containing an ideal subgroup).  Finally, several equivalent conditions ...

Automatic Group-Outlier Detection

We propose in this paper a new measure called GOF (Group Outlier Factor) to detect groups outliers. To validate this measure we integrated it in a clustering process using Self-organizing Map. The proposed approach is based on relative density of each group of data and simultaneously provides a partitioning of data and a quantitative indicator (GOF). The obtained results are very encouraging to...

Automatic Group Sparse Coding

Sparse Coding (SC), which models the data vectors as sparse linear combinations over basis vectors (i.e., dictionary), has been widely applied in machine learning, signal processing and neuroscience. Recently, one specific SC technique, Group Sparse Coding (GSC), has been proposed to learn a common dictionary over multiple different groups of data, where the data groups are assumed to be pre-de...

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