Given a finite group G of even order, which graphs Γ have a 1−factorization admitting G as automorphism group with a sharply transitive action on the vertex-set? Starting from this question, we prove some general results and develop an exhaustive analysis when Γ is a complete multipartite graph and G is cyclic.

Due to the time complexity in composing recommendations, matrix factorization-based approaches are inefficient in dealing with large scale datasets. In this paper, we propose a similar user indexbased parallel matrix factorization approach. Since the group of similar users is indexed in advance, there is no need to compute similarities between all users in datasets. Furthermore, the size of a m...

A motion segmentation algorithm based on factorization method and discriminant criterion is proposed. This method uses a feature with the most useful similarities for grouping, selected using motion information calculated by factorization method and discriminant criterion. A group is extracted based on discriminant analysis for the selected feature’s similarities. The same procedure is applied ...

The term “proxy multi-signature” refers to the situation in which a proxy signer is authorized to sign a message on behalf of a group of original signers. Combined with identity-based cryptography, we proposed an efficient identity-based proxy multi-signature scheme using cubic residues without bilinear pairing. Our scheme is secure against existential forgery on adaptive chosenmessage and iden...

We formalize the notion of a factorization of a word, a so-called F -factorization, introduced in [7] when solving some open problems on word equations. We show that most of the factorizations considered in the literature t well into that framework, and in particular that central algorithmic problems, such as the uniqueness or the synchronizability, remain polynomial time solvable for an import...

Every action of a group on a set decomposes the set into orbits. The group acts on each of the orbits and an orbit does not have sub-orbits (unequal orbits are disjoint), so the decomposition of a set into orbits could be considered as a “factorization” of the set into “irreducible” pieces for the group action. Our focus here is on these irreducible parts, namely group actions with a single orbit.

We define Sobolev norms of arbitrary real order for a Banach representation $(\pi, E)$ Lie group, with regard to single differential operator $D=d\pi(R^2+\Delta)$. Here, $\Delta$ is Laplace element in the universal enveloping algebra, and $R>0$ depends explicitly on growth rate representation. In particular, we obtain spectral gap $D$ space smooth vectors $E$. The main tool novel factorization ...