Generating the alternating group by cyclic triples

Decomposing triples into cyclic designs

Dirac generating operators and Manin triples

Given a pair of Lie algebroid structures on a vector bundle A (over M) and its dual A∗, and provided the A∗-module L = (∧A ⊗ ∧T ∗M) 1 2 exists, there exists a canonically defined differential operator D̆ on Γ(∧A ⊗ L ). We prove that the pair (A,A∗) constitutes a Lie bialgebroid if, and only if, D̆ is a Dirac generating operator as defined by Alekseev & Xu [1].

Cyclic alternating pattern

Key points • Expressed by the physiological phasic events of NREM sleep, including arousals, cyclic alternating pattern represents the most complex arrangement of sleep microstructure. • Cyclic alternating pattern is organized in sequences organized in successive cycles. Each cyclic alternating pattern cycle is composed of a phase A (phasic events) and a phase B (background rhythm). • Cyclic al...

The Product Replacement Graph on Generating Triples of Permutations

We prove that the product replacement graph on generating 3-tuples of An is connected for n ≤ 11. We employ an efficient heuristic based on [P1] which works significantly faster than brute force. The heuristic works for any group. Our tests were confined to An due to the interest in Wiegold’s Conjecture, usually stated in terms of T -systems (see [P2]). Our results confirm Wiegold’s Conjecture ...

Group Sparse Optimization by Alternating Direction Method

This paper proposes efficient algorithms for group sparse optimization with mixed `2,1-regularization, which arises from the reconstruction of group sparse signals in compressive sensing, and the group Lasso problem in statistics and machine learning. It is known that encoding the group information in addition to sparsity will lead to better signal recovery/feature selection. The `2,1-regulariz...