Existing grouped variable selection methods rely heavily on prior group information, thus they may not be reliable if an incorrect group assignment is used. In this paper, we propose a family of shrinkage variable selection operators by controlling the k-th largest norm (KAN). The proposed KAN method exhibits some flexible group-wise variable selection naturally even though no correct prior gro...

Institutions were introduced by Goguen and Burstall 8, 9, 10, 11] to formally capture the notion of logical system. Interpreting institutions as functors, and morphisms and representations of institutions as natural transformations, we give elegant proofs for the completeness of the categories of institutions with morphisms and representations, respectively, show that the duality between morphi...

Continuous lattices were characterised by Mart́ın Escardó as precisely the objects that are Kan-injective w.r.t. a certain class of morphisms. We study Kan-injectivity in general categories enriched in posets. An example: ω-CPO’s are precisely the posets that are Kan-injective w.r.t. the embeddings ω →֒ ω + 1 and 0 →֒ 1. For every class H of morphisms we study the subcategory of all objects Kan-in...

Brucella species can cause brucellosis, a zoonotic disease that causes serious livestock economic losses and represents a public health threat. The mechanism of virulence of Brucella spp. is not yet fully understood. Therefore, it is crucial to identify new molecules that serve as virulence factors to better understand this host-pathogen interplay. Here, we evaluated the role of the Brucella me...

Given an order-enriched category, it is known that all its KZ-monadic subcategories can be described by Kan-injectivity with respect to a collection of morphisms. We prove the analogous result for Kan-injectivity with respect to a collection H of commutative squares. A square is called a Kan-injective consequence of H if by adding it to H Kan-injectivity is not changed. We present a sound logic...

Cane and Candy are traceable to two Chinese words both pronounced Kan. One word means Cane or pole when Kan finally became cane in English. The other word Kan means sweet. Then there is the Chinese word Dih which means Drops when Kan-Dih became Candy and means Sweet Drops. Sugar crystals would be like sand in size. Candy of the size of drops. While Misri of small stones, the term Kan-Dih entere...

We establish a functor Kan from local Kan simplicial manifolds to weak Kan simplicial manifolds. It gives a solution to the problem of extending local Lie groupoids to Lie 2-groupoids.

Functional Kan simplicial sets are simplicial sets in which the horn-fillers required by the Kan extension condition are given explicitly by functions. We show the non-constructivity of the following basic result: if B and A are functional Kan simplicial sets, then A is a Kan simplicial set. This strengthens a similar result for the case of non-functional Kan simplicial sets shown by Bezem, Coq...

In Escherichia coli, the primosome assembly proteins, PriA, PriB, PriC, DnaT, DnaC, DnaB, and DnaG, are thought to help to restart DNA replication forks at recombinational intermediates. Redundant functions between priB and priC and synthetic lethality between priA2::kan and rep3 mutations raise the possibility that there may be multiple pathways for restarting replication forks in vivo. Herein...