It is shown that coherence conditions for monoidal categories concerning associativity are analogous to coherence conditions for symmetric or braided strictly monoidal categories, where associativity arrows are identities. Mac Lane’s pentagonal coherence condition for associativity is decomposed into conditions concerning commutativity, among which we have a condition analogous to naturality an...

N(6)-Methyladenosine (m(6)A) is emerging as a chemical mark that broadly affects the flow of genetic information in various biological processes in eukaryotes. Recently, Xiao et al. reported that the nuclear m(6)A reader protein YTHDC1 impacts mRNA splicing, providing a transcriptome-wide glance of splicing changes affected by this mRNA methylation reader protein.

When modeling the distribution of a set of data by a mixture of Gaussians, there are two possibilities: i) the classical one is using a set of parameters which are the proportions, the means and the variances; ii) the second is to consider the proportions as the probabilities of a discrete valued hidden variable. In the first case a usual prior distribution for the proportions is the Dirichlet ...

The category of admissible (in the appropriately modified sense of representation theory of totally disconnected groups) semi-linear representations of the automorphism group of an algebraically closed extension of infinite transcendence degree of the field of algebraic complex numbers is described. Let k be a field of characteristic zero containing all ℓ-primary roots of unity for a prime ℓ, F...

We prove that there does not exist a subset of the plane S that meets every isometric copy of the vertices of the unit square in exactly one point. We give a complete characterization of all three point subsets F of the reals such that there does not exists a set of reals S which meets every isometric copy of F in exactly one point.

The title compound, C(16)H(16)N(2)O·0.5H(2)O, is a substituted 1-phenyl-benzimidazole, which belongs to the class of ATP-site inhibitors of the platelet-derived growth-factor receptor. In the crystal, the components are linked by an O-H⋯N hydrogen bond.

We classify the Montesinos links up to mutation and 5-move equivalence, and obtain from this a Jones and Kauffman polynomial test for a Montesinos link.

As a consequence of the wave nature of light, invisibility devices based on isotropic media cannot be perfect. The principal distortions of invisibility are due to reflections and time delays. Reflections can be made exponentially small for devices that are large in comparison with the wavelength of light. Time delays are unavoidable and will result in wave-front dislocations. This paper consid...

Given a variety of algebras V, we study categories of algebras in V with a compatible structure of uniform space. The lattice of compatible uniformities of an algebra, Unif A, can be considered a generalization of the lattice of congruences ConA. Mal’cev properties of V influence the structure of Unif A, much the same as they do that of ConA. The category V[CHUnif] of complete, Hausdorff unifor...