A classical problem in statistics is to study relationships between several blocks of variables. The goal is to find variables of one block directly related to variables of other blocks. The Regularized Generalized Canonical Correlation Analysis (RGCCA) is a very attractive framework to study such a kind of relationships between blocks. However, RGCCA captures linear relations between blocks an...

We study the Ehresmann--Schauenburg bialgebroid of a noncommutative principal bundle as quantization gauge groupoid classical bundle. show that group is isomorphic to bisections bialgebroid, and we give crossed module structure for automorphisms bialgebroid. Examples illustrating these constructions include: Galois objects Taft algebras, monopole over quantum spheres not faithfully flat Hopf--G...

Crossed Uncrossed Differentials (CUDs) have long been used as surrogate for the interhemispheric transfer time (IHTT). Evidence is presented that macular vision is the province of the major hemisphere, wherein all commands are initiated regardless of the laterality of the effectors of such commands. Using clinical and time-resolved data it is shown also that the above arrangement (i.e. neural h...

Let τ be a linear map from a unital C∗-algebra A to a von Neumann algebra B and let C be a unital C∗-algebra. A map T from a Hilbert A-module E to a von Neumann C-B module F is called a τ -map if 〈T (x), T (y)〉 = τ(〈x, y〉) for all x, y ∈ E. A Stinespring type theorem for τ -maps and its covariant version are obtained when τ is completely positive. We show that there is a bijective correspondenc...

In this paper we present a new algorithmic approach for computing the Hilbert function of a finitely generated difference-differential module equipped with the natural double filtration. The approach is based on a method of special Gröbner bases with respect to “generalized term orders” on Nm × Zn and on difference-differential modules. We define a special type of reduction for two generalized ...

We reduce the problem on multiplicities of simple subquotients in an-stratiied Generalized Verma module to the analogous problem for classical Verma modules.

We study the ideal structure of C∗-algebras arising from C∗-correspondences. We prove that gauge-invariant ideals of our C∗-algebras are parameterized by certain pairs of ideals of original C∗-algebras. We show that our C∗-algebras have a nice property which should be possessed by generalization of crossed products. Applications to crossed products by Hilbert C∗-bimodules and relative Cuntz-Pim...

Secondary homotopy groups supplement the structure of classical homotopy groups. They yield a 2-functor on the groupoid-enriched category of pointed spaces compatible with fiber sequences, suspensions and loop spaces. They also yield algebraic models of (n− 1)-connected (n+1)-types for n ≥ 0. Introduction The computation of homotopy groups of spheres in low degrees in [Tod62] uses heavily secon...

Hyperoctahedral homology for involutive algebras is the theory associated to hyperoctahedral crossed simplicial group. It related equivariant stable homotopy via of infinite loop spaces. In this paper we show that there an E-infinity algebra structure on module computes homology. We deduce admits Dyer-Lashof operations. Furthermore, a Pontryagin product which gives associative, graded-commutati...