β-mixing sequence Reproducing kernel Hilbert spaces ℓ 2-empirical covering number Capacity dependent error bounds a b s t r a c t We study learning algorithms for classification generated by regularization schemes in reproducing kernel Hilbert spaces associated with a general convex loss function in a non-i.i.d. process. Error analysis is studied and our main purpose is to provide an elaborate ...

A complete list of homogeneous operators in the Cowen Douglas class Bn(D) is given. This classification is obtained from an explicit realization of all the homogeneous Hermitian holomorphic vector bundles on the unit disc under the action of the universal covering group of the bi-holomorphic automorphism group of the unit disc.

Chain complexes with a group of operators are a well known tool in algebraic topology, where they arise naturally as the chain complex C∗X̃ of cellular chains of the universal cover X̃ of a reduced CW -complex X. The group of operators here is the fundamental group of X. J.H.C. Whitehead in his classical but little read paper [31] showed that the chain complex C∗(X̃) is useful for the homotopy cla...

For a prime power q and for integers R, η with R > 0, 0 ≤ η ≤ R − 1, let A R,q = (Cni)i denote an infinite sequence of q-ary linear [ni, ni − ri]qR codes Cni with covering radius R and such that the following two properties hold: (a) the codimension ri = Rti + η, where (ti)i is an increasing sequence of integers; (b) the length ni of Ci coincides with f (η) q (ri), where f (η) q is an increasin...

Let X(∆) be the real toric variety associated to a smooth fan ∆. The main purpose of this article is: (i) to determine the fundamental group and the universal cover of X(∆), (ii) to give necessary and sufficient conditions on ∆ under which π1(X(∆)) is abelian, (iii) to give necessary and sufficient conditions on ∆ under which X(∆) is aspherical, and when ∆ is complete, (iv) to give necessary an...

Let Γ be an extended tilde geometry of rank n > 2 such that there exists a 1-covering γ : Γ → Φ where Φ is a c.Cn−1-geometry with orders 1, 2, . . . , 2. Suppose that the normalizer in Aut(Γ ) of the deck group of γ acts flag-transitively on Γ . We prove that, under these hypotheses, only three possibilities exist for the universal cover of Γ . c © 2007 Elsevier Ltd. All rights reserved.