24,646 research outputs found
Left-ordered inp-minimal groups
We prove that any left-ordered inp-minimal group is abelian, and we provide
an example of a non-abelian left-ordered group of dp-rank 2
Mean field variational Bayesian inference for support vector machine classification
A mean field variational Bayes approach to support vector machines (SVMs)
using the latent variable representation on Polson & Scott (2012) is presented.
This representation allows circumvention of many of the shortcomings associated
with classical SVMs including automatic penalty parameter selection, the
ability to handle dependent samples, missing data and variable selection. We
demonstrate on simulated and real datasets that our approach is easily
extendable to non-standard situations and outperforms the classical SVM
approach whilst remaining computationally efficient.Comment: 18 pages, 4 figure
Cubic Polynomial Maps with Periodic Critical Orbit, Part II: Escape Regions
The parameter space for monic centered cubic polynomial maps
with a marked critical point of period is a smooth affine algebraic curve
whose genus increases rapidly with . Each consists of a
compact connectedness locus together with finitely many escape regions, each of
which is biholomorphic to a punctured disk and is characterized by an
essentially unique Puiseux series. This note will describe the topology of
, and of its smooth compactification, in terms of these escape
regions. It concludes with a discussion of the real sub-locus of
.Comment: 51 pages, 16 figure
When is Galois cohomology free or trivial?
Let p be a prime and F a field containing a primitive pth root of unity. Let
E/F be a cyclic extension of degree p and G_E < G_F the associated absolute
Galois groups. We determine precise conditions for the cohomology group
H^n(E)=H^n(G_E,Fp) to be free or trivial as an Fp[Gal(E/F)]-module. We examine
when these properties for H^n(E) are inherited by H^k(E), k>n, and, by analogy
with cohomological dimension, we introduce notions of cohomological freeness
and cohomological triviality. We give examples of H^n(E) free or trivial for
each n in N with prescribed cohomological dimension.Comment: 29 pages; removed hypothesis on perfect fields in main results, and
added reference
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