67,489 research outputs found
Minimal classes of graphs of unbounded clique-width defined by finitely many forbidden induced subgraphs
We discover new hereditary classes of graphs that are minimal (with respect
to set inclusion) of unbounded clique-width. The new examples include split
permutation graphs and bichain graphs. Each of these classes is characterised
by a finite list of minimal forbidden induced subgraphs. These, therefore,
disprove a conjecture due to Daligault, Rao and Thomasse from 2010 claiming
that all such minimal classes must be defined by infinitely many forbidden
induced subgraphs.
In the same paper, Daligault, Rao and Thomasse make another conjecture that
every hereditary class of unbounded clique-width must contain a labelled
infinite antichain. We show that the two example classes we consider here
satisfy this conjecture. Indeed, they each contain a canonical labelled
infinite antichain, which leads us to propose a stronger conjecture: that every
hereditary class of graphs that is minimal of unbounded clique-width contains a
canonical labelled infinite antichain.Comment: 17 pages, 7 figure
Towards a theory of local Shimura varieties
This is a survey article that advertizes the idea that there should exist a
theory of p-adic local analogues of Shimura varieties. Prime examples are the
towers of rigid-analytic spaces defined by Rapoport-Zink spaces, and we also
review their theory in the light of this idea. We also discuss conjectures on
the -adic cohomology of local Shimura varieties.Comment: 53 page
Empirical Bayes selection of wavelet thresholds
This paper explores a class of empirical Bayes methods for level-dependent
threshold selection in wavelet shrinkage. The prior considered for each wavelet
coefficient is a mixture of an atom of probability at zero and a heavy-tailed
density. The mixing weight, or sparsity parameter, for each level of the
transform is chosen by marginal maximum likelihood. If estimation is carried
out using the posterior median, this is a random thresholding procedure; the
estimation can also be carried out using other thresholding rules with the same
threshold. Details of the calculations needed for implementing the procedure
are included. In practice, the estimates are quick to compute and there is
software available. Simulations on the standard model functions show excellent
performance, and applications to data drawn from various fields of application
are used to explore the practical performance of the approach. By using a
general result on the risk of the corresponding marginal maximum likelihood
approach for a single sequence, overall bounds on the risk of the method are
found subject to membership of the unknown function in one of a wide range of
Besov classes, covering also the case of f of bounded variation. The rates
obtained are optimal for any value of the parameter p in (0,\infty],
simultaneously for a wide range of loss functions, each dominating the L_q norm
of the \sigmath derivative, with \sigma\ge0 and 0<q\le2.Comment: Published at http://dx.doi.org/10.1214/009053605000000345 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Generating Functional in CFT on Riemann Surfaces II: Homological Aspects
We revisit and generalize our previous algebraic construction of the chiral
effective action for Conformal Field Theory on higher genus Riemann surfaces.
We show that the action functional can be obtained by evaluating a certain
Deligne cohomology class over the fundamental class of the underlying
topological surface. This Deligne class is constructed by applying a descent
procedure with respect to a \v{C}ech resolution of any covering map of a
Riemann surface. Detailed calculations are presented in the two cases of an
ordinary \v{C}ech cover, and of the universal covering map, which was used in
our previous approach. We also establish a dictionary that allows to use the
same formalism for different covering morphisms. The Deligne cohomology class
we obtain depends on a point in the Earle-Eells fibration over the
Teichm\"uller space, and on a smooth coboundary for the Schwarzian cocycle
associated to the base-point Riemann surface. From it, we obtain a variational
characterization of Hubbard's universal family of projective structures,
showing that the locus of critical points for the chiral action under fiberwise
variation along the Earle-Eells fibration is naturally identified with the
universal projective structure.Comment: Latex, xypic, and AMS packages. 53 pages, 1 figur
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