496 research outputs found
Transformations for multivariate statistics
This paper derives transformations for multivariate statistics that eliminate asymptotic skewness, extending the results of Niki and Konishi (1986, Annals of the Institute of Statistical Mathematics 38, 371-383). Within the context of valid Edgeworth expansions for such statistics we first derive the set of equations that such a transformation must satisfy and second propose a local solution that is sufficient up to the desired order. Application of these results yields two useful corollaries. First, it is possible to eliminate the first correction term in an Edgeworth expansion, thereby accelerating convergence to the leading term normal approximation. Second, bootstrapping the transformed statistic can yield the same rate of convergence of the double, or prepivoted, bootstrap of Beran (1988, Journal of the American Statistical Association 83, 687-697), applied to the original statistic, implying a significant computational saving. The analytic results are illustrated by application to the family of exponential models, in which the transformation is seen to depend only upon the properties of the likelihood. The numerical properties are examined within a class of nonlinear regression models (logit, probit, Poisson, and exponential regressions), where the adequacy of the limiting normal and of the bootstrap (utilizing the k-step procedure of Andrews, 2002, Econometrica 70, 119-162) as distributional approximations is assessed
Cyclic A-infinity Algebras and Calabi--Yau Structures in the Analytic Setting
This paper considers -algebras whose higher products satisfy an
analytic bound with respect to a fixed norm. We define a notion of right
Calabi--Yau structures on such -algebras and show that these give
rise to cyclic minimal models satisfying the same analytic bound. This
strengthens a theorem of Kontsevich--Soibelman, and yields a flexible method
for obtaining analytic potentials of Hua-Keller.
We apply these results to the endomorphism DGAs of polystable sheaves
considered by Toda, for which we construct a family of such right CY structures
obtained from analytic germs of holomorphic volume forms on a projective
variety. As a result, we can define a canonical cyclic analytic
-structure on the Ext-algebra of a polystable sheaf, which depends
only on the analytic-local geometry of its support. This shows that the results
of Toda can be extended to the quasi-projective setting, and yields a new
method for comparing cyclic -structures of sheaves on different
Calabi--Yau varieties.Comment: 41 pages, comments welcom
Stability over cDV singularities and other complete local rings
We characterise subcategories of semistable modules for noncommutative
minimal models of compound Du Val singularities, including the non-isolated
case. We find that the stability is controlled by an infinite polyhedral fan
that stems from silting theory, and which can be computed from the Dynkin
diagram combinatorics of the minimal models found in the work of Iyama--Wemyss.
In the isolated case, we moreover find an explicit description of the
deformation theory of the stable modules in terms of factors of the
endomorphism algebras of 2-term tilting complexes. To obtain these results we
generalise a correspondence between 2-term silting theory and stability, which
is known to hold for finite dimensional algebras, to the much broader setting
of algebras over a complete local Noetherian base ring.Comment: 23 pages, 6 figures, several lemmas concerning the silting fan in
section 2 have been clarified, Proposition 3.4 has been strengthened, and
many typos have been correcte
Signs of progression:MR image analysis for the management of low-grade glioma
Every year approximately one thousand people in the Netherlands are diagnosedwith diffuse glioma, a type of infiltrative brain tumor that originates from theglial cells. There is no curative treatment available for adults diagnosed witha diffuse glioma, although surgical resection, radiotherapy and chemotherapyare used to improve prognosis and decrease symptoms. Low-grade glioma canremain stable for long periods of time before, inevitably, malignant progressionoccurs. The radiological assessment of glioma through magnetic resonanceimaging (MRI) plays an important role in the management of glioma. Inthis thesis I explore the role of quantitative measurements, emerging imagingmarkers and predictive modelling in the management of glioma. These methodscan aid the radiologist to predict the timing, location and severity of tumorprogression, to ultimately improve the quality of life for glioma patients.<br/
Convex-Arc Drawings of Pseudolines
A weak pseudoline arrangement is a topological generalization of a line
arrangement, consisting of curves topologically equivalent to lines that cross
each other at most once. We consider arrangements that are outerplanar---each
crossing is incident to an unbounded face---and simple---each crossing point is
the crossing of only two curves. We show that these arrangements can be
represented by chords of a circle, by convex polygonal chains with only two
bends, or by hyperbolic lines. Simple but non-outerplanar arrangements
(non-weak) can be represented by convex polygonal chains or convex smooth
curves of linear complexity.Comment: 11 pages, 8 figures. A preliminary announcement of these results was
made as a poster at the 21st International Symposium on Graph Drawing,
Bordeaux, France, September 2013, and published in Lecture Notes in Computer
Science 8242, Springer, 2013, pp. 522--52
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