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D-modules on rigid analytic spaces I
(De GruyterJournal für die reine und angewandte Mathematik, 2016)
We introduce a sheaf of infinite order differential operators D on smooth rigid analytic spaces that is a rigid analytic quantisation of the cotangent bundle. We show that the sections of this sheaf over sufficiently small ...
Global Rates of Convergence in Log-Concave Density Estimation
(Institute of Mathematical StatisticsAnnals of Statistics, 2016)
The estimation of a log-concave density on $\Bbb R$$^d$ represents a central problem in the area of nonparametric inference under shape constraints. In this paper, we study the performance of log-concave density estimators ...
Injectivity and Stability for a Generic Class of Generalized Radon Transforms
(SpringerJournal of Geometric Analysis, 2016-06-30)
Let (M, g) be an analytic, compact, Riemannian manifold with boundary, of dimension n≥2. We study a class of generalized Radon transforms, integrating over a family of hypersurfaces embedded in M, satisfying the Bolker ...
Tests for separability in nonparametric covariance operators of random surfaces
(Institute of Mathematical StatisticsAnnals of Statistics, 2016)
The assumption of separability of the covariance operator
for a random image or hypersurface can be of substantial use in
applications, especially in situations where the accurate estimation
of the full covariance structure ...
A Fully Automatic Theorem Prover with Human-Style Output
(SpringerJournal of Automated Reasoning, 2016-06-11)
This paper describes a program that solves elementary mathematical problems, mostly in metric space theory, and presents solutions that are hard to distinguish from solutions that might be written by human mathematicians.
Homological Stability for Spaces of Embedded Surfaces
(Mathematical Sciences PublisherGeometry & Topology, 2016)
We study the space of oriented genus $\textit{g}$ subsurfaces of a fixed manifold $\textit{M}$, and in particular its homological properties. We construct a “scanning map” which compares this space to the space of sections ...
TORSION GALOIS REPRESENTATIONS OVER CM FIELDS AND HECKE ALGEBRAS IN THE DERIVED CATEGORY
(Cambridge University PressForum of Mathematics, Sigma, 2016-07-21)
We construct algebras of endomorphisms in the derived category of the cohomology of arithmetic manifolds, which are generated by Hecke operators. We construct Galois representations with coefficients in these Hecke algebras ...
Peter Hall’s Work on High-Dimensional Data and Classification
(Institute of Mathematical StatisticsAnnals of Statistics, 2016)
In this article, I summarise Peter Hall’s contributions to high-dimensional data, including their geometric representations and variable selection methods based on ranking. I also discuss his work on classification problems, ...
Invariant Distributions and Tensor Tomography for Gaussian Thermostats
(International PressCommunications in Analysis and Geometry, 2016)
In this paper we consider the Gaussian thermostat ray transforms on both closed Riemannian surfaces and compact Riemannian surfaces with boundary. We establish certain results on the injectivity of the thermostat ray ...
How old are you, really? Communicating chronic risk through ‘effective age’ of your body and organs
(BioMed CentralBMC Medical Informatics and Decision Making, 2016-08-05)
In communicating chronic risks, there is increasing use of a metaphor that can be termed ‘effective-age’: the age of a ‘healthy’ person who has the same risk profile as the individual in question. Popular measures include ...