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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 ...
An introduction to applications of wavelet benchmarking with seasonal adjustment
(WileyJournal of the Royal Statistical Society: Series A (Statistics in Society), 2016-11-05)
Before adjustment, low and high frequency data sets from national accounts are frequently inconsistent. Benchmarking is the procedure used by economic agencies to make such data sets consistent. It typically involves ...
The greedy basis equals the theta basis: A rank two haiku
(ElsevierJournal of Combinatorial Theory Series A, 2016-08-26)
We prove the equality of two canonical bases of a rank 2 cluster algebra, the greedy basis of Lee–Li–Zelevinsky and the theta basis of Gross–Hacking–Keel–Kontsevich.
Nonhyperbolic free-by-cyclic and one-relator groups
(New York Journal of MathematicsNew York Journal of Mathematicshttp://nyjm.albany.edu/j/2016/22-35.html, 2016-08-01)
We show that the free-by-cyclic groups of the form $F_2$ $\rtimes$ $\Bbb Z$ act properly cocompactly on CAT(0) square complexes. We also show using generalized Baumslag–Solitar groups that all known groups defined by a ...
Gromov-Hausdorff Collapsing of Calabi-Yau manifolds
(International PressCommunications in Analysis and Geometry, 2016-06-08)
This paper is a sequel to Collapsing of Abelian Fibered Calabi-Yau Manifolds [12]. We further study Gromov–Hausdorff collapsing limits of Ricci-flat Kähler metrics on abelian fibered Calabi–Yau manifolds. Firstly, we show ...
Arithmetic invariant theory and 2-descent for plane quartic curves
(Mathematical Sciences PublishersAlgebra & Number Theory, 2016-09-27)
Given a smooth plane quartic curve C over a field $\textit{k}$ of characteristic 0, with Jacobian variety $\textit{J}$, and a marked rational point P $\in$ C($\textit{k}$), we construct a reductive group $\textit{G}$ and ...
Isometric disks are holomorphic
(SpringerInventiones mathematicae, 2016-10-05)
This paper shows that every totally-geodesic isometry from the unit disk to a finite-dimensional Teichmüller space for the intrinsic Kobayashi metric is either holomorphic or anti-holomorphic; in particular, it is a ...
Handbook of Big Data [Book review]
(WileyStatistics in Medicine, 2016-12-01)