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Tubular free by cyclic groups act freely on CAT(0) cube complexes
(Canadian Mathematical SocietyCanadian Mathematical Bulletin, 2017-03-01)
We identify when a tubular group (the fundamental group of a finite graph of groups with $\mathbb{Z}$$^{2}$ vertex and $\mathbb{Z}$ edge groups) is free by cyclic and show, using Wise's equitable sets criterion, that every ...
Total Positivity in Markov Structures
(Institute of Mathematical StatisticsAnnals of Statistics, 2017-06)
We discuss properties of distributions that are multivariate totally positive of order two (MTP$_{2}$) related to conditional independence. In particular, we show that any independence model generated by an MTP$_{2}$ ...
Bayesian Nonparametric Ordination for the Analysis of Microbial Communities
(Taylor & FrancisJournal of the American Statistical Association, 2017-07-10)
Human microbiome studies use sequencing technologies to measure the abundance of bacterial species or Operational Taxonomic Units (OTUs) in samples of biological material. Typically the data are organized in contingency ...
Trend to equilibrium for the Becker–Döring equations: an analogue of Cercignani's conjecture
(Mathematical Sciences PublishersAnalysis and PDE, 2017-08-01)
We investigate the rate of convergence to equilibrium for subcritical solutions to the Becker–Döring equations with physically relevant coagulation and fragmentation coefficients and mild assumptions on the given initial ...
Homological mirror symmetry for hypersurface cusp singularities
(SpringerSelecta Mathematica, 2017-06-03)
We study versions of homological mirror symmetry for hypersurface cusp singularities and the three hypersurface simple elliptic singularities. We show that the Milnor fibres of each of these carries a distinguished Lefschetz ...
Trust in numbers
(WileyJournal of the Royal Statistical Society. Series A: Statistics in Society, 2017-10-01)
Those who value quantitative and scientific evidence are faced with claims both of a reproducibility crisis in scientific publication, and of a post-truth society abounding in fake news and alternative facts. Both issues ...
Discussion of "The ASA’s p-value statement, one year on" by Robert Matthews
(Wiley-BlackwellSignificance, 2017-05-03)
Maximal Abelian Sets of Roots
(American Mathematical SocietyMemoirs of the American Mathematical Society, 2017-11)
In this work we let Φ be an irreducible root system, with Coxeter group W. We consider subsets of Φ which are abelian, meaning that no two roots in the set have sum in Φ∪{0}. We classify all maximal abelian sets (i.e., ...
On a Heegaard Floer theory for tangles
(University of CambridgeDPMMS, 2017-03-10)
The purpose of this thesis is to define a “local” version of Ozsváth and Szabó’s Heegaard Floer homology HFL^ for links in the 3-sphere, i.e. a Heegaard Floer homology HFT^ for tangles in the 3-ball. The decategorification ...
The Planar Ising Model and Total Positivity
(SpringerJournal of Statistical Physics, 2017-01-01)
A matrix is called totally positive (resp. totally nonnegative) if all its minors are positive (resp. nonnegative). Consider the Ising model with free boundary conditions and no external field on a planar graph G. Let ...