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Simple Containers for Simple Hypergraphs
(Cambridge University PressCombinatorics Probability and Computing, 2016-05-01)
We give an easy method for constructing containers for simple hypergraphs. The method also has consequences for non-simple hypergraphs. Some applications are given; in particular, a very transparent calculation is offered ...
Detecting and Localizing Differences in Functional Time Series Dynamics: A Case Study in Molecular Biophysics
(Taylor & FrancisJournal of the American Statistical Association, 2016-03-22)
Motivated by the problem of inferring the molecular dynamics of DNA in solution, and linking them with its base-pair composition, we consider the problem of comparing the dynamics of functional time series (FTS), and of ...
Free groups and the axiom of choice
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 2016-01-05)
The Nielsen–Schreier theorem states that subgroups of free groups are free. As all of its proofs use the Axiom of Choice, it is natural to ask whether the theorem is equivalent to the Axiom of Choice. Other questions arise ...
Effectivity of Iitaka fibrations and pluricanonical systems of polarized pairs
(SpringerPublications mathématiques de l'IHÉS, 2016-01-18)
For every smooth complex projective variety W of dimension d and nonnegative Kodaira dimension, we show the existence of a universal constant m depending only on d and two natural invariants of the very general fibres of ...
Proof of a conjecture of Batyrev and Nill
(Johns Hopkins University PressAmerican Journal of Mathematics, 2016)
We prove equivalences of derived categories for the various mirrors in the Batyrev-Borisov construction. In particular, we obtain a positive answer to a conjecture of Batyrev and Nill. The proof involves passing to an ...
Modelling Interactions in High-dimensional Data with Backtracking
(Journal of Machine Learning ResearchJournal of Machine Learning Research, 2016)
We study the problem of high-dimensional regression when there may be interacting variables. Approaches using sparsity-inducing penalty functions such as the Lasso (Tibshirani, 1996) can be useful for producing interpretable ...
On the Cauchy Problem for the Homogeneous Boltzmann-Nordheim Equation for Bosons: Local Existence, Uniqueness and Creation of Moments
(SpringerJournal of Statistical Physics, 2016)
The Boltzmann-Nordheim equation is a modification of the Boltzmann equation, based on physical considerations, that describes the dynamics of the distribution of particles in a quantum gas composed of bosons or fermions. ...
Non-reductive automorphism groups, the Loewy filtration and K-stability
(l'Institut FourierAnnales de l'Institut Fourier, 2016-03-18)
We study the K-stability of a polarised variety with non-reductive automorphism group. We associate a canonical filtration of the co-ordinate ring to each variety of this kind, which destabilises the variety in several ...
Alpha invariants and coercivity of the Mabuchi functional on Fano manifolds
(Université Paul SabatierAnnales de la Faculté des Sciences de Toulouse, 2016)
We give a criterion for the coercivity of the Mabuchi functional for general Kàhler classes on Fano manifolds in terms of Tian's alpha invariant. This generalises a result of Tian in the anti-canonical case implying the ...
On K-stability of finite covers
(Oxford University PressJournal of the London Mathematical Society, 2016)
We show that certain Galois covers of K-semistable Fano varieties are K-stable. We use this to give some new examples of Fano manifolds admitting Kähler-Einstein metrics, including hypersurfaces, double solids and threefolds.