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Generalised additive and index models with shape constraints
(WileyJournal of the Royal Statistical Society: Series B (Statistical Methodology), 2015-10-26)
We study generalized additive models, with shape restrictions (e.g. monotonicity, convexity and concavity) imposed on each component of the additive prediction function. We show that this framework facilitates a non-parametric ...
On the motive of some hyperKaehler varieties
(De GruyterJournal für die reine und angewandte Mathematik, 2015-06-05)
We show that the motive of the Hilbert scheme of length-n subschemes on a K3 surface or on an abelian surface admits a decomposition similar to the decomposition of the motive of an abelian variety obtained by Shermenev, ...
Transversals as Generating Sets in Finitely Generated Groups
(Cambridge University PressBulletin of the Australian Mathematical Society, 2015-08-19)
We explore transversals of finite index subgroups of finitely generated groups. We show that when H is a subgroup of a rank n group G and H has index at least n in G then we can construct a left transversal for H which ...
Near-optimal estimation of jump activity in semimartingales
(Institute of Mathematical StatisticsThe Annals of Statistics, 2015-07-15)
In quantitative finance, we often model asset prices as semimartingales, with drift, diffusion and jump components. The jump activity index measures the strength of the jumps at high frequencies, and is of interest both ...
F-Saturation Games
(ElsevierDiscrete Mathematics, 2015-06-23)
We study F-saturation games, first introduced by Füredi, Reimer and Seress [4] in 1991, and named as such by West [5]. The main question is to determine the length of the game whilst avoiding various classes of graph, ...
Deformations of Cayley submanifolds
(University of CambridgeDepartment of Pure Mathematics and Mathematical StatisticsTrinity College, 2016-03-01)
Cayley submanifolds of R^8 were introduced by Harvey and Lawson as an instance of calibrated submanifolds, extending the volume-minimising properties of complex submanifolds in Kähler manifolds. More generally, Cayley ...
Chaos and Entropic Chaos in Kac's Model Without High Moments
(Institute of Mathematical StatisticsElectronic Journal of Probability, 2013-08-27)
In this paper we present a new local Lévy Central Limit Theorem, showing convergence to stable states that are not necessarily the Gaussian, and use it to find new and intuitive entropically chaotic families with underlying ...
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 Villani's conjecture concerning entropy production for the Kac Master equation
(America Institute of Mathematical SciencesKinetic and Related Models, 2011-06-01)
In this paper we take an idea presented in recent paper by Carlen, Carvalho, Le Roux, Loss, and Villani ([3]) and push it one step forward to find an exact estimation on the entropy production. The new estimation essentially ...