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Type theoretic weak factorization systems
(University of CambridgeDepartment of Pure Mathematics and Mathematical StatisticsKing's, 2017-06-01)
This thesis presents a characterization of those categories with weak factorization systems that can interpret the theory of intensional dependent type theory with Σ, Π, and identity types.
We use display map categories ...
Efficient advert assignment
(InformsOperations Research, 2016-07-01)
We develop a framework for the analysis of large-scale ad auctions where adverts are assigned over a continuum of search types. For this pay-per-click market, we provide an efficient mechanism that maximizes social welfare. ...
Existence of Mori fibre spaces for 3-folds in char p
(ElsevierAdvances in Mathematics, 2017-06-20)
We prove the following results for projective klt pairs of dimension 3 over an algebraically closed field of characteristic $p$>5: the cone theorem, the base point free theorem, the contraction theorem, finiteness of minimal ...
Critical Exponents on Fortuin-Kasteleyn Weighted Planar Maps
(SpringerCOMMUNICATIONS IN MATHEMATICAL PHYSICS, 2017-10-01)
In this paper we consider random planar maps weighted by the self-dual Fortuin--Kasteleyn model with parameter $q \in (0,4)$. Using a bijection due to Sheffield and a connection to planar Brownian motion in a cone we obtain ...
RANDOM WALKS ON THE RANDOM GRAPH
(ANNALS OF PROBABILITY, 2018-01)
Homological stability for spaces of embedded surfaces
(Mathematical Sciences PublisherGeometry and Topology, 2017-05-10)
© 2017, Mathematical Sciences Publishers. All rights reserved.We study the space of oriented genus-g subsurfaces of a fixed manifold M and, in particular, its homological properties. We construct a “scanning map” which ...
Small-amplitude swimmers can self-propel faster in viscoelastic fluids
(ElsevierJournal of Theoretical Biology, 2015-07-08)
Many small organisms self-propel in viscous fluids using travelling wave-like deformations of their bodies or appendages. Examples include small nematodes moving through soil using whole-body undulations or spermatozoa ...
The stress–pressure relationship in simulations of MRI-induced turbulence
(Oxford University PressMonthly Notices of the Royal Astronomical Society, 2016-01-01)
We determine how MRI (magnetorotational instability)-turbulent stresses depend on gas pressure via a suite of unstratified shearing box simulations. Earlier numerical work reported only a very weak dependence at best, ...
Growth of eccentric modes in disc–planet interactions
(Oxford University PressMonthly Notices of the Royal Astronomical Society, 2016-03-07)
We formulate a set of linear equations that describe the behaviour of small eccentricities in a protoplanetary system consisting of a gaseous disc and a planet. Eccentricity propagates through the disc by means of pressure ...
Destruction of large-scale magnetic field in nonlinear simulations of the shear dynamo
(Oxford University PressMonthly Notices of the Royal Astronomical Society, 2016-03-03)
The Sun's magnetic field exhibits coherence in space and time on much larger scales than the turbulent convection that ultimately powers the dynamo. In the past the α-effect (mean-field) concept has been used to model the ...