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Structured light enables biomimetic swimming and versatile locomotion of photoresponsive soft microrobots
(Nature Publishing GroupNature Materials, 2016-02-15)
Microorganisms move in challenging environments by periodic changes in body shape. In contrast, current artificial microrobots cannot actively deform, exhibiting at best passive bending under external fields. Here, by ...
Dynamics of laterally confined marine ice sheets
(Cambridge University PressJournal of Fluid Mechanics, 2016-02-03)
We present an experimental and theoretical study of the dynamics of laterally confined marine ice sheets in the natural limit in which the long, narrow channel into which they flow is wider than the depth of the ice. A ...
Quantum communication complexity advantage implies violation of a Bell inequality
(National Academy of SciencesProceedings of the National Academy of Sciences, 2016-03-08)
We obtain a general connection between a large quantum advantage in communication complexity and Bell non-locality. We show that given any protocol offering a sufficiently large quantum advantage in communication complexity, ...
The response of the lower stratosphere to zonally symmetric thermal and mechanical forcing.
(American Meteorological SocietyJournal of the Atmospheric Sciences, 2016-04-15)
The response of the atmosphere to zonally symmetric applied heating and mechanical forcing is considered, allowing for the fact that the response may include a change in the wave force (or ‘wave drag’). A scaling argument ...
The double peak in upwelling and heating in the tropical lower stratosphere.
(American Meteorological SocietyJournal of the Atmospheric Sciences, 2016-04-15)
The processes responsible for double peak latitudinal structures in the time averaged tropical lower stratospheric upwelling, centred near 70hPa and 20º N–S, previously noted in ERA-Interim and other reanalysis and model ...
Statistical and computational trade-offs in estimation of sparse principal components
(Institute of Mathematical StatisticsAnnals of Statistics, 2016)
In recent years, Sparse Principal Component Analysis has emerged as an extremely popular dimension reduction technique for highdimensional data. The theoretical challenge, in the simplest case, is to estimate the leading ...
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 ...
Level-raising and symmetric power functoriality, III
(Duke University PressDuke Mathematical Journal, 2016-12-09)
The simplest case of the Langlands functoriality principle asserts the existence of
the symmetric powers Symn of a cuspidal representation of GL.2/ over the adèles of
F , where F is a number field. In 1978, Gelbart and ...
A 2-adic automorphy lifting theorem for unitary groups over CM fields
(SpringerMathematische Zeitschrift, 2016)
We prove a ‘minimal’ type automorphy lifting theorem for 2-adic Galois representations of unitary type, over imaginary CM fields. We use this to improve an automorphy lifting theorem of Kisin for GL_2.
Spectral methods and computational trade-offs in high-dimensional statistical inference
(Department of Pure Mathematics and Mathematical Statistics, University of CambridgeUniversity of CambridgeDepartment of Pure Mathematics and Mathematical StatisticsFaculty of MathematicsSt John's College, 2016-10-04)
Spectral methods have become increasingly popular in designing fast algorithms for modern highdimensional datasets. This thesis looks at several problems in which spectral methods play a central role. In some cases, we ...