ORCID Profile
0000-0002-4281-6388
Current Organisations
Massachusetts Institute of Technology
,
Australian National University
,
University of Leeds
,
Université de Bretagne Occidentale
,
University of Manchester
,
University of Warwick
,
University of Oxford
,
University of Melbourne
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Publications
Riemannian twistors and Hermitian structures on low-dimensional space forms
Publisher: AIP Publishing
Date: 10-1992
DOI: 10.1063/1.529935
Abstract: A Riemannian Kerr Theorem is described, which associates to an integrable Hermitian structure (with singularities) on S4 a complex analytic surface in CP3. To such a Hermitian structure can be associated a harmonic morphism defined on each of the four-dimensional space forms with values in a Riemann surface. This unifies the classifications for the three-dimensional space forms of Baird and Wood and the recent classifications for R4 and S4 by Wood, into one simple equation. As a consequence we derive the classification for harmonic morphisms defined on four-dimensional hyperbolic space with values in a Riemann surface and a new implicit form for harmonic morphisms defined on three-dimensional hyperbolic space. Unification of the Kerr Theorems for S4 and for compactified Minkowski space M is achieved at the complex level after suitably embedding the spaces in compactified, complexified Minkowski space.
Identification Of Quantum Encoder Matrix From A Collection Of Pauli Errors
Publisher: IEEE
Date: 11-2019
Quadratic cyclic sequences
Publisher: Springer Science and Business Media LLC
Date: 06-08-2020
A threshold loading device for testing of inspiratory muscle performance
Publisher: European Respiratory Society (ERS)
Date: 03-1995
DOI: 10.1183/09031936.95.08030463
Abstract: Threshold loading is a method of incrementally loading the inspiratory muscles, which requires development of an adjustable threshold pressure (Pth) before air will flow. In the ideal device, flow is independent of pressure once Pth is exceeded. A "weighted plunger" apparatus is commonly used, but devices described previously perform unreliably at high inspiratory load. We have modified this apparatus using the diaphragm and valve seating from a threshold valve used to deliver positive airway pressure (AMBU 10, AMBU International, Denmark) to yield improved pressure-flow characteristics. With this device, there was a linear relationship between Pth and weight on the plunger (r = 0.998), and flow was largely independent of pressure once Pth was exceeded: pressure developed at an inspiratory flow of 1.3 +/- 0.1 l.s-1 was 13.6 +/- 7.0% below Pth. Our modified weighted plunger apparatus allows consistent and reliable threshold loading of inspiratory muscles, even at high inspiratory loads.
Emergence of geometry in a combinatorial universe
Publisher: Elsevier BV
Date: 12-2013
Harmonic Maps and Morphisms from Multilinear Norm-Preserving Mappings
Publisher: World Scientific Pub Co Pte Lt
Date: 03-1997
DOI: 10.1142/S0129167X97000093
Abstract: We extend the notion of orthogonal multiplication to multilinear norm-preserving mapping, using them to construct new eigenmaps into spheres. We characterize those which are harmonic morphisms. By the method of reduction we construct interesting families of harmonic morphisms into S 2 from the product manifolds H 2 × S 3 and S 3 × S 3 of hyperbolic spaces and spheres. The corresponding reduction equation depends on two independent variables. We are able to solve the first-order horizontal conformality problem explicitly in terms of elliptic functions and then render the map harmonic by a conformal deformation of the metric.
Harmonic morphisms and conformal foliations by geodesics of three-dimensional space forms
Publisher: Cambridge University Press (CUP)
Date: 08-1991
DOI: 10.1017/S1446788700033358
Abstract: A complete classification is given of harmonic morphisms to a surface and conformal foliations by geodesics, with or without isolated singularities, of a simply-connected space form. The method is to associate to any such a holomorphic map from a Riemann surface into the space of geodesics of the space form. Properties such as nonintersecting fibres (or leaves) are translated into conditions on the holomorphic mapping which show it must have a simple form corresponding to a standard ex le.
Why Linear? An Illustration Using a Geometric Model of Quantum Interaction
Publisher: Springer International Publishing
Date: 2016
Harmonic morphisms and bicomplex manifolds
Publisher: Elsevier BV
Date: 2011
A class of analytic pairs of conjugate functions in dimension three
Publisher: Walter de Gruyter GmbH
Date: 21-06-2019
DOI: 10.1515/ADVGEOM-2018-0034
Abstract: We exploit an ansatz in order to construct power series expansions for pairs of conjugate functions defined on domains of Euclidean 3-space. Convergence properties of the resulting series are investigated. Entire solutions which are not harmonic are found as well as a 2-parameter family of ex les which contains the Hopf map.
On Functions with a Conjugate
Publisher: Cellule MathDoc/CEDRAM
Date: 2015
DOI: 10.5802/AIF.2931
Liouville-type theorems for biharmonic maps between Riemannian manifolds
Publisher: Walter de Gruyter GmbH
Date: 2010
DOI: 10.1515/ACV.2010.003
Weierstrass representations for harmonic morphisms on Euclidean spaces and spheres.
Publisher: Det Kgl. Bibliotek/Royal Danish Library
Date: 12-1997
Unique continuation of semi-conformality for a harmonic mapping onto a surface
Publisher: Springer Science and Business Media LLC
Date: 07-11-2008
An integral formula for a class of biharmonic maps from Euclidean 3-space
Publisher: Elsevier BV
Date: 10-2018
Hypercube quantum search: exact computation of the probability of success in polynomial time
Publisher: Springer Science and Business Media LLC
Date: 15-03-2023
DOI: 10.1007/S11128-023-03883-9
Abstract: In the emerging domain of quantum algorithms, Grover’s quantum search is certainly one of the most significant. It is relatively simple, performs a useful task and more importantly, does it in an optimal way. However, due to the success of quantum walks in the field, it is logical to study quantum search variants over several kinds of walks. In this paper, we propose an in-depth study of the quantum search over a hypercube layout. First, through the analysis of elementary walk operators restricted to suitable eigenspaces, we show that the acting component of the search algorithm takes place in a small subspace of the Hilbert workspace that grows linearly with the problem size. Subsequently, we exploit this property to predict the exact evolution of the probability of success of the quantum search in polynomial time.
Conformal subfoliations of prescribed geodesic curvature
Publisher: Det Kgl. Bibliotek/Royal Danish Library
Date: 12-2003
DOI: 10.7146/MATH.SCAND.A-14420
Abstract: Given a $2$-dimensional conformal foliation $\\mathcal F$ of a Riemannian manifold $M$, the problem of finding a $1$-dimensional subfoliation $\\mathcal G$, conformal in $M$, whose leaves have prescribed geodesic curvature in the leaves of $\\mathcal F$ is equivalent to a Pfaff differential system on a circle bundle over $M$. We study such pairs of foliations on a $3$- and $4$-manifold.
CR geometry and conformal foliations
Publisher: Springer Science and Business Media LLC
Date: 19-11-2012
Harmonic Morphisms, Seifert Fibre Spaces and Conformal Foliations
Publisher: Wiley
Date: 1992
Harmonic morphisms, conformal foliations and shear-free ray congruences
Publisher: The Belgian Mathematical Society
Date: 1998
Conformal and semi-conformal biharmonic maps
Publisher: Springer Science and Business Media LLC
Date: 08-05-2008
Prescribed Q
Publisher: Elsevier BV
Date: 02-2009
Three-dimensional Ricci solitons which project to surfaces
Publisher: Walter de Gruyter GmbH
Date: 27-01-2007
Constant mean curvature polytopes and hypersurfaces via projections
Publisher: Elsevier BV
Date: 03-2014
Ray congruences that generate conformal foliations
Publisher: AIP Publishing
Date: 03-2012
DOI: 10.1063/1.3692168
Abstract: Given a Riemannian 3-manifold (M3, g0) endowed with a unit vector field U0 that is tangent to a conformal foliation, we require that the pair extend to a space-time \\documentclass[12pt]{minimal}\\begin{document}$({\\mathcal M}, {\\mathcal G})$\\end{document}(M,G) endowed with a space-like unit vector field Ut in such a way that Ut simultaneously generates null geodesics and is tangent to a conformal foliation on space-like slices t = constant. The property that the foliation be conformal is intimately related to CR-geometry.
Bernstein theorems for harmonic morphisms from R3 andS 3
Publisher: Springer Science and Business Media LLC
Date: 12-1988
DOI: 10.1007/BF01450078
Q-curvature flow on 4-manifolds
Publisher: Springer Science and Business Media LLC
Date: 06-04-2006
Stress-energy tensors and the Lichnerowicz Laplacian
Publisher: Elsevier BV
Date: 10-2008
Twistor Theory on a Finite Graph
Publisher: Springer Science and Business Media LLC
Date: 22-04-2011
KNOT SINGULARITIES OF HARMONIC MORPHISMS
Publisher: Cambridge University Press (CUP)
Date: 02-2001
DOI: 10.1017/S0013091598001278
Abstract: A harmonic morphism defined on $\\mathbb{R}^3$ with values in a Riemann surface is characterized in terms of a complex analytic curve in the complex surface of straight lines. We show how, to a certain family of complex curves, the singular set of the corresponding harmonic morphism has an isolated component consisting of a continuously embedded knot. AMS 2000 Mathematics subject classification: Primary 57M25. Secondary 57M12 58E20
The Geometric Spectrum of a Graph and Associated Curvatures
Publisher: Springer International Publishing
Date: 2017
Feedback Loops: A Fundamental Ingredient of Information Processing
Publisher: Springer International Publishing
Date: 2015
Heat flow for harmonic maps from graphs into Riemannian manifolds
Publisher: Elsevier BV
Date: 06-2022
Biharmonic Conformal Maps in Dimension Four and Equations of Yamabe-Type
Publisher: Springer Science and Business Media LLC
Date: 28-02-2018
Conservation Laws, Equivariant Harmonic Maps and Harmonic Morphisms
Publisher: Wiley
Date: 1992
An invariance property for frameworks in Euclidean space
Publisher: Elsevier BV
Date: 2014
Gene expression levels as endophenotypes in genome-wide association studies of Alzheimer disease
Publisher: Ovid Technologies (Wolters Kluwer Health)
Date: 08-02-2010
Static fields on three-dimensional space forms in terms of contour integrals of twistor functions
Publisher: Elsevier BV
Date: 08-1993
On Constructing Biharmonic Maps and Metrics
Publisher: Springer Science and Business Media LLC
Date: 2003
Biharmonic maps from biconformal transformations with respect to isoparametric functions
Publisher: Elsevier BV
Date: 02-2017
A B�chner technique for harmonic mappings from a 3-manifold to a surface
Publisher: Springer Science and Business Media LLC
Date: 1992
DOI: 10.1007/BF00128338
Harmonic morphisms on heaven spaces
Publisher: Wiley
Date: 11-03-2009
DOI: 10.1112/BLMS/BDP006
p-harmonic maps and minimal submanifolds
Publisher: Springer Science and Business Media LLC
Date: 12-1992
DOI: 10.1007/BF01934344
A Hamiltonian system on hyperbolic space and associated harmonic maps
Publisher: Elsevier BV
Date: 11-1992
A class of three-dimensional Ricci solitons
Publisher: Mathematical Sciences Publishers
Date: 12-01-2009
Related Organisations
Massachusetts Institute Of Technology
Location: United States of America
University Of Leeds
Location: United Kingdom of Great Britain and Northern Ireland
University Of Manchester
Location: United Kingdom of Great Britain and Northern Ireland
University Of Warwick
Location: United Kingdom of Great Britain and Northern Ireland
University Of Oxford
Location: United Kingdom of Great Britain and Northern Ireland
Related Funding Activities
No related grants have been discovered for Paul Baird.