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Chalfont Saint Giles, United Kingdom

Vincent J.-P.,UK National Institute for Medical Research | Fletcher A.G.,Mathematical Institute | Baena-Lopez L.A.,UK National Institute for Medical Research
Nature Reviews Molecular Cell Biology | Year: 2013

When fast-growing cells are confronted with slow-growing cells in a mosaic tissue, the slow-growing cells are often progressively eliminated by apoptosis through a process known as cell competition. The underlying signalling pathways remain unknown, but recent findings have shown that cell crowding within an epithelium leads to the eviction of cells from the epithelial sheet. This suggests that mechanical forces could contribute to cell elimination during cell competition. © 2013 Macmillan Publishers Limited. All rights reserved. Source


Penrose R.,Mathematical Institute
Foundations of Physics | Year: 2014

This paper argues that the case for "gravitizing" quantum theory is at least as strong as that for quantizing gravity. Accordingly, the principles of general relativity must influence, and actually change, the very formalism of quantum mechanics. Most particularly, an "Einsteinian", rather than a "Newtonian" treatment of the gravitational field should be adopted, in a quantum system, in order that the principle of equivalence be fully respected. This leads to an expectation that quantum superpositions of states involving a significant mass displacement should have a finite lifetime, in accordance with a proposal previously put forward by Diósi and the author. © 2014 The Author(s). Source


Penrose R.,Mathematical Institute
Foundations of Physics | Year: 2014

The 2nd Law of thermodynamics was driven by the Big Bang being extraordinary special, with hugely suppressed gravitational degrees of freedom. This cannot have been simply the result of a conventional quantum gravity. Conformal cyclic cosmology proposes a different picture, of a classical evolution from an aeon preceding our own. The ultimate Hawking evaporation of black holes is key to the 2nd Law and requires information loss, violating unitarity in a strongly gravitational context. © 2013 The Author(s). Source


Dellar P.J.,Mathematical Institute
Computers and Mathematics with Applications | Year: 2013

The lattice Boltzmann space/time discretisation, as usually derived from integration along characteristics, is shown to correspond to a Strang splitting between decoupled streaming and collision steps. Strang splitting offers a second-order accurate approximation to evolution under the combination of two non-commuting operators, here identified with the streaming and collision terms in the discrete Boltzmann partial differential equation. Strang splitting achieves second-order accuracy through a symmetric decomposition in which one operator is applied twice for half timesteps, and the other operator is applied once for a full timestep. We show that a natural definition of a half timestep of collisions leads to the same change of variables that was previously introduced using different reasoning to obtain a second-order accurate and explicit scheme from an integration of the discrete Boltzmann equation along characteristics. This approach extends easily to include general matrix collision operators, and also body forces. Finally, we show that the validity of the lattice Boltzmann discretisation for grid-scale Reynolds numbers larger than unity depends crucially on the use of a Crank-Nicolson approximation to discretise the collision operator. Replacing this approximation with the readily available exact solution for collisions uncoupled from streaming leads to a scheme that becomes much too diffusive, due to the splitting error, unless the grid-scale Reynolds number remains well below unity. © 2013 Published by Elsevier Ltd. Source


Olver S.,Mathematical Institute
BIT Numerical Mathematics | Year: 2010

We present a numerically stable way to compute oscillatory integrals. For each additional frequency, only a small, well-conditioned linear system with a Hessenberg matrix must be solved, and the amount of work needed decreases as the frequency increases. Moreover, we can modify the method for computing oscillatory integrals with stationary points. This is the first stable algorithm for oscillatory integrals with stationary points which does not lose accuracy as the frequency increases and does not require deformation into the complex plane. © Springer Science + Business Media B.V. 2010. Source

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