Recall the definition of Y in (1.5). The anticanonical divisor on Y is −KY=O(3,1) which provides the height H defined as follows. For a point (x,y)∈P3Q×P3Q, we choose x,y∈Z4prim, unique up to sign, so that (x,y)=([x],[y]) and we let

We prove a lower bound that agrees with Manin's prediction for the number of rational points of bounded height on the Fermat cubic surface. As an app…

We prove that a Lebesgue measure-preserving linked-twist map defined in the plane is metrically isomorphic to a Bernoulli shift (and thus strongly mixing). This is the first such result for an explicitly defined linked-twist map on a manifold other …

We prove that a Lebesgue measure-preserving linked-twist map defined in the plane is metrically isomorphic to a Bernoulli shift (and thus strongly mi…

In this chapter we review some of the most recent computational advances in the rapidly expanding field of statistical social network analysis using …

We are very appreciative of comments on a draft manuscript that we received from Eliahu Cohen, Casey McCoy and Ken Wharton. We are also very grateful for the support of the University of Bristol Institute for Advanced Studies and the School of Arts …

This paper provides a prospectus for a new way of thinking about the wavefunction of the universe: a $\Psi$-epistemic quantum cosmology. We present a…

We introduce Latent Gaussian Process Regression which is a latent variable extension allowing modelling of non-stationary multi-modal processes using…

The efficient calculation of Hamiltonian spectra, a problem often intractable on classical machines, can find application in many fields, from physic…

Quantum metrology enables estimation of optical phase shifts with precision beyond the shot-noise limit. One way to exceed this limit is to use squee…

We demonstrate photon-pair generation in a reverse proton exchanged waveguide fabricated on a periodically poled magnesium doped stoichiometric lithi…

Using techniques from symplectic geometry, we prove that a pure state of three qubits is up to local unitaries uniquely determined by its one-particl…

We determine the solvent mediated contribution to the effective potentials for model colloidal or nano- particles dispersed in a binary solvent that …

This paper presents the verification of control systems implemented in Simulink. The goal is to ensure that high-level requirements on control perfor…

This paper examines the verification of stability, a control requirement, over discrete control systems represented as Simulink diagrams, using diffe…

We investigate the static and dynamic properties of a weakly polydisperse hard sphere system in the deeply supercooled state, i.e. at densities highe…

On-chip integrated photonic circuits are crucial to further progress towards quantum technologies and in the science of quantum optics. Here we repor…

Various 3D reconstruction methods have enabled civil engineers to detect damage on a road surface. To achieve the millimetre accuracy required for ro…

The folded node is a singularity associated with loss of normal hyperbolicity in systems where mixtures of slow and fast timescales arise due to sing…

We present a deep person re-identification approach that combines semantically selective, deep data augmentation with clustering-based network compre…

TOPCAT, the Tool for OPerations on Catalogues And Tables, is an interactive desktop application for retrieval, analysis and manipulation of tabular d…

We are concerned with obtaining well-calibrated output distributions from regression models. Such distributions allow us to quantify the uncertainty …

Hardy and Littlewood's approximate functional equation for quadratic Weyl sums (theta sums) provides, by iterative application, a powerful tool for t…

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