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The dynamics of quasiregular maps of punctured space (2019)
Journal Article
Nicks, D. A., & Sixsmith, D. J. (2019). The dynamics of quasiregular maps of punctured space. Indiana University Mathematics Journal, 68(1), 323-352. https://doi.org/10.1512/iumj.2019.68.7556

The Fatou-Julia iteration theory of rational and transcendental entire functions has recently been extended to quasiregular maps in more than two real dimensions. Our goal in this paper is similar; we extend the iteration theory of analytic self-maps...

Principal nested shape space analysis of molecular dynamics data (2019)
Journal Article
Dryden, I. L., Kim, K., Laughton, C. A., & Le, H. (2019). Principal nested shape space analysis of molecular dynamics data. Annals of Applied Statistics, 13(4), 2213-2234. https://doi.org/10.1214/19-AOAS1277

Molecular dynamics simulations produce huge datasets of temporal sequences of molecules. It is of interest to summarize the shape evolution of the molecules in a succinct, low-dimensional representation. However, Euclidean techniques such as principa...

Tail expectile process and risk assessment (2019)
Journal Article
Daouia, A., Girard, S., & Stupfler, G. (2020). Tail expectile process and risk assessment. Bernoulli, 26(1), 531-556. https://doi.org/10.3150/19-BEJ1137

Expectiles define a least squares analogue of quantiles. They are determined by tail expectations rather than tail probabilities. For this reason and many other theoretical and practical merits, expectiles have recently received a lot of attention, e...

Nonlinear shear of entangled polymers from nonequilibrium molecular dynamics (2019)
Journal Article
Anwar, M., & Graham, R. S. (2019). Nonlinear shear of entangled polymers from nonequilibrium molecular dynamics. Journal of Polymer Science Part B: Polymer Physics, https://doi.org/10.1002/polb.24904

This work aims to improve the use of Molecular Dynamics simulations of Kremer-Grest chains to inform future developments of models of entangled polymer dynamics. We perform non-equilibrium molecular dynamics simulations, under shear flow, for well en...

From bore-soliton-splash to a new wave-to-wire wave-energy model (2019)
Journal Article
Bokhove, O., Kalogirou, A., & Zweers, W. (2019). From bore-soliton-splash to a new wave-to-wire wave-energy model. Water Waves, 1(2), 217-218. https://doi.org/10.1007/s42286-019-00022-9

We explore extreme nonlinear water-wave amplification in a contraction or, analogously, wave amplification in crossing seas. The latter case can lead to extreme or rogue-wave formation at sea. First, amplification of a solitary-water-wave compound ru...

Two-Grid hp-DGFEMs on Agglomerated Coarse Meshes (2019)
Journal Article
Congreve, S., & Houston, P. (2019). Two-Grid hp-DGFEMs on Agglomerated Coarse Meshes. PAMM, 19(1), https://doi.org/10.1002/pamm.201900175

We generalise the a priori error analysis of two‐grid hp‐version discontinuous Galerkin finite element methods for strongly monotone second‐order quasilinear elliptic partial differential equations to the case when coarse meshes consisting of general...

Mathematical modelling of telomere length dynamics (2019)
Journal Article
Wattis, J. A., Qi, Q., & Byrne, H. M. (2019). Mathematical modelling of telomere length dynamics. Journal of Mathematical Biology, 1-38. https://doi.org/10.1007/s00285-019-01448-y

Telomeres are repetitive DNA sequences located at the ends of chromosomes. During cell division, an incomplete copy of each chromosome's DNA is made, causing telomeres to shorten on successive generations. When a threshold length is reached replicati...

Global uniform estimate for the modulus of 2D Ginzburg-Landau vortexless solutions with asymptotically infinite boundary energy (2019)
Journal Article
Ignat, R., Kurzke, M., & Lamy, X. (2019). Global uniform estimate for the modulus of 2D Ginzburg-Landau vortexless solutions with asymptotically infinite boundary energy. SIAM Journal on Mathematical Analysis,

For ε > 0, let uε : Ω → R 2 be a solution of the Ginzburg-Landau system −∆uε = 1 ε 2 uε(1 − |uε| 2) in a Lipschitz bounded domain Ω. In an energy regime that excludes interior vortices, we prove that 1 − |uε| is uniformly estimated by a positive powe...

Beyond tail median and conditional tail expectation: extreme risk estimation using tail Lp-optimisation (2019)
Journal Article
Gardes, L., Girard, S., & Stupfler, G. (2019). Beyond tail median and conditional tail expectation: extreme risk estimation using tail Lp-optimisation. Scandinavian Journal of Statistics, https://doi.org/10.1111/sjos.12433

The Conditional Tail Expectation is an indicator of tail behaviour that, contrary to the quantile or Value-at-Risk, takes into account the frequency of a tail event together with the probabilistic behaviour of the variable of interest on this event....

Pair-based likelihood approximations for stochastic epidemic models (2019)
Journal Article
Stockdale, J. E., Kypraios, T., & O'Neill, P. D. (in press). Pair-based likelihood approximations for stochastic epidemic models. Biostatistics,

Fitting stochastic epidemic models to data is a non-standard problem because data on the infection processes defined in such models are rarely observed directly. This in turn means that the likelihood of the observed data is intractable in the sense...

General Principles for the Validation of Proarrhythmia Risk Prediction Models: An Extension of the CiPA In Silico Strategy (2019)
Journal Article
Li, Z., Mirams, G. R., Yoshinaga, T., Ridder, B. J., Han, X., Chen, J. E., …Strauss, D. G. (2019). General Principles for the Validation of Proarrhythmia Risk Prediction Models: An Extension of the CiPA In Silico Strategy. Clinical Pharmacology and Therapeutics, https://doi.org/10.1002/cpt.1647

This white paper presents principles for validating proarrhythmia risk prediction models for regulatory use as discussed at the In Silico Breakout Session of a Cardiac Safety Research Consortium/Health and Environmental Sciences Institute/US Food and...

An agglomeration-based massively parallel non-overlapping additive Schwarz preconditioner for high-order discontinuous Galerkin methods on polytopic grids (2019)
Journal Article
Antonietti, P. F., Houston, P., Pennesi, G., & Suli, E. (in press). An agglomeration-based massively parallel non-overlapping additive Schwarz preconditioner for high-order discontinuous Galerkin methods on polytopic grids. Mathematics of Computation,

In this article we design and analyze a class of two-level non-overlapping additive Schwarz preconditioners for the solution of the linear system of equations stemming from discontinuous Galerkin discretizations of second-order elliptic partial diffe...

Asymptotic modelling and direct numerical simulations of multilayer pressure-driven flows (2019)
Journal Article
Kalogirou, A., Cimpeanu, R., & Blyth, M. (2019). Asymptotic modelling and direct numerical simulations of multilayer pressure-driven flows. European Journal of Mechanics - B/Fluids, https://doi.org/10.1016/j.euromechflu.2019.10.011

The nonlinear dynamics of two immiscible superposed viscous fluid layers in a channel is examined using asymptotic modelling and direct numerical simulations (DNS). The flow is driven by an imposed axial pressure gradient. Working on the assumption t...

Designing quantum experiments with a genetic algorithm (2019)
Journal Article
Nichols, R., Mineh, L., Rubio, J., Matthews, J. C. F., & Knott, P. A. (2019). Designing quantum experiments with a genetic algorithm. Quantum Science and Technology, 4(4), https://doi.org/10.1088/2058-9565/ab4d89

We introduce a genetic algorithm that designs quantum optics experiments for engineering quantum states with specific properties. Our algorithm is powerful and flexible, and can easily be modified to find methods of engineering states for a range of...

Moving boundary problems for quasi-steady conduction limited melting (2019)
Journal Article
Morrow, L. C., King, J. R., Moroney, T. J., & Mccue, S. (2019). Moving boundary problems for quasi-steady conduction limited melting. SIAM Journal on Applied Mathematics, 79(5), 2107-2131. https://doi.org/10.1137/18M123445X

The problem of melting a crystal dendrite is modelled as a quasi-steady Stefan 5 problem. By employing the Baiocchi transform, asymptotic results are derived in the limit that 6 the crystal melts completely, extending previous results that hold for a...

A master stability function approach to cardiac alternans (2019)
Journal Article
Lai, Y. M., Veasy, J., Coombes, S., & Thul, R. (2019). A master stability function approach to cardiac alternans. Applied Network Science, 4(1), https://doi.org/10.1007/s41109-019-0199-z

During a single heartbeat, muscle cells in the heart contract and relax. Under healthy conditions, the behaviour of these muscle cells is almost identical from one beat to the next. However, this regular rhythm can be disturbed giving rise to a varie...

How a nonassociative algebra reflects the properties of a skew polynomial (2019)
Journal Article
Brown, C., & Pumpluen, S. (in press). How a nonassociative algebra reflects the properties of a skew polynomial. Glasgow Mathematical Journal,

Let $S$ be a unital associative ring and $S[t;\sigma,\delta]$ be a skew polynomial ring, where $\sigma$ is an injective endomorphism of $S$ and $\delta$ a left $\sigma$-derivation. For each $f\in S[t;\sigma,\delta]$ of degree $m>1$ with a unit as lea...

Virtual Element Method for Quasilinear Elliptic Problems (2019)
Journal Article
Cangiani, A., Chatzipantelidis, P., Diwan, G., & Georgoulis, E. (2019). Virtual Element Method for Quasilinear Elliptic Problems. IMA Journal of Numerical Analysis, 1-18. https://doi.org/10.1093/imanum/drz035

A Virtual Element Method (VEM) for the quasilinear equation −div(κ κ κ(u)gradu) = f using general polygonal and polyhedral meshes is presented and analysed. The nonlinear coefficient is evaluated with the piecewise polynomial projection of the virtua...