## Preprint Series

### 2014

MPS-2014-01 "An adaptive finite element method for the infinity Laplacian" by Omar Lakkis and Tristan Pryer

MPS-2014-02 "Discontinuous Galerkin methods for a class of nonvariational problems" by Andreas Dedner and Tristan Pryer

MPS-2014-03 "Discontinuous Galerkin methods for the *P*-biharmonic equation from a discrete variational perspective" by Tristan Pryer

MPS-2014-04 "Energy consistent discontinuous Galerkin methods for a quasi-incompressible diffuse two phase flow model" by Jan Giesselmann and Tristan Pryer

MPS-2014-05 "Variations on the sum-product problem" by Brendan Murphy, Oliver Roche-Newton and Ilya Shkredov

MPS-2014-06 "The tube axis and entanglements in polymer melts" by Alexei E. Likhtman

MPS-2014-07 "Microscopic definition of polymer entanglements" by Alexei E. Likhtman and M. Ponmurugan

MPS-2014-08 "Conditioning and Preconditioning of the Optimal State Estimation Problem" by S.A. Haben, A.S. Lawless and N.K. Nichols

MPS-2014-09 "Schatten Class Toeplitz Operators on Generalized Fock Spaces" by Joshua Isralowitz, Jani Virtanen and Lauren Wolf

MPS-2014-10 "Interpolation of Hilbert and Sobolev Spaces: Quantitative Estimates and Counterexamples" by S.N. Chandler-Wilde, D.P. Hewett and A. Moiola

MPS-2014-11 "Noisy Monte Carlo: Convergence of Markov chains with approximate transition kernels" by P. Alquier, N. Friel, R.G. Everitt and A. Boland

MPS-2014-12 "A shape calculus based method for a transmission problem with random interface" by Alexey Chernov, Duong Pham and Thanh Tran

MPS-2014-13 "Estimation of arbitrary order central statistical moments by the Multilevel Monte Carlo Method" by Claudio Bierig and Alexey Chernov

MPS-2014-14 "A finite difference moving mesh method based on conservation for moving boundary problems" by T.E. Lee, M.J. Baines and S. Langdon

MPS-2014-15 "Quasi-analyticity and determinacy of the full moment problem from finite to infinite dimensions" by Maria Infusino

MPS-2014-16 "Reduced relative entropy techniques for a priori analysis of multiphase problems in elastodynamics" by Jan Giesselmann and Tristan Pryer

MPS-2014-17 "Reduced relative entropy techniques for a posteriori analysis of multiphase problems in elastodynamics" by Jan Giesselmann and Tristan Pryer

MPS-2014-18 "The Error of Representation: Basic Understanding" by Daniel Hodyss and Nancy Nichols

MPS-2014-19 "A posteriori analysis of discontinuous Galerkin schemes for systems of hyperbolic conservation laws" by Jan Giesselmann, Charalambos Makridakis and Tristan Pryer

MPS-2014-20 "Lazy ABC" by Dennis Prangle

MPS-2014-21 "Acoustic scattering: high frequency boundary element methods and unified transform methods" by S.N. Chandler-Wilde and S. Langdon

MPS-2014-22 "Weighted α-rate dominating sets in social networks" by Danica Vukadinovic Greetham, Anush Poghosyan and Nathaniel Charlton

MPS-2014-23 "Review article: Advances in the study of boundary value problems for nonlinear integrable PDEs" by Beatrice Pelloni

### 2013

MPS-2013-01 "Scheduling satellite-based SAR acquisition for sequential assimilation of water level observations into flood modelling" by Javier Garcia-Pintado, Jeff C. Neal, David C. Mason, Sarah L. Dance and Paul D. Bates

MPS-2013-02 "Hybrid numerical-asymptotic approximation for high frequency scattering by penetrable convex polygons" by Samuel P. Groth, David P. Hewett and Stephen Langdon

MPS-2013-03 "Primary Evolving Networks and the Comparative Analysis of Robust and Fragile Structures" by Peter Grindrod, Zhivko V. Stoyanov and Garry M. Smith

MPS-2013-04 "Aperiodic dynamics in a deterministic model of attitude formation in social groups" by Jonathan A. Ward and Peter Grindrod

MPS-2013-05 "Clustering-based improvement of nonparametric functional time series forecasting. Application to intraday household-level load curves" by Mohamed Chaouch

MPS-2013-06 "Spectral theory of some non-selfadjoint linear differential operators" by B. Pelloni and D.A. Smith

MPS-2013-07 "Dependence of the climate prediction skill on spatio-temporal scales: internal versus radiatively-forced contribution" by D. Volpi, F.J. Doblas-Reyes, J. Garcia-Serrano and V. Guemas

MPS-2013-08 "Kernel-smoothed conditional quantiles of randomly censored functional stationary ergodic data" by Mohamed Chaouch and Salah Khardani

MPS-2013-09 "Centrality and spectral radius in dynamic communication networks" by Danica Vukadinovic Greetham, Zhivko Stoyanov and Peter Grindrod

MPS-2013-10 "Regularisation of a Carbon Cycle Model-Data Fusion Problem" by S. Delahaies, I. Roulstone and N.K. Nichols

MPS-2013-11 "Implementation of an Interior Point Source in the Ultra Weak Variational Formulation through Source Extraction" by C.J. Howarth, P.N. Childs and A. Moiola

MPS-2013-12 "Relaxation of surface tension in the liquid-solid interfaces of Lennard-Jones liquids: Dynamic surface tension - myth or reality?" by A.V. Lukyanov and A.E. Likhtman

MPS-2013-13 "Plane Wave Discontinuous Galerkin Methods: Exponential Convergence of the *hp*-version" by R. Hiptmair, A. Moiola and I. Perugia

MPS-2013-14 "Estimating correlated observation errors with an ensemble transform Kalman filter" by J.A. Waller, S.L. Dance, A.S. Lawless and N.K. Nichols

MPS-2013-15 "'Quasi'-norm of an arithmetical convolution operator and the order of the Riemann zeta function" by Titus Hilberdink

MPS-2013-16 "The full infinite dimensional moment problem on semi-algebraic sets of generalized functions" by M. Infusino, T. Kuna and A. Rota

MPS-2013-17 "Acoustic scattering by fractal screens: mathematical formulations and wavenumber-explicit continuity and coercivity estimates" by S.N. Chandler-Wilde and D.P. Hewett

MPS-2013-18 "A frequency-independent boundary element method for scattering by two-dimensional screens and apertures" by D.P. Hewett, S. Langdon and S.N. Chandler-Wilde

MPS-2013-19 "Non-steady state heat conduction in composite walls" by Bernard Deconinck, Beatrice Pelloni and Natalie Sheils

MPS-2013-20 "Solutions of the Fully Compressible Semi-Geostrophic System" by M.J.P. Cullen, D.K. Gilbert and B. Pelloni

MPS-2013-21 "Online Bayesian Inference in Some Time-Frequency Representations of Non-Stationary Processes" by Richard G. Everitt, Christophe Andrieu and Manuel Davy

### 2012

MPS-2012-01 "Integration of a 3D Variational data assimilation scheme with a coastal area morphodynamic model of Morecambe Bay" by G.D. Thornhill, D.C. Mason, S.L. Dance, A.S. Lawless, N.K. Nichols and H.R. Forbes

MPS-2012-02 "The Unsteady Flow of a Weakly Compressible Fluid in a thin Porous Layer III: Three-dimensional Computations" by S. Langdon, D.J. Needham, B.A. Samson and J.P. Gilchrist

MPS-2012-03 "Wavenumber-explicit continuity and coercivity estimates in acoustic scattering by planar screens" by S.N. Chandler-Wilde and D.P. Hewett

MPS-2012-04 "A High Frequency Boundary Element Method for Scattering by a Class of Nonconvex Obstacles" by S.N. Chandler-Wilde, D.P. Hewett, S. Langdon and A. Twigger

MPS-2012-05 "On Error Dynamics and Instability in Data Assimilation" by Roland W.E. Potthast, Alexander J.F. Moodey, Amos S. Lawless and Peter Jan van Leeuwen

MPS-2012-06 "On Instabilities in Data Assimilation Algorithms" by Boris A. Marx and Roland W.E. Potthast

MPS-2012-07 "Flow and Shape Reconstruction from Remote Measurements" by Qazi Muhammad Zaigham Zia and Roland W.E. Potthast

MPS-2012-08 "On Discrimination Algorithms for Ill-Posed Problems with an Application to Magnetic Tomography" by Natalie Lowery, Roland Potthast, Maria Vahdati and William Holderbaum

MPS-2012-09 "The Stokes Conjecture for Waves with Vorticity" by Eugen Varvaruca and Georg S. Weiss

MPS-2012-10 "High frequency sound propagation in a network of interconnecting streets" by D.P.Hewett

MPS-2012-11 "Superfast non-linear diffusion in porous media: new regimes, universal model and power laws" by A.V. Lukyanov, M.M. Sushchikh, M.J. Baines and T.G. Theofanous

MPS-2012-12 "Resolution of sharp fronts in the presence of model error in variational data assimilation" by M.A. Freitag, N.K. Nichols and C.J. Budd

MPS-2012-13 "Nonlinear error dynamics for cycled data assimilation methods by Alexander J.F. Moodey, Amos S. Lawless, Roland W.E. Potthast and Peter Jan van Leeuwen

MPS-2012-14 "A New Error Measure for Forecasts of Household-level, High Resolution Electrical Energy Consumption" by Stephen Haben, Jonathan A. Ward, Danica Vukadinovic Greetham, Peter Grindrod and Colin Singleton

MPS-2012-15 "Acoustic trapped modes in a three-dimensional waveguide of slowly varying cross section" by Simon N. Gaulter and Nicholas R.T. Biggs

MPS-2012-16 "Relaxation of surface tension in the free-surface boundary layer of simple Lennard-Jones liquids" by A.V. Lukyanov and A.E. Likhtman

MPS-2012-17 "Data assimilation with correlated observation errors: analysis accuracy with approximate error covariance matrices" by L.M. Stewart, S.L. Dance and N.K. Nichols

MPS-2012-18 "Variational data assimilation for very large environmental problems" by A.S. Lawless

MPS-2012-19 "Representativity error for temperature and humidity using the Met Office high resolution model" by J.A. Pocock, S.L. Dance, A.S. Lawless, N.K. Nichols and J.R. Eyre

MPS-2012-20 "Computing Fresnel Integrals via Modified Trapezium Rules" by Mohammad Alazah, Simon N. Chandler-Wilde and Scott La Porte

MPS-2012-21 "Complex Dynamics in a Model of Social Norms" by Peter Grindrod and Mark C Parsons

MPS-2012-22 "Nonparametric Multivariate *L*_{1}-median Regression Estimation with Functional Covariates" by Mohamed Chaouch and Naamane Laib

MPS-2012-23 "Is the Helmholtz equation really sign-indefinite?" by Andrea Moiola and Euan Spence

MPS-2012-24 "Interventions in social networks: Impact on positive mood and network dynamics" by Danica Greetham, Robert Hurling, Abhijit Sengupta and Joy Wilkinson

MPS-2012-25 "Structure, pace and balance in Twitter conversations" by Danica Vukadinovic Greetham and Jonathan A. Ward

MPS-2012-26 "Estimating interchannel observation error correlations for IASI radiance data in the Met Office system" by L.M. Stewart, S.L. Dance, N.K. Nichols, J.R. Eyre and J. Cameron

MPS-2012-27 "Approximation by harmonic polynomials in star-shaped domains and exponential convergence of Trefftz *HP*-DGFEM" by R. Hiptmair, A. Moiola, I. Perugia and Ch. Schwab

### 2011

MPS-2011-01 "Use of the Ratio Plot in Capture-Recapture Estimation" by Dankmar Böhning, M. Fazil Baksh, Rattana Lerdsuwansri and James Gallagher

MPS-2011-02 "The Unsteady Flow of a Weakly Compressible Fluid in a Thin Porous Layer. II: Three-Dimensional Theory" by D.J. Needham, S. Langdon, B.A .Samson and J.P. Gilchrist

MPS-2011-03 "A moving mesh approach for modelling avascular tumour growth" by T.E. Lee, M.J. Baines, S. Langdon and M.J. Tindall

MPS-2011-04 "How Many Cases Are Missed When Screening Human Populations for Disease?" by Dankmar Böhning and Heinz Holling

MPS-2011-05 "Capture-Recapture Estimation Based Upon the Zero-Truncated Exponentially Mixed Poisson" by Sa-aat Niwitpong, Dankmar Böhning, Peter G.M. van der Heijden and Heinz Holling

MPS-2011-06 "Two Maps and Worldwide Ipod Interest" by Reason L. Machete

MPS-2011-07 "Bistability Through Triadic Closure" by Peter Grindrod, Desmond J. Higham and Mark C. Parsons

MPS-2011-08 "On the Spectra and Pseudospectra of a Class of Non-Self-Adjoint Random Matrices and Operators" by Simon N. Chandler-Wilde, Ratchanikorn Chonchaiya and Marko Lindner

MPS-2011-09 "Successful Networks in Security and Defence" by Peter Grindrod and David Sloggett

MPS-2011-10 "Equivalence of Weak Formulations of the Steady Water Waves Equations" by Eugen Varvaruca and Arghir Zarnescu

MPS-2011-11 "Spectrum of a Feinberg-Zee Random Hopping Matrix" by S N Chandler-Wilde and E B Davies

MPS-2011-12 "Superfast non-linear diffusion model of capillary transport in particulate porous media" by A.V. Lukyanov, M.M. Sushchikh, M.J. Baines and T.G. Theofanous

MPS-2011-13 "Resolution of sharp fronts in the presence of model error in variational data assimilation" by M.A. Freitag, N.K. Nichols and C.J. Budd

MPS-2011-14 "Competing Edge Networks" by Mark Parsons and Peter Grindrod

MPS-2011-15 "Contrasting Probabilistic Scoring Rules" by Reason L. Machete

MPS-2011-16 "Data assimilation for state and parameter estimation: application to morphodynamic modelling" by P.J. Smith, G.D. Thornhill, S.L. Dance, A.S. Lawless, D.C. Mason and N.K. Nichols

MPS-2011-17 "Limits to Predicting Predictability: A case study" by Reason L. Machete

MPS-2011-18 "A High Frequency *hp* Boundary Element Method for Scattering by Convex Polygons" by D.P. Hewett, S. Langdon and J.M. Melenk

### 2010

MPS_2010_01 "A high frequency boundary element method for scattering by convex polygons with impedance boundary conditions" by S.N. Chandler-Wilde, S. Langdon and M. Mokgolele

MPS_2010_02 "Social Networks: Evolving Graphs with Memory Dependent Edges" by Peter Grindrod and Mark Parsons

MPS_2010_03 "Boundary value problems for the elliptic sine-Gordon equation in a semi-strip" by A.S. Fokas and B. Pelloni

MPS_2010_04 "Resolution of sharp fronts in the presence of model error in variational data assimilation" by M.A. Freitag, N.K. Nichols and C.J. Budd

MPS_2010_05 "Numerical estimation of coercivity constants for boundary integral operators in acoustic scattering" by T. Betcke and E.A. Spence

MPS_2010_06 "Model order reduction for discrete unstable control systems using a balanced truncation approach" by C. Boess, N.K. Nichols and A. Bunse-Gerstner

MPS_2010_07 "A note on the analysis error associated with 3D-FGAT" by A.S. Lawless

MPS_2010_08 "Eigenvalue problem meets Sierpinski triangle: computing the spectrum of a non-self-adjoint random operator" by Simon N. Chandler-Wilde, Ratchanikorn Chonchaiya and Marko Lindner

MPS_2010_09 "Models for Evolving Networks: with Applications in Telecommunication and Online Activities" by Peter Grindrod and Desmond J. Higham

MPS_2010_10 "Breakdown of hydrostatic balance at convective scales in the forecast errors in the Met Office Unified Model" by Sanita Vetra-Carvalho, Mark Dixon, Stefano Migliorini, Nancy K. Nichols and Susan P. Ballard

MPS_2010_11 "Correlations of control variables in variational data assimilation" by D. Katz, N.K. Nichols, A.S. Lawless, M.J.P. Cullen and R.N. Bannister

MPS_2010_12 "Mathematical Modelling for the Digital Society" by Peter Grindrod

MPS_2010_13 "Four-dimensional variational data assimilation for high resolution nested models" by G.M. Baxter, S.L. Dance, A.S. Lawless and N.K. Nichols

MPS_2010_14 "Regularization Techniques for Ill-posed Inverse Problems in Data Assimilation" by M.A. Freitag, N.K. Nichols and C.J. Budd

MPS_2010_15 "State estimation using model order reduction for unstable systems" by C. Boess, A.S. Lawless, N.K. Nichols and A. Bunse-Gerstner

MPS_2010_16 "Conditioning and Preconditioning of the Variational Data Assimilation Problem" by S.A. Haben, A.S. Lawless and N.K. Nichols

MPS_2010_17 "A hybrid data assimilation scheme for model parameter estimation: application to morphodynamic modelling" by Polly J. Smith, Sarah L. Dance, Nancy K. Nichols

MPS_2010_18 "State Estimation using the Particle Filter with Mode Tracking" by J.A. Pocock, S.L. Dance and A.S. Lawless

MPS_2010_19 "Ensemble data assimilation in the presence of cloud" by S. Vetra-Carvalho, S. Migliorini, N.K. Nichols

MPS_2010_20 "Flow-Dependent Balance Conditions for Incremental Data Assimilation: Elliptic Operators" by S.J. Fletcher, N.K. Nichols and I. Roulstone

MPS_2010_21 "__Condition number estimates for combined potential integral operators in acoustics and their boundary element discretisation__" by T. Betcke, S.N. Chandler-Wilde, I.G. Graham, S. Langdon and M. Lindner

MPS_2010_22 "Conditioning of incremental variational data assimilation, with application to the Met Office system" by S.A. Haben, A.S. Lawless and N.K. Nichols

MPS_2010_23 "A Statistical Mechanical Approach for the Computation of the Climatic Response to General Forcings" by Valerio Lucarini and Stefania Sarno

MPS_2010_24 "From Grievance to Martyrdom: A Mathematical Perspective on the Journey of Radicalisation" by Peter Grindrod and David Sloggett

MPS_2010_25 "Population Size Estimation Based upon Ratios of Recapture Probabilities" by Irene Rocchetti, John Bunge and Dankmar Böhning

MPS_2010_26 "An Extension of Chao's Estimator of Population Size Based on the First Three Capture Frequency Counts" by K. Lanumteang and D. Böhning

MPS_2010_27 "A moving mesh approach to ice sheet modelling" by D. Partridge and M.J. Baines

MPS_2010_28 "Initial Distribution Spread: A density forecasting approach" by R.L. Machete and I.M. Moroz

MPS_2010_29 "Wave trapping in a two-dimensional sound-soft acoustic waveguide of slowly-varying width" by Nicholas R.T. Biggs

MPS_2010_30 "Capture-Recapture Estimation by Means of Empirical Bayesian Smoothing with an Application to the Geographical Distribution of Hidden Scrapie in Great Britain" by Dankmar Böhning, Ronny Kuhnert and Victor Del Rio Vilas

MPS_2010_31 "Velocity-based moving mesh methods for nonlinear partial differential equations" by M.J. Baines, M.E. Hubbard and P.K. Jimack

MPS_2010_32 "Communicability Across Evolving Networks" by Peter Grindrod, Desmond J. Higham, Mark C. Parsons and Ernesto Estrada

MPS_2010_33 "NLEVP: A Collection of Nonlinear Eigenvalue Problems" by Timo Betcke, Nicholas J. Higham, Volker Mehrmann, Christian Schröder and Françoise Tisseur

MPS_2010_34 "Early Warning with Calibrated and Sharper Probabilistic Forecasts by Machete, R.L.

### 2009

MPS_2009_01 "The Unsteady Flow of a Weakly Compressible Fluid in a Thin Porous Layer. II: Three-Dimensional Theory" by D.J. Needham, S. Langdon, B.A. Samson and J.P. Gilchrist

MPS_2009_02 "Variational data assimilation for parameter estimation: application to a simple morphodynamic model" by P.J. Smith, S.L. Dance, M.J. Baines, N.K. Nichols and T.R. Scott

MPS_2009_03 "__Condition number estimates for combined potential integral operators in acoustics and their boundary element discretisation__" by S. N. Chandler-Wilde, I. G. Graham, S. Langdon and M. Lindner

MPS_2009_04 "Mathematical concepts of data assimilation" by N.K. Nichols

MPS_2009_05 "Perturbation, Computation and Refinement of Invariant Pairs for Matrix Polynomials" by T. Betcke and D. Kressner

MPS_2009_06 "Symmetry-break, mixing, instability, and low frequency variability in a minimal Lorenz-like system" by V. Lucarini and K. Fraedrich

MPS_2009_07 "Symmetry-break in Voronoi Tessellations" by V. Lucarini

MPS_2009_08 "An exponentially convergent nonpolynomial finite element method for time-harmonic scattering from polygons" by A. H. Barnett and T. Betcke

MPS_2009_09 "Liquid flow over a substrate structured by seeded nanoparticles" by A.V. Lukyanov

MPS_2009_10 "Experimental Model of the Interfacial Instability in Aluminium Reduction Cells" by A. Pedchenko, S. Molokov, J. Priede, A. Lukyanov and P.J. Thomas

MPS_2009_11 "Classification of instability modes in a model of aluminium reduction cells with a uniform magnetic field" by Sergei Molokov, Gennady El and Alexander Lukyanov

MPS_2009_12 "Evolving Graphs: Dynamical Models, Inverse Problems and Propagation" by Peter Grindrod and Desmond J. Higham

MPS_2009_13 "On the spectra of certain Integro-Differential-Delay problems with applications in neurodynamics" by Peter Grindrod and Dimitris Pinotsis

MPS_2009_14 "A Nyström Method for a Boundary Value Problem arising in Unsteady Water Wave" by Mark D. Preston, Peter G. Chamberlain and Simon N. Chandler-Wilde

MPS_2009_15 "The flow induced dynamic surface tension effects at nanoscale" by A.V. Lukyanov

MPS_2009_16 "The elliptic sine-Gordon equation in a half plane" by B. Pelloni and D.A. Pinotsis

MPS_2009_17 "Variational Approach in Weighted Sobolev Spaces to Scattering by Unbounded Rough Surfaces" by Simon Chandler-Wilde and Johannes Elschner

### 2008

MPS_2008_01 " The No Response Test for the Reconstruction of Polyhedral Objects in Electromagnetics" by Roland Potthast and Mourad Sini

MPS_2008_02 " Existence of Solutions to the Neural Field Equation" by Roland Potthast and Peter beim Graben

MPS_2008_03 " Periodic solutions for nonlinear dilation equations" by Peter Grindrod

MPS_2008_04: " The PML for Rough Surface Scattering" by Simon N. Chandler-Wilde and P. Monk

MPS_2008_05: " Repulsion Exerted on a Spherical Particle by a Polymer Brush" by Jaeup U. Kim and Mark W. Matsen

MPS_2008_06: " High frequency scattering by convex curvilinear polygons" by S. Langdon, M. Mokgolele and S. N. Chandler-Wilde

MPS_2008_07: " Individual Based Model With Competition in Spatial Ecology" by Dmitri Finkelshtein, Yuri Kondratiev and Oleksandr Kutoviy

MPS_2008_08: " On convergence of dynamics of hopping particles to a birth-and-death process in continuum" by Dmitri Finkelshtein, Yuri Kondratiev and Eugene Lytvynov

MPS_2008_09: " Boundary integral methods in high frequency scattering" by Simon N. Chandler-Wilde and Ivan G. Graham

MPS_2008_10: " Algorithms for magnetic tomography - on the role of a priori knowledge and constraints" by Karl-Heinz Hauer, Roland Potthast and Martin Wannert,

MPS_2008_11: " Particle Distributions in a Block Copolymer Nanocomposite" by M. W. Matsen and R. B. Thompson

MPS_2008_12: " Limit Operators, Collective Compactness, and the Spectral Theory of Infinite Matrices" by Simon N. Chandler-Wilde and Marko Lindner

MPS_2008_13: " Phase Transitions and Quantum Stabilization in Quantum Anharmonic Crystals" by Alina Kargol, Yuri Kondratiev and Yuri Kozitsky

MPS_2008_14: " Language Processing with Dynamic Fields" by Peter beim Graben, Dimitris Pinotsis, Douglas Saddy and Roland Potthast

MPS_2008_15: " Condition Number Estimates for Combined Potential Boundary Integral Operators in Acoustic Scattering" by Simon Chandler-Wilde, Ivan G. Graham, Stephen Langdon and Marko Lindner