Outputs (159)

Stationary waves on nonlinear quantum graphs. II. Application of canonical perturbation theory in basic graph structures (2016)
Journal Article
Gnutzmann, S., & Waltner, D. (in press). Stationary waves on nonlinear quantum graphs. II. Application of canonical perturbation theory in basic graph structures. Physical Review E, 94(6), Article 062216. https://doi.org/10.1103/PhysRevE.94.062216

We consider exact and asymptotic solutions of the stationary cubic nonlinear Schrödinger equation on metric graphs. We focus on some basic example graphs. The asymptotic solutions are obtained using the canonical perturbation formalism developed in o... Read More about Stationary waves on nonlinear quantum graphs. II. Application of canonical perturbation theory in basic graph structures.

Adaptivity and Blow-Up Detection for Nonlinear Evolution Problems (2016)
Journal Article
Cangiani, A., Georgoulis, E. H., Kyza, I., & Metcalfe, S. (2016). Adaptivity and Blow-Up Detection for Nonlinear Evolution Problems. SIAM Journal on Scientific Computing, 38(6), A3833-A3856. https://doi.org/10.1137/16m106073x

This work is concerned with the development of a space-time adaptive numerical method, based on a rigorous a posteriori error bound, for a semilinear convection-diffusion problem which may exhibit blow-up in finite time. More specifically, a posterio... Read More about Adaptivity and Blow-Up Detection for Nonlinear Evolution Problems.

A geometric approach to visualization of variability in functional data (2016)
Journal Article
Xie, W., Kurtek, S., Bharath, K., & Sun, Y. (in press). A geometric approach to visualization of variability in functional data. Journal of the American Statistical Association, 112(519), https://doi.org/10.1080/01621459.2016.1256813

We propose a new method for the construction and visualization of boxplot-type displays for functional data. We use a recent functional data analysis framework, based on a representation of functions called square-root slope functions, to decompose o... Read More about A geometric approach to visualization of variability in functional data.

Event series prediction via non-homogeneous Poisson process modelling (2016)
Presentation / Conference Contribution
Goulding, J., Preston, S. P., & Smith, G. (2016, December). Event series prediction via non-homogeneous Poisson process modelling. Presented at 2016 IEEE International Conference on Data Mining (ICDM), Barcelona, Spain

Data streams whose events occur at random arrival times rather than at the regular, tick-tock intervals of traditional time series are increasingly prevalent. Event series are continuous, irregular and often highly sparse, differing greatly in nature... Read More about Event series prediction via non-homogeneous Poisson process modelling.

The deterministic Kermack‒McKendrick model bounds the general stochastic epidemic (2016)
Journal Article
Wilkinson, R. R., Ball, F. G., & Sharkey, K. J. (2016). The deterministic Kermack‒McKendrick model bounds the general stochastic epidemic. Journal of Applied Probability, 53(4), 1031-1040. https://doi.org/10.1017/jpr.2016.62

We prove that, for Poisson transmission and recovery processes, the classic Susceptible $\to$ Infected $\to$ Recovered (SIR) epidemic model of Kermack and McKendrick provides, for any given time $t>0$, a strict lower bound on the expected number of s... Read More about The deterministic Kermack‒McKendrick model bounds the general stochastic epidemic.

Modelling and Bayesian analysis of the Abakaliki smallpox data (2016)
Journal Article
Stockdale, J. E., Kypraios, T., & O’Neill, P. D. (2017). Modelling and Bayesian analysis of the Abakaliki smallpox data. Epidemics, 19, https://doi.org/10.1016/j.epidem.2016.11.005

The celebrated Abakaliki smallpox data have appeared numerous times in the epidemic modelling literature, but in almost all cases only a specific subset of the data is considered. The only previous analysis of the full data set relied on approximatio... Read More about Modelling and Bayesian analysis of the Abakaliki smallpox data.

Compensated convexity methods for approximations and interpolations of sampled functions in Euclidean spaces: theoretical foundations (2016)
Journal Article
Zhang, K., Crooks, E., & Orlando, A. (in press). Compensated convexity methods for approximations and interpolations of sampled functions in Euclidean spaces: theoretical foundations. SIAM Journal on Mathematical Analysis, 48(6), https://doi.org/10.1137/15M1045673

We introduce Lipschitz continuous and C¹,¹ geometric approximation and interpolation methods for sampled bounded uniformly continuous functions over compact sets and over complements of bounded open sets in Rn by using compensated convex transforms.... Read More about Compensated convexity methods for approximations and interpolations of sampled functions in Euclidean spaces: theoretical foundations.

Differential cohomology and locally covariant quantum field theory (2016)
Journal Article
Becker, C., Schenkel, A., & Szabo, R. J. (2017). Differential cohomology and locally covariant quantum field theory. Reviews in Mathematical Physics, 29(1), Article 1750003. https://doi.org/10.1142/S0129055X17500039

We study differential cohomology on categories of globally hyperbolic Lorentzian manifolds. The Lorentzian metric allows us to define a natural transformation whose kernel generalizes Maxwell's equations and fits into a restriction of the fundamental... Read More about Differential cohomology and locally covariant quantum field theory.

Geometrical structure of two-dimensional crystals with non-constant dislocation density (2016)
Journal Article
Parry, G. P., & Zyskin, M. (in press). Geometrical structure of two-dimensional crystals with non-constant dislocation density. Journal of Elasticity, 127(2), https://doi.org/10.1007/s10659-016-9612-3

We outline mathematical methods which seem to be necessary in order to discuss crystal structures with non-constant dislocation density tensor(ddt) in some generality. It is known that, if the ddt is constant (in space), then material points can be i... Read More about Geometrical structure of two-dimensional crystals with non-constant dislocation density.

The nonconforming virtual element method for the stokes equations (2016)
Journal Article
Cangiani, A., Gyrya, V., & Manzini, G. (2016). The nonconforming virtual element method for the stokes equations. SIAM Journal on Numerical Analysis, 54(6), 3411-3435. https://doi.org/10.1137/15M1049531

© 2016 Society for Industrial and Applied Mathematics. We present the nonconforming virtual element method (VEM) for the numerical approximation of velocity and pressure in the steady Stokes problem. The pressure is approximated using discontinuous p... Read More about The nonconforming virtual element method for the stokes equations.