Geometric Integration of ODEs Using Multiple Quadratic Auxiliary Variables

Geometric integration of conservative polynomial ODEs ✩

We consider systems whose Hamiltonian is of the form H(q,p) = 2p + V (q), where the potential V is either cubic or quartic with no cubic terms. For most of these systems (in the measure sense) we give an explicit numerical integration method that preserves both phase space volume and the value of the Hamiltonian. This is exemplified in the Hénon–Heiles system. An application is to the hybrid Mo...

Exterior algebra, ODEs and geometric integration References

References [1] A. Adrover, S. Cerbelli & M. Giona. Exterior algebra-based algorithms to estimate Liapunov spectra and stretching statistics in high-dimensional and distributed systems, Int. [4] L. Allen & T.J. Bridges. Flow past a swept wing with a compliant surface: stabilizing the attachment line boundary layer, Stud. Hydrodynamic stability of the Ekman boundary layer including interaction wi...

Survival analysis using auxiliary variables via non-parametric multiple imputation.

We develop an approach, based on multiple imputation, that estimates the marginal survival distribution in survival analysis using auxiliary variables to recover information for censored observations. To conduct the imputation, we use two working survival models to define a nearest neighbour imputing risk set. One model is for the event times and the other for the censoring times. Based on the ...

Membrane geometry with auxiliary variables and quadratic constraints

Consider a surface described by a Hamiltonian which depends only on the metric and extrinsic curvature induced on the surface. The metric and the curvature, along with the basis vectors which connect them to the embedding functions defining the surface, are introduced as auxiliary variables by adding appropriate constraints, all of them quadratic. The response of the Hamiltonian to a deformatio...

Exact Sampling Using Auxiliary Variables