Natural Metric for Quantum Information Theory

We study in detail a very natural metric for quantum states. This new proposal has two basic ingredients: entropy and purification. The metric for two mixed states is defined as the square root of the entropy of the average of representative purifications of those states. Some basic properties are analyzed and its relation with other distances is investigated. As an illustrative application, the proposed metric is evaluated for 1-qubit mixed states.Comment: v2: enlarged; presented at ISIT 2008 (Toronto

Multirate timestepping methods for hyperbolic conservation laws

This paper constructs multirate time discretizations for hyperbolic conservation laws that allow different time-steps to be used in different parts of the spatial domain. The discretization is second order accurate in time and preserves the conservation and stability properties under local CFL conditions. Multirate timestepping avoids the necessity to take small global time-steps (restricted by the largest value of the Courant number on the grid) and therefore results in more efficient algorithms

On Extrapolated Multirate Methods

In this manuscript we construct extrapolated multirate discretization methods that allow to efficiently solve problems that have components with different dynamics. This approach is suited for the time integration of multiscale ordinary and partial differential equations and provides highly accurate discretizations. We analyze the linear stability properties of the multirate explicit and linearly implicit extrapolated methods. Numerical results with multiscale ODEs illustrate the theoretical findings

Achieving Very High Order for Implicit Explicit Time Stepping: Extrapolation Methods

In this paper we construct extrapolated implicit-explicit time stepping methods that allow to efficiently solve problems with both stiff and non-stiff components. The proposed methods can provide very high order discretizations of ODEs, index-1 DAEs, and PDEs in the method of lines framework. These methods are simple to construct, easy to implement and parallelize. We establish the existence of perturbed asymptotic expansions of global errors, explain the convergence orders of these methods, and explore their linear stability properties. Numerical results with stiff ODEs, DAEs, and PDEs illustrate the theoretical findings and the potential of these methods to solve multiphysics multiscale problems

The effect of population variation on the accuracy of sex estimates derived from basal occipital discriminant functions

Multiple discriminant functions that estimate sex from the dimensions of the basal occipital have been published. However, as there is limited exploration of basal dimension variation between groups, the accuracy of these functions when applied to archaeological material is unknown. This study compares basal dimensions between four known sex-at-death post-medieval European samples and explores how metric differences impact on the accuracy of sex assessment discriminant functions. Published data from St Bride’s, London (n = 146) and the Georges Olivier collection, Paris (n = 68) were compared with new data from the eighteenth to nineteenth century Dutch Middenbeemster sample (n = 74) and the early twentieth century Rainer sample, Romania (n = 282) using independent t tests. The Middenbeemster and Rainer data were substituted into six published discriminant functions derived from the St Bride’s and the Georges Olivier samples, and the results were compared to their known sex. Multiple statistically significant differences were found between the four groups. Of the six discriminant functions tested, five failed to reach the published accuracy and fell below chance. In addition, even where the samples were statistically comparable in means, trends for difference also impacted the accuracy of discriminant functions. Enough variation in basal occipital dimensions existed in the European groups to decrease the accuracy of sex estimation discriminant functions to unusable. Possible inter-observer error, varying genetic, socioeconomic, and geographical factors are likely causes of dimension variation. This research further highlights the dangers of using sex estimation discriminant functions on samples that differ to the original derivative population and demonstrates the need for more rigorous testing