Interannual climate variability seen in the Pliocene Model Intercomparison Project

Following reconstructions suggesting weakened temperature gradients along the Equator in the early Pliocene, there has been much speculation about Pliocene climate variability. A major advance for our knowledge about the later Pliocene has been the coordination of modelling efforts through the Pliocene Model Intercomparison Project (PlioMIP). Here the changes in interannual modes of sea surface temperature variability will be presented across PlioMIP. Previously, model ensembles have shown little consensus in the response of the El Niño–Southern Oscillation (ENSO) to imposed forcings – either for the past or future. The PlioMIP ensemble, however, shows surprising agreement, with eight models simulating reduced variability and only one model indicating no change. The Pliocene's robustly weaker ENSO also saw a shift to lower frequencies. Model ensembles focussed on a wide variety of forcing scenarios have not yet shown this level of coherency. Nonetheless, the PlioMIP ensemble does not show a robust response of either ENSO flavour or sea surface temperature variability in the tropical Indian and North Pacific oceans. Existing suggestions linking ENSO properties to to changes in zonal temperature gradient, seasonal cycle and the elevation of the Andes Mountains are investigated, yet prove insufficient to explain the consistent response. The reason for this surprisingly coherent signal warrants further investigation

Mutually Unbiased Bases and Semi-definite Programming

A complex Hilbert space of dimension six supports at least three but not more than seven mutually unbiased bases. Two computer-aided analytical methods to tighten these bounds are reviewed, based on a discretization of parameter space and on Grobner bases. A third algorithmic approach is presented: the non-existence of more than three mutually unbiased bases in composite dimensions can be decided by a global optimization method known as semidefinite programming. The method is used to confirm that the spectral matrix cannot be part of a complete set of seven mutually unbiased bases in dimension six.Comment: 11 pages

On properties of Karlsson Hadamards and sets of Mutually Unbiased Bases in dimension six

The complete classification of all 6x6 complex Hadamard matrices is an open problem. The 3-parameter Karlsson family encapsulates all Hadamards that have been parametrised explicitly. We prove that such matrices satisfy a non-trivial constraint conjectured to hold for (almost) all 6x6 Hadamard matrices. Our result imposes additional conditions in the linear programming approach to the mutually unbiased bases problem recently proposed by Matolcsi et al. Unfortunately running the linear programs we were unable to conclude that a complete set of mutually unbiased bases cannot be constructed from Karlsson Hadamards alone.Comment: As published versio