Equiangular tight frames and fourth root seidel matrices

AbstractIn this paper we construct complex equiangular tight frames (ETFs). In particular, we study the grammian associated with an ETF whose off-diagonal entries consist entirely of fourth roots of unity. These ETFs are classified, and we also provide some computational techniques which give rise to previously undiscovered ETFs

Deep sea tests of a prototype of the KM3NeT digital optical module

The first prototype of a photo-detection unit of the future KM3NeT neutrino telescope has been deployed in the deepwaters of the Mediterranean Sea. This digital optical module has a novel design with a very large photocathode area segmented by the use of 31 three inch photomultiplier tubes. It has been integrated in the ANTARES detector for in-situ testing and validation. This paper reports on the first months of data taking and rate measurements. The analysis results highlight the capabilities of the new module design in terms of background suppression and signal recognition. The directionality of the optical module enables the recognition of multiple Cherenkov photons from the same (40)Kdecay and the localisation of bioluminescent activity in the neighbourhood. The single unit can cleanly identify atmospheric muons and provide sensitivity to the muon arrival directions

Complex equiangular tight frames and erasures

AbstractIn this paper we demonstrate that there are distinct differences between real and complex equiangular tight frames (ETFs) with regards to erasures. For example, we prove that there exist arbitrarily large non-trivial complex equiangular tight frames which are optimal against three erasures, and that such frames come from a unique class of complex ETFs. In addition, we extend certain results in Bodmann and Paulsen (2005) [2] to complex vector spaces as well as show that other results regarding real ETFs are not valid for complex ETFs