616,057 research outputs found
Applications of finite geometry in coding theory and cryptography
We present in this article the basic properties of projective geometry, coding theory, and cryptography, and show how
finite geometry can contribute to coding theory and cryptography. In this way, we show links between three research areas, and in particular, show that finite geometry is not only interesting from a pure mathematical point of view, but also of interest for applications. We concentrate on introducing the basic concepts of these three research areas and give standard references for all these three research areas. We also mention particular results involving ideas from finite geometry, and particular results in cryptography involving ideas from coding theory
Extension of information geometry for modelling non-statistical systems
In this dissertation, an abstract formalism extending information geometry is
introduced. This framework encompasses a broad range of modelling problems,
including possible applications in machine learning and in the information
theoretical foundations of quantum theory. Its purely geometrical foundations
make no use of probability theory and very little assumptions about the data or
the models are made. Starting only from a divergence function, a Riemannian
geometrical structure consisting of a metric tensor and an affine connection is
constructed and its properties are investigated. Also the relation to
information geometry and in particular the geometry of exponential families of
probability distributions is elucidated. It turns out this geometrical
framework offers a straightforward way to determine whether or not a
parametrised family of distributions can be written in exponential form. Apart
from the main theoretical chapter, the dissertation also contains a chapter of
examples illustrating the application of the formalism and its geometric
properties, a brief introduction to differential geometry and a historical
overview of the development of information geometry.Comment: PhD thesis, University of Antwerp, Advisors: Prof. dr. Jan Naudts and
Prof. dr. Jacques Tempere, December 2014, 108 page
Large bandwidth, highly efficient optical gratings through high index materials
We analyze the diffraction characteristics of dielectric gratings that
feature a high index grating layer, and devise, through rigorous numerical
calculations, large bandwidth, highly efficient, high dispersion dielectric
gratings in reflection, transmission, and immersed transmission geometry. A
dielectric TIR grating is suggested, whose -1dB spectral bandwidth is doubled
as compared to its all-glass equivalent. The short wavelength diffraction
efficiency is additionally improved by allowing for slanted lamella. The
grating surpasses a blazed gold grating over the full octave. An immersed
transmission grating is devised, whose -1dB bandwidth is tripled as compared to
its all-glass equivalent, and that surpasses an equivalent classical
transmission grating over nearly the full octave. A transmission grating in the
classical scattering geometry is suggested, that features a buried high index
layer. This grating provides effectively 100% diffraction efficiency at its
design wavelegth, and surpasses an equivalent fused silica grating over the
full octave.Comment: 15 pages, 7 figure
- …