title: On the chromatic index of Latin squares

authors: Cavenagh, Nicholas J.

abstract: A proper coloring of a Latin square of order n is an assignment of colors to its elements triples such that each row, column and symbol is assigned n distinct colors. Equivalently, a proper coloring of a Latin square is a partition into partial transversals. The chromatic index of a Latin square is the least number of colors needed for a proper coloring. We study the chromatic index of the cyclic Latin square which arises from the addition table for the integers modulo n. We obtain the best possible bounds except for the case when n=2 is odd and divisible by 3. We make some conjectures about the chromatic index, suggesting a generalization of Ryser's conjecture (that every Latin square of odd order contains a transversal).

text: On the chromatic index of Latin squares A proper coloring of a Latin square of order n is an assignment of colors to its elements triples such that each row, column and symbol is assigned n distinct colors. Equivalently, a proper coloring of a Latin square is a partition into partial transversals. The chromatic index of a Latin square is the least number of colors needed for a proper coloring. We study the chromatic index of the cyclic Latin square which arises from the addition table for the integers modulo n. We obtain the best possible bounds except for the case when n=2 is odd and divisible by 3. We make some conjectures about the chromatic index, suggesting a generalization of Ryser's conjecture (that every Latin square of odd order contains a transversal).

year: 2015

title: Resolving Multiple Propagation Paths in Time of Flight Range Cameras using Direct and Global Separation Methods

authors: Whyte, Refael

subjects: time of flight imaging

abstract: Time of flight (ToF) range cameras illuminate the scene with an amplitude-modulated continuous wave light source and measure the returning modulation envelopes: phase and amplitude. The phase change of the modulation envelope encodes the distance travelled. This technology suffers from measurement errors caused by multiple propagation paths from the light source to the receiving pixel. The multiple paths can be represented as the summation of a direct return, which is the return from the shortest path length, and a global return, which includes all other returns. We develop the use of a sinusoidal pattern from which a closed form solution for the direct and global returns can be computed in nine frames with the constraint that the global return is a spatially lower frequency than the illuminated pattern. In a demonstration on a scene constructed to have strong multipath interference, we find the direct return is not significantly different from the ground truth in 33∕136 pixels tested; where for the full-field measurement, it is significantly different for every pixel tested. The variance in the estimated direct phase and amplitude increases by a factor of eight compared with the standard time of flight range camera technique.

text: Resolving Multiple Propagation Paths in Time of Flight Range Cameras using Direct and Global Separation Methods Time of flight (ToF) range cameras illuminate the scene with an amplitude-modulated continuous wave light source and measure the returning modulation envelopes: phase and amplitude. The phase change of the modulation envelope encodes the distance travelled. This technology suffers from measurement errors caused by multiple propagation paths from the light source to the receiving pixel. The multiple paths can be represented as the summation of a direct return, which is the return from the shortest path length, and a global return, which includes all other returns. We develop the use of a sinusoidal pattern from which a closed form solution for the direct and global returns can be computed in nine frames with the constraint that the global return is a spatially lower frequency than the illuminated pattern. In a demonstration on a scene constructed to have strong multipath interference, we find the direct return is not significantly different from the ground truth in 33∕136 pixels tested; where for the full-field measurement, it is significantly different for every pixel tested. The variance in the estimated direct phase and amplitude increases by a factor of eight compared with the standard time of flight range camera technique.

year: 2015

title: An analysis of the rhetorical organisation of selected authentic Maori texts belonging to the text-types argument and information report

authors: Houia-Roberts, Ngaere

subjects: Te reo Māori

abstract: I report here on the findings of an analysis of the overall rhetorical structure of authentic Māori texts belonging to two different text-types – argument and information report – which were written by highly competent users of the language. I also suggest ways in which this type of analysis could underpin the development of teaching resources designed for Māori-medium educational settings.

text: An analysis of the rhetorical organisation of selected authentic Maori texts belonging to the text-types argument and information report I report here on the findings of an analysis of the overall rhetorical structure of authentic Māori texts belonging to two different text-types – argument and information report – which were written by highly competent users of the language. I also suggest ways in which this type of analysis could underpin the development of teaching resources designed for Māori-medium educational settings.

year: 2004