Magic numbers in the discrete tomography of cyclotomic model sets

We report recent progress in the problem of distinguishing convex subsets of cyclotomic model sets $\varLambda$ by (discrete parallel) X-rays in prescribed $\varLambda$-directions. It turns out that for any of these model sets $\varLambda$ there exists a `magic number' $m_{\varLambda}$ such that any two convex subsets of $\varLambda$ can be distinguished by their X-rays in any set of $m_{\varLambda}$ prescribed $\varLambda$-directions. In particular, for pentagonal, octagonal, decagonal and dodecagonal model sets, the least possible numbers are in that very order 11, 9, 11 and 13.Comment: 6 pages, 1 figure; based on the results of arXiv:1101.4149 [math.MG]; presented at Aperiodic 2012 (Cairns, Australia

Discrete Tomography of Penrose Model Sets

Various theoretical and algorithmic aspects of inverse problems in discrete tomography of planar Penrose model sets are discussed. These are motivated by the demand of materials science for the reconstruction of quasicrystalline structures from a small number of images produced by quantitative high resolution transmission electron microscopy.Comment: 7 pages, 1 figure; paper presented at Aperiodic 2006 (Zao, Japan

Handbook for Computerized Reliability Analysis Method /CRAM/

Method for analyzing reliability by use of computer

Performance and evaluation of the Viking lander camera performance prediction program

A computer program is described for predicting the performance of the Viking lander cameras. The predictions are primarily concerned with two objectives: (1) the picture quality of a reference test chart (of which there are three on each lander) to aid in diagnosing camera performance; and (2) the picture quality of cones with surface properties of a natural terrain to aid in predicting favorable illumination and viewing geometries and operational camera commands. Predictions made with this program are verified by experimental data obtained with a Viking-like laboratory facsimile camera

An analysis of the facsimile-camera response to radiant point sources

In addition to imaging the surrounding terrain, planetary lander cameras may also be used to survey the stars to aid in locating the lander site. The response of the facsimile camera, which was selected for the Viking lander missions to Mars, to a radiant point source is formulated and shown to result in a statistical rather than deterministic signal. The signal statistics are derived and magnitudes are evaluated for the brighter visual and red stars. The probability of detecting the resultant statistical signals in photosensor and preamplifier noise and the associated probability of false alarms are also determined