On a question of Beidleman and Robinson

In (1, Theorem A), Beidleman and Robinson proved that if a group satisfies the permutizer condition, it is soluble, its chief factors have order a prime number or 4 and G induces the full group of automorphisms in the chief factors of order 4. In this paper, we show that the converse of this theorem is false by showing some counterexamples. We also find some sufficient conditions for a group satisfying the converse of that theorem to satisfy the permutizer condition

MultiSciView: Multivariate Scientific X-ray Image Visual Exploration with Cross-Data Space Views

X-ray images obtained from synchrotron beamlines are large-scale, high-resolution and high-dynamic-range grayscale data encoding multiple complex properties of the measured materials. They are typically associated with a variety of metadata which increases their inherent complexity. There is a wealth of information embedded in these data but so far scientists lack modern exploration tools to unlock these hidden treasures. To bridge this gap, we propose MultiSciView, a multivariate scientific x-ray image visualization and exploration system for beamline-generated x-ray scattering data. Our system is composed of three complementary and coordinated interactive visualizations to enable a coordinated exploration across the images and their associated attribute and feature spaces. The first visualization features a multi-level scatterplot visualization dedicated for image exploration in attribute, image, and pixel scales. The second visualization is a histogram-based attribute cross filter by which users can extract desired subset patterns from data. The third one is an attribute projection visualization designed for capturing global attribute correlations. We demonstrate our framework by ways of a case study involving a real-world material scattering dataset. We show that our system can efficiently explore large-scale x-ray images, accurately identify preferred image patterns, anomalous images and erroneous experimental settings, and effectively advance the comprehension of material nanostructure properties. Keywords: Scientific x-ray image visualization, Multi-level scatterplot, Cross-data space exploratio