The chromaticity of wheels with a missing spoke II

AbstractIn the previous paper, it was shown that the graph Un + 1 obtained from the wheel Wn + 1 by deleting a spoke is uniquely determined by its chromatic polynomial if n ⩾ 3 is odd. In this paper, we show that the result is also true for even n ⩾ 4 except when n = 6 in which case, the graph W given in the paper is the only graph having the same chromatic polynomial as that of U7. The relevant tool is the notion of nearly uniquely colorable graph

Telescope to Observe Planetary Systems (TOPS): a high throughput 1.2-m visible telescope with a small inner working angle

The Telescope to Observe Planetary Systems (TOPS) is a proposed space mission to image in the visible (0.4-0.9 micron) planetary systems of nearby stars simultaneously in 16 spectral bands (resolution R~20). For the ~10 most favorable stars, it will have the sensitivity to discover 2 R_E rocky planets within habitable zones and characterize their surfaces or atmospheres through spectrophotometry. Many more massive planets and debris discs will be imaged and characterized for the first time. With a 1.2m visible telescope, the proposed mission achieves its power by exploiting the most efficient and robust coronagraphic and wavefront control techniques. The Phase-Induced Amplitude Apodization (PIAA) coronagraph used by TOPS allows planet detection at 2 lambda/d with nearly 100% throughput and preserves the telescope angular resolution. An efficient focal plane wavefront sensing scheme accurately measures wavefront aberrations which are fed back to the telescope active primary mirror. Fine wavefront control is also performed independently in each of 4 spectral channels, resulting in a system that is robust to wavefront chromaticity.Comment: 12 pages, SPIE conference proceeding, May 2006, Orlando, Florid

Beta Invariant and Chromatic Uniqueness of Wheels

A graph G is chromatically unique if its chromatic polynomial completely determines the graph. An n-spoked wheel, Wn, is shown to be chromatically unique when n ≥ 4 is even [S.-J. Xu and N.-Z. Li, The chromaticity of wheels, Discrete Math. 51 (1984) 207–212]. When n is odd, this problem is still open for n ≥ 15 since 1984, although it was shown by di erent researchers that the answer is no for n = 5, 7, yes for n = 3, 9, 11, 13, and unknown for other odd n. We use the beta invariant of matroids to prove that if M is a 3-connected matroid such that |E(M)| = |E(Wn)| and β (M) = β (M(Wn)), where β (M) is the beta invariant of M, then M ≅ M(Wn). As a consequence, if G is a 3-connected graph such that the chromatic (or flow) polynomial of G equals to the chromatic (or flow) polynomial of a wheel, then G is isomorphic to the wheel. The examples for n = 3, 5 show that the 3-connectedness condition may not be dropped. We also give a splitting formula for computing the beta invariants of general parallel connection of two matroids as well as the 3-sum of two binary matroids. This generalizes the corresponding result of Brylawski [A combinatorial model for series-parallel networks, Trans. Amer. Math. Soc. 154 (1971) 1–22]

Visual assessment of object color chroma and colorfulness

A series of visual experiments were designed to determine whether naive observers typically evaluate chroma or colorfulness when judging color appearance. A total of 7 observers were asked to determine a color appearance match between Munsell samples under the same illuminant (C) at different levels of illuminance. Color appearance matches were determined for 12 Munsell samples, under five reference and matching scene illuminance conditions, for four experimental techniques. The four experimental techniques were haploscopic, simultaneous inspection, successive inspection, and short-term memory matching. Results suggested that a chroma match was most important when observers were evaluating the color appearance of two scenes at different levels of illuminance. Results were also compared to predictions of two color appearance models. While similar trends were apparent between the experimental results and the two model\u27s predictions, only the Hunt model\u27s chroma term satisfactorily predicted experimental observations

Demonstrating a multi-primary high dynamic range display system for vision experiments.

We describe the design, construction, calibration, and characterization of a multi-primary high dynamic range (MPHDR) display system for use in vision research. The MPHDR display is the first system to our knowledge to allowfor spatially controllable, high dynamic range stimulus generation using multiple primaries.We demonstrate the high luminance, high dynamic range, and wide color gamut output of the MPHDR display. During characterization, the MPHDR display achieved a maximum luminance of 3200 cd=m2, a maximum contrast range of 3; 240; 000 V 1, and an expanded color gamut tailored to dedicated vision research tasks that spans beyond traditional sRGB displays. We discuss how the MPHDR display could be optimized for psychophysical experiments with photoreceptor isolating stimuli achieved through the method of silent substitution. We present an example case of a range of metameric pairs of melanopsin isolating stimuli across different luminance levels, from an available melanopsin contrast of117%at 75 cd=m2 to a melanopsin contrast of23%at 2000 cd=m2

APPARATUSES, SYSTEMS, AND METHODS FOR CALIBRATING DISPLAYS

A display calibration system may include (i) a spectrometry device positioned to capture light emitted by a group of sub-pixels in a sub-region of a display that is both (a) located within a light-emitting region of the display and (b) is smaller than the light-emitting region, (ii) at least one camera device positioned to capture light emitted by a plurality of sub-pixels, in the light-emitting region of the display, that includes the group of sub-pixels, and (iii) a calibration computing device that is (a) communicatively coupled to both the spectrometry device and the at least one camera device and that (b) generates calibration data for driving the plurality of sub-pixels in the light-emitting region of the display based on information received from the spectrometry device and the at least one camera device. Corresponding calibration apparatuses and methods are also disclosed