The goal of this work is to develop a portable and accurate colorblind test that has advantages over the HRR and Ishihara plate tests, including that it is easier and faster to perform, does not require the subject to identify alphanumeric characters or geometric shapes, provides unambiguous results to the provider without interpretation, and is at least 8 times faster. The advantage over prior anomaloscopes is that it can be made in a hand-held version, uses binary matching choices rather than having the subject match colors with a tuning knob, and uses optimal reference color choices determined from established knowledge of human color perception. To successfully achieve this, cone spectral sensitivity curves and all subsets of four LEDs from a set of eight spanning the visible spectrum, the 1x4 metamer solution for a reference color for normal vision, deuteranomaly, and protanomaly are calculated. From these solutions, the optimized set of 4 LEDS was determined by maximizing the average angle between the normal, deuteranomaly, and protanomaly metamer solution vectors in the XYZ color space. To perform the test, the subject is asked to determine the best match for color and brightness in side-by-side display panels illuminated with distinctly different reference metamer color pairs for normal, deuteranomaly, and protanomaly vision. This allows the operator to directly and unambiguously determine the subject’s color vision type. The average duration to perform the tests are 30, 253, and 281 seconds for the anomaloscope, Ishihara 38 plate test, and HRR 24 plate test, respectively. When determining whether the subject has normal vision or is colorblind, the anomaloscope and HRR test results agreed for all 102 subjects. Because this rendition of the anomaloscope was designed to only distinguish between normal, deuteranomalous, and protanomalous vision, the 7 subjects that the HRR determined to be tritanomalous were not included in the results presented hereafter. The HRR 24 plate test and the anomaloscope agreed in their diagnosis 91/95 = 96% of the time, the Ishihara 38 plate test and the anomaloscope agreed in their diagnosis 94/101 = 93% of the time, and the HRR and the Ishihara agreed in their diagnosis 89/95 = 94% of the time. The approach described here can be extended to other types of color blindness.

Axion stars are hypothetical objects formed of axions, obtained as localized and coherently oscillating solutions to their classical equation of motion. Depending on the value of the field amplitude at the core |θ₀| ≡ |θ(r = 0)|, the equilibrium of the system arises from the balance of the kinetic pressure and either self-gravity or axion self-interactions. Starting from a general relativistic framework, we obtain the set of equations describing the configuration of the axion star, which we solve as a function of |θ₀|. For small |θ₀| [< over ~] 1, we reproduce results previously obtained in the literature, and we provide arguments for the stability of such configurations in terms of first principles. We compare qualitative analytical results with a numerical calculation. For large amplitudes |θ₀| [> over ~] 1, the axion field probes the full non-harmonic QCD chiral potential and the axion star enters the dense branch. Our numerical solutions show that in this latter regime the axions are relativistic, and that one should not use a single frequency approximation, as previously applied in the literature. We employ a multi-harmonic expansion to solve the relativistic equation for the axion field in the star, and demonstrate that higher modes cannot be neglected in the dense regime. We interpret the solutions in the dense regime as pseudo-breathers, and show that the life-time of such configurations is much smaller than any cosmological time scale.

It is commonly anticipated that gravity is subjected to the standard principles of quantum mechanics. Yet some — including Einstein — have questioned that presumption, whose empirical basis is weak. Indeed, recently Dyson has emphasized that no conventional experiment is capable of detecting individual gravitons. However, as we describe, if inflation occurred, the universe, by acting as an ideal graviton amplifier, affords such access. It produces a classical signal, in the form of macroscopic gravitational waves, in response to spontaneous (not induced) emission of gravitons. Thus recent BICEP2 observations of polarization in the cosmic microwave background (CMB) will, if confirmed, provide firm empirical evidence for the quantization of gravity. Their details also support quantitative ideas concerning the unification of strong, electromagnetic and weak forces, and of all these with gravity.