We derive a set of symmetry relations for the three-neutrino mixing angles, including the MSW matter effect. Though interesting in their own right, these relations are used to choose the physical region of the mixing angles such that oscillations are parameterized completely and uniquely. We propose that the preferred way of setting the bounds on the mixing angles should be $\theta_{12} \in [0,\pi/2]$, $\theta_{13} \in [-\pi/2,\pi/2]$, $\theta_{23}\in [0,\pi/2]$, and $\delta \in [0,\pi)$. No CP violation then results simply from setting $\delta=0$. In the presence of the MSW effect, this choice of bounds is a new result. Since the size of the asymmetry about $\theta_{13} = 0$ is dependent on the details of the data analysis and is a part of the results of the analysis, we argue that the negative values of $\theta_{13}$ should not be ignored.Comment: 4 page

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Searches for dispersive effects in the propagation of light at cosmological distances have been touted as sensitive probes of Lorentz invariance violation (LIV) and of theories of quantum gravity. Frequencydependent time lags between simultaneously emitted pulses of light can signal a modification in the photon dispersion relation; however, matter engenders the cosmos with a dispersive index of refraction to similar effect. We construct a theoretical framework for the analysis of such effects, contrasting these dispersive terms with those from LIV models. We consider all matter, both luminous and dark. Though the only known mode of interaction for dark matter (DM) is gravitational, most models of dark matter also allow for electromagnetic interactions, if only at the one-loop level in perturbation theory. Generically, the leading order dispersive effects due to matter scale with photon energy as ! À2 for a charged DM candidate and ! 2 for a neutral DM candidate. Terms linear in ! can arise in the index of refraction if parity and charge-parity asymmetries are present at the Lagrangian or system level. Herein, we compute the index of refraction for a millicharged dark matter candidate at the one-loop level, a neutral scalar DM candidate introduced by Boehm and Fayet [Nucl. Phys. B 683, 219 (2004)], and the minimal supersymmetric standard model's neutralino. For a neutral DM candidate, we determine that matter effects can compete with LIV effects that depend quadratically on energy whenever the photon energy is beyond 10 29 GeV, well beyond the Greisen-Zatsepin-Kuzmin cutoff. The dispersive matter effects that scale linearly with ! are model dependent, and their existence results in circular birefringence.

Age-related decreases in the conduction velocity (CV) of action potentials along myelinated axons have been linked to morphological changes in the myelin sheath. In particular, evidence suggests the presence of segmental demyelination and remyelination of axons. In remyelinated segments, the distance between adjacent nodes of Ranvier is typically shorter, and myelin sheaths are thinner. Both experimental and computational evidence indicates that shortened internodes slows CV. In this computational study, we determine the impact of progressive segmental demyelination and remyelination, modeled by shorter internodes with thinner myelin sheaths interspersed with normal ones, upon the CV. We find that CV progressively decreases as the number of remyelinated segments increases, but this decrease is greater than one would expect from an estimate of the CV based merely upon the number of short and long internodes. We trace the additional suppression of the CV to transitions between long and short internodes. Our study presents an important consideration for the precise modeling of neural circuits with remyelinated neurons.