The Opacity of the Intergalactic Medium Measured Along Quasar Sightlines at z∼6z\sim 6

We publicly release a new sample of $34$ medium resolution quasar spectra at $5.77\leq z_{\rm em}\leq6.54$ observed with the Echellette Spectrograph and Imager (ESI) on the Keck telescope. This quasar sample represents an ideal laboratory to study the intergalactic medium (IGM) during the end stages of the epoch of reionization, and constrain the timing and morphology of the phase transition. For a subset of $23$ of our highest signal-to-noise ratio spectra (S/N$>7$, per $10\,{\rm km\,s^{-1}}$ pixel), we present a new measurement of the Lyman-$\alpha$ (Ly$\alpha$) forest opacity spanning the redshift range $4.8\lesssim z\lesssim6.3$. We carefully eliminate spectral regions that could be causing biases in our measurements due to additional transmitted flux in the proximity zone of the quasars, or extra absorption caused by strong intervening absorption systems along the line of sight. We compare the observed evolution of the IGM opacity with redshift to predictions from a hydrodynamical simulation with uniform ultraviolet background (UVB) radiation, as well as two semi-numerical patchy reionization models, one with a fluctuating UVB and another with a fluctuating temperature field. Our measurements show a steep rise in opacity at $z\gtrsim5.0$ and an increased scatter and thus support the picture of a spatially inhomogeneous reionization process, consistent with previous work. However, we measure significantly higher optical depths at $5.3\lesssim z\lesssim5.7$ than previous studies, which reduces the contrast between the highest opacity Gunn-Peterson troughs and the average opacity trend of the IGM, which may relieve some of the previously noted tension between these measurements and reionization models.Comment: accepted for publication at Ap

A New Method to Measure the Post-Reionization Ionizing Background from the Joint Distribution of Lyman-α\alpha and Lyman-β\beta Forest Transmission

The amplitude of the ionizing background that pervades the intergalactic medium (IGM) at the end of the epoch of reionization provides a valuable constraint on the emissivity of the sources which reionized the Universe. While measurements of the ionizing background at lower redshifts rely on a simulation-calibrated mapping between the photoionization rate and the mean transmission of the Ly$\alpha$ forest, at $z\gtrsim6$ the IGM becomes increasingly opaque, and transmission arises solely in narrow spikes separated by saturated Gunn-Peterson troughs. In this regime, the traditional approach of measuring the average transmission over large $\sim 50$ Mpc$/h$ regions is less sensitive and sub-optimal. Additionally, the five times smaller oscillator strength of the Ly$\beta$ transition implies the Ly$\beta$ forest is considerably more transparent at $z\gtrsim6$, even in the presence of contamination by foreground $z\sim 5$ Ly$\alpha$ forest absorption. In this work we present a novel statistical approach to analyze the joint distribution of transmission spikes in the co-spatial $z\sim 6$ Ly$\alpha$ and Ly$\beta$ forests. Our method relies on Approximate Bayesian Computation (ABC), which circumvents the necessity of computing the intractable likelihood function describing the highly correlated Ly$\alpha$ and Ly$\beta$ transmission. We apply ABC to mock data generated from a large-volume hydrodynamical simulation combined with a state-of-the-art model of ionizing background fluctuations in the post-reionization IGM, and show that it is sensitive to higher IGM neutral hydrogen fractions than previous techniques. As a proof of concept, we apply this methodology to a real spectrum of a $z=6.54$ quasar and measure the ionizing background from $5.4\leq z \leq 6.4$ along this sightline with $\sim0.2$ dex statistical uncertainties.Comment: 15 pages, 18 figures, ApJ submitte

On the structure of the virtual Compton amplitude with additional final-state meson in the extended Bjorken region

Using the framework of the non-local light-cone expansion a systematic study is performed for the structure of the twist-2 contributions to the virtual Compton amplitude in polarized deep-inelastic non-forward scattering for general nucleon spin with an additional scalar meson in the final state. A useful kinematic parameterization allowing for appropriate triple-valued off-forward parton distribution amplitudes is given. One-variable amplitudes being adapted to the fixed parameters of the extended Bjorken region are introduced by decomposing the Compton amplitude into collinear and non-collinear components. These amplitudes obey Wandzura-Wilczek and Callan-Gross like relations. The evolution equations for all the distribution amplitudes are determined showing that the additional meson momentum does not appear in the evolution kernels. The generalization to $n$ outgoing mesons is given

Disordered Topological Insulators via C∗C^*-Algebras

The theory of almost commuting matrices can be used to quantify topological obstructions to the existence of localized Wannier functions with time-reversal symmetry in systems with time-reversal symmetry and strong spin-orbit coupling. We present a numerical procedure that calculates a Z_2 invariant using these techniques, and apply it to a model of HgTe. This numerical procedure allows us to access sizes significantly larger than procedures based on studying twisted boundary conditions. Our numerical results indicate the existence of a metallic phase in the presence of scattering between up and down spin components, while there is a sharp transition when the system decouples into two copies of the quantum Hall effect. In addition to the Z_2 invariant calculation in the case when up and down components are coupled, we also present a simple method of evaluating the integer invariant in the quantum Hall case where they are decoupled.Comment: Added detail regarding the mapping of almost commuting unitary matrices to almost commuting Hermitian matrices that form an approximate representation of the sphere. 6 pages, 6 figure

On a counterexample to a conjecture by Blackadar

Blackadar conjectured that if we have a split short-exact sequence 0 -> I -> A -> A/I -> 0 where I is semiprojective and A/I is isomorphic to the complex numbers, then A must be semiprojective. Eilers and Katsura have found a counterexample to this conjecture. Presumably Blackadar asked that the extension be split to make it more likely that semiprojectivity of I would imply semiprojectivity of A. But oddly enough, in all the counterexamples of Eilers and Katsura the quotient map from A to A/I is split. We will show how to modify their examples to find a non-semiprojective C*-algebra B with a semiprojective ideal J such that B/J is the complex numbers and the quotient map does not split.Comment: 6 page

Restricted diffusion of calretinin in cerebellar granule cell dendrites implies Ca²⁺-dependent interactions via its EF-hand 5 domain

Ca²⁺-binding proteins (CaBPs) are important regulators of neuronal Ca²⁺ signaling, acting either as buffers that shape Ca²⁺ transients and Ca²⁺ diffusion and/or as Ca²⁺ sensors. The diffusional mobility represents a crucial functional parameter of CaBPs, describing their range-of-action and possible interactions with binding partners. Calretinin (CR) is a CaBP widely expressed in the nervous system with strong expression in cerebellar granule cells. It is involved in regulating excitability and synaptic transmission of granule cells, and its absence leads to impaired motor control. We quantified the diffusional mobility of dye-labelled CR in mouse granule cells using two-photon fluorescence recovery after photobleaching (FRAP). We found that movement of macromolecules in granule cell dendrites was not well described by free Brownian diffusion and that CR diffused unexpectedly slow compared to fluorescein dextrans of comparable size. During bursts of action potentials, which were associated with dendritic Ca²⁺ transients, the mobility of CR was further reduced. Diffusion was significantly accelerated by a peptide embracing EF-hand 5 of CR. Our results suggest long-lasting, Ca²⁺-dependent interactions of CR with large and/or immobile binding partners. These interactions render CR a poorly mobile Ca²⁺ buffer and point towards a Ca²⁺ sensor function of CR