Effect of Our Galaxy's Motion on Weak Lensing Measurements of Shear and Convergence

In this work we investigate the effect on weak-lensing shear and convergence measurements due to distortions from the Lorentz boost induced by our Galaxy's motion. While no ellipticity is induced in an image from the Lorentz boost to first order in beta = v/c, the image is magnified. This affects the inferred convergence at a 10 per cent level, and is most notable for low multipoles in the convergence power spectrum C {\kappa}{\kappa} and for surveys with large sky coverage like LSST and DES. Experiments which image only small fractions of the sky and convergence power spectrum determinations at l > 5 can safely neglect the boost effect to first order in beta.Comment: 4 pages, replaced to reflect changes made for publication to MNRA

Image reconstruction from photon sparse data

We report an algorithm for reconstructing images when the average number of photons recorded per pixel is of order unity, i.e. photon-sparse data. The image optimisation algorithm minimises a cost function incorporating both a Poissonian log-likelihood term based on the deviation of the reconstructed image from the measured data and a regularization-term based upon the sum of the moduli of the second spatial derivatives of the reconstructed image pixel intensities. The balance between these two terms is set by a bootstrapping technique where the target value of the log-likelihood term is deduced from a smoothed version of the original data. When compared to the original data, the processed images exhibit lower residuals with respect to the true object. We use photon-sparse data from two different experimental systems, one system based on a single-photon, avalanche photo-diode array and the other system on a time-gated, intensified camera. However, this same processing technique could most likely be applied to any low photon-number image irrespective of how the data is collected

Speed-of-light pulses in a nonlinear Weyl equation

We introduce a prototypical nonlinear Weyl equation, motivated by recent developments in massless Dirac fermions, topological semimetals and photonics. We study the dynamics of its pulse solutions and find that a localized one-hump initial condition splits into a localized two-hump pulse, while an associated phase structure emerges in suitable components of the spinor field. For times larger than a transient time $t_s$ this pulse moves with the speed of light (or Fermi velocity in Weyl semimetals), effectively featuring linear wave dynamics and maintaining its shape (both in two and three dimensions). We show that for the considered nonlinearity, this pulse represents an exact solution of the nonlinear Weyl (NLW) equation. Finally, we comment on the generalization of the results to a broader class of nonlinearities and on their emerging potential for observation in different areas of application.Comment: 7 pages, 6 figure

The Fourth Amendment and the Control of Police Discretion

The fourth amendment protects the security of people\u27s persons, houses, papers, and effects in two distinct (if overlapping) ways. First, it requires a sufficiently weighty public interest before the government\u27s agents are allowed to search or seize. Thus, for example, probable cause is required for arrest. Whatever uncertainty there may be in the phrase probable cause (and, for that matter, however indefinite the idea of arrest may have become), in this context, at least, the probable cause standard requires the demonstration of objective facts that point with some probability to the guilt for some particular offense of the person arrested. As the Supreme Court stated in its 1949 decision, Brinegar v. United States, [p]robable cause exists where \u27the facts and circumstances within their [the officers\u27] knowledge and of which they had reasonably trustworthy information [are] sufficient in themselves to warrant a man of reasonable caution in the belief that\u27 an offense has been or is being committed [by the arrestee]. The governmental interest ultimately served by arrest is of course the enforcement of the criminal laws. The arrest brings the suspected wrong-doer to book, and it may also permit discovery of additional incriminating evidence. Yet the probable cause standard insists upon a sufficient likelihood that this interest will in fact be served before an arrest may be made. It assesses the relative worth of the opposing interests - the public interest in law enforcement and the individual\u27s right to be left alone - and identifies when the one must give way to the other. It tolerates some but not too much risk of the arrest of the innocent. This is the interest-balancing role of the fourth amendment. Second, the fourth amendment also performs a discretion control function. Even when the governmental interest at stake might otherwise justify a search or seizure, that search or seizure may be illegal if allowing it would confer too broad a discretionary authority on the police. There is, it is thought, a separate evil in leaving the police too much discretion to decide on their own where to search and whom and what to seize, under their own perhaps unknowable standards or under no standards at all. The Brinegar opinion adverted to this idea when it mentioned that permitting arrests on less than probable cause would leave law-abiding citizens at the mercy of the officers\u27 whim or caprice. Anthony Amsterdam seems to have been ref erring to these two functions of the fourth amendment when he asked whether a fourth amendment that limits the opportunity for indiscriminate searches should not also be concerned with discriminatory ones