Magneto-chiral scattering of light: a new optical manifestation of chirality

We have investigated multiple scattering of light in systems subject to magneto-chiral (MC) effects. Our medium consists of magneto-optically active dipoles placed in a chiral geometry under the influence of an external magnetic field. We have calculated, for the first time, the total and the differential scattering MC cross sections of this system, explicitely showing that they are proportional to pseudoscalar quantities. This provides a new optical measure for the degree of chirality, a pseudoscalar g, of an arbitrary geometrical configuration of scatterers based on its scattering properties. We have calculated g for some simple chiral systems and we have even used it to probe the degree of optical chirality of random systems. Finally, we have compared $g$ with other recently defined chiral measures in literature.Comment: 18 pages, 6 figures, RevTeX. Submitted to PR

Uncertainty And Risk Analysis Of Macroeconomic Forecasts: Fan Charts Revisited

Since 1996 the Bank of England (BoE) has been publishing estimates of probability distribution of the future outcomes of inflation and output growth. These density forecasts, known as "fan charts", became very popular with other central banks (e.g. Riskbank) as a tool to quantify uncertainties and risks of conditional point forecasts. The BoE's procedure is mainly a methodology to determine the distribution of a linear combination of independent random variables. In this article we propose an alternative methodology that addresses two issues with the BoE procedure that may affect the estimation of the densities. The first issue relates to a statistical shortcut taken by the BoE that implicitly considers that the mode of the linear combination of random variables is the (same) linear combination of the modes of those variables. The second issue deals with the assumption of independence, which may be restrictive. An illustration of the new methodology is presented and its results compared with the BoE approach.

Explosion of smoothness for conjugacies between multimodal maps

Let $f$ and $g$ be smooth multimodal maps with no periodic attractors and no neutral points. If a topological conjugacy $h$ between $f$ and $g$ is $C^{1}$ at a point in the nearby expanding set of $f$, then $h$ is a smooth diffeomorphism in the basin of attraction of a renormalization interval of $f$. In particular, if $f:I \to I$ and $g:J \to J$ are $C^r$ unimodal maps and $h$ is $C^{1}$ at a boundary of $I$ then $h$ is $C^r$ in $I$.Comment: 22 page