14,694 research outputs found
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
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 and be smooth multimodal maps with no periodic attractors and no
neutral points. If a topological conjugacy between and is
at a point in the nearby expanding set of , then is a smooth
diffeomorphism in the basin of attraction of a renormalization interval of .
In particular, if and are unimodal maps and
is at a boundary of then is in .Comment: 22 page
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