Rodrigues formulas for the Macdonald polynomials

We present formulas of Rodrigues type giving the Macdonald polynomials for arbitrary partitions through the repeated application of creation operators on the constant 1. Three expressions for the creation operators are derived one from the other. When the last of these expressions is used, the associated Rodrigues formula readily implies the integrality of the (q,t)-Kostka coefficients. The proofs given in this paper rely on the connection between affine Hecke algebras and Macdonald polynomialsComment: 15 pages, AmsLaTe

A high resolution spatiotemporal model for in-vehicle black carbon exposure : quantifying the in-vehicle exposure reduction due to the Euro 5 particulate matter standard legislation

Several studies have shown that a significant amount of daily air pollution exposure is inhaled during trips. In this study, car drivers assessed their own black carbon exposure under real-life conditions (223 h of data from 2013). The spatiotemporal exposure of the car drivers is modeled using a data science approach, referred to as microscopic land-use regression (mu LUR). In-vehicle exposure is highly dynamical and is strongly related to the local traffic dynamics. An extensive set of potential covariates was used to model the in-vehicle black carbon exposure in a temporal resolution of 10 s. Traffic was retrieved directly from traffic databases and indirectly by attributing the trips through a noise map as an alternative traffic source. Modeling by generalized additive models (GAM) shows non-linear effects for meteorology and diurnal traffic patterns. A fitted diurnal pattern explains indirectly the complex diurnal variability of the exposure due to the non-linear interaction between traffic density and distance to the preceding vehicles. Comparing the strength of direct traffic attribution and indirect noise map-based traffic attribution reveals the potential of noise maps as a proxy for traffic-related air pollution exposure. An external validation, based on a dataset gathered in 2010-2011, quantifies the exposure reduction inside the vehicles at 33% (mean) and 50% (median). The EU PM Euro 5 PM emission standard (in force since 2009) explains the largest part of the discrepancy between the measurement campaign in 2013 and the validation dataset. The mu LUR methodology provides a high resolution, route-sensitive, seasonal and meteorology-sensitive personal exposure estimate for epidemiologists and policy makers