In this paper, we study multivariate ranks and quantiles, defined using the theory of optimal transport, build on work Chernozhukov et al. (Ann. Statist. 45 (2017) 223–256) Hallin 49 (2021) 1139–1165). We characterization, computation properties rank quantile functions their empirical counterparts. derive uniform consistency these estimates to population versions, under certain assumptions. fac...

In this paper we present a method of parameter optimization, relative trust-region learning, where the trust-region method and the relative optimization [21] are jointly exploited. The relative trust-region method finds a direction and a step size with the help of a quadratic model of the objective function (as in the conventional trust-region methods) and updates parameters in a multiplicative...

This study reports the simulation of a photocatalytic system process and the photocatalytic property of self-cleaning asphalt concrete (SCAC) with four typical asphalt mixtures. A photocatalytic system was simulated based on the pollutant concentration data, which were collected on three types of city roads. Two photocatalytic indexes were proposed to evaluate the photocatalytic property of sel...

In the first part of this paper we prove the multiplicativ property of the relative Quillen Chern character. Then we obtain a Riemann-Roch formula between the relative Chern character of the Bott morphism and the relative Thom form.