APFELgrid: a high performance tool for parton density determinations

We present a new software package designed to reduce the computational burden of hadron collider measurements in Parton Distribution Function (PDF) fits. The APFELgrid package converts interpolated weight tables provided by APPLgrid files into a more efficient format for PDF fitting by the combination with PDF and $\alpha_s$ evolution factors provided by APFEL. This combination significantly reduces the number of operations required to perform the calculation of hadronic observables in PDF fits and simplifies the structure of the calculation into a readily optimised scalar product. We demonstrate that our technique can lead to a substantial speed improvement when compared to existing methods without any reduction in numerical accuracy.Comment: 13 pages, 2 figures. Submitted to CPC. Code available from https://github.com/nhartland/APFELgri

Statistical analysis of probability density functions for photometric redshifts through the KiDS-ESO-DR3 galaxies

Despite the high accuracy of photometric redshifts (zphot) derived using Machine Learning (ML) methods, the quantification of errors through reliable and accurate Probability Density Functions (PDFs) is still an open problem. First, because it is difficult to accurately assess the contribution from different sources of errors, namely internal to the method itself and from the photometric features defining the available parameter space. Second, because the problem of defining a robust statistical method, always able to quantify and qualify the PDF estimation validity, is still an open issue. We present a comparison among PDFs obtained using three different methods on the same data set: two ML techniques, METAPHOR (Machine-learning Estimation Tool for Accurate PHOtometric Redshifts) and ANNz2, plus the spectral energy distribution template fitting method, BPZ. The photometric data were extracted from the KiDS (Kilo Degree Survey) ESO Data Release 3, while the spectroscopy was obtained from the GAMA (Galaxy and Mass Assembly) Data Release 2. The statistical evaluation of both individual and stacked PDFs was done through quantitative and qualitative estimators, including a dummy PDF, useful to verify whether different statistical estimators can correctly assess PDF quality. We conclude that, in order to quantify the reliability and accuracy of any zphot PDF method, a combined set of statistical estimators is required.Comment: Accepted for publication by MNRAS, 20 pages, 14 figure

Modelling and control of the flame temperature distribution using probability density function shaping

This paper presents three control algorithms for the output probability density function (PDF) control of the 2D and 3D flame distribution systems. For the 2D flame distribution systems, control methods for both static and dynamic flame systems are presented, where at first the temperature distribution of the gas jet flames along the cross-section is approximated. Then the flame energy distribution (FED) is obtained as the output to be controlled by using a B-spline expansion technique. The general static output PDF control algorithm is used in the 2D static flame system, where the dynamic system consists of a static temperature model of gas jet flames and a second-order actuator. This leads to a second-order closed-loop system, where a singular state space model is used to describe the dynamics with the weights of the B-spline functions as the state variables. Finally, a predictive control algorithm is designed for such an output PDF system. For the 3D flame distribution systems, all the temperature values of the flames are firstly mapped into one temperature plane, and the shape of the temperature distribution on this plane can then be controlled by the 3D flame control method proposed in this paper. Three cases are studied for the proposed control methods and desired simulation results have been obtained