\documentclass[10pt]{article}

\usepackage{fullpage}
\usepackage{setspace}
\usepackage{parskip}
\usepackage{titlesec}
\usepackage[section]{placeins}
\usepackage{xcolor}
\usepackage{breakcites}
\usepackage{lineno}
\usepackage{hyphenat}





\PassOptionsToPackage{hyphens}{url}
\usepackage[colorlinks = true,
            linkcolor = blue,
            urlcolor  = blue,
            citecolor = blue,
            anchorcolor = blue]{hyperref}
\usepackage{etoolbox}
\makeatletter
\patchcmd\@combinedblfloats{\box\@outputbox}{\unvbox\@outputbox}{}{%
  \errmessage{\noexpand\@combinedblfloats could not be patched}%
}%
\makeatother


\usepackage{natbib}




\renewenvironment{abstract}
  {{\bfseries\noindent{\abstractname}\par\nobreak}\footnotesize}
  {\bigskip}

\titlespacing{\section}{0pt}{*3}{*1}
\titlespacing{\subsection}{0pt}{*2}{*0.5}
\titlespacing{\subsubsection}{0pt}{*1.5}{0pt}


\usepackage{authblk}


\usepackage{graphicx}
\usepackage[space]{grffile}
\usepackage{latexsym}
\usepackage{textcomp}
\usepackage{longtable}
\usepackage{tabulary}
\usepackage{booktabs,array,multirow}
\usepackage{amsfonts,amsmath,amssymb}
\providecommand\citet{\cite}
\providecommand\citep{\cite}
\providecommand\citealt{\cite}
% You can conditionalize code for latexml or normal latex using this.
\newif\iflatexml\latexmlfalse
\providecommand{\tightlist}{\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}%

\AtBeginDocument{\DeclareGraphicsExtensions{.pdf,.PDF,.eps,.EPS,.png,.PNG,.tif,.TIF,.jpg,.JPG,.jpeg,.JPEG}}

\usepackage[utf8]{inputenc}
\usepackage[ngerman,english]{babel}



\usepackage{float}








\begin{document}

\title{Analysis of Electron Distribution Functions using the Gaussian Mixture
Model}



\author[1]{Beniamino Sanò}%
\author[2]{Nathan N. Maes}%
\author[3]{David L. Newman}%
\author[3]{Martin V. Goldman}%
\author[4]{Francesco Valentini}%
\author[5]{Giovanni Lapenta}%
\affil[1]{University of Trento / University of Calabria}%
\affil[2]{University of Leuven}%
\affil[3]{University of Colorado Boulder}%
\affil[4]{Dipartimento di Fisica, Università della Calabria}%
\affil[5]{Univ Leuven, KU Leuven, Dept Wiskunde}%


\vspace{-1em}



  
  \date{May 25, 2024}


\begingroup
\let\center\flushleft
\let\endcenter\endflushleft
\maketitle
\endgroup





\selectlanguage{english}
\begin{abstract}
Velocity distribution functions (VDFs) measured by the Magnetospheric
Multiscale (MMS) mission are complex 3D datasets that can be represented
as a superposition of multiple beams (M. V. Goldman et al., 2020). A
recent work (Dupuis et al., 2020) proposed the use of the Gaussian
Mixture Model (GMM). Here we investigate the approach by considering
first synthetic distributions made by artificially creating beams of
either Maxwellian distributions or kappa distributions with varying
power law index. By varying the inter-beam average difference and the
beam standard deviation we evaluate the ability of the GMM in
recognizing correctly the beam. We then apply the method systematically
to MMS data in the tail and in the dayside. In this case, the data need
preparation before being processed by the GMM to account for the
specifics of the instrument and in particular the lack of data at low
energy and to account for the noise in the counts. The conclusion of the
analysis is that the GMM is capable of detecting the presence of
multiple beams when their distinction is significant. The GMM can define
reliably the complexity of a measured dataset in terms of the number of
optimal beams provided by information theory criteria. Visual inspection
confirms this automatic definition of complexity.%
\end{abstract}%



\sloppy




\selectlanguage{english}
\FloatBarrier
\end{document}

