\documentclass[12pt,a4paper]{article}

\usepackage{calc}
\usepackage{fancyhdr,lastpage}
\usepackage{array,longtable}
\usepackage{graphics}
\usepackage{charter}
\usepackage{epsfig,amssymb,amsmath,psfrag,epstopdf,color}
\usepackage{graphicx}

\setlength{\oddsidemargin}{0pt}
\setlength{\evensidemargin}{0pt}
\setlength{\topmargin}{-0.75in}
\addtolength{\headheight}{3pt}
\setlength{\textwidth}{\paperwidth-2in}
\setlength{\textheight}{9.8in}

\def\smallfrac#1#2{\hbox{$\frac{#1}{#2}$}}
\newcommand{\be}{\begin{equation}}
\newcommand{\ee}{\end{equation}}
\newcommand{\bea}{\begin{eqnarray}}
\newcommand{\eea}{\end{eqnarray}}
\newcommand{\bi}{\begin{itemize}}
\newcommand{\ei}{\end{itemize}}
\newcommand{\ben}{\begin{enumerate}}
\newcommand{\een}{\end{enumerate}}
\newcommand{\la}{\left\langle}
\newcommand{\ra}{\right\rangle}
\newcommand{\lc}{\left[}
\newcommand{\rc}{\right]}
\newcommand{\lp}{\left(}
\newcommand{\rp}{\right)}
\newcommand{\as}{\alpha_s}
\newcommand{\aq}{\alpha_s\left( Q^2 \right)}
\newcommand{\amz}{\alpha_s\left( M_Z^2 \right)}
\newcommand{\aqq}{\alpha_s \left( Q^2_0 \right)}
\newcommand{\aqz}{\alpha_s \left( Q^2_0 \right)}
\def\toinf#1{\mathrel{\mathop{\sim}\limits_{\scriptscriptstyle
{#1\rightarrow\infty }}}}
\def\tozero#1{\mathrel{\mathop{\sim}\limits_{\scriptscriptstyle
{#1\rightarrow0 }}}}
\def\toone#1{\mathrel{\mathop{\sim}\limits_{\scriptscriptstyle
{#1\rightarrow1 }}}}
\def\frac#1#2{{{#1}\over {#2}}}
\def\gsim{\mathrel{\rlap{\lower4pt\hbox{\hskip1pt$\sim$}}
    \raise1pt\hbox{$>$}}}         %greater than or approx. symbol
\def\lsim{\mathrel{\rlap{\lower4pt\hbox{\hskip1pt$\sim$}}
    \raise1pt\hbox{$<$}}}         %less than or approx. symbol
\newcommand{\mrexp}{\mathrm{exp}}
\newcommand{\dat}{\mathrm{dat}}
\newcommand{\one}{\mathrm{(1)}}
\newcommand{\two}{\mathrm{(2)}}
\newcommand{\art}{\mathrm{art}} 
\newcommand{\rep}{\mathrm{rep}}
\newcommand{\net}{\mathrm{net}}
\newcommand{\stopp}{\mathrm{stop}}
\newcommand{\sys}{\mathrm{sys}}
\newcommand{\stat}{\mathrm{stat}}
\newcommand{\diag}{\mathrm{diag}}
\newcommand{\pdf}{\mathrm{pdf}}
\newcommand{\tot}{\mathrm{tot}}
\newcommand{\minn}{\mathrm{min}}
\newcommand{\mut}{\mathrm{mut}}
\newcommand{\partt}{\mathrm{part}}
\newcommand{\dof}{\mathrm{dof}}
\newcommand{\NS}{\mathrm{NS}}
\newcommand{\cov}{\mathrm{cov}}
\newcommand{\gen}{\mathrm{gen}}
\newcommand{\cut}{\mathrm{cut}}
\newcommand{\parr}{\mathrm{par}}
\newcommand{\val}{\mathrm{val}}
\newcommand{\tr}{\mathrm{tr}}
\newcommand{\checkk}{\mathrm{check}}
\newcommand{\reff}{\mathrm{ref}}
\newcommand{\Mll}{M_{ll}}
\newcommand{\extra}{\mathrm{extra}}
\newcommand{\draft}[1]{}
\newcommand{\comment}[1]{{\bf \it  #1}}
\def\beq{\begin{equation}}  
\def\eeq{\end{equation}}  
\renewcommand{\familydefault}{ptm}


\pagestyle{fancy}
\fancyhf{}
\rfoot{\thepage}


\setcounter{secnumdepth}{-2}

\makeatletter
\renewcommand{\section}{\@startsection
  {section}{1}{0pt}{-\baselineskip}{2\baselineskip}{\LARGE\bfseries\center}}
\makeatother


\begin{document}

\setlength{\parindent}{0pt}
\setlength{\parskip}{1em}


\begin{enumerate}

\clearpage
\item From the authors
\begin{figure}[t]
\begin{center}
  \includegraphics[scale=0.38]{2-pdffitting/plots/DIS-main.pdf}
   \caption{\small Schematic representation of
   the deep-inelastic scattering process.
   %
   An energetic lepton (electron, muon or neutrino) scatters
   off one of the quarks
   in the proton by means of the interchange of a gauge boson
   ($\gamma, W^{\pm}$ or $Z$).
   %
   The large virtuality of the gauge boson, $Q\gg \Lambda_{\rm QCD}$,
   ensures that the process can be described within QCD
   factorization in terms of coefficient functions
   and parton distributions.
    \label{fig:DIS-main}
  }
\end{center}
\end{figure}
\clearpage
\item From the authors
\begin{figure}[t]
\begin{center}
  \includegraphics[scale=1.0]{2-pdffitting/plots/pdf4lhcq10.pdf}\qquad\quad
   \includegraphics[scale=1.0]{2-pdffitting/plots/pdf4lhcq1000.pdf}
%\includegraphics[scale=0.75]{2-pdffitting/plots/nnpdf30evolution.pdf}
   \caption{\small The effect of the DGLAP evolution in the PDF4LHC NNLO Hessian set (with 100 eigenvectors), comparing
   the PDFs at a low scale of $Q^2=10$ GeV$^2$ (left) with the same PDFs evolved
   up to a typical LHC scale of $Q^2=10^4$ GeV$^2$ (right plot).
   %
   In this plot the PDFs are shown together with the corresponding
   one-sigma PDF uncertainty band.
    \label{fig:pdf4lhcevolution}
  }
\end{center}
\end{figure}
\clearpage
\item From Left: R. Thorne, The effect on PDFs and αS (MZ2 ) due to changes in flavour scheme and higher twist contributions, Eur.Phys.J. C74 (7) (2014) 2958. arXiv:1402.3536; Right: M. Guzzi, P. M. Nadolsky, H.-L. Lai, C.-P. Yuan, General-Mass Treatment for Deep Inelastic Scattering at Two-Loop Accuracy, Phys.Rev. D86 (2012) 053005 
\begin{figure}[t]
\begin{center}
  \includegraphics[scale=0.45]{2-pdffitting/plots/f2c.pdf}
   \caption{\small Left plot: the inclusive proton structure
   function $F_2^2(x,Q^2)$ at NNLO as a function of $Q^2$ for two different
   values of $x$ in the RT' GM-VFNS as compared to the FFNS calculation.
   %
   Right plot: the NNLO charm structure function $F_2^c(x,Q)$
   as a function of $Q$ for $x=0.01$ comparing the S-ACOT-$\chi$
   GM scheme with the corresponding ZM and FFN scheme calculations.
    \label{fig:f2c}
  }
\end{center}
\end{figure}
\clearpage
\item From R. D. Ball, et al., Parton distributions from high-precision collider dataarXiv:1706.00428 
\begin{figure}[t]
\begin{center}
  \includegraphics[scale=0.60]{3-datatheory/plots/kinplot-report.pdf}
  \caption{\small Typical kinematical coverage in the
    $(x,Q^2)$ plane for the dataset included in a global
    analysis, in this case NNPDF3.1.
    %
    For hadronic observables, leading order kinematics
    are assumed to map each data bin to a pair of $(x,Q^2)$
    values.
    %
    The various datasets are clustered into families of
    related processes.
    \label{fig:kinplot-report} 
  }
\end{center}
\end{figure}
\clearpage
\item From the authors
\begin{figure}[t]
\begin{center}
  \includegraphics[scale=0.42]{3-datatheory/plots/dis-diagrams.pdf}
   \caption{\small Left plot: $D$ meson production
   in charged-current neutrino-induced DIS.
   %
   This is known as the dimuon process since events are tagged
   where the $D$ meson decays semi-leptonically, with
   the pair of oppositely charged muons providing a clean signature.
   %
   Right plot:
   %
   Charm production in neutral current DIS at leading order,
   highlighting the sensitivity of this process to the gluon
   PDF.
    \label{fig:dis-diagrams}
  }
\end{center}
\end{figure}
\clearpage
\item From Left: J. Currie, E. W. N. Glover, A. Gehrmann-De Ridder, T. Gehrmann, A. Huss, J. Pires, Single jet inclusive production for the individual jet pT scale choice at the LHC, in: 23rd Cracow Epiphany Conference on Particle Theory Meets the First Data from LHC Run 2 Cracow, Poland, January 9-12, 2017, 2017. arXiv:1704.00923; Right: the authors
\begin{figure}[h]
\begin{center}
  \includegraphics[scale=0.19]{3-datatheory/plots/autoATLAS7R4fracLO.pdf}
  \includegraphics[scale=1.35]{3-datatheory/plots/jetcorr.pdf}
   \caption{\small
   Left: Fractional contributions from different partonic channels to the single inclusive jet
   production at the LHC 7 TeV at LO in the central rapidity region~\cite{Currie:2017ctp}.
   %
   Right: Correlations between binning cross sections from ATLAS on the single inclusive jet
   production at the LHC 7 TeV and the gluon PDF; dashed curves correspond to
   experiment bins at low $p_T$. 
    \label{fig:jet3}
  }
\end{center}
\end{figure}
\clearpage
\item From Left: G. Aad, et al., Measurement of the inclusive jet cross-section in proton-proton collisions at s = 7 TeV using 4.5 fb1 of data with the ATLAS detector, JHEP 02 (2015) 153, [Erratum: JHEP09,141(2015)]. arXiv:1410.8857, doi:10.1007/JHEP02(2015)153, 10.1007/JHEP09(2015)141; Right: S. Chatrchyan, et al., Measurement of the ratio of inclusive jet cross sections using the anti-kT algorithm with ra- dius parameters R=0.5 and 0.7 in pp collisions at √s = 7TeV, Phys. Rev. D90 (7) (2014) 072006. arXiv:1406.0324, doi:10.1103/PhysRevD.90.072006
\begin{figure}[h]
\begin{center}
  \includegraphics[scale=0.3]{3-datatheory/plots/SystSummaryR06_Y0.pdf}
  \includegraphics[scale=0.45]{3-datatheory/plots/InclusiveExperimentalUnc_Ybin0.pdf}
   \caption{\small
    Representative systematic errors in single inclusive jet measurement at
    LHC 7 TeV in the central rapidity region, from ATLAS (left)~\cite{Aad:2014vwa}
    and CMS (right)~\cite{Chatrchyan:2014gia}. 
    The luminosity error is not included in the ATLAS plot. 
   \label{fig:jet4}
  }
\end{center}
\end{figure}
\clearpage
\item From J. Currie, E. W. N. Glover, A. Gehrmann-De Ridder, T. Gehrmann, A. Huss, J. Pires, Single jet inclusive production for the individual jet pT scale choice at the LHC, in: 23rd Cracow Epiphany Conference on Particle Theory Meets the First Data from LHC Run 2 Cracow, Poland, January 9-12, 2017, 2017. arXiv:1704.00923
\begin{figure}[h]
\begin{center}
  \includegraphics[scale=0.2]{3-datatheory/plots/ATLAS7R4ratiotoNLO.pdf}
  \hspace{0.1in}
  \includegraphics[scale=0.2]{3-datatheory/plots/ATLAS7R4NNLOratiotodata.pdf}
   \caption{\small
   Left: Predictions on single inclusive jet production at the LHC 7 TeV
   using ATLAS binning and anti-$k_T$ algorithm with $R=0.4$, with a central scale choice of leading
   jet $p_T$ and scale variations by varying renormalization and factorization
   scales simultaneously by a factor of 2~\cite{Currie:2017ctp}. 
   %
   Right: For the same setup comparing the NNLO predictions using a central
   scale choice of the leading jet $p_T$ (green) and the individual jet $p_T$ (red)~\cite{Currie:2017ctp}.
    \label{fig:jet1}
  }
\end{center}
\end{figure}
\clearpage
\item From A. M. Sirunyan, et al., Measurement of the triple-differential dijet cross section in proton-proton collisions at sqrt(s) = 8 TeV and constraints on parton distribution functionsarXiv:1705.02628
\begin{figure}[h]
\begin{center}
  \includegraphics[scale=0.23]{3-datatheory/plots/CMSdijet1.pdf}
  \hspace{0.3in}
  \includegraphics[scale=0.23]{3-datatheory/plots/CMSdijet2.pdf}
   \caption{\small
   Effects of the CMS 8 TeV jet data on the gluon PDF when adding up to a
   PDF fit with HERA DIS data only. The left plot compares the fit with
   only DIS data and the fit with CMS dijet data in addition. The right
   plot compares the fit to HERA DIS plus CMS dijet data and fit to HERA
   DIS plus CMS single jet data~\cite{Sirunyan:2017skj}.   
   \label{fig:jet5}
  }
\end{center}
\end{figure}
\clearpage
\item From M. Aaboud, et al., Precision measurement and interpretation of inclusive W+, W− and Z/γ∗ production cross sections with the ATLAS detectorarXiv:1612.03016
 \begin{figure}
  \begin{center}
 \includegraphics[width=0.37\textwidth]{3-datatheory/plots/Zpeak_cen_NNLO_combined}\qquad\qquad
 \includegraphics[width=0.37\textwidth]{3-datatheory/plots/Wasym25_NNLO_combined}
  \end{center}
\caption{ATLAS 7 TeV measurement of $Z$ rapidity distribution (left) and $W$ asymmetry (right), taken from~\cite{Aaboud:2016btc}.}\label{fig:ATLASWZdata}
\end{figure}
\clearpage
\item From Left: V. Khachatryan, et al., Measurement of the differential cross section and charge asymmetry for inclusive pp → W± + X production at √s = 8 TeV, Eur. Phys. J. C76 (8) (2016) 469. arXiv:1603.01803; Right: M. Aaboud, et al., Precision measurement and interpretation of inclusive W+, W− and Z/γ∗ production cross sections with the ATLAS detectorarXiv:1612.03016
\begin{figure}
  \begin{center}
 \includegraphics[width=0.4\textwidth]{3-datatheory/plots/Figure_004-b}
  \includegraphics[width=0.5\textwidth]{3-datatheory/plots/Rs_com_new}
  \end{center}
\caption{(Left) Down valence distribution, with the CMS fit to HERA I+II data only, and including the CMS 8 TeV W production data. Taken from~\cite{Khachatryan:2016pev}. (Right) The ratio of the strange quark to the light quark sea, $R_s$, with different PDF predictions and the result of the ATLAS fit to HERA I+II data and the high precision $W$ and $Z/\gamma^*$ data shown. Taken from~\cite{Aaboud:2016btc}.}\label{fig:WZpdf}
\end{figure}
\clearpage
\item From R. Boughezal, A. Guffanti, F. Petriello, M. Ubiali, The impact of the LHC Z-boson transverse momentum data on PDF determinations, JHEP 07 (2017) 130. arXiv:1705.00343, doi:10.1007/JHEP07(2017)130
\begin{figure}[h]
\begin{center}
  \includegraphics[scale=0.5]{3-datatheory/plots/NNPDF30_nlo_as_0118_ATLASZPT8TEVYDIST-BIN1_ptZ_vs_gdu.pdf}
   \caption{\small 
   Correlations between the cross sections in various $p_{T}$ bins and the gluon, down- and
   up-quark PDFs as a function of $x$~\cite{Boughezal:2017nla}. The binning corresponds to the ATLAS measurement~\cite{Aad:2015auj} with rapidity interval $0<|y_Z|<0.4$. 
    \label{fig:ptz4}
  }
\end{center}
\end{figure}
\clearpage
\item From Left:G. Aad, et al., Measurement of the transverse momentum and φ∗η distributions of DrellYan lepton pairs in proton- proton collisions at √s = 8 TeV with the ATLAS detector, Eur. Phys. J. C76 (5) (2016) 291; Right: V. Khachatryan, et al., Measurement of the Z boson differential cross section in transverse momentum and rapidity in protonproton collisions at 8 TeV, Phys. Lett. B749 (2015) 187–209. arXiv:1504.03511 
\begin{figure}[h]
\begin{center}
  \includegraphics[scale=0.3]{3-datatheory/plots/ZmumuptSyst1.pdf}
  \hspace{0.5in}
  \includegraphics[scale=0.3]{3-datatheory/plots/uncert_normed_xsec_dpt_y0-2.pdf}
   \caption{\small 
   Left plot: relative experimental errors on the measured normalized $p_T$ spectra
   of the $Z$ boson in dimuon channel (dressed) from ATLAS 8 TeV~\cite{Aad:2015auj} .
   %
   Right plot: relative experimental errors on the measured normalized $p_T$ spectra
   of the $Z$ boson in dimuon channel from CMS 8 TeV~\cite{Khachatryan:2015oaa} .
    \label{fig:ptz3}
  }
\end{center}
\end{figure}
\clearpage
\item From A. Gehrmann-De Ridder, T. Gehrmann, E. W. N. Glover, A. Huss, T. A. Morgan, NNLO QCD corrections for Drell-Yan pZT and φ∗ observables at the LHC, JHEP 11 (2016) 094. arXiv:1610.01843
\begin{figure}[h]
\begin{center}
  \includegraphics[scale=0.4]{3-datatheory/plots/ATLAS_ptz_bin_ratNLO_NNLOFull.pdf}
  \includegraphics[scale=0.4]{3-datatheory/plots/ATLASnorm_ptz_bin_ratNLO_NNLOFull.pdf}
   \caption{\small 
   Left(right) plot shows the unnormalized(normalized) transverse momentum distribution
   of the inclusive $Z$ boson production at LHC 8 TeV~\cite{Gehrmann-DeRidder:2016jns}.
   The green and blue bands denote
   the NLO and NNLO predictions with scale variations. The fiducial cuts on charged
   leptons are $p_{T,l}>20\,{\rm GeV}$ and $|\eta_l|<2.4$.  
    \label{fig:ptz2}
  }
\end{center}
\end{figure}
\clearpage
\item From R. D. Ball, et al., Parton distributions from high-precision collider dataarXiv:1706.00428
\begin{figure}[h]
\begin{center}
  \includegraphics[scale=0.4]{3-datatheory/plots/xg-31-nnlo-ZpT.pdf}
  \includegraphics[scale=0.4]{3-datatheory/plots/xsp-31-nnlo-ZpT.pdf}
   \caption{\small
   Impact of the $Z$ boson transverse momentum measurements from
   ATLAS and CMS 8 TeV on the gluon PDF and the total strangeness in the
   NNPDF3.1 global analyses~\cite{Ball:2017nwa}.  
    \label{fig:ptimp}
  }
\end{center}
\end{figure}
\clearpage
\item From D. d’Enterria, J. Rojo, Quantitative constraints on the gluon distribution function in the proton from collider isolated-photon data, Nucl.Phys. B860 (2012) 311–338. arXiv:1202.1762
\begin{figure}[t]
  \begin{center}
 \includegraphics[width=0.45\textwidth]{3-datatheory/plots/subproc_ppgamma_jetphox_lhc_inc_stack}
\includegraphics[width=0.45\textwidth]{3-datatheory/plots/subproc_ppgamma_jetphox_lhc_is_stack.pdf}
  \end{center}
\caption{Relative contributions from Compton ($qg$), annihilation ($q\overline{q}$) and fragmentation to prompt photon production at central rapidities at the 14 TeV LHC, before (left) and after (right) the application of isolation cuts. Figures taken from~\cite{d'Enterria:2012yj}.}\label{fig:isol}
\end{figure}
\clearpage
\item From D. d’Enterria, J. Rojo, Quantitative constraints on the gluon distribution function in the proton from collider isolated-photon data, Nucl.Phys. B860 (2012) 311–338. arXiv:1202.1762
\begin{figure}
  \begin{center}
 \includegraphics[width=0.4\textwidth]{3-datatheory/plots/g_PDFerr_red_Qs}
%  \includegraphics[width=0.4\textwidth]{3-datatheory/plots/ggF_higgs_nnpdf}
  \end{center}
\caption{Relative reduction in the NNPDF2.1 NLO gluon PDF uncertainty when including a 36 ${\rm pb}^{-1}$ LHC 7 TeV isolated photon data set via reweighting. Taken from~\cite{d'Enterria:2012yj}.}\label{fig:isolPDF}
\end{figure}
\clearpage
\item From the authors
\begin{figure}[t]
\begin{center}
  \includegraphics[scale=0.75]{3-datatheory/plots/topdiffcorrelation.pdf}
   \caption{\small The correlation coefficient between the gluon
   PDF at $Q=100$ GeV and the theory predictions for
   the differential distributions in $y_{t\bar{t}}$
   (left) and $m_{t\bar{t}}$ (right plot) at $\sqrt{s}=8$ TeV,
   as a function of $x$.
   %
   Each curve corresponds to a specific measurement bin.
   %
   The higher the absolute value of the correlation coefficient, the
   bigger the sensitivity to the gluon in those specific values of $x$.
    \label{fig:topdiffcorr}
  }
\end{center}
\end{figure}
\clearpage
\item From Left: M. Czakon, M. L. Mangano, A. Mitov, J. Rojo, Constraints on the gluon PDF from top quark pair production at hadron colliders, JHEP 1307 (2013) 167. arXiv:1303.7215; Right: M. Czakon, N. P. Hartland, A. Mitov, E. R. Nocera, J. Rojo, Pinning down the large-x gluon with NNLO top-quark pair differential distributions, JHEP 04 (2017) 044. arXiv:1611.08609 
\begin{figure}[t]
\begin{center}
  \includegraphics[scale=0.45]{3-datatheory/plots/ttbar-impact.pdf}
   \caption{\small Left plot: the impact of the LHC 7 and 8 TeV inclusive
   top-quark pair cross-section data on the large-$x$ gluon of
   NNPDF2.3~\cite{Czakon:2013tha}.
   %
   Right plot: the impact of the LHC 8 TeV differential distributions in
    top-quark pair production on the $gg$ luminosity~\cite{Czakon:2016olj}, compared with a baseline fit
    based on the NNPDF3.0 global analysis without the jet data.
    \label{fig:ttbar-impact}
  }
\end{center}
\end{figure}
\clearpage
\item From Left: the authors; Right: M. Aaboud, et al., Measurement of the inclusive cross-sections of single top-quark and top-antiquark t-channel pro- duction in pp collisions at √s = 13 TeV with the ATLAS detector, JHEP 04 (2017) 086. arXiv:1609.03920
\begin{figure}[h]
\begin{center}
  \includegraphics[scale=0.40]{3-datatheory/plots/singletop}
   \caption{\small Left plot: one of the Feynman diagrams for single-top production
   at leading order, illustrating its sensitivity to the $b$-quark
   PDF.
   %
   Right plot: comparison of the theoretical predictions for the ratio $R_t=\sigma_t/\sigma_{\bar{t}}$
   from different PDF sets and the corresponding ATLAS measurements at $\sqrt{s}=13$ TeV
   from~\cite{Aaboud:2016ymp}.
    \label{fig:singletop}
  }
\end{center}
\end{figure}
\clearpage
\item From the authors
\begin{figure}[t]
\begin{center}
  \includegraphics[scale=0.38]{3-datatheory/plots/gPDF_rwgt.pdf}
   \caption{\small Left plot: comparison between the small-$x$ gluon
   at $Q^2=4$ GeV$^2$
   in NNPDF3.0 with the corresponding result after different
   combinations of the charm production data at
   LHCb have been included in the fit.
   %
   We show the central value and one-sigma PDF uncertainty
   bands for the $N^7+N^{13/5}$ and the $N^5+N^7+N^{13}$
   combinations, as well as the central value for the
   $N^5+N^{13/7}$ case
    \label{fig:gPDF_rwgt}
  }
\end{center}
\end{figure}
\clearpage
\item From arXiv:1307.7099
\begin{figure}[t]
  \begin{center}

 \includegraphics[width=0.32\textwidth]{3-datatheory/plots/cep}
  \end{center}
\caption{Figure from 1307.7099. {\bf perhaps don't need a figure- if we decide to keep, will find better one...}}\label{fig:cep}
\end{figure}
\clearpage
\item From the authors
\begin{figure}[t]
\begin{center}
  \includegraphics[scale=0.46]{3-datatheory/plots/fastinterfaces.pdf}
   \caption{\small Right plot: the ratio between the {\tt NLOjet++} calculation
   of inclusive jet production at 7 TeV in the rapidity interval
   $2 \le y \le 3$ and the corresponding {\it a posteriori} calculation
   based on {\tt APPLgrid}, for different values of the factorization
   and renormalization scales.
   %
   Left plot: the transverse momentum distribution of photons in the $pp\to \gamma+{\rm jet}$
   process at 7 TeV, comparing the original {\tt MadGraph5\_aMC@NLO} calculation with the
   {\it a posteriori} result based on {\tt aMCfast} and {\tt APPLgrid}.
   %
   The lower insets show the ratio between the two calculations for different
   choices of $\mu_R$ and $\mu_F$.
    \label{fig:fastinterfaces}
  }
\end{center}
\end{figure}
\clearpage
\item From the authors
\begin{figure}[t]
\begin{center}
  \includegraphics[scale=0.65]{3-datatheory/plots/apfelgrid.pdf}
   \caption{\small Comparison of the timings per data point between the
   original {\tt APPLgrid} computation of hadronic cross-sections,
   Eq.~(\ref{eq:applgrid2}), with the same calculation
   based on the {\tt APFELgrid} combination, Eq.~(\ref{eq:apfelgrid}), for a variety of
   LHC datasets.
   %
   We find that the improvement in computational speed is between a factor 100 and a factor 1000
   depending on the specific dataset.
    \label{fig:apfelgrid}
  }
\end{center}
\end{figure}
\clearpage
\item From A. D. Martin, W. J. Stirling, R. S. Thorne, G. Watt, Parton distributions for the LHC, Eur. Phys. J. C63 (2009) 189. arXiv:0901.0002
\begin{figure}[t]
\begin{center}
  \includegraphics[scale=0.70]{4-fitting/plots/mstw08-tolerance.pdf}
   \caption{\small 
  The individual tolerance for each eigenvector, determined
  by the criterion that each separate experiment should be described
  within 90\% CL.
  %
  In each case the figure indicates the name of the experiment
  that determines the tolerance for the various eigenvector directions.
    \label{fig:mstw08-tolerance}
  }
\end{center}
\end{figure}
\clearpage
\item From L. Del Debbio, S. Forte, J. I. Latorre, A. Piccione, J. Rojo, Unbiased determination of the proton structure function f2(p) with estimation, JHEP 03 (2005) 080. arXiv:hep-ph/0501067
\begin{figure}[t]
\begin{center}
  \includegraphics[scale=0.79]{4-fitting/plots/f2p-scatter.pdf}
   \caption{\small 
  The scatter between the mean values (left) and variances (right plot)
  of all the data points included in the analysis of~\cite{DelDebbio:2004qj}, comparing
  the original experimental values with the results obtained from the MC representation
  for different number $N_{\rm rep}$ of replicas.
    \label{fig:f2p-scatter}
  }
\end{center}
\end{figure}
\clearpage
\item From M. Dittmar, et al., Parton Distributions, arXiv:0901.2504
\begin{figure}[t]
\begin{center}
  \includegraphics[scale=0.79]{4-fitting/plots/heralhc.pdf}
   \caption{\small 
  The gluon PDF at $Q=2$ GeV in the HERA-LHC benchmark fit of
  Ref.~\cite{Dittmar:2009ii}, where the one-sigma PDF uncertainties
  computed with the Hessian method (black lines) are compared to
  those of the Monte Carlo method (red lines), finding good agreement.
  %
  Each of the green curves corresponds to an individual MC replica.
  %
  In the left fit, the normalization
  and systematic
  uncertainties in the MC replicas from Eq.~(\ref{eq:replicas}) fluctuate
  according to a multi-Gaussian distribution, while in the right
  fit they fluctuate instead according to a log-normal distribution.
    \label{fig:heralhc}
  }
\end{center}
\end{figure}
\clearpage
\item From the authors
\begin{figure}[t]
\begin{center}
  \includegraphics[scale=0.79]{4-fitting/plots/LM.pdf}
   \caption{\small Schematic representation of the Lagrange Multiplier method.
   %
   In the left plot we show a two-dimensional projection of the PDF parameter space,
   indicating the contours in $\chi^2$ for fixed values of
   the physical quantity $\mathcal{F}$.
   %
   In the right plot we show how the PDF uncertainty associated to $\mathcal{F}$
   for a given confidence interval is determined by the condition that the
   global $\chi^2$ should not grow beyond the tolerance $\Delta\chi^2$.
    \label{fig:LM}
  }
\end{center}
\end{figure}
\clearpage
\item From Left: L. A. Harland-Lang, A. D. Martin, P. Motylinski, R. S. Thorne, Uncertainties on αS in the MMHT2014 global PDF analysis and implications for SM predictionsarXiv:1506.05682; Right: R. D. Ball, V. Bertone, L. Del Debbio, S. Forte, A. Guffanti, et al., Precision NNLO determination of αs(MZ) using an unbiased global parton set, Phys.Lett. B707 (2012) 66–71. arXiv:1110.2483
\begin{figure}[h]
\begin{center}
  \includegraphics[scale=0.65]{4-fitting/plots/globalNNLO.pdf}
  \includegraphics[scale=0.6]{4-fitting/plots/alphasfit-21-nnlo-global.pdf}
   \caption{\small
  Left plot: the profile of global $\chi^2$ as in a scan of $\alpha_s(M_Z)$
  in MMHT2014 NNLO analysis~\cite{Harland-Lang:2015nxa}.
  %
  Right plot: the profile of global $\chi^2$ as in a scan of $\alpha_s(M_Z)$
  in NNPDF2.1 NNLO analysis~\cite{Ball:2011us}. The error bars indicate fluctuations of
  the $\chi^2$ due to finite number of MC replicas. 
    \label{fig:as1}
  }
\end{center}
\end{figure}
\clearpage
\item From H.-L. Lai, et al., Uncertainty induced by QCD coupling in the CTEQ global analysis of parton distributions, Phys. Rev. D82 (2010) 054021. arXiv:1004.4624
\begin{figure}[h]
\begin{center}
  \includegraphics[scale=0.4]{4-fitting/plots/pA224a_vs_ct66_0_mu2.pdf}
  \includegraphics[scale=0.4]{4-fitting/plots/pA224a_vs_ct66_4_mu2.pdf}
   \caption{\small
   Comparison of the PDF+$\alpha_s$ uncertainties for gluon and charm quark
   PDFs as from the full eigenvectors including $\alpha_s(M_Z)$ in the Hessian
   matrix (filled error band with dotted borders) and the seperate PDF and
   $\alpha_s$ uncertainties added in quadrature
   (hatched band with solid borders)~\cite{Lai:2010nw}. The dashed lines
   represent the PDF uncertianties only.
    \label{fig:as2}
  }
\end{center}
\end{figure}
\clearpage
\item From T.-J. Hou, S. Dulat, J. Gao, M. Guzzi, J. Huston, P. Nadolsky, C. Schmidt, J. Winter, K. Xie, C. P. Yuan, CT14 Intrinsic Charm Parton Distribution Functions from CTEQ-TEA Global AnalysisarXiv:1707.00657.
\begin{figure}[h]
\begin{center}
  \includegraphics[scale=0.5]{4-fitting/plots/CT14ICSEAmcs_WpWm_kf2_Vrap.pdf}
  \hspace{0.2in}
  \includegraphics[scale=0.5]{4-fitting/plots/CT14ICSEAmcs_ZH_kf2_Vrap.pdf}
   \caption{\small
   Dependence of total cross sections of weak boson and Higgs boson productions
   at LHC 13 TeV on the choice of charm quark mass in CT14 NNLO analysis~\cite{Hou:2017khm}.
   The ellipse indicates PDF uncertainties at 90\% C.L. Also shown are dependence
   of the cross sections on the assumed momentum fraction carried by non-perturbative
   charm PDF at the initial scale. 
    \label{fig:as3}
  }
\end{center}
\end{figure}
\clearpage
\item From J. Butterworth, et al., PDF4LHC recommendations for LHC Run II, J. Phys. G43 (2016) 023001. arXiv:1510.03865
\begin{figure}[h]
\begin{center}
  \includegraphics[scale=0.4]{4-fitting/plots/xg-mc900_vs_mch100_vs_meta30.pdf}
  \includegraphics[scale=0.4]{4-fitting/plots/xg-mc900_vs_cmc100.pdf}
  \includegraphics[scale=0.4]{4-fitting/plots/xdbar-mc900_vs_mch100_vs_meta30.pdf}
  \includegraphics[scale=0.4]{4-fitting/plots/xdbar-mc900_vs_cmc100.pdf}
   \caption{\small
   Comparison of the gluon and $\bar d$-quark PDFs at a scale of $Q^2=100\,{\rm GeV}^2$
   between the prior and the two reduced Hessian sets, and between the prior and
   the compressed MC set, normalized to the central value of the prior~\cite{Butterworth:2015oua}. 
    \label{fig:comb1}
  }
\end{center}
\end{figure}
\clearpage
\item From Left: S. Camarda, et al., QCD analysis of W- and Z-boson production at Tevatron, Eur. Phys. J. C75 (9) (2015) 458. arXiv:1503.05221; Right: the authors
\begin{figure}[t]
\begin{center}
  \includegraphics[scale=0.48]{4-fitting/plots/rw.pdf}
   \caption{\small 
     Left plot: the impact of the Tevatron $W$ and $Z$ data
     on the MMHT2014 NLO fit, estimated by the Hessian
     profiling method of Ref.~\cite{Camarda:2015zba}.
  %
     Right plot: the gluon PDF in the NNPDF3.0 closure tests,
     quantifying the impact of the collider inclusive jet data,
     and comparing the results of the Bayesian reweighting
     with those of a direct refit. 
    \label{fig:rw}
  }
\end{center}
\end{figure}
\clearpage
\item From A. Buckley, J. Ferrando, S. Lloyd, K. Nordstrm, B. Page, et al., LHAPDF6: parton density access in the LHC precision era, Eur.Phys.J. C75 (2015) 132. arXiv:1412.7420
\begin{figure}[t]
\begin{center}
  \includegraphics[scale=0.45]{4-fitting/plots/lhapdf6.pdf}
   \caption{\small 
  Left plot: the relative difference between LHAPDF v5 and v6
  for $g(x,Q)$ for different values of $x$ as a function of $Q$, using
  CT10 as input PDF.
  %
  Right plot: the timing improvement in v6 as compared to v5, $t_6/t_5$,
  for a cross-section integration of 1M phase space points
  with {\tt Sherpa} and for CKKW event generation of
  100k $pp \to 4$ jet events.
    \label{fig:lhapdf6}
  }
\end{center}
\end{figure}
\clearpage
\item From S. Dulat, T.-J. Hou, J. Gao, M. Guzzi, J. Huston, P. Nadolsky, J. Pumplin, C. Schmidt, D. Stump, C. P. Yuan, New parton distribution functions from a global analysis of quantum chromodynamics, Phys. Rev. D93 (3) (2016) 033006
\begin{figure}[h]
\begin{center}
  \includegraphics[scale=0.6]{5-pdfgroups/plots/ct14dou.pdf}
   \caption{\small
   A comparison of 90\% C.L. uncertainties on the $d/u$ PDF ratio at $Q=10$ GeV for
   CT14 NNLO (solid blue) and CT10 NNLO (dashed red), and CJ12 (green lines) error ensembles~\cite{Dulat:2015mca}. 
    \label{fig:ct1}
  }
\end{center}
\end{figure}
\clearpage
\item From S. Dulat, T.-J. Hou, J. Gao, M. Guzzi, J. Huston, P. Nadolsky, J. Pumplin, C. Schmidt, D. Stump, C. P. Yuan, New parton distribution functions from a global analysis of quantum chromodynamics, Phys. Rev. D93 (3) (2016) 033006
\begin{figure}[h]
\begin{center}
  \includegraphics[scale=0.45]{5-pdfgroups/plots/ct14sn.pdf}
   \caption{\small
   Best-fit values of the equivalent Gaussian variables for 33 experiments
   in the CT14 NNLO global analysis~\cite{Dulat:2015mca}. 
    \label{fig:ct2}
  }
\end{center}
\end{figure}
\clearpage
\item From S. Dulat, T.-J. Hou, J. Gao, M. Guzzi, J. Huston, P. Nadolsky, J. Pumplin, C. Schmidt, D. Stump, C. P. Yuan, New parton distribution functions from a global analysis of quantum chromodynamics, Phys. Rev. D93 (3) (2016) 033006
\begin{figure}[h]
\begin{center}
  \includegraphics[scale=0.55]{5-pdfgroups/plots/ct14ha.pdf}
  \hspace{0.3in}
  \includegraphics[scale=0.55]{5-pdfgroups/plots/ct14hb.pdf}
   \caption{\small
   Dependence of the increase in $\chi^2$ in the constrained CT14 fit on the expected
   cross section $\sigma_H$ at the LHC 8 and 13 TeV~\cite{Dulat:2015mca}, for $\alpha_s(M_Z)$=0.118. The solid
   and dashed curves are for the constrained fits without and with the Tier-2 penalties,
   respectively. The red dots correspond to the upper and lower 90\% C.L. limits calculated
   by the Hessian method.  
    \label{fig:cthiggs}
  }
\end{center}
\end{figure}
\clearpage
\item From L. A. Harland-Lang, A. D. Martin, P. Motylinski, R. S. Thorne, Parton distributions in the LHC era: MMHT 2014 PDFs, Eur. Phys. J. C75 (5) (2015) 204. arXiv:1412.3989
\begin{figure}[t]
\begin{center}
  \includegraphics[scale=0.70]{5-pdfgroups/plots/deutCJcomp.pdf}
   \caption{\small Fitted MMHT14 deuteron correction factors with uncertainty, compared to the CJ12~\cite{Owens:2012bv} predictions. Taken from~\cite{Harland-Lang:2014zoa}.
    \label{fig:deutcorr}
  }
\end{center}
\end{figure}
\clearpage
\item From L. A. Harland-Lang, A. D. Martin, P. Motylinski, R. S. Thorne, Uncertainties on αS in the MMHT2014 global PDF analysis and implications for SM predictionsarXiv:1506.05682
\begin{figure}[t]
\begin{center}
  \includegraphics[scale=0.63,trim={0 -2cm 0 0},clip]{5-pdfgroups/plots/globalNNLO.pdf}\quad
   \includegraphics[scale=0.83]{5-pdfgroups/plots/NNLOlimits.pdf}
   \caption{\small (Left) Global $\chi^2$ values as a function of $\alpha_S(M_Z^2)$. (Right) Best fit $\alpha_S(M_Z^2)$ together with the upper and lower 1$\sigma$ constraints from the most constraining data sets. Both figures correspond to NNLO fits and are taken from~\cite{Harland-Lang:2015nxa}.
    \label{fig:MMHTalphas}
  }
\end{center}
\end{figure}
\clearpage
\item From the authors
\begin{figure}[t]
\begin{center}
  \includegraphics[scale=0.45]{5-pdfgroups/plots/20momsumrule.pdf}
   \caption{\small 
   Left plot: comparison between the NNPDF2.0 and 2.1 predictions
   for the inclusive $W+$ production cross-section at the LHC 7 TeV,
   which illustrates the phenomenological impact of heavy quark mass effects.
   %
   Right plot: the distribution of the momentum integral Eq.~(\ref{eq:momentumintegral})
   among the MC replicas for the variants of the NNPDF2.1 LO, NLO and NNLO fits that
   do not impose explicitly the momentum sum rule.
    \label{fig:20momsumrule}
  }
\end{center}
\end{figure}
\clearpage
\item From R. D. Ball, et al., Parton distributions for the LHC Run II, JHEP 04 (2015) 040. arXiv:1410.8849
\begin{figure}[t]
\begin{center}
  \includegraphics[scale=0.45]{5-pdfgroups/plots/nnpdf30closuretests.pdf}
   \caption{\small Representative results of the closure tests presented
   in the NNPDF3.0 analysis.
   %
   Left plot: in a level 0 closure tests, where the pseudo-data is generated
   without any statistical fluctuations, the $\chi^2$ should decrease monotonically
   as a function of the number of GA iterations, down to arbitrarily small values.
   %
   Right plot: the distribution of the difference between theory and data
   in units of the error of the latter among each of the Monte Carlo replicas.
   %
   This distribution is consistent with the Gaussian predicted by statistics.
    \label{fig:nnpdf30closuretests}
  }
\end{center}
\end{figure}
\clearpage
\item From S. Alekhin, J. Blumlein, S. Moch, R. Placakyte, Parton Distribution Functions, αs and Heavy-Quark Masses for LHC Run IIarXiv:1701.05838
\begin{figure}
\begin{center}
  \includegraphics[scale=0.3]{5-pdfgroups/plots/htwist.pdf}\qquad
   \includegraphics[scale=0.3]{5-pdfgroups/plots/gluhigh.pdf}
   \caption{\small (Left) The higher twist coefficient for the $F_2$ structure function from the ABMP16 fit, including 1--$\sigma$ uncertainty. (Right) Percentage difference in ABMP $n_f=3$ gluon distribution between the default result and fits performed with higher $W^2$ cuts, without higher twist corrections. The 1--$\sigma$ uncertainty bands are shown. Plots taken from~\cite{Alekhin:2017kpj}.
    \label{fig:ABMhtwist}
  }
\end{center}
\end{figure}
\clearpage
\item From S. Alekhin, J. Blumlein, S. Moch, R. Placakyte, Parton Distribution Functions, αs and Heavy-Quark Masses for LHC Run IIarXiv:1701.05838
\begin{figure}
\begin{center}
  \includegraphics[scale=0.3]{5-pdfgroups/plots/scanalp.pdf}
   \caption{\small The $\overline{{\rm MS}}$ value of the top quark mass $m_t(m_t)$ obtained in the ABMP16 fit for variants of $\alpha_S(M_Z^2)$ (data points) and for the best fit values (hatched bands). Plot taken from~\cite{Alekhin:2017kpj}.
    \label{fig:ABMmt}
  }
\end{center}
\end{figure}
\clearpage
\item From A. Accardi, L. T. Brady, W. Melnitchouk, J. F. Owens, N. Sato, Constraints on large-x parton distributions from new weak boson production and deep-inelastic scattering data, Phys. Rev. D93 (11) (2016) 114017. arXiv:1602.03154
\begin{figure}[h]
\begin{center}
  \includegraphics[scale=0.45]{5-pdfgroups/plots/cj_du_err.pdf}
  \includegraphics[scale=0.46]{5-pdfgroups/plots/cj_du_pdfs.pdf}
   \caption{\small 
   Left plot: relative error (90\% C.L.) on the $d/u$ PDF ratio as a function of $x$ at
   $Q^2=10\,{\rm GeV}^2$ from the CJ15 fit compared with errors obtained in fits excluding
   certain data sets~\cite{Accardi:2016qay}.
   %
   Right plot: comparison of the $d/u$ ratio at $Q^2=10\,{\rm GeV}^2$ for different PDF
   sets, including CJ15, MMHT14, CT14, and JR14, with PDF uncertainties shown for 90\%
   C.L. except for MMHT14 at 68\% C.L.~\cite{Accardi:2016qay}
    \label{fig:cj2}
  }
\end{center}
\end{figure}
\clearpage
\item From A. Accardi, L. T. Brady, W. Melnitchouk, J. F. Owens, N. Sato, Constraints on large-x parton distributions from new weak boson production and deep-inelastic scattering data, Phys. Rev. D93 (11) (2016) 114017. arXiv:1602.03154
\begin{figure}[h]
\begin{center}
  \includegraphics[scale=0.45]{5-pdfgroups/plots/cj_F2dN_wfn.pdf}
   \caption{\small 
   Ratio of deuteron to isoscalar nucleon structure functions $F_2^d/F_2^N$ at
   $Q^2=10\,{\rm GeV}$ for CJ15 fits with different models of wave functions~\cite{Accardi:2016qay};
   colored band is the 90\% C.L. error for CJ15 main fit (with AV18 wave functions). 
    \label{fig:cj3}
  }
\end{center}
\end{figure}
\clearpage
\item From F. Aaron, et al., Combined Measurement and QCD Analysis of the Inclusive e± p Scattering Cross Sections at HERA, JHEP 1001 (2010) 109. arXiv:0911.0884
\begin{figure}[t]
\begin{center}
  \includegraphics[scale=0.50]{5-pdfgroups/plots/xfitter.pdf}
   \caption{\small Left plot: the HERAPDF1.0 determination of parton distributions,
   based on the analysis of the combined HERA structure functions from
   Run I.
   %
   Right plot: schematic representation of the {\tt xFitter} code structure, see text
   for more details.
    \label{fig:xfitter}
  }
\end{center}
\end{figure}
\clearpage
\item From Left: S. Camarda, et al., QCD analysis of W- and Z-boson production at Tevatron, Eur. Phys. J. C75 (9) (2015) 458. arXiv:1503.05221; Right: V. Bertone, et al., A determination of mc(mc) from HERA data using a matched heavy-flavor scheme, JHEP 08 (2016) 050. arXiv:1605.01946
\begin{figure}[t]
\begin{center}
  \includegraphics[scale=0.70]{5-pdfgroups/plots/xfitter2.pdf}
   \caption{\small Two representative analyses of PDF-related studies
   performed by the {\tt xFitter} Developer's Team.
   Left plot: the impact on $d_V$ of the Tevatron $W$ and $Z$ data on a HERA-only
   fit, comparing the impact of the lepton-level measurements with that of the boson-level
   measurements, from Ref.~\cite{Camarda:2015zba}.
   %
   Right plot: the $\chi^2$ profile of a fit based on the inclusive
   HERA and charm data, as a function of the running mass $m_c(m_c)$ from
   Ref.~\cite{Bertone:2016ywq}.
   %
   In this analysis charm structure functions were computed with {\tt APFEL}
   in the FONLL-C general mass scheme.
    \label{fig:xfitter2}
  }
\end{center}
\end{figure}
\clearpage
\item From Left: G. Aad, et al., Measurement of the inclusive jet cross section in pp collisions at √s=2.76 TeV and comparison to the inclusive jet cross section at √s=7 TeV using the ATLAS detector, Eur.Phys.J. C73 (2013) 2509; Right: M. Aaboud, et al., Precision measurement and interpretation of inclusive W+, W− and Z/γ∗ production cross sections with the ATLAS detectorarXiv:1612.03016
\begin{figure}[t]
\begin{center}
  \includegraphics[scale=0.45]{5-pdfgroups/plots/atlaspdffits.pdf}
   \caption{\small Two representative results of the PDF fitting efforts
   performed within the ATLAS collaboration.
   %
   Left plot: a PDF fit quantifying the effect on the gluon from the HERA-only fit
   of the ATLAS inclusive jet measurements at $\sqrt{s}=2.76$ TeV
   and 7 TeV, from Ref.~\cite{Aad:2013lpa}.
   %
   Right plot: the determination of the strangeness ratio $R_s(x=0.023,Q^2=1.9\,{\rm GeV}^2)$
   for a fit to HERA data and the 2011 ATLAS measurements of the $W^{\pm}$ and $Z$
   rapidity distributions at 7 TeV, where the results of the {\tt xFitter} analysis,
   denoted by ATLAS-epWZ16, are compared with the predictions from various PDF fits.
    \label{fig:atlaspdffits}
  }
\end{center}
\end{figure}
\clearpage
\item From
\begin{figure}[t]
\begin{center}
  \includegraphics[scale=0.40]{6-structure/plots/xg-abs-pdfcomp-lowQ.pdf}
  \includegraphics[scale=0.40]{6-structure/plots/xg-pdfcomp-highQ.pdf}
   \caption{\small 
     The gluon PDF $xg(x,Q^2)$ at $Q=1.7$ GeV (left)
     and $Q=100$ GeV (right) comparing the ABMP16, CT14, MMHT14,
     and NNPDF3.1 NNLO sets with $\alpha_{S}(m_Z)=0.118$.
     %
     In the right plots, results are normalized to the central value
     of NNPDF3.1.
    \label{fig:pdfcomp-xg}
  }
\end{center}
\end{figure}
\clearpage
\item From
\begin{figure}[t]
\begin{center}
  \includegraphics[scale=0.44]{6-structure/plots/largexgluon.pdf}
   \caption{\small 
     Left: comparison of the NNPDF3.1 NNLO global fit at $Q=100$ GeV with
     the corresponding fits where the $Z$ $p_T$, top quark, or inclusive
     jet data have been removed.
     %
     Right plot: same as before, now comparing with the NNPDF3.1 NNLO fit
     where the ATLAS and CMS 7 TeV inclusive jet data have been treated
     using exact NNLO theory.
    \label{fig:largexgluon}
  }
\end{center}
\end{figure}
\clearpage
\item From
\begin{figure}[t]
\begin{center}
  \includegraphics[scale=0.39]{6-structure/plots/xu-pdfcomp-highQ.pdf}
  \includegraphics[scale=0.39]{6-structure/plots/xd-pdfcomp-highQ.pdf}
  \includegraphics[scale=0.39]{6-structure/plots/xubar-pdfcomp-highQ.pdf}
  \includegraphics[scale=0.39]{6-structure/plots/xdbar-pdfcomp-highQ.pdf}
   \caption{\small 
     Same as Fig.~\ref{fig:pdfcomp-xg} (right), now comparing the
     up, down, anti-up, and anti-down quark PDFs.
    \label{fig:pdfcomp-quarkseparation}
  }
\end{center}
\end{figure}
\clearpage
\item From
\begin{figure}[t]
\begin{center}
  \includegraphics[scale=0.39]{6-structure/plots/xDeltaS-abs-pdfcomp-lowQ.pdf}
  \includegraphics[scale=0.39]{6-structure/plots/xtriplet-abs-pdfcomp-lowQ.pdf}
    \caption{\small 
     Same as Fig.~\ref{fig:pdfcomp-xg} (left), now comparing the
     sea quark asymmetry $\Delta_S=\bar{d}-\bar{u}$ (left) and the quark
     isotriplet $T_3=u+\bar{u}-d-\bar{d}$ (right plot).
    \label{fig:pdfcomp-quarkseparation-2}
  }
\end{center}
\end{figure}
\clearpage
\item From
\begin{figure}[t]
\begin{center}
  \includegraphics[scale=0.39]{6-structure/plots/xu-abs-pdfcomp-highQ.pdf}
  \includegraphics[scale=0.39]{6-structure/plots/xd-abs-pdfcomp-highQ.pdf}
    \caption{\small 
      Same as Fig.~\ref{fig:pdfcomp-quarkseparation}, now focusing
      on the large-$x$ region of the up quark (left) and down quark
      (right plot) PDFs.
    \label{fig:pdfcomp-quarkseparation-largex}
  }
\end{center}
\end{figure}
\clearpage
\item From
\begin{figure}[t]
\begin{center}
\includegraphics[scale=0.40]{6-structure/plots/xsp-abs-pdfcomp-lowQ.pdf}
\includegraphics[scale=0.40]{6-structure/plots//xsp-pdfcomp-highQ.pdf}
     \caption{\small 
      Same as Fig.~\ref{fig:pdfcomp-xg} for the total strangeness
      $xs^+(x,Q^2)$.
      \label{fig:pdfcomp-xsp}
  }
\end{center}
\end{figure}
\clearpage
\item From
\begin{figure}[t]
\begin{center}
\includegraphics[scale=0.45]{6-structure/plots/strangeratio-summary.pdf}
     \caption{\small 
     The ratio of strange to non-strange sea quarks
     $R_s (x,Q^2)$, Eq.~(\ref{eq:rs}) for $x=0.023$
     and $Q^2=1.9$ GeV$^2$.
     %
     We compare the results of various global PDF fits with those
     of the ATLAS/{\tt xFitter} interpretation study as well as with
     those of a NNPDF3.1 fit based on the same dataset as the ATLAS
     study.
     %
     The vertical lines indicate two possible scenarios for the strange
     PDFs, namely a suppression of size $R_{s}\simeq 0.5$ and then
     a strange sea which is symmetric with the non-strange one,
     $R_{S}\simeq 1$.
      \label{fig:Rsx}
  }
\end{center}
\end{figure}
\clearpage
\item From
\begin{figure}[t]
\begin{center}
\includegraphics[scale=0.40]{6-structure/plots/xRs-abs-RslowQ.pdf}
\includegraphics[scale=0.40]{6-structure/plots/xRs-abs-RshighQ.pdf}
     \caption{\small 
     The ratio of strange to non-strange sea quarks
     $R_s (x,Q^2)$, Eq.~(\ref{eq:rs}), as a function of $x$
     for $Q=1.38$ GeV (left plot) and for $Q=100$ GeV (right plot).
               \label{fig:Rsxplot}
  }
\end{center}
\end{figure}
\clearpage
\item From
\begin{figure}[t]
\begin{center}
\includegraphics[scale=0.44]{6-structure/plots/ct14ic.pdf}
     \caption{\small 
     Left: the deviation of the $\chi^2$ in the CT14IC fits,
with respect to the
     best-fit value of the CT14 fit with perturbative charm,
     as a function of $\la x\ra_{\rm IC}$
     %
     Results are shown for the BHPS and SEA models, with the
    ``1'' points labeling the preferred value of  $\la x\ra_{\rm IC}$,
    with those labelled with ``2'' indicate the largest
    values of the charm momentum fraction allowed by the
    fit tolerance criteria.
    %
    Right: the transverse momentum distribution of $Z$ bosons
    in the $pp \to Z+c$ process at 13 TeV, comparing the CT14 NNLO
    result with various of the CT14 IC models, as a function
    of $p_T^Z$.
      \label{fig:ct14ic}
  }
\end{center}
\end{figure}
\clearpage
\item From
\begin{figure}[t]
\begin{center}
\includegraphics[scale=0.40]{6-structure/plots/Cplot.pdf}
\includegraphics[scale=0.40]{6-structure/plots/Cplot-highQ.pdf}
     \caption{\small 
       The momentum fraction carried by charm quarks, $C(Q)$
       Eq.~(\ref{eq:charmmomfrac}),
       both at a low scale $Q=1.51$ GeV (left) and at a high scale
       $Q=M_Z$ (right plot).
       %
       We compare NNPDF3.0 (perturbative charm) with NNPDF3.1 (based on
       fitted charm) with and without the inclusion of the EMC charm
       data, as well as with the BHPS and SEA scenarios of the
       CT14IC fits.
       %
       See text for more details.
      \label{fig:charmfrac}
  }
\end{center}
\end{figure}
\clearpage
\item From
\begin{figure}[h]
\begin{center}
\includegraphics[scale=0.40]{6-structure/plots/nnpdf31ic.pdf}
     \caption{\small 
      Left: comparison of the fitted charm PDF at $Q=1.65$ GeV
      between the NNPDF3IC set and the different models
      of the CT14IC analysis.
      %
      Right: the dependence of the quark-antiquark
      PDF luminosity at the LHC 13 TeV in the NNPDF3IC fits
      with the value of the charm mass $m_c$ used in the fit.
      \label{fig:nnpdf31ic}
  }
\end{center}
\end{figure}
\clearpage
\item From the authors.
\begin{figure}
  \begin{center}
    \includegraphics[width=0.28\textwidth]{7-QED/plots/photon}
    \includegraphics[width=0.45\textwidth]{7-QED/plots/lumi13r.pdf}
  \end{center}
  \caption{\small Left: schematic diagram for the photon--initiated production of a system $X$, and the corresponding photon PDFs.
    %
    Right: the $\gamma\gamma$ luminosity as a function of the invariant mass, $M_X$, of the produced final-state, taken from~\cite{Giuli:2017oii}.
The ratio to results with $O(\alpha\alpha_S)$ and $O(\alpha^2)$ to the leading $O(\alpha)$ DGLAP evolution shown. 
  }\label{fig:photfeyn} \label{fig:qedevol}
\end{figure}
\clearpage
\item From 1607.04266
\begin{figure}[t]
  \begin{center}
    \includegraphics[width=0.99\textwidth]{7-QED/plots/LUXqed.pdf}
  \end{center}
  \vspace{-0.6cm}
  \caption{\small Left: overview of the various contributions to the photon
    PDF $\gamma(x,Q^2)$ in the LUXqed approach as a function of $x$
    at $Q=100$ GeV.
    %
    Right: comparison of the photon PDFs from CT14qed\_inc, MRST2004, NNPDF2.3/3.0
    and LUXqed, normalized to the central value of the latter.
  }\label{fig:LUXqed}
\end{figure}
\clearpage
\item From
\begin{figure}[t]
  \begin{center}
 \includegraphics[width=0.45\textwidth]{7-QED/plots/lumi13m}
  \includegraphics[width=0.45\textwidth]{7-QED/plots/lumi13r1}
  \end{center}
\caption{$\gamma\gamma$ luminosities at $\sqrt{s}=13$ TeV. (Left) Absolute values for the HKR16,  NNPDF3.0QED and LUXqed sets. (Right) Ratios of the CT14QED, HKR16 and {\tt xFitter\_HMDYep} sets to the LUXqed prediction. 68\% uncertainty bands are shown, with the exception of the HKR16 set, where the error is due to model variation in the inelastic input (lower edge corresponds to elastic only).}\label{fig:photlumi}
\end{figure}
\clearpage
\item From 1607.04635 (left) and the authors (right)
\begin{figure}[t]
  \begin{center}
 \includegraphics[width=0.45\textwidth]{7-QED/plots/crosslux.pdf}
  \includegraphics[width=0.45\textwidth]{7-QED/plots/crossluxfcc.pdf}
  \end{center}
\caption{The differential lepton pair production cross sections at $\sqrt{s}=$ 13 TeV and 100 TeV with respect to the invariant mass of the pair $M_{ll}$, for lepton $|\eta| <2.5$ and $p_\perp  > 20$ GeV. The photon--initiated contributions predicted using the LUXqed and NNPDF3.0QED sets, including the 68\% C.L. uncertainty bands. The NLO Drell--Yan cross section, calculated with \texttt{MCFM}~\cite{Campbell:2011bn}, is also shown.}\label{fig:lepphot}
\end{figure}
\clearpage
\item From
\begin{figure}[t]
  \begin{center}
 \includegraphics[width=0.99\textwidth]{7-QED/plots/EWcorr.pdf}
  \end{center}
  \vspace{-0.6cm}
  \caption{\small Two representative examples of NLO EW corrections
    for processes relevant for PDF determinations, computed with {\tt MCFM}
    at $\sqrt{s}=13$ TeV~\cite{Campbell:2016dks}.
    %
    In the left plot, we show the percentage NLO EW correction for high-mass dilepton
    production as a function of $M_{ll}$, comparing also with the
    corresponding {\tt ZGRAD} calculation.
    %
    In the right plot, we show the same quantity, now for dijet production
    as a function of the invariant mass of the dijet $M_{jj}$.
    %
    The two curves correspond to two possible ways to combine NLO
    QCD and EW corrections, known as additive ($\delta_{\rm add}$)
    and multiplicative ($\delta_{\rm prod}$).
    \label{fig:Sect7-EWcorr}}
\end{figure}
\clearpage
\item From 1607.04635 
\begin{figure}[h]
\begin{center}
  \includegraphics[scale=0.61]{8-pheno/plots/higgs-summary.pdf}
  \caption{\small The PDF dependence of the
  most important Higgs production inclusive
    cross-sections at the LHC 13 TeV.
    %
    The results are normalized to the central value of NNPDF3.1,
    and only PDF uncertainties are shown.
    %
    See text for more details of the theoretical
    calculation.
    \label{fig:higgs}
  }
\end{center}
\end{figure}
\clearpage
\item From
\begin{figure}[h]
\begin{center}
  \includegraphics[scale=0.45]{8-pheno/plots/higgs-differential.pdf}
  \caption{\small Left: the PDF uncertainties in the
  $p_T^h$ distribution of Higgs bosons produced in the gluon-fusion
  mode at the LHC 13 TeV for $0 \le p_T^h \le 200$ GeV,
  computed using the PDF4LHC15 sets.
  %
  Right: the gluon-gluon PDF luminosity with the same
  set now extending up to higher values of the invariant mass
  of the final state $M_X$.
    \label{fig:higgs_differential}
  }
\end{center}
\end{figure}
\clearpage
\item From
\begin{figure}[t]
\begin{center}
  \includegraphics[scale=0.40]{8-pheno/plots/gg_lumi-tev.pdf}
  \includegraphics[scale=0.40]{8-pheno/plots/qg_lumi-tev.pdf}
  \includegraphics[scale=0.40]{8-pheno/plots/qq_lumi-tev.pdf}
  \includegraphics[scale=0.40]{8-pheno/plots/q2_lumi-tev.pdf}
  \caption{\small Comparison of PDF luminosities in the large
    invariant mass $M_X$ region between MMHT14, ABMP16, CT14 and
    NNPDF3.1.
    %
    From left to right and from top to bottom we show the results
    of the gluon-gluon, gluon-quark, quark-antiquark
    and quark-quark luminosities, normalized
    to the central value of MMHT14.
    %
    In this comparison, NNLO PDFs with $\alpha_s(m_Z)=0.118$
    sets are used.
    \label{fig:BSMlumi}
  }
\end{center}
\end{figure}
\clearpage
\item From
\begin{figure}[t]
\begin{center}
  \includegraphics[scale=0.45]{8-pheno/plots/BSMhighmass.pdf}
  \caption{\small Left: the PDF uncertainties for high-mass
  graviton production in the Randall-Sundrum scenario
  induced by gluon-fusion at the LHC 8 TeV, computed
  with {\tt MadGraph5}.
  %
  We compare the results of the NNPDF2.3 fit with that
  of the same fit including the constraints
  from top-quark production cross-sections.
  %
  Right: the $K$-factor for the NLO+NLL cross-section,
  including PDF uncertainties, for the production
  of a squark-anti-squark pair $\tilde{q}\tilde{q}^*$
  at the LHC 13 TeV with various PDF sets.
    \label{fig:BSMhighmass}
  }
\end{center}
\end{figure}
\clearpage
\item From
\begin{figure}[t]
\begin{center}
  \includegraphics[scale=0.45]{8-pheno/plots/mw.pdf}
  \caption{\small Left: comparison of the direct
  measurements of $m_W$, $m_t$, and $m_h$ from ATLAS
  with the predictions from the global electroweak fit,
  from~\cite{Aaboud:2017svj}.
  %
  Right: estimate of the PDF uncertainties in the $m_W$
  determination using different PDF sets and collider scenarios,
  from~\cite{Bozzi:2015hha} 
  %
  This estimate has been obtained from template fits to the
  $p_T^l$ distribution, imposing the constraint that $p_T^W\le 15$ GeV.
    \label{fig:mw}
  }
\end{center}
\end{figure}
\clearpage
\item From
\begin{figure}[t]
\begin{center}
  \includegraphics[scale=0.45]{8-pheno/plots/alphasrunning.pdf}
  \caption{\small Left: the modification
  in the running of $\alpha_s(Q)$ induced
  by a new heavy colored fermion of mass $m=0.5$ TeV as compared to the SM
  prediction, for various representations of its color gauge group,
  from~\cite{Becciolini:2014lya}.
  %
  Right: comparison of recent direct determinations of $\alpha_s(Q)$ at the Tevatron
  and the LHC as a function of $Q$, together with the PDG 2016 world
  average and with the results of the global ATLAS TEEC 2012 fit.
    \label{fig:alphasrunning}
  }
\end{center}
\end{figure}
\clearpage
\item From
\begin{figure}[h]
\begin{center}
  \includegraphics[scale=0.45]{9-future/plots/Higgs_Fig2.pdf}
   \caption{\small
   The cross section for Higgs production in gluon fusion calculated
   at increasing perturbative orders~\cite{Forte:2013mda}.
   At each order the theoretical uncertainty is shown for 
   using scale variation (red circles), the CH method (blue crosses),
   and the $\overline {\rm CH}$ method (green squares); at N$^3$LO the
   Passarino-David uncertainty based on series acceleration method
   is also shown (purple diamonds).
    \label{fig:thunc1}
  }
\end{center}
\end{figure}
\clearpage
\item From
\begin{figure}[h]
\begin{center}
  \includegraphics[scale=0.37]{9-future/plots/gluon_jcc21x_to_cy29c_1.pdf}
  \hspace{0.1in}
  \includegraphics[scale=0.38]{9-future/plots/cteq-jets3.pdf}
   \caption{\small 
   Left plot: dependence of the gluon PDFs on the choice of QCD scales in 
   calculation of inclusive jet cross sections in CT10 NNLO fits~\cite{Gao:2013xoa}.
   %
   Right plot: impact of the theoretical uncertainties of inclusive jet
   cross sections on the gluon PDFs in CT10 NNLO fits~\cite{Rojo:2015acz} .
    \label{fig:thunc2}
  }
\end{center}
\end{figure}
\clearpage
\item From
\begin{figure}[h]
\begin{center}
  \includegraphics[scale=0.37]{9-future/plots/xg-th_nnlo_vs_nlo.pdf}
  \hspace{0.1in}
  \includegraphics[scale=0.37]{9-future/plots/xsinglet-th_nnlo_vs_nlo.pdf}
   \caption{\small
   Left(right) plot shows comparisons between the conventional PDF uncertainties and
   the differences of the central PDFs determined at NLO and NNLO for the
   gluon(total singlet) PDF as from NNPDF3.0~\cite{Ball:2014uwa}. 
    \label{fig:thunc3}
  }
\end{center}
\end{figure}
\clearpage
\item From
\begin{figure}[t]
\begin{center}
  \includegraphics[scale=0.50]{9-future/plots/PDFlattice.pdf}
   \caption{\small 
                       \label{fig:PDFlattice}
                       Left plot: the $u(x)-d(x)$ difference
                       as a function of Bjorken $x$, where the
                       results of a recent lattice QCD calculation
  based on quasi-PDFs is compared with the MSTW08 and CJ12 results.
  %
  Right plot: the momentum fraction carried by sum of
  up and down quarks, $\la x \ra_{u+d}$ for different values
  of the parameter $t_s$ (points with
  errors), compared with the results from recent global
  PDF fits (horizontal band).
  }
\end{center}
\end{figure}
\clearpage
\item From
\begin{figure}[t]
\centering
\includegraphics[width=0.93\textwidth]{9-future/plots/lhec.pdf}
\caption{\small Left plot: kinematic coverage in the $(x,Q^2)$
of several existing and proposed deep-inelastic scattering experiments.
%
Starting from the fixed-target experiments and then moving to HERA, the
LHeC and finally the FCC-eh, as the center of mass energy increases,
the kinematic reach extends both towards higher $Q^2$ and smaller $x$ values.
%
Right plot: results of an {\tt xFitter} PDF feasibility study that
compares the impact on the gluon PDF of adding either LHeC or FCC-eh (or both)
pseudo-data in addition to the HERA inclusive structure function dataset.
}
\label{fig:kinplotLHeC}
\end{figure}
\clearpage
\item From
\begin{figure}[t]
\begin{center}
\includegraphics[scale=0.38]{9-future/plots/F2p_lhec.pdf}
\includegraphics[scale=0.38]{9-future/plots/FLp_lhec.pdf}
\includegraphics[scale=0.38]{9-future/plots/F2p_fcceh.pdf}
\includegraphics[scale=0.38]{9-future/plots/FLp_fcceh.pdf}
\caption{\small The theoretical predictions  for the $F_2$ and $F_L$ structure functions at the
LHeC (upper) and FCC-eh (lower plots) using the NNPDF3.1sx NNLO
   and NNLO+NLL$x$ fits at $Q^2=5$ GeV$^2$.
%
In the case of the $F_2^p$ structure function, we also show the expected total experimental uncertainties
   based on the simulated pseudo-data, assuming the NNLO+NLL$x$ values as central prediction.
       \label{fig:LHeCpredictions}
  }
\end{center}
\end{figure}
\clearpage
\item From
\begin{figure}[t]
\centering
\includegraphics[width=0.93\textwidth]{9-future/plots/kinplot}
\caption{\small Kinematic coverage in the $(x,M_X)$ plane of a
  $\sqrt{s}=100$ TeV 
  hadron collider (solid blue line),
  compared with the corresponding coverage of the LHC at
  $\sqrt{s}=14$ TeV (dot-dashed red line).
}
\label{fig:kinplot}
\end{figure}
\clearpage
\item From
\begin{figure}[t]
\begin{center}
  \includegraphics[scale=0.60]{9-future/plots/fcc-xsecs.pdf}
   \caption{\small 
     Comparison of cross-sections for different representative
     processes at the FCC with $\sqrt{s}=100$ TeV,
     between the NNPDF3.0 predictions and those of the NNPDF3.0+LHCb
     sets, as discussed in the text.
     %
     The acceptance cuts are different in each process.
     %
     In the left plot we show the results for direct photon
     production, off-peak Drell-Yan cross-sections, and inclusive
     weak boson production.
     %
     In the right plot we show the fiducial cross-sections for
     $c\bar{c}$ and $b\bar{b}$ production.
    \label{fig:fcc-xsecs}
  }
\end{center}
\end{figure}
\clearpage
\item From
\begin{figure}[t]
\begin{center}
  \includegraphics[scale=0.44]{9-future/plots/FCCtopEW.pdf}
   \caption{\small 
    Left: the PDF of the $W^+$ boson normalized to that of the gluon,
    as a function of $x$ for different scales: $q=10^4$ GeV,
    $10^6$ GeV, $10^8$ GeV, from Ref.~\cite{Bauer:2017isx}.
    %
    Right: the cross-section inclusive Higgs production by $t\bar{t}$ associated
    production, comparing the results of the $n_f=5$ scheme ($gg\to h t\bar{t}$),
    the $n_f=6$ scheme ($t\bar{t}\to h$), and of their interpolation by means
    of the ACOT general-mass scheme.
\label{fig:FCCtopEW}
  }
\end{center}
\end{figure}



\end{enumerate}

\end{document}
