text:
\subsubsection{Searches for Jet Quenching in \mbox{$pA$}\xspace\ collisions}

Given the recent wealth of data showing evidence for
collective behavior in
\pPb, \pp\ collisions (for a recent review see Ref.~\cite{Nagle:2018nvi}),
it is natural to search for
jet quenching effects in these systems.  As of this writing
no effects of jet quenching have been observed in \pPb\ or \pp\ collisions.
Here we discuss several searches for jet quenching in \mbox{$pA$}\xspace\ collisions.

The nuclear modification factor \RpA\ has been measured both in
\mbox{$d$$+$Au}\xspace\ collisions at RHIC and \pPb\ collisions at the LHC
for both jets~\cite{Adare:2015gla,Adam:2015hoa,ATLAS:2014cpa} and
charged particles~\cite{Adams:2003im,Adler:2003ii,Khachatryan:2016odn}.
No evidence for jet quenching was found in these measurements.
However, the precision of these measurements is limited by the
normalization uncertainties associated with the nuclear modification
factor coming from the luminosity and \TAA\ determination (along
with other sources).

In order to be sensitive to potentially smaller jet quenching
effects, measurements of self-normalized observables (e.g. normalized per-jet, or per-trigger
particle) have been done.
ALICE measured the charged-particle jets opposite to a high-transverse momentum
trigger hadron~\cite{Acharya:2017okq} and reported their per-trigger normalized yield over a broad kinematic range.
The advantage of the per trigger particle normalisation is that no \TAA\ scaling of the reference is needed and thus no Glauber modelling and interpretation of the event activity (EA) in terms of geometry is required.
Events are classified according to how hits in a forward scintillator in the Pb-going
direction or hits in a zero-degree neutron detector also in the Pb-going direction.
Figure \ref{fig:pPbjqALICE}, shows the ratio of the observable in the two EA classes. The ratio is consistent with no energy loss. The red line indicates a limit, at $90\%$ confidence level, on the average $p_{T}$ shift of 0.4 GeV/c, which is an estimate of the maximum energy that is transported outside the jet cone.

\begin{figure}[h!]
 \centering
  \includegraphics[width=0.45\textwidth]{plots/2018-May-20-ppb5_RCP_limit90_AKT04_V0A_W1.pdf}
 \caption{ Ratio of recoil jet $p_{\rm{T}}$ distribution in \pPb\ events with high and low event activity measured in the forward detectors. From Ref. \cite{Aaboud:2017tke}}
 \label{fig:pPbjqALICE}
 \end{figure}

 ATLAS measured fragmentation functions in \pPb\ collisions~\cite{Aaboud:2017tke}.
 As shown in Figure~\ref{fig:pPbjq} in contrast
 to \mbox{Pb$+$Pb}\xspace\ collisions, no significant deviation was found between the \pPb\ fragmentation
 functions and the \pp\ ones for the soft particles in the jet.
 There is some excess of less than 10\% in the central values
 for charged-particles between approximately 1--5~GeV between
 the fragmentation functions in \pPb\ and \pp\ collisions but it is within the
 size of the systematic uncertainties.
 Also shown in Figure~\ref{fig:pPbjq} is the measurement from CMS of
 the dijet asymmetry in \pPb\ collisions selected on the forward
 energy in the Pb-going direction~\cite{Chatrchyan:2014hqa}.
 They evaluated the mean of this distribution
 and found that quantity to be independent of the forward energy to within their
 uncertainties.

 \begin{figure}[h!]
 \centering
 \includegraphics[width=0.59\textwidth]{plots/atlas_pPb_FF.pdf}
 \includegraphics[width=0.4\textwidth]{plots/CMS_pPb_xJ.pdf}
 \caption{(left) Ratios of the fragmentation functions in \pPb\ collisions
 to those in \pp\ collisions for various \mbox{$p_{\mathrm{T}}^{\mathrm{jet}}$}\ selections as a
 function of charged particle \mbox{${p_T}$}\xspace.  (right) Mean value
 of the ratio of the subleading to leading \mbox{$p_{\mathrm{T}}^{\mathrm{jet}}$} (\mbox{$x_{J}$})
 as a function of the transverse energy in the Pb-going direction.  Figures
 are from Ref.~\cite{Aaboud:2017tke} (left) and Ref.~\cite{Chatrchyan:2014hqa} (right). }
 \label{fig:pPbjq}
 \end{figure}

There is ongoing interest in more sensitive measurements which might
be more sensitive to any jet quenching signal but the existing measurements
clearly show that any jet quenching which might exist in \pPb\ collisions
is much smaller than that in heavy ion collisions.

\subsubsection{Light ion collisions}
 In order to map the transition
between large systems (e.g. central heavy ion collisions collisions) with large
energy loss and small \mbox{$pA$}\xspace\ systems without observed energy
loss, there is a lot of interest in having small, symmetric
collision systems with which to potentially observe the turn-off of jet
quenching.

Some data from collision systems smaller than \mbox{Pb$+$Pb}\xspace\ or
\auau\ does exist.  Most recently, the LHC delivered
\xexe\ collisions in 2017.  Those results showed that the
value of \RAA\ for charged particles depends primarily
on the size of the collision system (as measured by the charged particle
multiplicity)~\cite{Acharya:2018eaq}.
However, the utility of the \xexe\ measurements to answer this question
is limited by the
fact that \xexe\ collisions are much closer in charged-particle
multiplicity and \Npart\ to \mbox{Pb$+$Pb}\xspace\ collisions than they are to \pPb\
collisions.

In light of this there remains a great interest in colliding a
much smaller collision system, with an \Npart\ close to that
of \pPb\ collisions but with a larger geometrical transverse overlap that increases the in-medium path length and thus potentially, quenching.
The preferred collision system
is \OO~\cite{Huss:2020dwe,Brewer:2021kiv}. The experimental projections for the nuclear modification factor of charged hadrons measured in a short \OO\ run of $0.5$ nb$^{-1}$ \cite{ALICE-PUBLIC-2021-004} were compared to theoretical expectations for jet quenching ~\cite{Huss:2020dwe,Huss:2020whe}. The comparison indicates that partonic energy loss signal might be observed at transverse momentum of approximately 20~GeV.

In the spring of 2021
RHIC ran \OO\ collisions for the STAR experiment.
The data from that run has not yet been analyzed but will
be the first look at this important question.

\section{Introduction}
\input{intro}
\section{A brief summary of the theoretical advances in jet quenching}
\input{theory}
\section{Jet Measurements in Heavy Ion Collisions}
\subsection{Jet Reconstruction}
\input{techniques}
\subsection{Jet tools}
\label{subsect:jettools}
\input{tools}
\subsection{Jet Observables}
\input{observables}
\section{What have we learned from jet measurements at the LHC and RHIC?}

We have organised available heavy-ion jet data around  three physics
questions. First, what are the mechanisms responsible for the transport of energy from high-energy to low-energy modes within the QGP? Second, can we observe jets
probing free quarks and gluons within the QGP?
And finally, what is the critical size for the QGP formation?
The first class of measurements constrains the mechanisms of jet-medium interactions since it comprises a vast set of observables that are differential in jet size, flavour, shape, substructure and in-medium path length. We reconstruct jets after they interacted with the QGP and we measure the properties of a specific selection of jets, hose which have survived. We aim to learn about flavour hierarchy in energy loss, about the role of the medium response, or the interplay between energy loss and color coherence. These aspects of jet quenching are interconnected and measurements attempt to isolate the effects, for instance, by separating large-angle and small-angle components or by selecting jets with a hard 2-prong substructure.
The second class of observables comprise searches of large momentum transfer interactions in the medium as a proof of point-like scatterers within the QGP fluid.  The third class of measurements comprises searches for jet quenching signatures in small systems like \pPb\
collisions that display signatures of collective effects.

\subsection{Jet energy transport within the QGP}

\input{transport}

\subsection{Effective Degrees of Freedom of the QGP}
\input{dof}

\subsection{Critical Size for QGP Formation}
\input{critical_size}

\section{Conclusions and Outlook}
\input{conclusions}
\section{Acknowledgements}
\input{thanks}

\section{References}
\bibliographystyle{unsrturl}

\subsubsection{How opaque is the QGP to jet propagation?}

Inclusive jets dominantly originate from light quarks and gluons.  The high rates of these
jets allow for measurements over a very large kinematic range. Figure~\ref{fig:incjetsRAA}
shows recent ALICE and ATLAS results of the
jet nuclear modification factor, \mbox{$R_{\mathrm{AA}}$}, measured in 0--10\%
central collisions from 60~GeV to 1~TeV
for \mbox{$R=0.4$}\ jets~\cite{Acharya:2019jyg,Aaboud:2018twu} for 5.02~TeV \mbox{Pb$+$Pb}\xspace\
collisions at the LHC.
\mbox{$R_{\mathrm{AA}}$}\ remains below unity over the entire measured
kinematic range.
At RHIC, the jet \mbox{$R_{\mathrm{CP}}$}\ was measured~\cite{Adam:2020wen} and been found to be
consistent with values from Ref.~\cite{Abelev:2013kqa} in 2.76~TeV \mbox{Pb$+$Pb}\xspace\ collisions,
see Figure~\ref{fig:starrcp}. Additionally, \RAA\ has
been measured for neutral pions~\cite{PHENIX:2012jha}.

\begin{figure}
\centering
 \includegraphics[width=0.44\textwidth]{plots/alice_r4_raa.pdf}
   \includegraphics[width=0.54\textwidth]{plots/RAA_ATLAS.pdf}
   \caption{Jet \mbox{$R_{\mathrm{AA}}$}\ as a function of \mbox{$p_{\mathrm{T}}^{\mathrm{jet}}$}\ in \mbox{Pb$+$Pb}\xspace\ collisions.  Figures are from Refs.~\cite{Acharya:2019jyg} (left) and \cite{Aaboud:2018twu} (right).}
   \label{fig:incjetsRAA}
\end{figure}

\begin{figure}
\centering
\includegraphics[width=0.95\textwidth]{plots/star_rcp_jet.pdf}
\caption{\mbox{$R_{\mathrm{CP}}$}\ for jets and charged particles at RHIC and the LHC
(as indicated on the plot)
for \mbox{$R=0.2$}\ (left) and \mbox{$R=0.3$}\ jets (right).  From Ref.~\cite{Adam:2020wen}.}
\label{fig:starrcp}
\end{figure}

In order to extract energy loss values from these measurements, it is necessary to have a
model.  Jet quenching models are reviewed in
Refs.~\cite{Qin:2015srf,Blaizot:2015lma,Cao:2020wlm}.
A great deal of theoretical work has gone into the development of these
models over many years.  However, constraining models with data has been a
challenge.
The use of Bayesian techniques to extract jet
quenching parameters is a recent but rapidly evolving field.
 This was first used in heavy ion collisions
to constrain the equation of state~\cite{Pratt:2015zsa} and is now used to extract
estimates for the QGP bulk properties including sheer and
bulk viscosity (see recent examples in
Refs.~\cite{Bernhard:2019bmu, JETSCAPE:2020mzn, Nijs:2020roc}).

From the LHC data, Ref.~\cite{He:2018gks} calculated that
jets have lost an average of 10--50 GeV for \mbox{$p_{\mathrm{T}}^{\mathrm{jet}}$}\ between 100 and 900~GeV.
These energy loss
values provide additional information based on
the \RAA\ values, but they are
not direct properties of the QGP.  The extraction of \qhat\ from energy
loss measurements was recently performed in Refs.~\cite{Ke:2020clc,Cao:2021keo} using
the LIDO and JETSCAPE software, respectively.
Both of these papers constrain the models to experimental data by evolving a jet
quenching calculation through a 2+1D hydrodynamic evolution (using event-averaged
initial conditions).    At high temperature, the
two \qhat\ extractions agree and constrain $\qhat / T^3$ to be approximately 1--5
over the range 300~$< T <$~500~MeV
but the result from LIDO increases
sharply to 10--15 for $T<$~300~MeV, while the result from JETSCAPE remains constant
in that same range (both of these extractions are for $p=$~100~GeV).
The extractions use different energy loss models
and a different selection of experimental data and it is not clear
which (or both) aspect of the models leads to the low-$T$ difference in \qhat.
Both extractions include data from RHIC, but LIDO
includes the STAR jet \mbox{$R_{\mathrm{CP}}$}\ result~\cite{Adam:2020wen} and the PHENIX \mbox{$\pi^{0}$}\
result~\cite{Adare:2012wg} while JETSCAPE only includes the PHENIX \mbox{$\pi^{0}$}\ result.
JETSCAPE has broken down the constraints on \qhat\ from RHIC and the
LHC data separately and shown that there is essentially no constraining power in the
RHIC data in their model due to the limited kinematic range of the measurement.
The limited kinematic range and
statistical precision of the available RHIC data mean that the extractions are dominated
by the LHC data at 5.02~TeV.  This should
change with data from the sPHENIX experiment~\cite{Adare:2015kwa}.

The ability to extract \qhat\ from the data via Bayesian analysis is a substantial step
forward in jet physics in heavy ion collisions.  The current analyses represent a proof of concept of the Bayesian techniques and are improvable in several ways. On the one hand, next generation of analysis will include more differential jet observables that pose more constrain to the models than single hadron or fixed-$R$ inclusive jet suppression. On the other hand, a wider set of model calculations and approximations should be included in the analysis.
Other aspects, like going beyond event-averaged geometry to be sensitive to geometrical fluctuations in energy loss are also to be addressed.

For the rest of this section, we discuss other measurements which can provide
more experimental information about the details of energy transport in the QGP.

\subsubsection{How does the amount of lost energy depend on path length?}
A fundamental question is how energy loss of jets depends on the
path length the jet travels through the QGP.
We cannot know the specific path length traveled by the jet because of:
\begin{itemize}
\item event-by-event variation of the QGP shape and size
\item the unknown position of the hard scattering process within the QGP
\item the random propagation direction of the jet within the QGP
\end{itemize}
Because of these there can be a large variation between the path lengths encountered
even by jets produced within the same hard scattering.  This variation,
along with the steeply falling jet cross section with transverse momentum
leads to a selection bias toward jets which have lost little energy and thus likely
also travelled through a smaller than average amount of QGP.  This
is called the \textit{surface bias}~\cite{Renk:2012ve}.

In addition to  path-length
variation there can also be  fluctuations in the energy loss
process~\cite{Milhano:2015mng}.
In order to isolate effects which are sensitive to path-length
variations, jet observables which are
differential in the QGP geometry can be measured.
Additionally, model calculations must incorporate
realistic event-by-event geometry into calculations in order to make
meaningful comparisons to data.  In this section, we will discuss
the physics processes thought to govern this question and the available measurements.
We will finish with some open questions.

In the perturbative description of energy loss, the spectrum of the emitted gluons is
expected to be $dI/d\omega \propto 1/\omega$ if the interactions with the medium are incoherent.
However the Landau–Pomeranchuk–Migdal (LPM)
effect in the QGP~\cite{Baier:1996kr,Wang:1994fx} leads to $dI/d\omega \propto 1/\omega^{3/2}$ for
$\omega < \omega_{c}$ and this leads to a quadratic dependence of the energy loss on the
in-medium path length, $L$, $\Delta E_{loss} \propto L^{2}$.
In a nonperturbative strong coupling model $\Delta E_{loss} \propto L^{3}$ is
expected~\cite{Chesler:2008uy}.

$\Delta E_{loss}(L)$ itself is not directly measurable.  Instead, the key element in
this study has been to measure the azimuthal anisotropy, \mbox{$v_{n}$}, of jets and high-\mbox{${p_T}$}\xspace\ particles.
Measurements from RHIC using hadrons showed a larger $v_2$ than expected
from pQCD-based energy loss calculations~\cite{Adare:2010sp}.  This
was taken as possible evidence for strong coupling energy loss with a stronger
 dependence on $L$ than expected from pQCD.  However,
conclusions made from these measurements were shown to be limited
by the use of non-fluctuating geometry; the addition
of geometrical fluctuations increased the value of \mbox{$v_{\mathrm{2}}$}\
expected from pQCD-based theoretical calculations~\cite{Noronha-Hostler:2016eow}.
At the LHC, measurements of jet~\cite{Aad:2013sla,Adam:2015mda,ATLAS:2020qxc} and
high-\mbox{${p_T}$}\xspace\ charged particle~\cite{Sirunyan:2017pan} \mbox{$v_{\mathrm{2}}$}\ have been performed at the LHC;
a compilation of the measurements for mid-central \mbox{Pb$+$Pb}\xspace\ collisions is shown in
Figure~\ref{fig:v2}.  The \mbox{$v_{\mathrm{2}}$}\ value varies from approximately 5\% for 20~GeV charged particles
to about 2\% for 200~GeV jets.  The \mbox{$v_{\mathrm{2}}$}\ values as a function of centrality follow
the geometrical expectations; a smaller \mbox{$v_{\mathrm{2}}$}\ value is seen in central collisions
than in mid-central and peripheral collisions~\cite{ATLAS:2020qxc}.  In order to further
constrain the path-length dependence of energy loss, measurements of \mbox{$v_{\mathrm{3}}$}\ and
\mbox{$v_{\mathrm{4}}$}\ have been made for jets~\cite{ATLAS:2020qxc} and high-\mbox{${p_T}$}\xspace\ charged
particles~\cite{Sirunyan:2017pan}; above 20~GeV, there is no evidence for non-zero
\mbox{$v_{\mathrm{3}}$}\ or \mbox{$v_{\mathrm{4}}$}\ in any collision system.   These higher-order
harmonics should introduce a smaller
path length difference between in-plane and out-of-plane directions than \mbox{$v_{\mathrm{2}}$}\
and so it is important to improve the precision of these measurements
in order experimentally constrain the path length dependence of energy loss.

\begin{figure}[ht]
\centering
\includegraphics[width=0.93\textwidth]{plots/jetvn_all.pdf}
\caption{A compilation of jet~\cite{Adam:2015mda,ATLAS:2020qxc} and
charged-particle~\cite{Sirunyan:2017pan} \mbox{$v_{\mathrm{2}}$}\
measurements.  Figure is from Ref.~\cite{ATLAS:2020qxc}.}
\label{fig:v2}
\end{figure}

Interestingly, a non-zero \mbox{$v_{\mathrm{2}}$}\ has  been measured for high-\mbox{${p_T}$}\xspace\ charged
particles in \pPb\ collisions~\cite{Aad:2019ajj}.  The measured \mbox{$v_{\mathrm{2}}$}\ is approximately
2\% for 20--50~GeV particles in central \pPb\ collisions.  In contrast to \mbox{Pb$+$Pb}\xspace\ collisions,
the \mbox{$v_{\mathrm{2}}$}\ in \pPb\ collisions is not accompanied by a large energy loss; in \pPb\
collisions \RpPb\ is consistent with unity~\cite{Adam:2015hoa,Khachatryan:2016odn}.
If this \mbox{$v_{\mathrm{2}}$}\ arises from path-length
dependent energy loss, the absolute size of the energy loss
would have to be sufficiently small to accommodate the
\RpPb\ results.  Thus far, there is no understanding of
whether the observed \mbox{$v_{\mathrm{2}}$}\ can be attributed to energy loss or
if some other source is required to explain the data.
If the \pPb\ \mbox{$v_{\mathrm{2}}$}\ is due to some other mechanism
than path-length-dependent energy loss, then the impact to the commonly accepted understanding of these measurements in heavy-ion
collisions needs to be assessed.

Dijet measurements provide a different sensitivity to the path-length
dependence of energy loss through geometry
than single-jet
measurements.
The first LHC results showed a significant depletion of balanced dijets
in \mbox{Pb$+$Pb}\xspace\ collisions~\cite{Aad:2010bu}.
The qualitative explanation for this is that one jet loses more energy than
the other, either through an asymmetry in the path length or through fluctuations in
the energy loss.
Current measurements show the same decrease in the fraction of balanced
jet pairs in central \mbox{Pb$+$Pb}\xspace\ collisions compared to \pp\ collisions,
up to leading jets of at least 400~GeV~\cite{ATLAS:2020jyp}
(see Figure~\ref{fig:xJ_ATLAS}).
For leading jet \mbox{${p_T}$}\xspace of 158--178~GeV the \mbox{$x_{J}$}\ distribution in central
\mbox{Pb$+$Pb}\xspace\ collisions is consistent with no \mbox{$x_{J}$}\ dependence over the range of 0.5~$< \mbox{$x_{J}$} <$~1.0.
This is a very broad distribution and suggests that there is a very wide
variation in the magnitude of energy loss experienced by the subleading jet in
these collisions.
At 2.76~TeV, the first unfolded dijet
measurements in \mbox{Pb$+$Pb}\xspace\ collisions also
showed the imbalanced pairs expected from energy loss, but also an apparent peak  in
the \mbox{$x_{J}$}\ distribution   at approximately 0.5~\cite{Aaboud:2017eww}.  Figure~\ref{fig:xJ_ATLAS}
shows the \mbox{$x_{J}$}\ distributions (after the unfolding) in central \mbox{Pb$+$Pb}\xspace\ collisions
for jets from 100~GeV to over 200~GeV.  The peak structure is clear for the lowest
\mbox{${p_T}$}\xspace\ jets and becomes insignificant for $\mbox{${p_T}$}\xspace >$~126~GeV.  The origin of this structure
is not known. New measurements at 5.02~TeV have been unable to reach as
low in jet \mbox{${p_T}$}\xspace to confirm this structure~\cite{ATLAS:2020jyp}.

\begin{figure}[ht]
\centering
\includegraphics[width=0.50\textwidth]{plots/xJ_ATLAS502.pdf}
\includegraphics[width=0.45\textwidth]{plots/xJ_ATLAS276.pdf}
\caption{Dijet momentum imbalance, \mbox{$x_{J}$}, at 5.02~TeV (left) and 2.76~TeV (right)
for 0--10\% central \mbox{Pb$+$Pb}\xspace\ collisions and \pp\ collisions. Figures are from Ref.~\cite{ATLAS:2020jyp} (left) and   Ref.~\cite{Aaboud:2017eww}  (right).}
\label{fig:xJ_ATLAS}
\end{figure}

Both the dijet imbalance and the jet azimuthal anisotropies
should be especially sensitive to the effects of fluctuations in the initial geometry and fluctuations in the energy loss process.
Due to this it is important to simultaneously experimentally constrain these quantities
and compare them with theoretical calculations.

\subsubsection{How does jet quenching depend on the characteristics of the jets?}

In the previous sections, jets were discussed as monolithic objects.
Here, we discuss measurements of the jet properties that were done in order to probe the medium-modifications of the internal jet radiation pattern. Such modifications can provide information on the microscopic details of the jet-QGP interactions.

The jet radiation pattern is explored via measurements of the jet shapes including fragmentation functions.
We also discuss varying the \textit{partonic flavor} of jets between quarks, gluons
and heavy quarks, to test the flavour and mass dependence of jet-medium interactions. Finally, we discuss measurements of the hard jet substructure which aim at probing the building blocks of the parton shower in medium.

{\bf Does jet quenching depend on the jet shape or are harder narrower jets quenched less?}

Differences in the parton shower evolution
are expected to lead to different energy loss, so it is reasonable to ask if
the structure of the jets which survive is modified from jets in \pp\ collisions.
This question is intrinsically related to the quark/gluon differences discussed in the next subsection
because gluon jets on average have a broader and softer fragmentation than
quark jets.

The most comprehensive measurement
of jet fragmentation in heavy-ion collisions is in Ref.~\cite{Aaboud:2018hpb}.
Figure~\ref{fig:FF_PbPb_z} shows the fragmentation functions in central \mbox{Pb$+$Pb}\xspace\ events
for \mbox{$R=0.4$}\ jets divided by the same quantity in \pp\ collisions for three jet
\mbox{${p_T}$}\xspace\ selections.  The momentum fraction of the jet carried by the charged particle,
\mbox{$z$}, is determined with respect to the \textit{observed} jet energy (as opposed
to the original, pre-quenching, parton energy).
At high-\mbox{$z$}\ the ratios of the fragmentation functions are consistent
for all three jet \mbox{${p_T}$}\xspace\ selections and there is an excess of high-\mbox{$z$}\ particles in \mbox{Pb$+$Pb}\xspace\
collisions. This excess can be explained as the result of a selection bias: the measured jets with high-$z$ hadrons are jets with a harder fragmentation that have
been quenched less.
Since quark jets have harder fragmentation on average than gluon jets, this
could also be understood as
evidence for a stronger energy loss for gluon jets than quark
jets~\cite{Spousta:2015fca} resulting on an enhanced quark fraction at given \mbox{$p_{\mathrm{T}}^{\mathrm{jet}}$}.

\begin{figure}
\centering
\includegraphics[width=0.55\textwidth]{plots/FF_z.pdf}
\caption{Ratios of the fragmentation functions in
central \mbox{Pb$+$Pb}\xspace\ collisions to those in \pp\ collisions
for three different \mbox{$p_{\mathrm{T}}^{\mathrm{jet}}$}\ selections as a function of \mbox{$z$}.  Figure is from Ref.~\cite{Aaboud:2018hpb}.}
\label{fig:FF_PbPb_z}
\end{figure}

In order to look at the angular distribution of energy in jets, jet angularities and other jet shapes have been measured~\cite{Chatrchyan:2013kwa,Acharya:2018uvf}.  The measurement in
 Ref.~\cite{Chatrchyan:2013kwa} measures
 the distribution of calorimeter energy inside the jets.
 Ref.~\cite{Acharya:2018uvf} is based on unfolded
 \mbox{$R=0.2$}\ track-based jets and includes $\mbox{$p_{\mathrm{T}}^{\mathrm{part}}$} >$~0.15 GeV and measures
 both the angularity, $g$ and the momentum dispersion $p_{T}D$.  These observables correspond to $\lambda_{0,2}$ and $\lambda_{1,1}$ in Equation \ref{equation:angularities} respectively.
  The small cone size of these jets emphasizes the core and
 minimizes the effect of any medium response.  The distributions of
 these quantities in \mbox{Pb$+$Pb}\xspace\ collisions are shown in Figure~\ref{fig:alice_shapes}  and indicate that the measured quenched jets are narrower and have a harder fragmentation than the \mbox{\sc Pythia}\xspace~\cite{Sjostrand:2014zea}
 simulation of jets in the vacuum.
 This can, yet again,
 be interpreted as a selection bias by which broad jets with a softer fragmentation are more quenched and are filtered out from the selected reconstructed jet $p_{\rm{T}}$ bin.
 Interestingly, like in the fragmentation function measurements from ATLAS above, a harder and narrower fragmentation
 is consistent with a more quark-like fragmentation and the results agree well with \mbox{\sc Pythia}\xspace quark distributions as shown in~\cite{Acharya:2018uvf}.
It is however worth noting that the measurement of the jet charge \cite{CMS:2020plq} does not indicate a change of quark and gluon fractions in \mbox{Pb$+$Pb}\xspace\ relative to \pp\ collisions.

 \begin{figure}[ht]
 \centering
 \includegraphics[width=0.85\textwidth]{plots/alice_shapes.pdf}
 \caption{Jet girth and momentum dispersion in central Pb-Pb collisions compared to a vacuum simulation, from Ref.~\cite{Acharya:2018uvf}.}
 \label{fig:alice_shapes}
 \end{figure}

{\bf Does jet quenching depend on quark flavour and mass?}

 At leading order in vacuum QCD, differences between quark and gluon fragmentation are dictated by color factors: the splitting rate is
 enhanced by the color factor and is 2.25
 times higher for gluons than for quarks, leading to broader and softer parton showers.  The
 larger splitting rate leads to an expectation of
 more interactions between gluon jets and the QGP.

Inclusive jets are mixture of quark and gluon jets.  The mixture is governed by
the parton distributions functions (PDFs) of the colliding
nucleons.  At low-$x$, gluons dominate and toward the valence region
there is a greater fraction of quarks.
An attempt to measure the quark and gluon fractions in
 jets in \mbox{Pb$+$Pb}\xspace\ collisions has not found any
significant difference from that measured in \pp\ collisions~\cite{Sirunyan:2020qvi},
but such measurements have substantial systematic uncertainties and model dependence.
Other techniques have been
used to attempt to enhance the quark-jet fraction and to look at
the effect on the jet quenching.
One technique to enhance the quark-jet sample is to measure
the rapidity dependence of jet observables. At forward rapidities,
the fraction of quark initiated jets will be enhanced because the jet
partons come from higher-$x$ partons than at smaller rapidities.
Alternatively, one can consider jets recoiling from isolated photons or Z-bosons. \mbox{\sc Pythia}\xspace simulations \cite{CMS:2021vsp} indicate quark fractions nearly a factor three higher in Z-jet events than in central dijet events for $R=0.4$ jets of $p_{\rm{T}}<200$ GeV at 13 TeV.
Lastly, heavy flavour jet tagging allows to study the effect of large
quark mass on jet quenching.

\begin{itemize}
    \item \underline{Rapidity dependence of energy loss}
    Figure~\ref{fig:incjetsRAA_rap}
 shows the first evidence for
a rapidity dependence of \mbox{$R_{\mathrm{AA}}$}~~\cite{Aaboud:2018twu}.
There are two competing effects that could be expected.
First, the gluon jet fraction in the inclusive jet sample decreases toward increasing rapidity at
fixed jet transverse momentum, \mbox{$p_{\mathrm{T}}^{\mathrm{jet}}$}, (see, for example Ref.~\cite{Spousta:2015fca} where the PYTHIA8 calculations show that the quark fraction almost doubles at forward rapidities $1.2 < |y| <2.1$  compared to $|y| <0 .3$ for jets of $p_{\rm{T}}=100$ GeV.)
As quarks are
expected to lose less energy than gluons in the QGP, the
value of \mbox{$R_{\mathrm{AA}}$}\ would
be expected to increase as $|\mbox{$y^{\mathrm{jet}}$}|$, and thus
the fraction of quark jets in the inclusive jet sample at a fixed \mbox{$p_{\mathrm{T}}^{\mathrm{jet}}$},
increases.  Second, the \mbox{$p_{\mathrm{T}}^{\mathrm{jet}}$}\ spectra become steeper with
increasing $|\mbox{$y^{\mathrm{jet}}$}|$ (see, for example Ref.~\cite{Aaboud:2017dvo}); this would cause a reduction in the \mbox{$R_{\mathrm{AA}}$}\
value for the same energy loss.  Figure~\ref{fig:incjetsRAA_rap}, \mbox{$R_{\mathrm{AA}}$}\ is shown to decrease with increasing
$|\mbox{$y^{\mathrm{jet}}$}|$ for jets with $\mbox{$p_{\mathrm{T}}^{\mathrm{jet}}$} >$~300~GeV,
suggesting that the second effect dominates for these jets.

\begin{figure}

 \centering
   \includegraphics*[width=0.54\textwidth]{plots/ydep_raa.pdf}
   \caption{
      \mbox{$R_{\mathrm{AA}}$}\ as a function of the jet rapidity
      normalized by $\mbox{$R_{\mathrm{AA}}$}(|y| < 0.3)$
      for four \mbox{$p_{\mathrm{T}}^{\mathrm{jet}}$}\ selections. Figure is from Refs.~\cite{Aaboud:2018twu}.}
   \label{fig:incjetsRAA_rap}
\end{figure}

    \item \underline{Photon-tagged jet observables}

    Jets opposite in azimuth from a high momentum photon can also provide
    an enhancement of quark-jets over inclusive jets because these photon-jet
    pairs are  primarily produced via $g+ q \to \gamma + q$ scattering.
    Additionally,
the photon does not lose energy in the QGP via the strong interaction and therefore
provides information about the initial hard scattering momentum transfer.
However, these jets have a different geometrical bias than inclusive jets;
 since the photon does not lose energy, the geometrical bias toward jets
produced near the surface is removed for photon-jet measurements.

Previous measurements have shown the \mbox{${p_T}$}\xspace\ of the jet relative to that of the photon is reduced
in heavy-ion
collisions relative to \pp\ collisions~\cite{Chatrchyan:2012gt}.
Measurements allow the study of the photon-jet
momentum balance as a function of the photon \mbox{${p_T}$}\xspace~\cite{Sirunyan:2017qhf,Aaboud:2018anc}.  The ATLAS
results are unfolded and
are shown in Figure~\ref{fig:photonjets} for 100-158~GeV photons in 0--10\% central collisions.
Going from peripheral to central collisions, the fraction of balanced photon-jet
pairs (those with $\mbox{$x_{J\gamma}$} \approx 1$) decreases and the fraction of pairs in which the photon
has more \mbox{${p_T}$}\xspace\ than the jet increases.  This is
qualitatively as expected from jet quenching, but due to the different
geometrical bias and observable than the inclusive jets it is not possible
to say without a model if these quark-enhanced jets have lost less energy,
as would be expected.  The most probable value
of \mbox{$x_{J\gamma}$}\ in the most central collisions is about 0.3, indicating that
many jets have lost a large fraction of their transverse momentum.  However, it is
interesting that even in the most central collisions, there remain
a substantial fraction of jets which are nearly
balanced--indicating that they have not lost a large amount of energy.
Measurements with $Z$-bosons as the tag have also been done~\cite{CMS:2017eqd};
the message is similar to that of the photon-tagged measurements but the
statistical precision is worse.

\begin{figure}[ht]
\centering
      \includegraphics[width=0.95\linewidth]{plots/gammajet_ATLAS.pdf}\\
      \caption{ Ratio of the jet transverse momentum to the
      photon \mbox{${p_T}$}\xspace, $x_{J\gamma}$, in \pp\ and \mbox{Pb$+$Pb}\xspace\ collisions~\cite{Aaboud:2018anc}. }
      \label{fig:photonjets}
\end{figure}

 First measurements of
the fragmentation of the jets opposite a photon have been performed~\cite{Sirunyan:2018qec,Aaboud:2019oac}.
As discussed above,
these fragmentation functions differ from inclusive fragmentation functions in a few ways.
First, the
jets are possibly quenched more due to geometrical bias from the photon selection.
Second, the jets are at  lower \mbox{$p_{\mathrm{T}}^{\mathrm{jet}}$}\ than the inclusive jet fragmentation functions
because the tagging with the photon limits the statistics and provides a cleaner identification
of jets at lower \mbox{$p_{\mathrm{T}}^{\mathrm{jet}}$}\ than in the inclusive case.
Finally, these jets have a much higher fraction of quark jets than the inclusive jet sample
do to the leading order dominance of the $q + g \to q + \gamma$ process in these events.
Measurements of photon-hadron correlations had been made at RHIC~\cite{Adare:2012qi,Abelev:2009gu,Ge:2017irb},
but
only recently were measurements made of the hadrons in reconstructed jets back-to-back with
a photon in \mbox{Pb$+$Pb}\xspace\ collisions~\cite{Sirunyan:2018qec,Aaboud:2019oac}.
Figure~\ref{fig:photonjetFF} shows the ratio fragmentation functions
in \mbox{Pb$+$Pb}\xspace\ collisions compared to \pp\ collisions for both jets opposite a photon
and inclusive jets.  A stronger deviation of this ratio from unity is seen in
central collisions than in peripheral collisions for both jet selections.  Interestingly,
when comparing the central data directly to the peripheral data, the centrality
dependence is significantly larger in the photon-tagged jets than in the inclusive jets.
It is not known if this is caused by the lower
\mbox{$p_{\mathrm{T}}^{\mathrm{jet}}$}\ range for the photon-tagged fragmentation functions or the different
geometrical biases of the two samples, but being able to measure the fragmentation of
photon-tagged jets at the same \mbox{$p_{\mathrm{T}}^{\mathrm{jet}}$}\ has inclusive jets would be an obvious
way to constrain the source of this difference.

\begin{figure}[ht]
\centering
      \includegraphics[width=0.95\linewidth]{plots/photonjetFF.pdf}
      \caption{The ratio of the fragmentation function as a function of
      charged particle \mbox{${p_T}$}\xspace\ in central \mbox{Pb$+$Pb}\xspace\ collisions to \pp\ collisions
      for jets opposite a photon
      (squares) and inclusive jet fragmentation functions~\cite{Aaboud:2017bzv}
      (circles). Figure is from Ref.~\cite{Aaboud:2019oac}.}
      \label{fig:photonjetFF}
\end{figure}

    \item \underline{Heavy Flavour}

    In vacuum, besides the aforementioned differences between the radiation pattern of jets initiated by light quarks and gluons, dictated at LO by the color factors, quark mass plays a role. In QCD (an in gauge theories in general), radiation off a massive quark Q is suppressed in a cone of angle $\theta_{C}=m_{Q}/E_{Q}$. This is the
    so-called dead cone effect \cite{Dokshitzer:1991fd} that causes heavy quarks to radiate less than light quarks. In heavy ion collisions, medium-induced radiation off heavy quarks is expected to fill the dead-cone region, but is predicted to be suppressed for high energy radiation as compared to light quarks \cite{Armesto:2003jh} resulting on a quark mass-dependence to energy loss.

The measurement of energy loss of heavy flavor jets
is very challenging.  The overall rate of these jets is very low (a few percent of the
inclusive jet cross section) and identifying them relies on measurements sensitive to the decay of the $B$ or $D$ hadron carrying the quark
of interest inside the jet.
CMS has made a measurement of the \mbox{$b$}-jet\xspace\ \RAA\ in 2.76 TeV
collisions~\cite{Chatrchyan:2013exa} and found consistent \RAA\ values
between inclusive and
\mbox{$b$}-jets\xspace.  Additionally, they measured the momentum imbalance of back-to-back \mbox{$b$}-jets\xspace\
and found them to be comparable to those measured for inclusive jets in 5.02~TeV \mbox{Pb$+$Pb}\xspace\ collisions~\cite{Sirunyan:2018jju}, see Figure~\ref{fig:bdijet}. Both
measurements have sizeable uncertainties and
\mbox{$b$}-jet\xspace\ measurements will be an important part of the LHC physics program in Run 3 and beyond.

\begin{figure}[ht]
\centering
      \includegraphics[width=0.95\linewidth]{plots/CMS-HIN-16-005_Figure_006.pdf}
      \caption{The momentum imbalance in inclusive and b-dijets as function of collision centrality in \mbox{Pb$+$Pb}\xspace \,collisions compared to \pp \,. Figure is from Ref.~\cite{Sirunyan:2018jju}}.
      \label{fig:bdijet}
\end{figure}

The application of substructure techniques to heavy flavour jets in \pp\ collisions has recently lead to the first direct observation of the dead cone in QCD~\cite{ALICE:2021aqk}. The exploration of such techniques in heavy ion collisions is yet to happen.
Substructure of double HF-tagged jets (discussed in Ref.~\cite{Ilten:2017rbd} in the context of disentangling heavy flavour processes in pp collisions) might allow to identify the c$\overline{\rm{c}}$ or b$\overline{\rm{b}}$ antenna without the ambiguities of the inclusive SD analysis that are subject of strong contamination of combinatorial prongs.

Heavy quark measurements are expected to be substantially improved in the near
future with higher luminosity and detector upgrades
at the LHC Runs 3 and 4~\cite{Citron:2018lsq} and the ability
to tag \mbox{$b$}-jets\xspace\ at sPHENIX at RHIC~\cite{PHENIX:2015siv}.

\end{itemize}

{\bf Does jet quenching depend on the hard substructure?}

As described in Section~\ref{subsect:jettools}, the grooming procedure stops when the SD condition is met. The corresponding $z_{12}$ and angular separation $\Delta R_{12}$ are called groomed momentum balance and groomed jet radius and are denoted by $z_{g}$ and $R_{g}$ respectively.
In vacuum, $z_{g}$ is connected to the Altarelli-Parisi splitting function and displays
a universal behavior in $1/z$~\cite{Larkoski:2017bvj}. In Pb-Pb collisions,
the interpretation of the observable is more difficult because medium-induced radiation is expected to violate angular ordering~ \cite{Mehtar-Tani:2011hma}
while the CA reclustering forces angular ordering on the jet constituents, among other reasons.

Several different mechanisms can contribute to the modification of $z_{g}$
and $R_{g}$ in heavy ion collisions. If medium-induced radiation is hard enough, it can increase the number of prongs that pass the SD cut. On the other hand, jet prongs and constituents lose energy in the medium, which can
reduce the number of subjet prongs passing the SD cut, $n_{SD}$.
In addition, the amount of jet energy loss is dictated by color coherence: jets with a resolved substructure will lose more energy because they contain more prongs that interact with the medium incoherently.

The $z_{g}$ distribution in heavy-ion collisions
was first measured by CMS \cite{Sirunyan:2017bsd}, then by STAR~\cite{Adam:2015doa} and ALICE~\cite{Acharya:2019djg}.
The CMS and ALICE measurements are shown in Figure~\ref{fig:zg01}.
\begin{figure}[ht!]
\centering
      \includegraphics[width=0.8\linewidth]{plots/CMS-HIN-16-006_Figure_004.pdf}
      \includegraphics[width=0.8\linewidth]{plots/Overlayed4x2-100601.pdf}
      \caption{Upper plot: CMS self-normalized results for the momentum balance $z_{g}$ in different jet momentum bins.
      Figure is from Ref.~\cite{Sirunyan:2017bsd}. Lower plot: ALICE $z_{g}$ results for jets in a fixed momentum interval of $80<p_{T,jet}^{ch}<120$ GeV and as function of the groomed splitting angle $R_{g}$ ($\Delta R^{rec}$).
      Figure is from Ref.~\cite{Acharya:2019djg}.}
      \label{fig:zg01}
\end{figure}
The main feature of the ALICE  track-based measurement was a suppression of the $z_{g}$ distribution with increasing $R_{g}$ and a hint of an enhancement at small angles. CMS did not perform a scan on the splitting opening angle (the default value is $R_{g}>0.1$) but did examine the jet $p_{T}$ dependence of the modification.
Both of these measurements were not fully corrected to particle-level. Rather, the \pp\ reference was modified to consider the impact of strong combinatorial background at the level of subjet prongs that dominates the low-$z_{g}$ region. ALICE also reported the measurement of the Les Houches multiplicity $n_{SD}$ which gives the number of prongs within the jet that pass the SD cut. The $n_{SD}$ distribution is shifted to lower values in PbPb relative to the vacuum calculation as expected if energy loss of the prongs reduces the number of subleading prongs passing the SD cut.

The next generation of groomed observables by ALICE were fully corrected and, for the sake of the unfolding stability, performed with a different selection of smaller jet $R$ and tighter SD grooming cuts ($z_{cut}=0.2,z_{cut}=0.4$) \cite{ALICE:2021obz}. The results are shown in Figure \ref{fig:zg02}. A similar message is distilled: small-angle splittings are enhanced while large-angle splittings are suppressed. And the $z_{g}$, when integrating over all angles, shows no modifications.

The data were compared to a set of models, including JetMed (denoted as Caucal et al), the Hybrid model (denoted as Pablos et al) and JETSCAPE~\cite{Kauder:2018cdt}.
The narrowing of $\theta_{g}$ is observed in these three different models, and this might seems surprising given the different nature of the implemented medium effects. So it is worth asking what is  the most relevant common feature in these models, and one answer is the dominance of vacuum physics at early, high-energy stages of the shower~\cite{Du:2021pqa,Caucal:2018dla}. This brings in a key element for the interpretation:  large $\theta_g$ biases to more activity in the early vacuum shower. Since vacuum structures with more prongs lead to more quenched jets, the shape of $\theta_{g}$ is the consequence of a selection bias; high $\theta_{g}$ jets are more quenched and migrate to lower jet $p_{T}$ bins. Other models in the plot like the one denoted by Yuan et al indicate that flavour-dependent energy loss can also play a role.

\begin{figure}[h!]
\centering
      \includegraphics[width=0.5\linewidth]{plots/h_theta_g_0-10_R02_zcut02_Theory.pdf}
          \caption{Normalized groomed jet radius $\theta_{g}$ in central collisions and small-R jets measured by ALICE~\cite{ALICE:2021obz},
          compared to the same observable measured in pp collisions and state of the art model and theory calculations. }
      \label{fig:zg02}
\end{figure}

Another substructure observable of interest is the $N$-subjettiness, denoted by $\tau_{N}$, which quantifies the degree to which a jet has a $N$(or fewer)-pronged substructure~\cite{Thaler:2010tr}

 The ratio of $\tau_{2}/\tau_{1}$ is used to tag boosted hadronically-decaying objects such as the W and top quarks, which are typically 2-prong objects as compared to QCD jets, which are mostly 1-pronged. ALICE measured $\tau_{2}/\tau_{1}$\cite{Acharya:2021ibn} using several declustering metrics, including exclusive $k_{T}$ and CA+SD. The results do not reveal a significant change in the prong-structure of the jet relative to \mbox{\sc Pythia}\xspace, which describes the observable well in pp collisions.

\begin{figure}[h]
\centering
       \includegraphics[width=0.45\linewidth]{plots/fig_06b.pdf}
      \includegraphics[width=0.45\linewidth]{plots/fig_07b.pdf}

      \caption{Left: Fully corrected $k_{T}$ distance measured for $R=1$ trimmed jets in the range $251<p_{T,jet}<316$ GeV for different centrality classes. Right: Nuclear modification factor as function of the $k_{T}$ distance. Figures are
      from Ref.~\cite{ATLAS:2019rmd}.}

      \label{fig:ktscale}
\end{figure}
ATLAS performed the first fully corrected measurement of the $k_{T}$ distance of large$-R$ jets in heavy ion collisions~\cite{ATLAS:2019rmd}.
First, \mbox{$R=0.2$}\ calorimeter jets were reconstructed via the usual
procedure.  Then jets with $\mbox{$p_{\mathrm{T}}^{\mathrm{jet}}$} > $~35~GeV
jets were taken as constituents for anti-$k_{T}$
jets clustered with $R = 1$.
Their constituents were reclustered with the $k_{T}$ algorithm~\cite{Dokshitzer:1997in,Ellis:1993tq}  and then the last clustering step was unwound to register the $k_{\rm{T}}$ scale or distance, defined as
\begin{equation}
\sqrt{d_{12}}=min(p_{T,1}^2,p_{T,2}^2) \Delta R_{12}^{2} \end{equation}
where indexes $1$ and $2$ refer to the two prongs that were clustered last.
Large $\sqrt{d_{12}}$ selects jets with distinct hard prongs separated at large angles.
If an $R=1$ jet consists of only a single sub-jet (SSJ), $\sqrt{d_{12}}$ is not defined.
Figure~\ref{fig:ktscale} shows the $k_{T}$ distance distribution for different centralities and indicates that the majority of the jets consist of a
single sub-jet. Two-prong configurations are suppressed by more than 2 orders of magnitude.

The plot on the right shows the nuclear modification factor
is qualitatively different between those jets which have a single sub-jet
and those which have more than one.  Those jets with a single sub-jet are suppressed
approximately 50\% less in central collisions than those jets which have multiple
sub-jets.

In parallel to the writing of this review, other observables are being explored. An example is the subjet energy fraction, which considers the fraction of energy carried by the leading subjet within the signal jet. Another example is the transverse momentum $k_{\rm{T}}$ of the splitting found with dynamical grooming \cite{Mehtar-Tani:2019rrk}, $k_{\rm{T,dyn}}$, which selects the hardest splitting within the CA-ordered jet tree.

All the discussed jet shape and  jet substructure observables must be correlated to some degree, by construction. For illustration, in Fig. \ref{fig:Correlations} we show the linear correlation coefficients for PYTHIA8  \cite{Sjostrand:2007gs} jets reconstructed with $R=0.4$ with \mbox{$p_{\mathrm{T}}^{\mathrm{jet}}$}\ $>100$ GeV. We observe that the $k_{\rm{T}}$ distance is strongly correlated to the girth and to $k_{\rm{T,dyn}}$ and strongly anti-correlated to the leading subjet fraction. The $n_{\rm{SD}}$, which is a measure of the intrajet multiplicity is naturally anti-correlated to the $p_{\rm{TD}}$ which is related to the dispersion in momentum of the jet constituents.
The $z_{g}$ measures a momentum balance while $R_{g}$ is an angle and they are not correlated. We also note the strong correlation between the girth and $R_{g}$, $k_{\rm{T,dyn}}$, and the $k_{\rm{T}}$ distance.
Finding a set of minimally correlated observables can be useful to perform systematic comparisons to models and calculations. An example of such procedure in \pp\ collisions is the recent extraction of $\alpha_{S}$ using jet substructure in $t\bar{t}$ events by CMS, where $R_{g}$,$z_{g}$,$\epsilon$ and jet multiplicity were identified as a set of minimally correlated variables among more than $30$ substructure observables \cite{CMS:2018ypj}.

The selection bias was discussed in the context of the $R_{g}$ but applies to most of the discussed observables. In order to mitigate this selection bias, and to increase the weight of quenched jets in the measured samples, different strategies are envisaged. An obvious one considers the substructure of jets recoiling from Z or $\gamma$ bosons. Other interesting approaches based on ML have been proposed~\cite{Du:2021pqa}.

\begin{figure}[h!]
\centering
       \includegraphics[width=0.7\linewidth]{plots/CorrelationMatrix_Full_Tagged.pdf}

      \caption{Linear Correlation matrix of the different jet shapes and substructure observables discussed in this chapter.}

      \label{fig:Correlations}
\end{figure}

\subsubsection{What happens to the energy lost from jets in the QGP?}

The main physics aim here is to understand the process by which
energy lost by the jet is incorporated into the QGP.  There are
two reasons why this is important:
\begin{itemize}
\item this provides access to the hydrodynamization process
\item the energy from the medium response is correlated with the
jet and affects other observables which are used to quantify the strength
of energy loss~\cite{He:2018xjv,Pablos:2019ngg}.
\end{itemize}

Three kinds of observables have been used to search for this effect:
\begin{itemize}
\item cone size dependence of jet \RAA
\item correlations between jets and tracks
\item fragmentation functions and jet shapes

\end{itemize}

In order to capture the full dynamics of jet quenching, large-$R$ jets and access to their internal structure is desired. Cross sections and the ratios of cross sections for different $R$ are IRC-safe observables that can be analytically calculated and pose strong constrains to the theory.
The heavy-ion underlying event creates combinatorial or fake jets that prevent unfolding and only at very high jet $p_{\rm{T}}$ the measurement of the inclusive large-$R$ jet is feasible. Below 100 GeV, the different collaborations have measured
jet cross sections and their ratios for different $R$ up to $R=0.5$~\cite{ATLAS:2012tjt,ALICE:2015mdb}.

In the energy range of a few hundred GeV up to the 1 TeV, CMS has reported the first measurement of jet nuclear modification factors for jets with radii from $R=0.2$ up to $R=1$, for different centrality classes.
In central collisions, and up to $R=0.4$ (where there are still sufficient data points to observe a trend), the nuclear modification factor increases with jet $p_{\rm{T}}$, in agreement with the ATLAS result for $R=0.4$ jets~\cite{ATLAS:2018gwx}. Above 500~GeV, where a full scan of the $R$ dependence is possible, the data is consistent with no dependence of the \RAA with jet $R$. The comparison of the data to models and calculations reveals significant tensions in the simultaneous description of the nuclear modification factor and its $R$ dependence. In Fig. \ref{fig:CMSR} an example of comparisons to analytical calculations is shown.

What is common to many of the models compared to the CMS data, is the strong role of the medium response which gives a larger contribution at large $R$. In models like the Hybrid model, the $R$ dependence of $R_{\rm{AA}}$ can be explained as the result of the balance of a stronger suppression for broader jets, and the ability to include more
medium response inside the cone.
The high transverse momentum of the $R=1.0$ jets in the CMS measurement could limit the
effect of medium response.  Measurements with a larger kinematic
range will allow for better discrimination between models.

Other measurement that emphasizes the role of the medium response at large $R$ is for instance the jet mass \cite{ALICE:2017nij} for $R=0.4$ jets. No modifications in \mbox{Pb$+$Pb}\xspace\ collisions relative to \pPb\ collisions
were observed, possibly due to a balance of energy loss and medium response effects~\cite{KunnawalkamElayavalli:2017hxo}.

 \begin{figure}[h!]
 \centering
 \includegraphics[width=0.9\textwidth]{plots/CMS_raa_ratio_1.pdf}
 \caption{ Ratio of the $R_{\rm{AA}}$ for different jet $R$ and $R_{\rm{AA}}$ for $R=0.2$, in different jet $p_{\rm{T}}$ intervals and compared to several calculations. Fig. from Ref.~\cite{CMS:2021vui}.}
 \label{fig:CMSR}
 \end{figure}

 In order to look for medium response, measurements
 of low momentum tracks around jets in heavy-ion collisions have been
 performed.
There has been interest in measuring fragmentation
functions as a function of \mbox{$p_{\mathrm{T}}^{\mathrm{part}}$}, the
transverse momentum of the particle in the jet.  This
is motivated to search for an
absolute scale in the modification of the fragmentation.
When looking at the jets fragmentation functions plotted as a function
of \mbox{$p_{\mathrm{T}}^{\mathrm{part}}$}, the low-\mbox{$p_{\mathrm{T}}^{\mathrm{part}}$}, $\mbox{$p_{\mathrm{T}}^{\mathrm{part}}$}\ <$~4~GeV, part of these ratios are approximately equal
for the three jet \mbox{${p_T}$}\xspace\ selections.
The low-\mbox{$p_{\mathrm{T}}^{\mathrm{part}}$}\ excess is thought to be due to the response of the
medium to the passage of the jet.  The approximate scaling and extent in \mbox{$p_{\mathrm{T}}^{\mathrm{part}}$}\
of the excess would be then sensitive to some scale in the QGP associated with the
response.

\begin{figure}[h!]
\centering
\includegraphics[width=0.43\textwidth]{plots/FF_pt.pdf}
\includegraphics[width=0.55\textwidth]{plots/track_jetatlas_pt.pdf}
\caption{Left: Ratios of the fragmentation functions in
central \mbox{Pb$+$Pb}\xspace\ collisions to those in \pp\ collisions
for three different \mbox{$p_{\mathrm{T}}^{\mathrm{jet}}$}\ selections as a function of charged-particle \mbox{${p_T}$}\xspace.
Right: The same quantity as in the left plot only differential in the distance, \r,
from the jet axis as well (different sets of points).
Figures are from Ref.~\cite{Aaboud:2018hpb} (left) and ~\cite{Aad:2019igg}
(right).}
\label{fig:FF_PbPb}
\end{figure}

 In order to study both the angular and longitudinal directions at once,
 both CMS and ATLAS have measured two-dimensional fragmentation
 functions~\cite{Khachatryan:2016erx,Khachatryan:2016tfj,Sirunyan:2018jqr,Aad:2019igg,Sirunyan:2021jty}.
 In the longitudinal fragmentation functions we noted that the low-\mbox{$p_{\mathrm{T}}^{\mathrm{part}}$}\
 excess was for particles below approximately 4 GeV.  The two-dimensional
 fragmentation functions in Refs.~\cite{Khachatryan:2016erx,Sirunyan:2018jqr,Aad:2019igg}
 provide support for that approximate scale both in 2.76 and 5.02 TeV \mbox{Pb$+$Pb}\xspace\ collisions
 at the LHC.  Figure~\ref{fig:FF_PbPb} shows the ratio of the two-dimensional
 fragmentation function in central \mbox{Pb$+$Pb}\xspace\ collisions to that in \pp\ collisions
 as a function of \mbox{$p_{\mathrm{T}}^{\mathrm{part}}$}\ for different values of distance $r$ to the jet axis.
 The magnitude of the modifications changes as a function of $r$, but the location
 in \mbox{$p_{\mathrm{T}}^{\mathrm{part}}$}\ of the transition from suppression to enhancement is at approximately
 4 GeV for all $r$ values.
 This same 4~GeV scale is also seen in measurements of $Z$-hadron
 correlations at ATLAS~\cite{ATLAS:2020wmg}.

redpajama_set_name: RedPajamaArXiv


text:
Home Community 'Are You Smarter Than a Fifth Grader?' Wins Best Game Show Award
'Are You Smarter Than a Fifth Grader?' Wins Best Game Show Award
by Lizzy Spangler
https://www.instagram.com/p/CB11yZrJuGx/
At the Reality Television Awards on June 24, Nickelodeon's reimagined "Are You Smarter Than A Fifth Grader?" won the Reality Television Award for Best Game/Variety Show.
The reimagined game show features Southlake student Colin Heintz, who nabbed a spot on the show last year. Competing as the only student from Texas, Colin's favorite subject is social studies.
"It was strange and exciting to see myself competing on TV. We were on a swim trip in Florida when the first episode I was in aired. We were watching with my family, teammates and coaches," Colin says. "It was really fun. We were only able to watch about half of the show until the storms got so bad they knocked the TV off the satellite. I was so happy to be reminded of what a fun time we all had on the show and see how happy everyone was when they watched it."

redpajama_set_name: RedPajamaCommonCrawl


text:
Q: Deriving sine difference formula I'm stuck proofing the difference formula $\sin (\alpha - \beta) = \sin \alpha \cos \beta - \cos \alpha \sin \beta$.
Given this diagram:

$$\sin (\alpha - \beta) = CD/AC = PQ/AC = (BQ-BP)/AC=BQ/AC-BP/AC$$
Now we need to relate that back to sine and cosine of alpha and beta:
$$BQ/AC = ???$$
I'm stuck here because $\sin \alpha = BQ/AB$ and $\cos \beta = AC/AB$. Multiplying those fractions together won't give me $BQ/AC$.
I thought I had the right idea, but I'm stuck. Hints are appreciated.

A: Let's instead prove the sum formula: $\sin(\alpha)=\sin(\alpha-\beta)\cos(\beta) + \sin(\beta)\cos(\alpha-\beta)$.
To do this, explain why the first summand on the right equals $CD/AB$, while the second summand on the right equals $BP/AB$ (hint: use similar triangles!). Combining these two gives you the sum formula.
To get the difference formula, draw the same diagram but with $\beta$ going clockwise.

redpajama_set_name: RedPajamaStackExchange


RUGBY LEAGUE expert Chris Thomas (@SolidPunts) uncovers the ante-post value ahead of Super League XXIV.
Warrington are the Liverpool of Super League. It's always going to be their year, and much like their Merseyside counterparts, this year, it actually might be.
Last year's Grand Finalists come into the campaign after collecting two runners-up medals last time out. Defeated by Catalans in the Challenge Cup, and Wigan in Super League, Wire were once again the bridesmaids.
But this year things look set to change – the arrival of Blake Austin is seismic. The best line breaking, metre-making, tackle-evading halfback on the planet has come to the Wolves. And much like Ben Barba did last year for St Helens, Austin looks set to light up Super League and should be supported as the 8/1 (William Hill) favourite to win the Man of Steel.
The Wolves have also made a host of other superb additions, including Jakke Mamo, Jason Clark and wonderkid Danny Walker, making it hard to look past Steve Price's men at 4/1 (BetBright) to lift the Super League trophy aloft for the very first time.
Defending champions Wigan are my other horse in this outright race at a generous 11/2 (Betway). The Cherry & Whites won last year with tenacious defence and ruthless efficiency and I'm not sure new coach Adrian Lam can undo outgoing boss Shaun Wane's wondrous achievements.
Lam has promised an attacking ethos and has added impetus with the signings of bad boy Zak Hardaker and the mercurial Jarrod Sammut. However, it's England international George Williams I'll be backing as their best shot at Man of Steel at a nice 33/1 (SkyBet).
This is it – my moment to make myself a genius or a fool… Hull KR are my dark horse! The Robins are my outsider to keep onside, a statement that may look silly come October.
Hull KR boast a great halves combination in Danny McGuire and new signing Josh Drinkwater, and their big pack can mix it up with the best of them under ex-Australia head coach Tim Sheens.
It could be worth having KR onside to make the top-five at 8/1 (William Hill) though I'll take my brave pill and back the Robins to win the Challenge Cup instead at a mouthwatering 50/1 (Ladbrokes).


What happens to my stock when I cancel a sent Stock Transfer? – How can we help?
What happens to my stock when I cancel a sent Stock Transfer?
The inventory will be returned to the source outlet and your stock on hand will not be adjusted in the destination outlet.


We can be reasonably sure that the first person to use wood as a tool didn't have a detailed knowledge of cellular biology, DNA, atomic binding forces and the mechanism of photo-synthesis.
Yet we can easily imagine that person communicating how to hit an antelope over the head with a branch, or covering some branches in leaves to make a rudimentary shelter.
We were building multi-storey buildings, ocean going vessels and mechanical tools of all kinds from wood years, centuries and millenia before we understood atomic matter, molecules and cells.
It was enough to understand that wood is relatively tough, and that wood from this part of this tree is harder than wood from this other part of this other tree.
A skilled carpenter remains a skilled carpenter even without a doctorate in physics, chemistry and biology.
Clearly we don't need to explain wood in order to work with it. So long as we can point to some instances of wood, and describe the relationships between different woods and our use for those woods the atomic structure of wood is of little relevance.
If a precise knowledge of all aspects of wood was necessary to communicate we would never have gotten past hitting antelope over the head.
Wood has always been a meaningful concept to humans - but not because we have defined what wood is - because we have a relationship with wood.
There are no exceptions to this principle. Provided we can point to an example, we don't need to define that example down to the most fundamental physical properties.


text:
Bernard Matthews
Big Al's
Daloon
Fenton Barns
Fine Food Specialist
Funnybones
German Bakery UK Ltd
Green Gourmet
Bernard MatthewsBig Al's
Fenton BarnsFine Food Specialist
German Bakery UK LtdGolden ValleyGreen Gourmet
Katerking
Longday FoodsLongra
MawbeefMeadowvaleMenuserveMoy Park
Peakhouse Foodspl
Plumtree Farms
SPAM With Bacon
THE WEST COUNTRY FISH CLUBThomas RidleyTorten Deko Shop
Wicks Manor
Show price trends for the category Grocery: Meat, Poultry & Game
Sausage & Bacon
"Meat, Poultry & Game" in the category Grocery
Welcome to Wunderstore, Britains's largest product search site with price comparison. You are currently in the Grocery category in the "Meat, Poultry & Game" department. With Wunderstore, you can browse more than 100 online shops for offers. In this way, you'll find almost every product from the Grocery: Meat, Poultry & Game section on our site that is currently available to buy online. And the best thing: not only will we show you which online shop you can currently buy the particular product you're looking for from, but we'll also let slip where you can buy that product at the best price!
To conduct a more targeted search, you can restrict the product selection to specific sub-sections such as "Beef", "Chicken & Turkey" or "Game". You can also run a specific targeted search for products from particular brands with us. Use the search field or the filter at the side for this. In this way, you can restrict the product selection to Country Range, Meadowvale, Fine Food Specialist or Bernard Matthews, for example. You can also use the filter at the side to search for products in specific colours or within certain price segments. And if you're on the hunt for a bargain, use the "Sale Filter" to find currently reduced items. In any case, we hope that we can help you with your search for good, well-priced offers on the internet using our price comparison tool.
Meat, Poultry & Game: How you can benefit from comparing prices
Price trend for the Meat, Poultry & Game product range in the Grocery product group
Online shops constantly optimise their prices. Some prices are updated several times a day and adapted in line with competitors' offers. Our price trend shows you the trend development of prices for products in the Grocery/Meat, Poultry & Game product range over the last few weeks and months.
We also, however, tell you when you can typically pick up products from the Grocery/Meat, Poultry & Game product range at a particularly attractive price. A good time is, for example, on tuesdays. For more details, see the price analysis graphs below.
Show details: When are products in the Meat, Poultry & Game product range in the Grocery product group particularly cheap?
Have you already thought about the right time to purchase of products in the Meat, Poultry & Game product range in the Grocery product group? We tell you the days of the week and specific times when the prices are particularly attractive.
On mondays, products from the Meat, Poultry & Game product range in the "Grocery" product group tend to be cheaper than the weekly average. The prices are around 3.6% lower than the average weekly price.
On tuesdays, products from the Meat, Poultry & Game product range in the "Grocery" product group tend to be cheaper than the weekly average. The prices are around 3.5% lower than the average weekly price.
On wednesdays, products from the Meat, Poultry & Game product range in the "Grocery" product group are slightly more expensive than the weekly average. The prices are around 11.7% higher than the average weekly price.
On thursdays, products from the Meat, Poultry & Game product range in the "Grocery" product group are slightly more expensive than the weekly average. The prices are around 1.4% higher than the average weekly price.
On fridays, products from the Meat, Poultry & Game product range in the "Grocery" product group tend to be cheaper than the weekly average. The prices are around 2.2% lower than the average weekly price.
On saturdays, products from the Meat, Poultry & Game product range in the "Grocery" product group tend to be cheaper than the weekly average. The prices are around 3.3% lower than the average weekly price.
On sundays, products from the Meat, Poultry & Game product range in the "Grocery" product group tend to be cheaper than the weekly average. The prices are around 3.3% lower than the average weekly price.
The prices of products from the Meat, Poultry & Game product range in the "Grocery" product group fluctuate during the course of the day. Between 0:00 and 1:00, they are, however, largely in line with the daily average.
The prices of products from the Meat, Poultry & Game product range in the "Grocery" product group fluctuate during the course of the day. Between 9:00 and 10:00, they are, however, largely in line with the daily average.
The prices of products from the Meat, Poultry & Game product range in the "Grocery" product group fluctuate during the course of the day. Between 10:00 and 11:00, they are, however, largely in line with the daily average.
It is probably not a bad idea to shop online for Meat, Poultry & Game on tuesday between 12:00 and 18:00.
On mondays between 0:00 and 6:00, the prices of products from the Meat, Poultry & Game product range in the "Grocery" product group are on average the same as their respective average weekly price.
On mondays between 6:00 and 12:00, the prices of products from the Meat, Poultry & Game product range in the "Grocery" product group are on average around 2.2% lower than their respective average weekly price.
On mondays between 12:00 and 18:00, the prices of products from the Meat, Poultry & Game product range in the "Grocery" product group are on average around 4.3% lower than their respective average weekly price.
On tuesdays between 0:00 and 6:00, the prices of products from the Meat, Poultry & Game product range in the "Grocery" product group are on average around 3.4% lower than their respective average weekly price.
On tuesdays between 6:00 and 12:00, the prices of products from the Meat, Poultry & Game product range in the "Grocery" product group are on average around 7.3% lower than their respective average weekly price.
On tuesdays between 12:00 and 18:00, the prices of products from the Meat, Poultry & Game product range in the "Grocery" product group are on average around 7.6% lower than their respective average weekly price.
On tuesdays between 18:00 and 24:00, the prices of products from the Meat, Poultry & Game product range in the "Grocery" product group are on average the same as their respective average weekly price.
On wednesdays between 0:00 and 6:00, the prices of products from the Meat, Poultry & Game product range in the "Grocery" product group are on average around 5.5% higher than their respective average weekly price.
On wednesdays between 6:00 and 12:00, the prices of products from the Meat, Poultry & Game product range in the "Grocery" product group are on average around 7.4% higher than their respective average weekly price.
On wednesdays between 12:00 and 18:00, the prices of products from the Meat, Poultry & Game product range in the "Grocery" product group are on average around 6.4% higher than their respective average weekly price.
On thursdays between 0:00 and 6:00, the prices of products from the Meat, Poultry & Game product range in the "Grocery" product group are on average around 2.8% higher than their respective average weekly price.
On thursdays between 6:00 and 12:00, the prices of products from the Meat, Poultry & Game product range in the "Grocery" product group are on average around 5% higher than their respective average weekly price.
On thursdays between 12:00 and 18:00, the prices of products from the Meat, Poultry & Game product range in the "Grocery" product group are on average around 3.9% lower than their respective average weekly price.
On thursdays between 18:00 and 24:00, the prices of products from the Meat, Poultry & Game product range in the "Grocery" product group are on average the same as their respective average weekly price.
On fridays between 0:00 and 6:00, the prices of products from the Meat, Poultry & Game product range in the "Grocery" product group are on average around 2.4% higher than their respective average weekly price.
On fridays between 6:00 and 12:00, the prices of products from the Meat, Poultry & Game product range in the "Grocery" product group are on average around 1.2% lower than their respective average weekly price.
On fridays between 12:00 and 18:00, the prices of products from the Meat, Poultry & Game product range in the "Grocery" product group are on average the same as their respective average weekly price.
On fridays between 18:00 and 24:00, the prices of products from the Meat, Poultry & Game product range in the "Grocery" product group are on average around 1.1% lower than their respective average weekly price.
On saturdays between 0:00 and 6:00, the prices of products from the Meat, Poultry & Game product range in the "Grocery" product group are on average the same as their respective average weekly price.
On saturdays between 6:00 and 12:00, the prices of products from the Meat, Poultry & Game product range in the "Grocery" product group are on average around 2.6% lower than their respective average weekly price.
On saturdays between 12:00 and 18:00, the prices of products from the Meat, Poultry & Game product range in the "Grocery" product group are on average the same as their respective average weekly price.
On saturdays between 18:00 and 24:00, the prices of products from the Meat, Poultry & Game product range in the "Grocery" product group are on average around 3.6% lower than their respective average weekly price.
On sundays between 0:00 and 6:00, the prices of products from the Meat, Poultry & Game product range in the "Grocery" product group are on average around 2.1% higher than their respective average weekly price.
On sundays between 6:00 and 12:00, the prices of products from the Meat, Poultry & Game product range in the "Grocery" product group are on average around 2.5% lower than their respective average weekly price.
On sundays between 12:00 and 18:00, the prices of products from the Meat, Poultry & Game product range in the "Grocery" product group are on average the same as their respective average weekly price.
On sundays between 18:00 and 24:00, the prices of products from the Meat, Poultry & Game product range in the "Grocery" product group are on average around 2.3% lower than their respective average weekly price.
Most frequently purchasedNew products
Daloon Frozen Savoury Vegetable and Beef Spring Rolls - 4x10x90g
from Daloon
Meadowvale Frozen Crispy Chicken Hot Wings - 1x1kg
from Meadowvale
Kangaroo Fillet, +/- 750g, Frozen
from Fine Food Specialist
Country Range Frozen 80% Beef Burgers 2oz - 48x57g
from Country Range
Country Range Frozen Battered Chicken Breast Nuggets 22g - 1x1.06kg
Country Range Frozen BBQ Chicken Wings - 1x1kg
Fenton Frozen British Easy Carve Turkey Breast Uncooked - 1x2.72kg
from Fenton Barns
Meadowvale Frozen Crunchy Hot & Spicy Chicken Breast Bites - 1x1kg
Bernard Matthews Frozen Crispy Crumb Turkey Burgers - 1x40x71g
from Bernard Matthews
Plumtree Frozen Pork Chipolata Sausages 16s - 1x4.54kg
from Plumtree Farms
Prime Fillet Steak
from THE WEST COUNTRY FISH CLUB
Golden Valley Frozen Gluten Free Breaded Chicken Chunks - 2x1kg
from Golden Valley
Meadowvale Frozen Cooked Cajun Chicken Breast Slices - 1x1kg
KaterKing Frozen British Pork Fully Cooked Meatballs - 1x3kg
from Katerking
Country Range Frozen Pork and Beef Sausage 8's - 1x4.54kg
Plumtree Frozen Lincolnshire Sausages 8s - 1x4.54kg
Country Range Frozen Battered Chicken Breast Steaks 85g - 1x1.02kg
Country Range Frozen Hot and Spicy Chicken Wings - 1x1kg
Country Range Frozen Butchers Cumberland Sausages 6's - 1x3.63kg
Browse here
Frozen Uncooked British Beef Mince Freeflow 95% - 1x2.5kg
from Thomas Ridley
Wagyu Flat Iron Steak, BMS 4-5, +/-700g, Frozen
Suckling Pig, Frozen, -4.5kg
100% Iberico Belotta Rib Rack, Frozen, +/-1.8kg
Country Range Frozen Pork Sausages 8s - 1x4.54kg


text:
Il distretto di Sangin è un distretto dell'Afghanistan situato nell'area orientale della provincia dell'Helmand. La popolazione è interamente Pashtun e al 2005 contava 50.900 abitanti. Il capoluogo del distretto è Sangin.

Altri progetti

Collegamenti esterni
Profilo del distretto dell'UNHCR , datato 01/12/2002, consultato il 04/08/2006 (PDF).
Mappa del distretto di Sangin  (PDF)

Sangin

redpajama_set_name: RedPajamaWikipedia


Looking for an effective and inexpensive way to advertise your business, event or item for sale? Local Channel 46 is the perfect spot. Your ad will reach over 3,600 Mason County residents. The static ad is on screen for approximately 15 seconds and rotates through about every 10 minutes – unbeatable exposure!
Please fill out the form below to submit your ad, or email your local channel advertisement to localchannel@hoodcanal.net. Ads must be submitted at least five (5) business days prior to desired start date. Artwork may be sent as a .jpg or .png file. The artwork dimensions are 10″ x 6.66″ or 720 x 480 pixels.
Microsoft PowerPoint or other presentation software is an easy to use option for creating ads. Keep in mind you are only creating a single slide and leave a margin around the text (between the edge of your background and the edge of your text box). If you do not own Microsoft PowerPoint options are available for free online. Suggested sites for free software are: http://www.openoffice.org/, http://drive.google.com, http://office.live.com.
If you would like us to create the advertisement for you, there is a onetime fee of $30. This fee applies to free and paid advertisements.
*Non-profit and other qualified charitable events may share their announcements through our Local Channel 46 free of charge, at the discretion of Hood Canal Communications.


We believe that Jesus Christ established the Church and commanded it to take the Gospel to the entire world. The Church is the collection of local, visible assemblies of scripturally baptized believers with a covenant agreement to carry out this command. Each assembly is independent with regard to function, self-governing in practice, yet under the leadership of Christ Himself. Furthermore, we believe that true, Bible based churches should associate and cooperate together for the spread of the Gospel message to the world. However, the amount of and extent of the cooperation is to be determined by the local Church. (Matt. 4:18-22, Matt. 16:18, Matt. 28:19, 20, Mark 1:14-20, John 1:35-51, Eph. 3:21, Acts chapters 1 & 2).
We believe that there are two divinely appointed offices in a church: pastors and deacons. These two offices are to be filled by men whose qualifications are set forth in Titus 1 and 1 Timothy 3.
We believe that God is the giver of all earthly and heavenly blessings and the giver of all that we have and all that we are. We have a spiritual responsibility to the whole world. We have a responsibility to share the gospel. We have a duty to be good managers of our possessions. We have the responsibility to serve Him with our time, talents, and material possessions. The Scriptures say that we, as God's children, should give a percentage of our income to His church, cheerfully, regularly, carefully, and generously. We should give for the progress of Christ's plan for His church here on earth. (Genesis 14:20, Leviticus 27:30-32, Deuteronomy 8:18, Malachi 3:8-12, Matthew 6:1-4,19-21, 19:21, 23:23, 25:14-29, Luke 12:16-21,42, 16:1-13, Acts 2:44-47, 5:1-11, 17:24-25, 20:35, Romans 6:6-22, 12:1-2, 1 Corinthians 4:1-2, 6:19-20, 12, 16:1-4, 2 Corinthians 8-9, 12:15, Philippians 4:10-19, 1 Peter 1:18-19).


text:
Charlotte Brontë 1847 gothic story of a plain English governess who falls in love with the mysterious Bryonic Edward Rochester has spurred over 36 movies, radio, musical and TV versions since 1910. This time the film directed by Cary Fukunaga (Sin Nombre) and screenwriter Moira Buffini (Tamara Drewe) have pared down the very detailed novel to a moody atmospheric plea for Jane's struggle to be treated like a independent human being.
The story opens with Jane (Mia Wasikowska) running away from from Thornfield Hall, getting caught in a storm on the moors. She is taken in by a brother and his sisters who nurse her back to health. St. John Rivers finds her a job teaching the local farmers daughters. The story then flashes back on how Jane came to be where she is now. As an orphaned child she was kicked out of her aunts home and sent to a charity school where she is accused of being decitful. Her sense of self worth is evident then as she does not back down from the attitude and self-righteous clergyman who runs the school. Her only friend Helen passes away from consumption. Somehow Jane survives the abuse at school and the loneliness, the movie doesn't really explain. Years later Jane receives the offer of a job teaching a French child at the estate of Thornfield Hall. Mrs. Fairfax (Judi Dench) the head housekeeper keeps the rooms ever ready as she never knows when Edward Rochester (Michael Fassbender) will be home. For once Jane feels comfortable and happy with her surroundings, despite the creepy noises that are coming from a wing of the sprawling mansion. When the dashing Mr. Rochester does come home her confidence and ability to speak her mind sparks his interest. Despite the slow build up Mr. Rochester with his swoon worthy eyes finds in Jane salvation from whatever it is that keeps him away from his home. They decide to wed, but soon that thump in the night becomes a fire in house, a person being shot, and Jane running away across the moors. She meets up with the River family and soon the brother (Jamie Bell) wants Jane to marry him and become a missionary wife. When Jane can't get Mr. Rochester out of her head, she returns only to find Thornfield burned to the ground.
Wasikowska is strong as the emotionally controlled Jane. Her Victorian era costumes with the many layered and corseted clothing in gray and her tawny hair in loose braids wrapped around her head is in direct contrast to Jane's curious and open mind. Fassbender is brooding and yet romantic. It's unfortunate that the chemistry between the two is somewhat lacking. Jane is so repressed that her surrender to Mr. Rochester's soulful glance is lacking. It was hard to believe that they fell in love so quickly. Where's the passion? It's still a movie worth watching even for whatever Brontë's feminist message may have been at the time. In the end Jane still goes back to the rich guy.
Labels: Jane Eyre review


Text Form for Signature Invitations — Fern Paper Co.
Here, you'll find the forms you need to submit your stationery wording to us. They're clearly labelled, so you can find the one you need depending on which design you've chosen. They have set character limits - this enables us to fit your text neatly within the framework of the designs.
If you're stuck and would like tips on how to word your invitations, you can find some examples here.


Many thanks to Erica Pike for donating an ebook copy of her recently released m/m romance, Little Stalker (College Fun & Gays #4), for a lucky commenter to win!
College student Coby is being stalked by a young guy and has no idea why…until someone suggests that the stalker may have a crush on him. The idea both excites and terrifies Coby, who is so deep in the closet he can barely manage to think the word "gay" without freaking out.
To enter, leave a comment stating that you are entering the contest. Contest closes 7 pm CST, Thursday, December 20.
Posted by Chris on Tuesday, December 11th, 2012, at 2:00 am, and filed under Contests, Reading.
I'm raising my hand to be added. Thank you Kindly!
Please count me in. I would love to read this one.


Cube breaks all traditional barriers in the foot massager category. Its internal system of dozens of air cells massage the entire lower body during one of four pre-programmed massage sessions. This affordable, readily accessible dual system of lower body massage chair and foot stool/table top is ideally suited for the space-conscious among us.
Electronically managed massage systems provides soothing and carefully choreographed pressure-point treatments through foot reflexology. Other benefits are gained through alleviating stiffness and pain in the calf and lower back areas.
©2013 An-Jye Health. All Rights Reserved.


Retail has never been a sector for the faint of heart, and its changing landscape and the entry of kickstarters make it a more challenging place to be than ever, particularly for long-established brands. Chily Fachler, CIO for Steinhoff UK Retail, spent much of 2017 devising and implementing a digital transformation strategy that would allow the multinational company's UK businesses Bensons for Beds and furniture retailer Harveys to thrive.
In has come a 'single version of the truth' database, with data interrogation tools and dashboards for over 300 staff (to be rolled out to 2,000 in all). Fachler's team have introduced warehouse management for the five distribution centres, improving stock control, warehouse productivity, operations and visibility, and reducing operating costs, working capital, shrinkage and unnecessary stock movements.
Office 365 has been deployed to 1,350 users, videoconferencing implemented (halving the travel spend, especially amongst senior executives, and bringing teams closer together), four different intranet sites have been rolled into a single Sharepoint-based version, and a time and attendance solution implemented in 350 locations. Routing and scheduling optimisation has already made the Bensons distribution teams more efficient, with Harveys to follow, introducing customer self-service for deliveries. Yammer has been deployed as internal social network, opening up a whole new conversation and mode of communication for colleagues.
And perhaps the icing on the cake is Fachler's introduction of mobile point of sale. It will let staff carry out assisted selling, product configuration and transactions while maximising customer engagement.
As well as bringing the businesses up to date, Fachler is welcoming the future with an augmented reality application incorporating a VR room planner to demonstrate what a particular bed/sofa/cabinet would look like (in three dimensions) in a room defined by the user.


Vivid Snaps Food Photography & Videography – Photography & videography for food business, including restaurant interior and chef portraits.
Our food photographers are all ready to present to you stunning pictures that tell stories about your restaurant, your menu and your dishes. Stimulate the appetite of your audience through our food photography!
Video the process, the making and the presentation of your plate through moving images that represent your masterpieces. Pique the taste buds of your audience through food videography!
Capture moments through still and moving images, to showcase the essence of your restaurant, cafes, or fine dining establishments. Impress your audience with our interior and exterior photography and videography.


OAK HARBOR, Washington, November 23. OLYMPIC champion Megan Jendrick stepped up for one race at the Whidbey Island short course meters Masters meet and set a Masters world record.
Jendrick, the 2000 Olympic champion in the 100 breaststroke, swam a 31.87 in the 50 breaststroke, erasing the world record in the 25-29 age group. The 26-year-old dipped under Nicole Heidemann's 31.97, set in December 2009.
The swim marks Jendrick's third Masters world record in 2010. She also holds the long course meters records in the 50 and 100 breaststrokes for the 25-29 age group, which she set in July.


text:
Q: partial deconstruction in pattern-matching (F#) Following a minimal example of an observation (that kind of astonished me):
type Vector = V of float*float

// complete unfolding of type is OK
let projX (V (a,_)) = a

// also works
let projX' x =
   match x with
   | V (a, _) -> a

// BUT:
// partial unfolding is not Ok
let projX'' (V x) = fst x

// consequently also doesn't work
let projX''' x =
   match x with
   | V y -> fst y

What is the reason that makes it impossible to match against a partially deconstructed type?
Some partial deconstructions seem to be ok:
// Works
let f (x,y) = fst y

EDIT:
Ok, I now understand the "technical" reason of the behavior described (Thanks for your answers & comments). However, I think that language wise, this behavior feels a bit "unnatural" compared to rest of the language:
"Algebraically", to me, it seems strange to distinguish a type "t" from the type "(t)". Brackets (in this context) are used for giving precedence like e.g. in "(t * s) * r" vs "t * (s * r)". Also fsi answers accordingly, whether I send
type Vector = (int * int)

or
type Vector = int * int

to fsi, the answer is always

type Vector = int * int

Given those observations, one concludes that "int * int" and "(int * int)" denote exactly the same types and thus that all occurrences of one could in any piece of code be replaced with the other (ref. transparency)... which as we have seen is not true.
Further it seems significant that in order to explain the behavior at hand, we had to resort to talk about "how some code looks like after compilation" rather than about semantic properties of the language which imo indicates that there are some "tensions" between language semantics an what the compiler actually does.

A: In F#
type Vector = V of float*float

is just a degenerated union (you can see that by hovering it in Visual Studio), so it's equivalent to:
type Vector =
    | V of float*float

The part after of creates two anonymous fields (as described in F# reference) and a constructor accepting two parameters of type float.
If you define
type Vector2 =
    | V2 of (float*float)

there's only one anonymous field which is a tuple of floats and a constructor with a single parameter. As it was pointed out in the comment, you can use Vector2 to do desired pattern matching.
After all of that, it may seem illogical that following code works:
let argsTuple = (1., 1.)
let v1 = V argsTuple

However, if you take into account that there's a hidden pattern matching, everything should be clear.
EDIT:
F# language spec (p 122) states clearly that parenthesis matter in union definitions:

Parentheses are significant in union definitions. Thus, the following two definitions differ:
type CType = C of int * int
type CType = C of (int * int)
The lack of parentheses in the first example indicates that the union case takes two arguments. The parentheses
  in the second example indicate that the union case takes one argument that is a first-class tuple value.

I think that such behavior is consistent with the fact that you can define more complex patterns at the definition of a union, e.g.:
    type Move =
        | M of (int * int) * (int * int)

Being able to use union with multiple arguments also makes much sense, especially in interop situation, when using tuples is cumbersome.
The other thing that you used:
type Vector = int * int

is a type abbreviation which simply gives a name to a certain type. Placing parenthesis around int * int does not make a difference because those parenthesis will be treated as grouping parenthesis.


It used to be more than now. Metra has become shy about enforcing rules regarding trespassers or troublemakers. Metra cops won't respond and when they do, they have been instructed not to arrest. Brain child of current management. I guess they are afraid they will lose a fare or two. I am sure the contract carriers have been instructed the same way. It doesn't make the employees all that gung ho to enforce anything since they don't get backed up. For example, you get bitched out about not collecting a fare, but yet try to enforce someone not paying said fare or surcharge you get reprimanded. Very confusing, disheartening and quite honestly a questionable practice. Those who don't respect the rules or procedures seem to be encouraged to get away with it and those who do end up paying for it in the long run. Don't understand it one bit, but welcome to the year 2018.


text:
Posts Tagged 'Greatest Show on Earth'
"Let us save what remains"*…
On Friday morning, January 25, 2013, 15 jihadis entered the restoration and conservation rooms on the ground floor of the Ahmed Baba Institute in Sankoré, a government library in Mali. The men swept 4,202 manuscripts off lab tables and shelves and carried them into the tiled courtyard. They doused the manuscripts—including 14th- and 15th-century works of physics, chemistry, and mathematics, their fragile pages covered with algebraic formulas, charts of the heavens, and molecular diagrams—in gasoline. Then they tossed in a lit match. The brittle pages and their dry leather covers ignited in a flash.
In minutes, the work of Timbuktu's greatest savants and scientists, preserved for centuries, hidden from the 19th-century jihadis and French conquerors, survivors of floods, bacteria, water, and insects, were consumed by the inferno.
In the capital city of Bamako 800 miles away, the founder of Timbuktu's Mamma Haidara Library, a scholar and community leader named Abdel Kader Haidara, saw the burning of the manuscripts as a tragedy—and a vindication of a remarkable plan he'd undertaken. Starting with no money besides the meager sum in his savings account, the librarian had recruited a loyal circle of volunteers, badgered and shamed the international community into funding the scheme, raised $1 million, and hired hundreds of amateur smugglers in Timbuktu and beyond. Their goal? Save books…
The whole heart-warming story at "The Great Library Rescue of Timbuktu."
* Thomas Jefferson
As we check it out, we might wish a spectacularly happy birthday to Phineas Taylor ("P.T.") Barnum; he was born on this date in 1810. Barnum founded and ran a small business, then a weekly newspaper in his native Connecticut before leaving for New York City and the entertainment business. He parlayed a variety troop and a "curiosities" museum (featuring the '"Feejee" mermaid' and "General Tom Thumb") into a fortune… which he lost in a series of legal setbacks. He replenished his stores by touring as a temperance speaker, then served as a Connecticut State legislator and as Mayor of Bridgeport (a role in which he introduced gas lighting and founded the Bridgeport hospital)… It wasn't until after his 60th birthday that he turned to endeavor for which he's best remembered– the circus.
"I am a showman by profession…and all the gilding shall make nothing else of me."
source: Library of Congress
Tagged with Barnum, books, Circus, Greatest Show on Earth, Library, preservation, showman, terrorism, Timbuktu
Mown down…
George C Ballas, Sr, the Houston, Texas, dance studio owner who changed the way America cut its grass when he invented the Weed Eater aka the weed whacker, died [late last month] of natural causes. He was 85. Ballas (seen here with an early prototype) got the idea for the mower while sitting in a car wash wondering if those spinning bristles could be modified to trim grass and weeds in areas a lawnmower couldn't reach. Turns out they could. He founded his Weed Eater company in 1971, made a bundle, and later sold the invention to Emerson Electric for an undisclosed sum. "A Weed Eater comes along once in a lifetime," he said. Although he's known as the Weed King, Ballas' life was dance. He was an Arthur Murray dance instructor and his own Dance Studio USA was the world's largest (43,000 square feet); his wife was a noted flamenco dancer; his son Corky is a champion ballroom dancer; and his grandson Mark is a professional dancer, a regular partner on Dancing With the Stars. (AP photo)
Via World of Wonder.
As we dance our way under those inconvenient hedges and into those pesky corners, we might wish a spectacularly happy birthday to Phineas Taylor ("P.T.") Barnum; he was born on this date in 1810. Barnum founded and ran a small business, then a weekly newspaper in his native Connecticut before leaving for New York City and the entertainment business. He parlayed a variety troop and a "curiosities" museum (featuring the '"Feejee" mermaid' and "General Tom Thumb") into a fortune… which he lost in a series of legal setbacks. He replenished his stores by touring as a temperance speaker, then served as a Connecticut State legislator and as Mayor of Bridgeport (a role in which he introduced gas lighting and founded the Bridgeport hospital)… It wasn't until after his 60th birthday that he turned to endeavor for which he's best remembered– the circus.
Tagged with Arthur Murray, Barnum, Circus, circus history, dance, Dance Studio USA, Dancing With the Stars, Emerson Electric, Feejee mermaid, General Tom Thumb, George Ballas, George C Ballas Sr, Greatest Show on Earth, Mark Ballas, P.T. Barnum, Phineas Taylor Barnum, Tom Thumb, Weed Eater, weed whacker, world's largest dance studio


Western Cape traffic officials have arrested yet another speedster in the Karoo. This time on the R61 between Aberdeen and Beaufort West. Provincial traffic chief, Kenny Africa says the 28-year-old driver was travelling at 162 kilometre an hour in a 120 zone. He had three passengers with him in his vehicle. The suspect is in custody at the Beaufort West Police station. He is the 12th driver to be caught in the Karoo this festive season for speeding. The highest speed recorded so far was 214 kilometres per hour in a 120 zone on the N1 near Laingsburg. All of the drivers are male.


text:
Q: Where does the space before \align* come from? In the following MWE, what is responsible for the large space before the align environment? How can I remove it (it doesn't appear if I change to \[ \] and remove amsmath) ?
\documentclass{article}

\usepackage[english]{babel}
\usepackage{amsmath,amssymb}
\usepackage{lipsum}

\begin{document}
\setlength{\parskip}{0pt}
\setlength{\abovedisplayskip}{0pt}
\setlength{\belowdisplayskip}{0pt}
\setlength{\abovedisplayshortskip}{0pt}
\setlength{\belowdisplayshortskip}{0pt}

\lipsum*[2]

\lipsum*[2]

\begin{align*}1, 2, 3\end{align*}

\lipsum*[2]

\lipsum*[2]
\end{document}

I have read Spacing around align environments (but it doesn't cover the case in which there's a \par before \align and Remove vertical space around align (but it attributes the space to \parskip, which seems wrong: setting \parskip to 0 pt doesn't remove the space). I also read Remove extra vertical space in amsmath's align environment and Remove vertical space around align equations, but they just say that one shouldn't leave a \par before an \align.  I'm curious to know what actually causes this blank space, even with all seemingly relevant lengths set to zero.
Edit for Reopen
Why does LaTeX insert space before formulas? is related, but it doesn't address the why: it says that leaving a blank line in the source causes the space but it doesn't say who is adding this space (and it's clearly an amsmath-specific this: the regular displaymath doesn't do that).

A: You ask,

Where does the [vertical] space before \align* come from?

It comes from an input mistake -- not a syntax error, mind you, but a mistake nevertheless -- in your code: Display-math environments should never, ever occur at the start of a paragraph.
In the following code, which preserves your \setlength instructions, the instance of align* that is not preceded by a paragraph break features no extra vertical whitespace; in contrast, the instance of align* that is preceded by a paragraph break does feature the dreaded extra whitespace. Observe that this happens even though the five length parameters have been set to 0pt.
To recap: Never begin a paragraph with a display-math environment. Not only is it poor practice from a typographic standpoint, it's also poor practice from a discursive/explanatory standpoint.

\documentclass{article}
\usepackage{amsmath,lipsum}

\begin{document}
\setlength{\parskip}{0pt}
\setlength{\abovedisplayskip}{0pt}
\setlength{\belowdisplayskip}{0pt}
\setlength{\abovedisplayshortskip}{0pt}
\setlength{\belowdisplayshortskip}{0pt}
\lipsum*[2]
\begin{align*}1, 2, 3\end{align*} % no paragraph break before  this 'align*'
\lipsum*[2]

\begin{align*}1, 2, 3\end{align*} % paragraph break before this 'align*'
\lipsum*[2]
\end{document}

A: Not sure of the actual reason but I manage to fix that by placing a \vspace{0.2em}
\begin{document}
\setlength{\parskip}{0pt}
\setlength{\abovedisplayskip}{0pt}
\setlength{\belowdisplayskip}{0pt}
\setlength{\abovedisplayshortskip}{0pt}
\setlength{\belowdisplayshortskip}{0pt}

\lipsum*[2]

\lipsum*[2]
\vspace{0.2em}
\begin{align*}1, 2, 3\end{align*}

\lipsum*[2]

\lipsum*[2]

\end{document}