text:
\section{Introduction}

Weak lensing mass calibration is a key to achieving the full potential of galaxy cluster cosmology \citep[for a discussion, see e.g.][]{vonderlinden2014}. Numerous lensing studies have provided cluster mass estimates over the last years \citep[e.g.][]{Gruen2014,vonderlinden2014,2015arXiv150201883H,okabesmith16,2017MNRAS.466.3103S,2017MNRAS.469.4899M,Dietrich17,2018arXiv180500039M}. The statistical power of such analyses is continuously growing with precise lensing source catalogs around large cluster samples coming from DES,\footnote{\href{https://www.darkenergysurvey.org}{https://www.darkenergysurvey.org}}, HSC,\footnote{\href{http://hsc.mtk.nao.ac.jp/ssp/}{http://hsc.mtk.nao.ac.jp/ssp/}} and KiDS\footnote{\href{http://kids.strw.leidenuniv.nl/}{http://kids.strw.leidenuniv.nl/}}, and future Euclid,\footnote{\href{https://www.euclid-ec.org/}{https://www.euclid-ec.org/}} LSST,\footnote{\href{https://www.lsst.org/}{https://www.lsst.org/}} or WFIRST\footnote{\href{https://wfirst.gsfc.nasa.gov/}{https://wfirst.gsfc.nasa.gov/}} data.
This improvement in statistics requires an equivalent push for reducing systematic uncertainties in measurement and modeling of lensing signals. State-of-the-art studies account for systematic effects such as deviations of the assumed model of the cluster matter density profile from the truth \citep[e.g.][]{2010arXiv1011.1681B}, systematics in lensing source catalogs \citep[e.g.][]{2017arXiv170801533Z}, excess contamination of the lensing source catalog with cluster member galaxies \citep[e.g.][]{2017MNRAS.469.4899M,2017arXiv170600427M}, and biases and calibration uncertainties in lensing source photometric redshifts inherent to the algorithms used for estimating them \citep[e.g.][]{2016arXiv161001160G,2017arXiv170801532H}. In recent studies, each of these effects cause uncertainty on cluster mass at the level of one to a few per cent \citep[e.g.][]{2017MNRAS.469.4899M}.

In this paper, we investigate another effect on redshift estimates of weak lensing sources -- the bias due to contamination of source photometry from diffuse intracluster light (ICL). In our ICL model, we consider light from the central galaxy and from unbound stars in the cluster potential \citep[see examples of studies or reviews in][]{1951PASP...63...61Z, 1952PASP...64..242Z, 2005ApJ...618..195G, 2005MNRAS.358..949Z, 2015IAUGA..2247903M, 2018MNRAS.474..917M, 2018AstL...44....8K} as well as the light of faint member galaxies below the survey selection threshold.
The diffuse light biases the flux and color measurements of lensing source galaxies, and causes a systematic change in photometric estimates of their redshift distributions. Among other effects, the spectral energy distribution (SED) of passive stellar populations at the cluster redshift introduces a mild cluster rest-frame D4000 break to the observed SED of the lensing source galaxy. These changes in flux and color affect the redshift assigned, especially for star-forming galaxies with weaker break features.

Careful analysis of color-magnitude space could be used to select galaxies less susceptible to these effects, and composite models for blended galaxies could in principle fully account for them. Given the complexity and algorithm dependence of source photometry and redshift estimation, we do not aim to provide a prescription for correcting ICL photo-$z$ contamination in this paper. Our goal is rather to evaluate approximately and, if possible, conservatively, what amplitude of bias we expect and identify the regimes in which it can be ignored.

In section 2, we describe our model for the surface brightness of intracluster light, using the results of \citet{zhang}. In section 3, we derive our estimate for how diffuse intracluster light of given surface brightness biases the lensing amplitude predicted from photometric redshifts, based on \citet{2016arXiv161001160G}.  Section 4 combines these two components of the model to estimate the bias in lensing excess density profiles in a typical current (DES-like) and future (LSST-like) survey, as a function of cluster redshift and separation from the cluster center. We conclude the study in section 5.

Estimates of a quantity $q$ are denoted as $\hat{q}$. All magnitudes given in the $u^{\star}g'r'i'z'$ bands are in CFHT/Megacam filters\footnote{\href{http://cfht.hawaii.edu/Instruments/Filters/megaprime.html}{http://cfht.hawaii.edu/Instruments/Filters/megaprime.html}} u.MP9301, g.MP9401, r.MP9601, i.MP9701, z.MP9801 and AB units until otherwise noted. Surface brightnesses are given in nJy arcsec$^{-2}$ units. These can be converted to counts per arcsec$^2$ at a magnitude zeropoint of 30 with a conversion factor of 3.63~nJy per count, i.e.~3.63~nJy arcsec$^{-2}$ correspond to 30 mag arcsec$^{-2}$. Cosmological distances for the scaling of lensing signal amplitudes are calculated in a flat $\Lambda$ cold dark matter cosmology with $\Omega_{m,0}=0.27$, and masses are expressed assuming a Hubble constant $H_0=70$km s$^{-1}$ Mpc$^{-1}$.

\section{Intracluster light model}
\label{sec:iclmodel}
The goal of this section is to derive a model for the surface brightness of ICL. We describe it as a function of cluster mass, cluster redshift, and projected physical distance from the cluster center.

The distribution of ICL is a debated topic in the literature. It is believed that the ICL contains a significant amount of stellar mass \citep{2013ApJ...770...57B, 2014MNRAS.437.3787C, 2018MNRAS.475..648P}, comparable to that of cluster central galaxies or the rest of the cluster galaxies. However, measurements of ICL in various samples \citep{2005MNRAS.358..949Z, 2005ApJ...618..195G, 2006AJ....131..168K, 2011MNRAS.414..602T,2012MNRAS.425.2058B, 2013ApJ...778...14G, 2014ApJ...794..137M, 2015MNRAS.448.1162D} do not necessarily find agreement on such a massive component, possibly due to methodological difference (such as differences in filter bands, or surface brightness thresholds and other criteria used to distinguish ICL from galaxies, see e.g. \citealt{2017ApJ...846..139M}, \citealt{2018MNRAS.474..917M} and the discussion in the latter), cluster-to-cluster variations \citep[e.g.,][]{2007AJ....134..466K}, cluster dynamic state \citep[e.g.,][]{2018ApJ...857...79J,2019A&A...622A.183J}, or redshift evolution and the surface brightness limits of ICL \citep[e.g.,][]{2015MNRAS.449.2353B}. By averaging the light profile of $\sim$ 300 optically selected clusters, \citet{zhang} quantified the ICL distribution at $z\sim 0.25$ for clusters more massive than $\sim 2 \times 10^{14} M_\odot$. A comparison of the stellar mass in the ICL component with the total stellar mass in DES Y1 \textsc{redMaPPer} clusters measured in \citet{palmese} shows that the ICL, together with the central galaxy, makes up $\sim 40\%$ of the total cluster stellar mass in the sample from \citet{zhang}. We make use of these measurements to model ICL.

There are three components empirically seen as diffuse light in clusters with the methodology of \citet{zhang}: pure ICL due to stars not bound to any galaxy, the light of faint cluster members below a detection/masking threshold, and scattered light of the cluster galaxies in the outskirts of the point-spread function (PSF).

We will call the first component, dominant in most regimes, \emph{pure} ICL.
Our model for pure ICL is based on the measurements presented in \citet{zhang}. In that work, sky brightness around centers of optically selected clusters is measured on co-added images. The latter are made by masking well-detected galaxies ($i<22.4$) on single-epoch DES images without background subtraction, and combining all frames of the full cluster sample while placing the cluster center at the center of the co-add image. Three effects contaminate the light measured such: background contamination due to random field galaxies, light of faint un-masked cluster member galaxies ($i>22.4$), and light of bright cluster member galaxies escaping the applied masking. These components are estimated and subtracted to yield the measurement of pure ICL.

As an additional contaminant, the PSF effect exists with every ground-based telescope at similar levels (see studies in \citealt{1969A&A.....3..455M, 1971PASP...83..199K, 1996PASP..108..699R,2007ApJ...666..663B, 2014A&A...567A..97S} and also discussions in \citealt{zhang}). It is a contaminant to the measurement in \citet{zhang}, yet greatly subdominant in the case of the DECam PSF, given that 97 per cent of light is contained within a 5'' radius of the PSF \citep[][their section 4]{zhang}, and intrinsic ICL is a much larger fraction of total cluster light. We find that the effect of PSF changes the ICL profile by less than 5 per cent in the relevant radial redshift ranges.

Our second term, the amount of light in \emph{undetected} galaxies, depends on the magnitude limit to which cluster members are detected and can be successfully deblended. We approximate this as a fixed limiting magnitude $m^{\rm lim}$.

The full function we are trying to model is thus
\begin{eqnarray}
\label{eqn:fmodel}
f_{\rm ICL}(M_{200m}, z_{d}, r, m^{\rm lim}) &=& f_{\rm pure\; ICL}(M_{200m}, z_{d}, r) \nonumber \\ &+& f_{\rm undetected}(M_{200m}, z_{d}, r, m^{\rm lim}) \; , \nonumber \\
\end{eqnarray}
with cluster mass $M_{\rm 200m}$, cluster redshift $z_{d}$, and projected physical distance $r$ from the cluster center. We describe our model for both terms in the following sections.

\subsection{Model for pure ICL}

\citet{zhang} have measured the pure ICL profile around a richness-redshift selected sample of redMaPPer clusters in DES Y1 data. In this subsection, we convert their measurement of pure ICL at these fixed parameters into a prediction for $f_{\rm pure\; ICL}(M_{200m}, z_{d}, r)$ based on the assumptions that
\begin{itemize}
\item The stellar mass density profile is self-similar, i.e.~indistinguishable between different clusters when expressed as a function of $r/r_{200m}\propto r\times M_{\rm 200m}^{-1/3}$. This is qualitatively consistent with the results of a richness-binned analysis in \citet{zhang}.
\item ICL has a fixed stellar mass density profile in physical coordinates across redshifts, which leads to a re-scaling of stellar mass per solid angle with the square of angular diameter distance. We note that there is an ongoing debate in the literature about the growth of ICL over cosmic time, which is discussed below.
\item ICL is passively evolving. As a function of redshift, it follows the corresponding luminosity evolution.
\end{itemize}

These three assumptions can be written as the three re-scaling terms on the right-hand side of the expression
\begin{eqnarray}
f_{\rm pure\; ICL}^{i'}(M_{200m}, z_{d}, r) &=&
f_{\rm ICL}^{\rm Zhang}\left(r\times \left(\frac{M_{200m}}{M_{200m}^{\rm fid}}\right)^{-1/3}\right) \nonumber \\
&\times& \left(\frac{D_{A}(z_d)}{D_{A}(z_{\rm fid})}\right)^2 \nonumber \\
&\times& 10^{-0.4\left(m_{i',z_d}-m_{\rm fid}\right)} \; .
\label{eqn:ftransform}
\end{eqnarray}
Here $f_{\rm ICL}^{\rm Zhang}(r)$ is the ICL surface brightness of \citet{zhang}, measured for a fiducial mass $M_{200m}^{\rm fid}=3\times10^{14} M_{\odot}$ and redshift $z_{\rm fid}=0.25$. $m_{i',z_d}-m_{\rm fid}$ is the apparent magnitude difference of a passively evolving galaxy seen at redshift $z_d$ in CFHT $i'$ band and at redshift $z_{\rm fid}$ in DES $r'$ band. For the purpose of this paper, we use a \citet{2003MNRAS.344.1000B} model with solar metallicity ($Z=0.02$), no dust, and with star formation beginning 10 Gyr before $z=0$ and subsequently declining as $e^{-t/\tau}$ with $\tau=0.1$ Gyr. The ratio of angular diameters $D_A$ corrects for the change of angular scale of the ICL profile with redshift.

Examples of ICL profiles transformed in cluster redshift, mass and filter band are shown in \autoref{fig:zhangtransform}. In this figure and all that follows, we apply azimuthal averaging and a smoothing of $\pm40$kpc at $r>150$kpc to reduce the noise of the pure ICL measurement of \citet{zhang} at large radii.

\begin{figure}
	\includegraphics[width=\columnwidth]{zhang_transform}
    \caption{Pure ICL profiles (solid lines) measured in DES (black) and transformed to higher mass (blue) and redshift (red) according to \autoref{eqn:ftransform}. Dotted lines show the additional ICL due to undetected cluster members (\autoref{eqn:fundet}) in a survey that detects galaxies down to $r=22.5$.}
    \label{fig:zhangtransform}
\end{figure}

Note that we assume ICL to not accrete or eject stars over time. It is often argued that ICL forms relatively late, assembling most of its total stellar mass during galaxy interactions after redshift 1.0 \citep{2006ApJ...648..936R,2006ApJ...652L..89M, 2007ApJ...668..826C, 2012MNRAS.425.2058B, 2013ApJ...770...57B, 2014MNRAS.437.3787C, 2016ApJ...816...98Z}. Since our model is based on ICL measurements at $z\sim 0.25$, the luminosity of ICL at higher redshift ($z>0.25$) is likely to be lower than, or at most equal to, the amount predicted from our passive evolution model. Hence, the photometric bias due to ICL at higher redshift ($z>0.25$) is likely to be less severe than that predicted in the paper. Passive evolution is a conservative assumption for the purpose of estimating photo-$z$ bias.

\begin{table}
\centering
\begin{tabular}{cccc}
$a$ & $b_r$ & $b_\lambda$&$b_z$\\
$[\mathrm{nJy}\; \mathrm{arcsec}^{-2}]$ & & & \\
\hline
$ 9.95 \pm 0.12 $ & $ 1.205 \pm 0.010 $ & $-0.831 \pm 0.037$ & $8.96 \pm 0.10$

\end{tabular}\caption{Best--fit values for eq. (\ref{eq:fmem}) for the DES $r'$ band flux from redMaPPer members. The reduced $\chi^2$ is 1.5.}\label{tab:fmem}
\end{table}

Finally, to set the ICL fluxes in other bands, we assume that at any redshift, ICL has the same color as the passive galaxy population. In reality, ICL could be somewhat bluer in color, especially at large cluster-centric distance. This is due to its lower metallicity, related to its build-up from tidal stripping of cluster members and disruption of dwarf galaxy members \citep[e.g.][]{2014ApJ...794..137M,2014A&A...565A.126P,2018MNRAS.475.3348H, 2018MNRAS.474..917M,demaio18,zhang,2019ApJ...871...24C}. We confirm that an excess in blue light of 0.1mag in $g$ band, comparable to the color effect of the expected metallicity offsets, would reduce our predicted bias, yet by less than 5 per cent, at all cluster redshifts studied here.

\subsection{ICL from undetected cluster members}

The light of undetected member galaxies is an additional contribution to diffuse light in the cluster. To add this to our full ICL model, we use the same methodology as \citet{zhang} apply for \emph{subtracting} the faint galaxy contribution towards a measurement of pure ICL (see their section 5). Namely, we assume that at any radius, the fraction of total cluster member light in faint galaxies is determined by a spatially homogeneous luminosity function. From the measured light in bright cluster members we can then predict the undetected contribution.

Formally, we write
\begin{eqnarray}
f_{\rm undetected}(M_{200m}, z_{d}, r, m^{\rm lim}) &=& f_{\rm members}(M_{200m}, z_{d}, r) \nonumber \\ &\times& S(z_d,m^{\rm lim},\infty) \; ,
\label{eqn:fundet}
\end{eqnarray}
where $S(z_d,m^{\rm lim},\infty)$ is the fraction of the integral over the cluster member luminosity function contributed by the faint end from $m^{\rm lim}$ to $\infty$.

For a \citet{1976ApJ...203..297S} luminosity function with faint-end slope $\alpha$,
\begin{equation}
\frac{\mathrm{d}N_{\rm gal}}{\mathrm{d}L}\propto\phi(L)\propto \left(\frac{L}{L^{\star}}\right)^{\alpha}\exp[L/L^{\star}]\; ,
\end{equation}
the integrated luminosity is given by
\begin{equation}
I(L_1,L_2)=\int_{L_1}^{L_2} L\;\phi(L)\,\mathrm{d}L \propto \left[\Gamma\left(\alpha+2,\frac{L_2}{L^{\star}}\right)-\Gamma\left(\alpha+2,\frac{L_1}{L^{\star}}\right)\right] \; ,
\label{eqn:lint}
\end{equation}
with the incomplete gamma function $\Gamma$. In this work, we assume $\alpha=-1$, as motivated by \citet{2014ApJ...785..104R}, thus
\begin{equation}
S(z_d,m_1,m_2)=\Gamma\left(1,10^{0.4(m^{\star}-m_1)}\right)-\Gamma\left(1,10^{0.4(m^{\star}-m_2)}\right)
\end{equation}
Note that for this luminosity function about 18\% of the total flux is contained in galaxies fainter than $0.2L_{\star}$ and more than 99\% of the total flux is contained in members brighter than $m^{\star}+5$.

The characteristic magnitude $m^{\star}$ \citep{2007ApJ...660..221K, 2014ApJ...785..104R} is a function of cluster redshift $z_d$, which we calculate from the \citet{2003MNRAS.344.1000B} model, normalized to match the SDSS DR8 \citep{2011ApJS..193...29A} redMaPPer catalog \citep{2014ApJ...785..104R} at $z=0.2$.

We approximate $f_{\rm members}$ from the light of redMaPPer cluster members $f_{\rm redMaPPer}$ in the "flux limited" DES Y1 catalog \citep{2018arXiv180500039M}. RedMaPPer estimates the probability of each galaxy along the line of sight to belong to the red cluster member population above $0.2 L_\star$ based on its position relative to the central galaxy and its color-magnitude relative to the empirically calibrated red sequence at the cluster redshift. The count of these galaxies within a cluster defines the redMaPPer richness $\lambda$. They are detected by DES over the full redshift range of the redMaPPer catalog, allowing us to empirically constrain the evolution of $f_{\rm members}$ with redshift. However, they are only the bright, red subset of the cluster galaxy population. For $f_{\rm members}$ in \autoref{eqn:fundet}, we thus use the luminosity function to re-scale $f_{\rm redMaPPer}$ by a factor $I(0.2 L^{\star},\infty)/I(0,\infty)=1.22$ from \autoref{eqn:lint}, for the missing members at $L<0.2 L_\star$. In the relevant radial range, these passive galaxies dominate the cluster member population \citep[e.g.][]{2016MNRAS.457.4360Z}, which is why we do not correct for the missing non-passive members.

From examining these light profiles, we find that the DES $r'$ band flux $f_{\rm members}$ of redMaPPer cluster members approximately follows a power law in projected radial distance, cluster richness and redshift, as:
\begin{equation}
f_{\rm members}(\lambda, z_{d}, r) = a \Big(\frac{r}{\tilde{r}} \Big)^{-b_r} \Big(\frac{\lambda}{\tilde{\lambda}}\Big)^{-b_\lambda} \Big(\frac{1+z_d}{1+\tilde{z}_d}\Big)^{-b_z} \,,\label{eq:fmem}
\end{equation}
where $\tilde{r}=240$ kpc, $\tilde{\lambda}=40$ and $\tilde{z}_d=0.5$ are the pivot values for richness and cluster redshift, and $a$ and $b_{r/\lambda/z}$ are our fit parameters for overall amplitude and power law exponents, respectively.

Eq. (\ref{eq:fmem}) is fit between 20 and 1000 kpc, and the best-fitting results from a $\chi^2$ minimization are given in Table \ref{tab:fmem} and $r$ is the comoving projected distance from the cluster center in kpc. The flux used is the SExtractor \texttt{AUTO} measurement in DES $r'$ band \citep{2017arXiv170801531D} and this is weighted for each galaxy from the redMaPPer catalog by the corresponding membership probability. The masked regions are taken into account when computing the flux per area, and the errors on the flux profiles are computed through a jackknife resampling. The bins in richness ($20<\lambda<140$) and redshift ($0.1<z<0.8$) are chosen to have a similar number of clusters in most bins.

To convert $f_{\rm members}(\lambda, z_{d}, r)$ to $f_{\rm members}(M_{200m}, z_{d}, r)$ we apply the $\langle\ln\lambda|M_{500c}\rangle$ relation of \citet{2015MNRAS.454.2305S}. We convert between $M_{200m}$ and their $M_{500c}$ using the mass-concentration relation of \citet{2008MNRAS.390L..64D}. We note that $\langle\lambda|M\rangle\neq e^{\langle\ln\lambda|M\rangle}$ due to intrinsic scatter in $\lambda$ at fixed $M$. For the purpose of this paper and consistency with our scaling of the \citet{zhang} model for pure ICL, we set the amplitude of the scaling relation such that $\langle\lambda|M_{200m}=3\times10^{14}M_{\odot},z=0.25\rangle$=30.

The $m_{\rm lim}$ to use with \autoref{eqn:fundet} is dependent on survey and detection strategy. For the DES Y1 Gold catalog \citet[][their Figure 8]{2017arXiv170801531D}, a conservative $m_{\rm lim}$ for the purpose of estimating the contribution of cluster members to diffuse light is a DES $i'$ band magnitude of 22.5.

We model the light of undetected members at a given cluster-centric radius as homogeneously distributed, rather than concentrated at the positions of the actual galaxies. If the surface brightness of ICL at the positions of actual undetected galaxies is small enough so that the linearity of photo-$z$ bias found in \autoref{sec:dbdf} holds, the predicted mean bias does not depend on this assumption of homogeneity. For member galaxies with larger surface brightness, non-linear blending effects will likely play a role - we consider these to be an issue separate to the ICL studied in this paper.

We note that the contribution of undetected cluster members becomes important at large cluster mass, high redshift, and for a shallow survey (see dotted lines in \autoref{fig:zhangtransform}). For our DES parameters, it contributes the majority of ICL for a cluster of $M_{200m}/M_{\odot}=10^{15}$ at $z_d>0.6$. For lower mass or redshift in DES, it is a subdominant component -- contributing, in the relevant regimes, between 10 and 40 per cent of ICL. For LSST it is negligible due to the completeness down to fainter magnitudes.

\section{Lensing photo-$z$ biases from diffuse light}

The goal of this section is to derive a model for the bias in the lensing measurement of cluster surface matter density due to leakage of ICL into lensing source galaxy photometry used for estimating source redshift ($z_s$) distributions. The source redshift dependent quantity needed for lensing measurements of a matter distribution at redshift $z_d$ is the predicted amplitude of the lensing signal. This amplitude is proportional to
\begin{equation}
\beta=D_{ds}/D_{s} \; ,
\end{equation}
the ratio of angular diameter distances between lens and source $D_{ds}$ and to the source $D_{s}$, defined as the ratios of physical to angular sizes of objects at $z_s$ seen by observers at $z_d$ and 0, respectively. The true value of $\beta$ could be calculated if redshifts were known for sources and lenses. In practice, the source redshift distributions are estimated from their photometry. Any bias in photo-$z$ thus manifests as a bias in the amplitude $\hat{\beta}$ estimated from them. In this work, we therefore primarily consider biases in $\hat{\beta}$, rather than in the redshift distribution more generally.

We define this bias as
\begin{equation}
\left(\hat{\beta}/\beta\right)-1\approx F(f_{\rm ICL}, z_{d},\mathrm{source\;magnitude\;limit}) \; ,
\label{eqn:dbdf}
\end{equation}
where $f_{\rm ICL}$ is the surface brightness of intracluster light present at the position of the lensing source galaxy in question and $z_d$ is the redshift of the lens. $F$ is the model for the ICL-related bias we derive in this section. The larger the statistical power of a lensing survey, the smaller a bias can be tolerated before it significantly affects the analysis. Current (and future) surveys aim for multiplicative biases to be below the few (to one) per cent level.

In the remainder of this section we describe the basic lensing formalism, followed by our framework for estimating the impact of ICL on empirical redshift estimates in \autoref{sec:betatree}. We then develop the right-hand side of \autoref{eqn:dbdf} in \autoref{sec:dbdf}. In this, $f_{\rm ICL}$ is denoting the level of ICL surface brightness at the position of the lensing source population -- the model for $f_{\rm ICL}$ as a function of cluster mass, redshift, and distance from the cluster center was presented in \autoref{sec:iclmodel}.

The image of a lensing source (or ensemble of sources) located on some annulus around a gravitational lens at angular diameter distance $D_{d}$ from the observer is subject to tangential gravitational shear \citep[e.g.][for a review]{2001PhR...340..291B}
\begin{equation}
\gamma_t=\Sigma_{\rm crit}^{-1}\times\Delta\Sigma= \frac{4\pi G D_{d}}{c^2}\times\beta\times\Delta\Sigma \; .
\label{eq:betagamma}
\end{equation}
The excess surface density $\Delta\Sigma$ at radius $r$ is the difference of the mean mass per area \emph{inside} and \emph{on the edge} of a circle of radius $r$,
\begin{equation}
\Delta\Sigma(r)=\langle\Sigma(<r)\rangle-\Sigma(r) \; .
\end{equation}

$\hat{\beta}$ can be estimated from the photo-$z$ redshift probability density $\hat{p}(z)$ as
\begin{equation}
\hat{\beta}=\int\hat{p}(z) \frac{D_{ds}(z_d,z)}{D_s(z)}\; \mathrm{d}z \; .
\label{eqn:pz}
\end{equation}
For the mean shear signal of an ensemble of lensing source galaxies $i$, each with weight $w_i$, this can be written as
\begin{equation}
\hat{\beta}=\frac{\sum_i w_i\times\hat{\beta}_i}{\sum_i w_i} \; ,
\label{eqn:nz}
\end{equation}
where $w_i$ is a source weight and $\hat{\beta}_i$ the estimated $\beta$ of source $i$ from \autoref{eqn:pz}. For the optimal (minimum variance) estimator of mean shear or surface mass overdensity, $w_i\propto\beta_i/\sigma_{e,i}^2$, or, in practice, $\propto\hat{\beta}_i/\sigma_{e,i}^2$ where $\sigma_{e}^2$ is the shape noise variance including intrinsic and measurement noise.

In the case of an unbiased estimate $\hat{\beta}$, this connects mean tangential shear $\langle\gamma_t\rangle$ and excess surface mass density $\Delta\Sigma$ as
\begin{equation}
\langle\gamma_t\rangle=\frac{\sum_i w_i\times\gamma_{t,i}}{\sum_i w_i}=\frac{4\pi G D_{d}}{c^2}\times\hat{\beta}\times\Delta\Sigma
\end{equation}
Thus, for example, if $\hat{\beta}$ is biased low, e.g.~due to a bias in photo-$z$, the estimated $\Delta\Sigma$ is biased high, and vice versa. This is the source of bias we evaluate in the following. For an indirect impact of the bias in photometric redshifts via the estimation of cluster member contamination of the lensing source sample, see Appendix~A.

\subsection{Framework for empirical redshift estimation}
\label{sec:betatree}

Our framework for estimating the effect of ICL on photo-$z$ is a simple empirical method that gives an unbiased estimate of $p(z|\bm{m})$, where $\bm{m}$ is a vector of colors and magnitude. The accuracy of its redshift distribution estimates are limited only by selection effects or sample variance of the available reference sample with known redshifts. In this work, we use the same sample for reference and bias determination, which cancels these effects: without ICL, the redshift distribution recovery is perfect by construction. Given this, and a model for the color of and total flux from diffuse light that enters each source, we can estimate how much the $\hat{\beta}$ of \autoref{eqn:nz} will be biased. We use this simple empirical method as a proxy for any photometric redshift estimation that could be performed using similar wide-band survey data, e.g.~from DES or, with the caveat that the fainter magnitude limit is not fully covered by our CFHT-based reference catalogs, LSST.

The empirical method is a simple decision tree described in detail in \citet{2016arXiv161001160G} and publicly available at \href{https://github.com/danielgruen/betatree/}{https://github.com/danielgruen/betatree/}. Given a complete reference sample of galaxies with photometric measurements in a set of bands and with known true redshift, the decision tree provides an unbiased and close to optimal estimate of $p(z)$ based on the color-magnitude information in any subset of these bands. The method splits the color-magnitude space spanned by the subset of bands into hyper-rectangles (leaves of the decision tree), and assigns to each galaxy as its $p(z)$ the histogram of true redshifts of reference galaxies in that leaf. We make the simplifying assumption that the lensing source sample is a magnitude limited sample of galaxies, i.e.~ignore additional explicit or implicit selections on pre-seeing size, shape or profile that are commonly present in such catalogs. For the purpose of these tests, and because no sufficiently faint magnitude limited sample of galaxies with spectroscopic $z$ is available, we use the same photo-$z$ sample and (unless otherwise noted) the same settings of the tree as in \citet{2016arXiv161001160G}. The galaxies used are measured from the Canada-France-Hawaii Telescope Legacy Survey (CFHTLS) Deep fields, four fields with one sq.~deg.~area each, for which 8-band photometry from CFHTLS and the WIRCam Deep Survey (WIRDS) is available. The sample is complete to $i'\approx25$, although we use a shallower magnitude limited sample for all analyses to follow. The combination of high signal-to-noise photometry for magnitude limits relevant for lensing source samples and large volume relative to e.g.~the COSMOS field make the sample well suited for our purpose.

\bigskip
Operationally, we estimate the bias of photo-$z$ due to intracluster light with the following procedures.

\begin{enumerate}
\item Build a decision tree from magnitude limited sample $20\leq i'\leq24$ (23.5, 24.5 as variants), optimized for a cluster redshift $z_d$, from $g'r'i'z'$ (also $u^{\star}g'r'i'z'$ as a variant) color-magnitude information. The magnitude limits are chosen to approximately match present and future samples of lensing source galaxies \citep[e.g.][]{2017arXiv170801533Z,2018PASJ...70S..25M}.
\item Estimate $\hat{\beta}$ in each leaf of the decision tree as the mean of $\beta_i$ of all reference galaxies in that leaf.
\item Determine the ICL $X-i'$ color $c_X$ as the median of the $X-i'$ color of all galaxies in the reference catalogs with $z\in[z_d-0.02,z_d+0.02]$ and a best-fit spectral energy distribution (SED) of a passive galaxy, where $X$ is one of ($u^{\star}$)$g'r'z'$. Note that this assumes that the ICL has the same SED as a red galaxy: this condition is satisfied in the clusters studied in \citet{zhang}, where the ICL colors are consistent with those from redMaPPer \citep{2014ApJ...785..104R} centrals within the inner 10 kpc, becoming bluer in the outer regions but still consistent with the red sequence galaxy population. Likewise, \citet{demaio18} found that ICL colors are consistent with red sequence galaxies over a wider redshift range ($0.29<z<0.89$) using HST imaging.
\item generate ICL-contaminated fluxes of each reference galaxy as $f_X^{\rm cont.}=f_X+\mu_A\times A\times f_{ICL,i}\times 10^{-0.4 c_X}$. In this, $A$ is defined to be the area of a circle with the post-seeing half-light radius of the galaxy. In our tests, we homogenized the data to a seeing half-light radius of 0.4'' to make this independent of the observing conditions of the CFHTLS-Deep fields. The factor $\mu_A$ accounts for the effective sensitivity of a method of measuring galaxy fluxes to diffuse light. We note that $\mu_A$ will depend strongly on the method used for extracting fluxes. By running \textsc{SExtractor} in dual-image mode with a detection image contaminated with diffuse flux, we find $\mu_{A}=2.5$ for \texttt{DETMODEL} model-fitting fluxes. \texttt{DETMODEL} fluxes are derived by fitting PSF convolved Sersic profile models to the galaxy images in a cut-out region. In our configuration, we follow the DES convention of fitting a PSF-convolved single exponential profile to the galaxies \citep{2017arXiv170801531D}. The value of $\mu_{A}=2.5$ is thus what we use in the following analysis.\footnote{In \texttt{AUTO} photometry, regardless of the explicit background subtraction settings, \textsc{SExtractor} measures and subtracts a background flux estimate locally. In this mode, it is hence insensitive to a diffuse background, i.e. $\mu_{A}^{\rm AUTO}=0$. There are other reasons, in particular the sensitivity to different point-spread function in different bands, that make \texttt{AUTO} photometry problematic for accurate multiband flux measurements in photometric surveys.}
\item Re-assign reference galaxies to leaves of the tree generated in (i), based on the contaminated color-magnitude information.
\item Estimate biased mean $\hat{\beta}$ for the contaminated case as the lensing-weighted mean (i.e.~with weight $w\propto\hat{\beta}$ of the leaf a galaxy falls into) of the respective $\hat{\beta}$ for each galaxy as determined in (ii) .
\item Estimate unbiased mean $\beta$ by weighting galaxies by their biased $\hat{\beta}$ as in (vi), but using their true reference redshifts to determine the $\beta$ to average.
\end{enumerate}

The ratio of the $\hat{\beta}$ of step (vi) and the unbiased true $\beta$ of step (vii), minus 1, is the bias we are trying to determine. Note that at $f_{\rm ICL}=0$, the two are, by construction, identical. In other words, the decision tree is an unbiased $\beta$ estimator unless the sample is affected by photometric biases or selection effects.

\subsection{Model}
\label{sec:dbdf}

In this section, we apply the scheme laid out in \autoref{sec:betatree} to derive an expression for the bias in $\Delta\Sigma$ as a function of ICL surface brightness, lens redshift, and magnitude limit of the source sample (\autoref{eqn:dbdf}).

Judging from the surface brightness of ICL observed in \citet{zhang}, the relevant range is $f_{\rm ICL}<40$~nJy~arcsec$^{-2}$ ($>27.4$~mag~arcsec$^{-2}$) as observed outside $\approx100$~kpc. In this range and given the sizes and magnitudes of lensing source galaxies,\footnote{Note that an $i'=24.5$ galaxy has a flux of 575~nJy, spread out over few arcsec$^2$.} ICL is a perturbation on top of the galaxies' intrinsic flux, such that we can attempt to approximate the effect of ICL on photo-$z$ as linear. We study the linearity of biases in $\hat{\beta}$ at a range of lens redshifts $z_d=0.2\ldots0.8$ in steps of 0.1 and limiting magnitudes of the source sample $m_{\rm lim}\in\{23.5,24.0,24.5\}$. \autoref{fig:boff} shows selected results for illustration that the bias is indeed well approximated as linear in $f_{\rm ICL}$ for the most relevant regimes. Only for the highest redshift clusters are non-linear effects visible at larger ICL flux levels. This is potentially related to the fact that the relevant source populations that are lensed by the cluster are located at high redshift. Their characteristic apparent magnitude is thus relatively faint and more susceptible to change due to ICL leakage. In the following, we will assume the bias on $\hat{\beta}$ due to ICL is linear in ICL flux, and use the measurement at $f_{\rm ICL}=14$~nJy~arcsec$^{-2}$ ($4$ counts per arcsec$^{-2}$ at ZP=30) to determine the slope. This choice is a trade-off: the added flux due to ICL is large enough to allow a high signal-to-noise measurement of the bias, but small enough that it does not suffer from non-linear effects or lead to problems due to sources that are below the $m<25.5$ limit of the CFHTLS-Deep catalog being boosted above the $m_{\rm lim}=23.5\ldots24.5$ magnitude limit of our source sample.

\begin{figure}
	\includegraphics[width=\columnwidth]{flux_bias_griz_24_0}
    \caption{Bias in $\Delta\Sigma$ (defined as the negative of the bias in $\hat{\beta}$) from $g'r'i'z'$ photo-$z$ bias for a sample of source galaxies at $20\leq i'\leq24$. Differently colored lines and points show results for different lens redshifts. 3.63~nJy arcsec$^{-2}$ correspond to 30 mag arcsec$^{-2}$.}
    \label{fig:boff}
\end{figure}
\begin{figure}
	\includegraphics[width=\columnwidth]{dbdf_model}
    \caption{Slope of $\Delta\Sigma$ bias with ICL surface brightness as a function of lens redshift. Circle symbols show measurements made as in \autoref{fig:boff}, upward and downward triangles the same measurements, but for deeper and shallower source samples. Solid line shows a quadratic model fit at the fiducial magnitude limit, dashed and dotted lines are the same model re-scaled by  $2^{m_{\rm lim}-24}$, where $m_{\rm lim}$ is the limiting magnitude of the sample.}
    \label{fig:dbdf_model}
\end{figure}

For a given source magnitude limit, the slope of bias with ICL surface brightness is a function of lens redshift. By measuring the slope at a range of redshifts, we empirically find that it can be described well, within the range of $z_d=0.2\ldots0.8$, by a quadratic function of $z_d$. Measurements and quadratic model (circles and solid line) are shown in \autoref{fig:dbdf_model}.

In addition, we empirically find that a re-scaling of the model by $2^{m_{\rm lim}-24}$ describes the measurements reasonably well at magnitude limits in the range $m_{\rm lim}\in(23.5,24.5)$ (downward and upward triangles with model as dotted and dashed curve in \autoref{fig:dbdf_model}). The following is the proposed model, for $g'r'i'z'$, fitted from in $z_d\in(0.2,0.8), m_{\rm lim}\in(23.5,24.5)$,
\begin{equation}
\label{eqn:dbdfmodel}
\frac{\mathrm{d}(\hat{\beta}/\beta)}{\mathrm{d}f_{\rm ICL}}\times [\mu\mathrm{Jy}\;\mathrm{arcsec}^{-2}] \approx\left(2.5 z_d^2-1.1z_d+0.028\right)\times 2^{m_{\rm lim}-24} \; .
\end{equation}
Repeating the same analysis including $u^{\star}$ band gives a somewhat smaller amplitude of
$(1.2z_d^2-0.063 z_d +0.10)$,
to be rescaled the same way as a function of magnitude limit.

\section{Bias predictions}

Using the models described in section 2 and 3, we study the bias in $\Delta\Sigma$ profiles due to contamination of source photometry with diffuse light around clusters.

Due to the dependence on cluster member detection limit of the ICL model (section 2), and the dependence on source population of the bias per unit ICL flux (section 3), we need to define a limiting magnitude for the lensing source catalog and for the detection of cluster members in a given survey. This, in addition to the mass and redshift of a cluster sample, determines our model prediction for ICL related photo-$z$ bias via equations (\ref{eqn:dbdfmodel}) and (\ref{eqn:fmodel}).

We study two cases, and again choose conservative limits (i.e.~faint limiting magnitudes for the lensing source catalog and conservative thresholds for complete cluster member detection): (1) an ongoing $griz$ wide-area survey, similar to DES, with lensing sources measured down to $r\approx23.5$ \citep{2017arXiv170801533Z} and cluster members completely detected and deblended down to $r\approx22.5$ \citep{2017arXiv170801531D}. And (2) an ongoing or future deep wide-area $ugriz$ survey, similar to HSC or LSST, with lensing sources measured and cluster members completely detected and deblended down to $r\approx25$.

Results for both cases are shown in \autoref{fig:model}, for clusters of two different masses approximately spanning the range currently used for optical cluster cosmology with \textsc{redMaPPer}. These should be compared to the statistical uncertainties of present and future surveys (currently of the order of a few per cent, optimistically of the order of one per cent) for a sense of whether the biases are relevant.

\begin{figure*}
	\includegraphics[width=\columnwidth]{model_des}
    \includegraphics[width=\columnwidth]{model_lsst}

	\includegraphics[width=\columnwidth]{model_des_15}
    \includegraphics[width=\columnwidth]{model_lsst_15}
    \caption{Predictions for the bias in $\Delta\Sigma$ profiles due to ICL-related source photo-$z$ bias for a DES-like (left-hand panels) and LSST-like (right-hand panels) survey, and a cluster of $M_{200m}/M_{\odot}=3\times10^{14}$ (top) and $10^{15}$ (bottom). The smallest scales (e.g.~$r<200 h_{70}^{-1}$ kpc in \citealt{2018arXiv180500039M}) that are most heavily affected by ICL are commonly excised from cluster lensing analyses for other reasons.}
    \label{fig:model}
\end{figure*}

We find that for a DES-like survey, even under the conservative assumptions made above, the $\Delta\Sigma$ signal estimated outside $200$kpc radius is biased mostly below the one per cent level, and only in extreme cases above the two per cent level, even for very massive and high redshift clusters. This implies that at the scale cuts and uncertainties of present DES cluster lensing studies \citep{2018arXiv180500039M}, ICL-related photo-$z$ bias is highly subdominant compared to the 5 per cent combined statistical and systematic uncertainty.

For a significantly deeper survey like LSST, biases at the level of two per cent are possible on the small to intermediate scales of $200-300$kpc that we hope to use for cluster lensing purposes. This is driven by the larger biases incurred by the fainter sources measured in these surveys. The availability of $u$ band information in addition to $griz$ somewhat alleviates the effect. Given the conservative assumptions made in our study, it is conceivable that the actual bias is only a fraction from our model prediction. But at least for the massive end of the clusters studied with these surveys, diffuse light photo-$z$ contamination requires either more detailed investigation or more conservative cuts in radius or limiting source magnitude.

\subsection{Limitations of our model}

In the context of these predictions, we summarize the simplifications made in our model, and their likely effect on the bias in practical applications.

Simplifications, i.e.~assumptions we had to make due to limited understanding of physical or algorithmic details:
\begin{itemize}
\item \textbf{Generic photo-$z$ algorithm:} For the purpose of this test, we used a simple empirical photo-$z$ algorithm. Assuming that all photo-$z$ algorithms estimate the same relation of multiband flux and redshift, results for other algorithms would likely be similar, yet not equal. We have made simplified tests using BPZ \citep{benitez2000,2017arXiv170801532H} that indicate that this is indeed the case.
\item \textbf{Leakage of ICL into galaxy photometry:} We assumed leakage to be proportional to a circular aperture with the post-seeing half-light radius of the galaxy. This is an approximation of how a matched aperture or, equivalently, model fitting algorithm for photometric measurements might perform. While we match the leakage scale in this work to the mean observed change in \textsc{SExtractor} \texttt{DETMODEL} flux, other photometry measurement algorithms might show very different results, and galaxy morphology might affect the leakage scale in a galaxy type and redshift dependent way. Also, small scale background subtraction could greatly reduce (or even invert) the effect. It is advisable that the leakage of diffuse light into galaxy photometry is estimated from image simulations for any lensing analysis that aims at a per cent level accuracy.
\item \textbf{Linearity of $\beta$ bias as a function of ICL flux:} Our model assumes that the change in estimated lensing amplitude $\hat{\beta}$ is linear in the ICL surface brightness. While this is appropriate for the relevant range of mean ICL surface brightness, inhomogeneity (i.e.~due to undetected yet localized cluster members) could affect the photo-$z$ more or less than predicted here. At the level of deblending possible with present and future lensing surveys, we expect this effect to be subdominant.
\item \textbf{Pure red cluster member population:} We have assumed that the cluster galaxy population only contains passive galaxies, similar in color to the ones identified by the \textsc{redMaPPer} algorithm. In practice, clusters contain star forming galaxies, especially at lower mass and higher redshift. The light of the undetected members among them is likely to have a similar, but not quite equal, effect on photo-$z$ bias as the light of red members. On the radial scales considered here, star-forming members are, however, not a majority of the population. In addition, the light of undetected cluster members is a subdominant component relative to pure ICL, hence we do not expect this assumption to significantly change our conclusions.
\item \textbf{Self-similar scaling of pure ICL:} We have assumed that pure ICL scales self-similarly with cluster mass, i.e.~its surface brightness is fixed at a given projected $r/r_{500}$. While this is consistent with simple comparisons made in \citet{zhang}, a more detailed study could reveal deviations.
\end{itemize}

Conservative assumptions, i.e.~ways in which we likely overestimate the effect of ICL in practice:
\begin{itemize}
\item \textbf{Passive SED of ICL:} We assume ICL to share the color of passive galaxies at the cluster redshift. A population of younger stars in the ICL would likely reduce its effect on photo-$z$ bias due to its similarity in color to lensing sources at higher redshift. We find that predicted bias is reduced, yet by less than 5 per cent, if ICL should be brighter in $g$ band by 0.1mag, which is approximately the level expected from reduced metallicity.
\item \textbf{Lack of ICL growth}: We fix the ICL surface density to a measurement at low redshift and predict the expected bias at higher redshift without accounting for any growth of ICL from early to late times. If ICL is assembled over time we thus overestimate biases for higher redshift clusters.
\item \textbf{Conservative deblending limits:} For DES, we have assumed cluster members to be deblended and thus not affecting source photo-$z$ down to a magnitude limit of $r=22.5$. At this level, DES Y1 is highly complete -- a significant fraction of cluster members below this limit are likely deblended successfully and, unlike assumed, do not in fact contribute to diffuse ICL. As a result, we likely overestimate the associated photo-$z$ bias in DES, in particular at large cluster mass and redshift.
\item \textbf{Magnitude limited source sample:} We used a simple magnitude cut to define our source sample. Realistic lensing source samples have additional selection criteria. A choice of limiting magnitude at the faint end of the population that is used in a given analysis allows for a conservative prediction of potential biases. For DES Y1/Y3 data, this was possible to do in this work.
\end{itemize}

Limitations, i.e.~regimes in which our model is not reliable:
\begin{itemize}
\item \textbf{Faint limit of source sample:} For LSST data, sufficiently faint reference samples of galaxies with known redshift and flux measurements do not exist to extend the modeling beyond $i'\approx 25$. Assuming that fainter lensing samples are used, the bias derived here is an underestimate of the bias encountered by such analyses.
\item \textbf{Blending with cluster members:} We only attempt to model diffuse ICL leaking into source photometry at a subdominant level. For the effect of blending between similarly bright cluster member and lensing source galaxies, the model developed here is not applicable. Besides, the success of correctly treating these cases will likely strongly depend on the choice of deblending algorithm.
\end{itemize}

\section{Conclusions}

We have developed a model for the bias in weak lensing estimates of cluster surface mass overdensity due to the contamination of lensed galaxy photometry from diffuse intracluster light. The latter systematically changes the flux, color, and thus photometric redshift estimate of the faint galaxies used as lensing sources.

Our model for diffuse light in clusters is simplistic yet conservative for the purpose of this exercise: a pure component of ICL due to un-bound stars in the cluster potential, measured at low redshift \citep{zhang} and re-scaled in mass and redshift by assuming self-similarity and passive evolution; and a component due to stars in undetected, faint cluster members, extrapolated from detected galaxies by means of the luminosity function. The effect of this surface brightness on photo-$z$ is estimated from an idealized empirical photo-$z$ estimation scheme \citep{2016arXiv161001160G}.

We find that for a DES-like cluster lensing experiment, i.e.~with cluster masses up to $M_{200m}=10^{15}M_{\odot}$, detection and deblending of cluster members brighter than $i'=22.5$, and a source sample no fainter than $i'=23.5$, ICL-related photo-$z$ bias does not significantly affect weak lensing mass reconstruction. Outside a cluster-centric radius of $200$kpc, which is commonly excluded in lensing studies for other reasons, biases are typically below 1 per cent for an $M_{200m}~3\times10^{14}M_{\odot}$ cluster, and below 2 per cent at $M_{200m}~10^{15}M_{\odot}$, even under the conservative assumptions we make. The effect of ICL on measured galaxy shapes may well be larger than that, and should be tested with dedicated image simulations.

Deeper source catalogs will be somewhat more susceptible to ICL-related photo-$z$ biases because the flux and color of faint source galaxies can be changed more strongly by ICL contamination. For massive clusters, lensing source catalogs down to $i'=25$ show one per cent biases at approximately twice the radius as the above DES-like survey. Even fainter sources will likely show even stronger effects, although this is difficult to quantify at present due to the lack of reliable color-magnitude-redshift information for such samples. An explicit treatment of measured fluxes as a composite of intracluster and lensing source galaxy light in photo-$z$ estimation could in principle remedy this effect. With moderately conservative scale and magnitude cuts, however, ICL bias of photo-$z$ will be a non-issue even in the next generation of surveys -- and with a less conservative examination of the effect, these could likely be moderately relaxed from the recommendations given in this work.

\section*{Acknowledgements}

Support for DG was provided by NASA through the Einstein Fellowship
Program, grant PF5-160138 and by Chandra Award Number GO8-19101A, issued by the Chandra X-ray Observatory Center. This work was supported in part by the U.S. Department of Energy under
contract number DE-AC02-76SF00515.

The authors thank Fabrice Brimioulle for providing the CFHTLS Deep photometry and photo-$z$ catalogs used in this work. This work has been promoted by fruitful discussions during the workshop series ``Becoming a One-Percenter''.

Funding for the DES Projects has been provided by the U.S. Department of Energy, the U.S. National Science Foundation, the Ministry of Science and Education of Spain,
the Science and Technology Facilities Council of the United Kingdom, the Higher Education Funding Council for England, the National Center for Supercomputing
Applications at the University of Illinois at Urbana-Champaign, the Kavli Institute of Cosmological Physics at the University of Chicago,
the Center for Cosmology and Astro-Particle Physics at the Ohio State University,
the Mitchell Institute for Fundamental Physics and Astronomy at Texas A\&M University, Financiadora de Estudos e Projetos,
Funda{\c c}{\~a}o Carlos Chagas Filho de Amparo {\`a} Pesquisa do Estado do Rio de Janeiro, Conselho Nacional de Desenvolvimento Cient{\'i}fico e Tecnol{\'o}gico and
the Minist{\'e}rio da Ci{\^e}ncia, Tecnologia e Inova{\c c}{\~a}o, the Deutsche Forschungsgemeinschaft and the Collaborating Institutions in the Dark Energy Survey.

The Collaborating Institutions are Argonne National Laboratory, the University of California at Santa Cruz, the University of Cambridge, Centro de Investigaciones Energ{\'e}ticas,
Medioambientales y Tecnol{\'o}gicas-Madrid, the University of Chicago, University College London, the DES-Brazil Consortium, the University of Edinburgh,
the Eidgen{\"o}ssische Technische Hochschule (ETH) Z{\"u}rich,
Fermi National Accelerator Laboratory, the University of Illinois at Urbana-Champaign, the Institut de Ci{\`e}ncies de l'Espai (IEEC/CSIC),
the Institut de F{\'i}sica d'Altes Energies, Lawrence Berkeley National Laboratory, the Ludwig-Maximilians Universit{\"a}t M{\"u}nchen and the associated Excellence Cluster Universe,
the University of Michigan, the National Optical Astronomy Observatory, the University of Nottingham, The Ohio State University, the University of Pennsylvania, the University of Portsmouth,
SLAC National Accelerator Laboratory, Stanford University, the University of Sussex, Texas A\&M University, and the OzDES Membership Consortium.

Based in part on observations at Cerro Tololo Inter-American Observatory, National Optical Astronomy Observatory, which is operated by the Association of
Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation.

The DES data management system is supported by the National Science Foundation under Grant Numbers AST-1138766 and AST-1536171.
The DES participants from Spanish institutions are partially supported by MINECO under grants AYA2015-71825, ESP2015-66861, FPA2015-68048, SEV-2016-0588, SEV-2016-0597, and MDM-2015-0509,
some of which include ERDF funds from the European Union. IFAE is partially funded by the CERCA program of the Generalitat de Catalunya.
Research leading to these results has received funding from the European Research
Council under the European Union's Seventh Framework Program (FP7/2007-2013) including ERC grant agreements 240672, 291329, and 306478.
We  acknowledge support from the Australian Research Council Centre of Excellence for All-sky Astrophysics (CAASTRO), through project number CE110001020, and the Brazilian Instituto Nacional de Ci\^encia
e Tecnologia (INCT) e-Universe (CNPq grant 465376/2014-2).

This manuscript has been authored by Fermi Research Alliance, LLC under Contract No. DE-AC02-07CH11359 with the U.S. Department of Energy, Office of Science, Office of High Energy Physics. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes.

Based in part on observations obtained with MegaPrime/MegaCam, a joint project of CFHT and CEA/IRFU, at the Canada-France-Hawaii Telescope (CFHT) which is operated by the National Research Council (NRC) of Canada, the Institut National des Science de l'Univers of the Centre National de la Recherche Scientifique (CNRS) of France, and the University of Hawaii. This work is based in part on data products produced at Terapix available at the Canadian Astronomy Data Centre as part of the Canada-France-Hawaii Telescope Legacy Survey, a collaborative project of NRC and CNRS.

This paper has gone through internal review by the DES collaboration.

\bibliographystyle{mnras}

redpajama_set_name: RedPajamaArXiv


text:
Q: Laravel 5.2 new query results get back to old when click on pagination I've applied search form in my app's index page. Results gets updated when I search for something. But when I click on the pagination, it gets me back to old results. So, I guess I've to update the pagination or clear cache or something and how to do it?
In routes.php
Route::get('/', 'BookmarkController@index');
Route::post('/', 'BookmarkController@search');

In BookmarkController.php
public function index(Request $request) {
    $tags_list = Tag::orderBy('tag', 'asc')->get();
    $bookmarks = Bookmark::orderBy('created_at', 'desc')->where('public', '1')->paginate(3);
    $bookmarks_all = Bookmark::orderBy('created_at','desc')->where('public', '1')->get();

    return view('welcome')
        ->with('bookmark', $bookmarks)
        ->with('tags_list', $tags_list)
        ->with('bookmarks_all', $bookmarks_all)
    ;
}

public function search(Request $request) {
    $search_value = $_POST['search'];
    $tags_list = Tag::orderBy('tag', 'asc')->get();
    $bookmarks = Bookmark::orderBy('created_at', 'desc')
        ->where('public', '1')
        ->where('title', 'rlike', $search_value)
        ->orwhere('description', 'rlike', $search_value)
        ->orwhere('contents', 'rlike', $search_value)
        ->orwhere('tags', 'rlike', $search_value)
        ->paginate(3)
    ;

    $bookmarks_all = Bookmark::orderBy('created_at', 'desc')->where('public', '1')->get();

    return view('welcome')
        ->with('bookmark', $bookmarks)
        ->with('tags_list', $tags_list)
        ->with('bookmarks_all', $bookmarks_all)
        ->render()
    ;
}

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    @if (count($bookmark) > 0)

            @foreach ($bookmark as $bookmark_single)

                                thumbnail}}" />

                                    {{ $bookmark_single->title }}

                                    {{ str_limit($bookmark_single->description, $limit = 50, $end = ' [...]') }}

<?php   $tags = $bookmark_single->tags;
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                                    @foreach ($tag_list as $tag)
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-  bookmarker }}">{{ $bookmark_single->bookmarker }}

                                url }}">Visit the link

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        @endif

Search form HTML in welcome.blade.php
<form id="demo-2" action="/" class="search-form col-sm-4" method="post">
    {{ csrf_field() }}

        <input id="search" class="form-control" placeholder="Search" name="search" value="" type="text">

            <button class="btn btn-primary" id="search-btn" type="submit"></button>

</form>

A: When you click on a pagination link you initiate a get request to the same page and end up on your first route that uses BookmarkController@index
One possible solution here is to change search route to get instead of post like:
Route::post('/search', 'BookmarkController@search');

and make sure your pagination applies to this new route like /search?page=2
If you want to keep the search login in the index method you need to make sure non of search filters apply if it's blank
public function index(Request $request) {
    $tags_list = Tag::orderBy('tag', 'asc')->get();
    $bookmarks_all = Bookmark::orderBy('created_at','desc')->where('public', '1')->get();

    $search_value = $request->input('search', '');

    $bookmarks = Bookmark::where(function($query) use ($search_value) {
        if (!empty($search_value)) {
            $query->where('title', 'rlike', $search_value)
            ->orwhere('description', 'rlike', $search_value)
            ->orwhere('contents', 'rlike', $search_value)
            ->orwhere('tags', 'rlike', $search_value)
        }
    })->where('public', '1')->orderBy('created_at', 'desc')->paginate(3);

    return view('welcome')
        ->with('bookmark', $bookmarks)
        ->with('tags_list', $tags_list)
        ->with('bookmarks_all', $bookmarks_all)
    ;
}

And change your search form method to get

redpajama_set_name: RedPajamaStackExchange


text:
Francisco Maspons y Labrós (Granollers, 1840-Bigues, 1901) fue un folklorista, escritor y jurista español.

Biografía
Nacido en 1840 en la localidad barcelonesa de Granollers del Vallés, siguió la carrera de Derecho hasta el doctorado y tomó el título de licenciado en derecho administrativo. Era abogado del colegio de Barcelona, notario e individuo de la Junta Directiva del colegio notarial de Barcelona. Fue fiscal municipal sustituto del municipio de San Pedro de Barcelona, juez de primera instancia en comisión de varios partidos judiciales y mantenedor del consistorio de los Juegos florales. También ocupó el cargo vocal de la junta directiva de la Asociación Artística-arqueológica de Barcelona en 1879, además de ser presidente del primer certamen científico literario de Granollers en 1881. Fue miembro del Congreso catalán de jurisconsultos reunido en Granollers en 1880 y delegado en el concurso por el partido judicial de Igualada, además de delegado por el colegio notarial de Barcelona en la Asamblea notarial de Madrid. Fue vicepresidente de la sección de Derecho e Historia de Cataluña del Centré Catalá en 1882 e individuo del congreso jurídico de Barcelona, celebrado con motivo de la Exposición Universal de 1888, así como del Congreso Económico Nacional de ese mismo año. También fue vocal de la sección arqueológica e individuo del jurado para las guías de Cataluña en la exposición mencionada más arriba, así como presidente de la Associació d'Excursions Catalana.

Colaboró en las revistas Lo Gay Saber, La Bandera Catalana, La Llumanera de Nova York, Revista Histórica, Lo Calendari Catalá, La Ilustració Catalana, Boletín y Anuari de la Associació de Excursións Catalana, Biblioteca Folk-lore, editada por dicha asociación, y de la Revista de Literatura Popular. En estas revistas publicó varios estudios históricos sobre las Cortes de Cataluña, forma de Gobierno de Barcelona, el convento de Jesús y los siguientes estudios folklóricos: Creencias populars catalanas, Lo poll y la pussa, La tonada maravillosa, Cuentos populars viennesos, Endevinallas populars francesas, Deixan lo dob, Literatura popular de Módica, Lo molí de San, Bibliografía forana, Llegendas rusas, Cuentos populares del Zulús, La festa dels morts, Los vehins, Lo cant de Ragnar, Las bruixas, Literatura popular italiana, Oswald de Furstench, Un cant popular hebreu, L'aprenentatje, S. Jordi, La llegenda de S. Jordi, Lo fort farall, Literatura popular bolonesa, El día de difuntos, La fola del Murchin, La scatola di cristallo, Lo puput, La fiesta de S. Juan, Lo ball de gitanas en lo Vallés.

En 1871 publicó la primera serie de una colección de cuentos populares catalanes con el título de Rondallayre, en 1872 la segunda y en 1875 la tercera. En la primera incluyó 26 cuentos, en la segunda y tercera 27 en cada una.

En 1885 completó Lo rondallayre con una cuarta serie que comprendía 20 cuentos, que formó parte de la biblioteca Fok-lore catalana publicada por la Associació d'Excursions Catalana. El escritor vienés Eduardo Poremvoiez escogió para el libreto de una ópera la acción del cuento «Las tres rosas», que figuró en La Rondallayre.

En 1874 publicó el Libro de la infancia. En 1877 envió a su amigo el doctor Pitré de Palermo con motivo de su casamiento un opúsculo en catalán en el que se describe una boda en las montañas del Principado. También fue autor de una obra titulada Siemprevivas (1885). Tuvo una afición especial en el estudio de la comarca del Vallés, sobre cuyas tradiciones, costumbres e historia escribió diversos textos. Fue socio de número de la Real Academia de Buenas Letras de Barcelona, además de miembro del International Folk-Lore Congress de Londres.

Falleció en 1901 en Bigues.

Obras

 La caza. Derechos y deberes del propietario y del cazador. Colección de disposiciones que la reglamentan cementados por D. José de Arullot y D. Francisco Maspons. Barcelona, imp. de El Porvenir, 1867.
 Lo Rondallayre. Colección de cuentos populares catalanes. Barcelona, imp. Verdaguer, 1871, 1872 y 1875.
 Jochs de la Infancia. Colleció de jochs populars catalans. Barcelona, imp. de Martí y Cantó, 1874.
 Tradicions del Vallés, Barcelona, imp. de la Renaixensa, 1876.
 Las bodas catalanas. Costums populars catalanas. Barcelona, imp. La Renaixensa, 1877.
 Lo Vallés, Barcelona, Estampa de Jaime Jepús, 1882.
 De Mollet á Bigas (extret del Anunari de la Associació d'Excursions Catalana, 1882).
 Crónica de Bruniquer, Barcelona, imp. de la Renaixensa, 1885.
 Excursió col-lectiva de la Conca baixa del Noya: Acta. Barcelona, Estampa dels Sucesors de N. Ramirez y Cª, 1886.
 Cuentus populars catalans. Cuarta serie, Barcelona, imp. Ramírez y Cª, 1885.
 Excursió col·lectiva á Gualba y al Gorch negre, Barcelona, Estampa dels Sucesors de N. Ramírez y C.ª, 1888.

Véase también
 María del Pilar Maspons y Labrós
 Mariano Maspons y Labrós

Referencias

Bibliografía

Nacidos en Granollers
Académicos de la Real Academia de Buenas Letras de Barcelona
Folcloristas de España del siglo XIX
Folcloristas de Cataluña

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New research indicates complacent New Zealanders are not following basic steps to prevent burglary.
– 20 percent leave home or go to bed without locking up.
As part of the inaugural Secure Homes Report, ADT Security surveyed 1,047 homeowners and renters in both metropolitan and regional areas of New Zealand. The research found one in three respondents has been subject to a break-in, with 17 percent of these intrusions happening while someone was at home.
Furthermore, 11 percent of those affected by burglary have experienced more than one break-in at their current residence.
Surprisingly, nearly 10 percent of break-ins occurred by way of unforced window entry, where the window or door had been left ajar or unlocked, highlighting the need for Kiwis to be more vigilant about securing their home.
ADT Security encourages householders to carry out a security assessment of their property and consider a monitored alarm system to better protect themselves from burglary and other crimes.
• A monitored home alarm is one of the most effective security measures. It's possible to isolate certain zones of the home to be monitored, so that alarms can be activated even when the home is occupied. In the event that an ADT alarm is triggered, a signal is sent to a 24 hour Security Response Centre where trained operators identify the cause and take appropriate action.


This bass and treble tone controller circuit is based on the classic Baxandall tone control circuitry and provides a maximum cut and boost of around 15dB at 10kHz and 100Hz. Since the Baxandall tone control circuit is a passive design, all frequencies are amplified. The position of the bass and treble control potentiometers and reactance of the capacitors affect the audio response.
The circuit up there is very popular Baxandall tone control configuration circuit. This Baxandall tone control has unity gain (gain=1) at midband and uses standard linear potentiometers. Low value, low cost, and small size capacitors is possible to apply because of the very high input impedance of CA3140. The frequency point is set at 100Hz and 10KHz by 15dB bass treble boost and cut. Full peak to peak output is available event at 20KHz because of excellent high slew rate characteristic of this opamp. The gain of this amplifier is decreased -3dB from flat response at 70KHz, and it's beyond audible frequency range to make sure this tone control circuit handle the audio range perfectly.


As far as I can tell I never set on particular theme or specific subject to paint or draw, however I always sketch what appears to me right there in front of my eyes. My endlessly fascination with observation allows me to study, analyze and revisit the same locations or objects number of times. Oftentimes I use these sketches in my studio to create new works and new ideas develop from there.
Although I don't have an exact theme to follow I constantly engage myself with social, political and cultural issues. Recently my works is focus on observation purely on everyday life, the environment and our mega cities with high rising building, powerful machines, wealth, consumers, mass consumption and the human's form.
I have always been fascinated with lines and spaces and what makes a composition to stand out. In my recent work, I simply use lines and contours to deconstruct, exaggerate and dictate my observation. Often times minimal amount of colors are added to the drawings which establish a real sense of place, suggests a notion of existence.


text:
Sendy Apollo
Sendy Apollo Review
By Kob Monney
Contact via Twitter
TV & Audio Editor
May 4, 2022 10:00 am BST
On their own, the Apollo offer a pleasantly engaging and warm sound. Combined with a DAC/headphone amplifier, these open-backed cans fulfil more of their potential.
Warm, pleasant sound
Great aesthetics
Amplification gets more performance from them
UKRRP: £459
USARRP: $499
EuropeRRP: €549
CanadaRRP: CA$709
AustraliaRRP: AU$809
Planar magnetic driversFeatures 68mm transducers to produce sound
Detachable earpadsEarpads can be detached and replaced
Sendy Audio is the sister brand of Chinese hi-fi outfit Sivga, and they share the ambition of producing high-quality cans that offer an audiophile listening experience.
The Apollo open-backed cans are the first headphones we've tested from Sendy, and the expectation is that they'll follow in the footsteps of the P-II and Robin SV021 models, delivering a warm presentation and aesthetically pleasing looks.
They're also the most expensive model we've looked at from either Sivga and Sendy, which raises those expectations further and poses the question as to whether they'll be able to meet them. Let's find out.
Terrific appearance and construction
Excellent comfort
Use goat's leather in headband
The Apollo are flat-out gorgeous in appearance. Handcrafted at the Sendy factory, the use of rosewood emphasises that natural handmade feel; the glossy finish is a stunner, with no imperfections or nicks on the review sample. The Apollo look great and feel great to touch, and that's part of the reason that people enjoy hi-fi so.
They're also lovely to wear. The size of the earcups and padding makes them best suited for bigger heads – smaller ones may feel swamped by their size. The hinges allow some scope for achieving the best fit, but I don't think you'll have much trouble there. The earcups simply swaddle your ears in high-protein padding.
At 385g, they weigh less than the P-II, and the earpad cushions that softly press against the head only become a little warm during use. The cans do feel loose at first, but the headband can be adjusted up or down to fit. Speaking of which…
The headband is made from soft and pliable goat's leather, with any pressure on the head barely noticeable – excellent for extended use; although vegans should probably give these headphones a swerve. Left and right earcups are denoted not just by the markings on the hinges but inside the earpads, too.
The open-back mesh housing features a striking sunlight design, a reference to Greek God of the Sun (and music), Apollo. The dotted membrane has both aesthetic and acoustic purposes, the arrangement of each hole said to influence the tuning of the headphone's sound. It's also worth remembering that as an open design, the headphones do leak sound.
Accompanying the headphones is a pear-shaped leather case for storage. It isn't particularly portable – placed in a rucksack, it's like a bag within a bag – but it certainly isn't the biggest carry case I've encountered (that would be the one for the Monolith M1070). Inside is a hemp case for carrying the cable and connectors; a 4.4mm balanced effort with 3.5mm adapter. The cable connection on the Apollo is slanted at an angle to avoid draping over the shoulder when in use.
One other aspect to note is that the earpads are detachable and can be replaced should they become damaged.
Low impendence
Wide frequency range
Planar magnetic drivers
The Sendy Apollo don't come with features in abundance, as you'd find with a wireless equivalent. Rattling through them, impendence is rated at 16-ohms, which is far less than the Sivga P-II or the Grado SR325x on-ears. A figure that low makes them easy to drive but also suggests that amplification is required since without it the volume the headphones will output at is low (unless you nudge the volume up on your source device).
Frequency response is 20Hz to 40kHz, which covers the Hi-Res Audio standard. If you have a) the necessary content and b) a source capable of playing that content, the Apollo should be able to do the rest. Sensitivity is 95dB.
The driver is planar magnetic. In ye olde days when planar technology was first introduced, it was big and heavy, resulting in headphones that were also big and heavy. The technology has advanced to the point where it has become both smaller and lighter, used in wired headphones with ambitions of being as portable as their wireless cousins.
The Apollo sport a 68mm large diaphragm transducer for its planar driver, and Sendy refers to the use of Quad Former technology in its description of the design. It uses two magnets next to a double-coil arrangement either side of the diaphragm in the middle. Sendy claims this offers "excellent" electroacoustic energy efficiency, extremely low distortion, and ups the Apollo's ability to reproduce music.
The detachable 6N OCC braided cable is 2m in length (another sign these wouldn't be best for portable use), and Sendy says the cable offers no signal loss in transmission. It also doesn't become too tangled – and when it does, it's easy to unpick, which adds a few points in the convenience stakes.
Warm soundstage with decent width
Smooth vocal performance
Not the most dynamic of performers
Having put the Apollo through the recommended 100 hours of burn-in before listening, the low impendence has been a slight cause for concern over the course of using them. I've plugged them into portable music players and systems and have always had to push up the volume significantly. If you're interested in the Apollo, it's a certainty that you'll need amplification such as a DAC to get the best from them.
In terms of expectations, the Apollo do meet what Sendy has asked of them. Listening to them reveals a soft-sounding and warm presentation that's pleasantly lush at times. They are, however, easy-going headphones to a fault.
Plugged into a source, the first thing I had to do was raise the volume – they can sound shy and reticent off the bat. Once a level has been found, the Apollo give up a degree of definition, punchiness and sharpness to a pair like Grado's SR325x on-ears.
This isn't a like-for-like comparison, of course – open-backed over-ears vs open-backed on-ears – but listening to the same tracks, the Grados offer more dynamism, greater expression and definition to instruments. On the other hand, the Sendy heaphones' warmth make bass sound soft, and they're not as able to pick out instruments with as much clarity and give them their own distinctly etched space within a soundstage.
However, give the Apollo a high-quality track and its attributes come to the fore rather well. A 24-bit/192kHz file of Coldplay's God Put A Smile Upon Your Face on an Astell & Kern SR25, and the Apollo deliver Chris Martin's voice with an inviting softness and warmth, capturing the changes in the pitch of his voice fine enough and extending the soundstage with width. However, I noticed that the repeated drumbeat wasn't delivered with much of a kick, and although the soundstage is wide, the sense of depth to music isn't quite felt.
Despite this, the Apollo are a consistently pleasant listen. Fleetwood Mac's The Chain (24-bit/96kHz) displays a decent amount of vigour and energy in the latter half of the track; there's solid definition to Lindsey Buckingham's Dobro guitar, as well as nice, vivid texture to instruments and reasonable amount of insight that's married to a respectable sense of timing – although, as mentioned, more definition and sharpness would help.
Used with a laptop and an EarMen Eagle DAC, there's more to be gained in terms of clarity, detail and definition. The Apollo + Eagle combination renders instruments more distinctly, expanding the soundstage even further, giving bass a firmer foundation as well as a punch in some more energy and excitement.
On their own, there's decent enough brightness reaped from Takuya Kuroda's Fade (16-bit/44.1khz), but more is elicited with the Eagle DAC for a richer, expressive and dynamic performance. Add a DAC to these headphones and you've got a winning combination; without one, the Apollo remain a solid and pleasant listen.
For the warm presentation and excellent looks Aesthetically, the look of the Sendy Apollo is great, they're comfortable to wear, and if you enjoy a warm hug of a sound then you'll likely find these appealing.
You'll need a DAC to get the best out of them The low impedance makes them easy to drive with amplification and adding a DAC to your setup will reap better performance.
The Sendy Apollo produce a soft, lush and warm presentation, but it's an approach that leaves them short in a few areas – namely definition and dynamism. For budding audiophiles, the Apollo may be a pair that will make you aware of the role headphone amplification and high-quality sources play in a hi-fi setup.
On their own, the Apollo are a pleasurable listening experience, although I'm always struck by the feeling I could be getting more from the music to which I'm listening. Pair these headphones with a DAC, and it helps the Apollo realise more of their potential.
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Tested with a range music files and streaming services
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What connectors does the Sendy Apollo over-ear come with?
The Apollo headphones are supplied with a 4.4mm balanced cable with a 3.5mm
UK RRP
USA RRP
EU RRP
CA RRP
AUD RRP
Driver (s)
68mm transducer planar magnetic
20 40000 – Hz
Midrange refers to the part of the frequency range that sits between the bass and treble. The midrange is the area that handles vocals and most of the instruments heard in a track. It can also be in reference to midrange loudspeaker drivers that replicate this area of the frequency range.
Hi-Res audio is referred to as a standard as well as a marketing term that describes digital audio files of better-than-CD quality (16-bit/44.1kHz).
Kob began his career at What Hi-Fi?, starting in the dusty stockroom before rising up the ranks to join the editorial and production team as the Buyer's Guide editor. Experienced in both magazine and …

redpajama_set_name: RedPajamaCommonCrawl


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Welcome to Anime Galaxy!Please read the ruls and have a happy posting!!!
Bun venit in comunitatea SKiLLz!Nu veti regreta.Have Fun !!!


You didn't expect me to leave this one behind, did you?
Take the icon if you wish, by all means.
And I suspect that he's really rather bored with what he's watching, all told.
a nother one that will make a good icon when resized I got off phillipthorpe's LJ.
I at least get to feel better that I no longer live in Jesusland! I live in the US of C!
I actually think I'd like that. I could have ghealth care without coping with moving and all the paperwork.
a quiet smug sense of superiority to those living in Jesusland... hell, I'm 1/3rd the way there already!


I wish the term 'poor' would stop defining me as a student.
This morning the government announced the scrapping of maintenance grants in favour of loans. While another policy is aimed at students, it seems the poorest of us are those who will suffer most.
Since a young age, the importance of intellect and education was instilled in me. It has become second nature to me to do well. So much so, at 11 I was accepted in to a grammar school after passing the entrance examination. I was one of many who achieved the highest GCSE's and A-Level qualifications and in my final year, I was given a specialist award for endeavour. Due to this, I was awarded a scholarship from Glasgow university to cover costs of books and any other equipment I may need.


In 2018, video is everywhere. Every day, people are interacting with family, friends and their favorite brands through a variety of dynamic multimedia experiences, from Facebook Live to Instagram Stories. Your customers and future customers expect to engage with your energy utility in similar ways.
For energy utility companies, video can enhance any of your marketing communications, from email campaigns to website landing pages.
The latest research finds that 53 percent of consumers want to see more video content from marketers.1 Video is no longer a nice-to-have component of your digital marketing strategy – it's an absolute must to meet the expectations of today's tech-savvy consumers, especially Millennials and Generation Z.
For energy utility marketers, video is an integral way to educate, engage and inspire residential and commercial customers at key touchpoints throughout the customer journey.
In fact, videos now comprise 20-30 percent of Questline's most recent Top Newsletter Content lists.4 Our most popular video, part of a "Smarter Living" quick tips series, garnered more than 100,000 views. Who knew a video about keeping the upstairs of your home cool could generate so much attention?
Customers are bombarded by hundreds of marketing campaigns each day, but a video has the ability to cut through the clutter and capture attention in a unique and powerful way. Viewers report remembering 95 percent of a message when watching a video versus only 10 percent when reading it in text.1 When one leading energy utility introduced a new bill, we created a short animated video to inform consumers. Compared to a text-only email, this successful video described the important changes in an easy-to-understand, digestible format.
Compared to other communication platforms (blog posts, articles, case studies), video has the power to tell an impactful story in less than a minute. It's also capable of conveying a great number of different moods and messages. During the holiday season, Questline created a heartwarming video on the vital role that lighting plays in creating a warm, inviting home. Each scene showed a different family opening their front door – illuminated by holiday lights – to welcome family and friends. As you can see here, this powerful message would be challenging to capture through text alone.
Video can be a lighthearted cartoon or an in-depth series featuring subject matter experts. No matter the topic, video provides a new way to bring your content to life.
When it comes to search engine optimization (SEO), video can help improve your website's standing in the eyes of Google. Search engines want to see content that engages viewers, and website landing pages with video will keep people on your page longer than text only. In fact, consumers will spend 88 percent more time on a landing page with video, compared to a text-only site.1 Showcasing the power of video, YouTube is now considered the second largest search engine with more than 500 million hours of video watched on a daily basis.5 By incorporating video into your marketing strategy, you have the opportunity to maximize your site's SEO.
From fun, animated videos to heartwarming feature stories, video marketing can show off your company's unique personality and brand voice. In turn, this helps build trust and loyalty among your customers. Continue to build on this foundation with ongoing videos that educate, inform and inspire. Create quick-hit videos on how to keep your home insulated or a reminder video of what to do during an outage. For example, our "You Can" series, featuring HGTV and DIY Network personality Jeff Wilson, educates consumers on various DIY home projects, such as insulating pipes and air sealing your attic. Wilson's knowledge of energy efficiency, coupled with his name recognition, builds trust and credibility. Check out one of our "You Can" videos here.
Did you know: Facebook has around 8 billion video views each day.6 This staggering statistic showcases why video is an ideal tactic for your social media strategy. Video features rich storytelling capabilities in an easy-to-digest format, making it well suited for busy, on-the-go audiences. Plus, people will often share videos they love with friends, so you have the opportunity to reach an even larger audience. Whether you're shooting on the latest 8k digital cinema camera or simply an iPhone, video can make a major impact on your engagement with customers.
Ready to rev up your video efforts?
We can help. Learn how Questline can bring your digital marketing strategy to life through the production of dynamic videos.


Punk Chain Leather and Steel Bracelet - Customisable!
Contemporary street punks highlight their style adorned with chains which Chrissie C has a passion for!
Punk fashion influenced the designs of Vivienne Westwood and Malcolm McLaren whose work Chrissie adores...rebellious, expressive and loaded with attitude!
This bracelet is crafted in a flat 10mm black or brown tan genuine leather and features stainless steel chain elements for the ultimate street punk look!
Finished with a stainless steel clasp!
Choose your colour and length so you have your own unique bracelet with the perfect fit!
I have used a stainless steel clasp for this bracelet and we adore stainless steel here at WOW jewellery as its SO durable and doesn't fade or tarnish like some other metals.
Express yourself with a personal bracelet crafted to your specification by Chrissie C at Wow Jewellery!
1: Measure your wrist with a flexible tape, strip of paper or piece of string, where you would normally wear the bracelet. The tape should be firm around the wrist but not tight.
2: If you are using a strip of paper or cord, mark your size with a pen or pencil then use a ruler to measure the length. That would be your exact wrist size.
3: To find your bracelet size, just add your wrist size with the appropriate measurements below.
For example, if you have a 17cm wrist and like a comfort fit, choose 18.5cm - 19cm braclet size from the drop down list.
We advise with all leather products to avoid bathing/showering in them and avoid wearing whilst swimming or engaging in water based activities to preserve the leather.


text:
FBI Director: 'Chinese students a counterintelligence risk to national security'
By Jon Dougherty • February 15, 2018
Domestic Intelligence
Intelligence Reporting
Tagged china, espionage, students
FBI Director Christopher Wray told the Senate Intelligence Committee that Chinese students in the United States may be covertly spying for the Chinese government.
During questioning, Sen. Marco Rubio, R-Fla., asked Wray about "the counterintelligence risk posed to U.S. national security from Chinese students, particularly those in advanced programs in science and mathematics."
"The use of non-traditional collectors, especially in the academic setting—whether it's professors, scientists, students—we see in almost every field office that the FBI has around the country," he said. "It's not just in major cities. It's in small ones as well, it's across basically every discipline. And I think the level of naivete on the part of the academic sector about this creates its own issues."
Wray also noted that the FBI is currently investigating some Chinese government-backed groups that facilitate dialogues between Chinese and American academics. He named one of them.
"We do share concerns about the Confucius Institutes," Wray said. "We've been watching that development for a while. It's just one of many tools that they take advantage of. We have seen some decrease recently in their own enthusiasm and commitment to that particular program, but it is something that we're watching warily and in certain instances have developed appropriate investigations into them."
In response to a question from Rubio about a large Chinese enrollment in STEM programs, Wray said, "They're exploiting the very open research and development environment that we have, which we all revere. But they're taking advantage of this. One of the things we're trying to do is to view the Chinese threat as not just a whole of government threat, but a whole-of-society threat, on their end. And I think it's going to take a whole-of-society response by us. It's not just the Intelligence Community, but it's raising awareness within our academic sector, within our private sector, as part of defense."
Wray is not the first FBI official to warn of Chinese espionage. Edward You, an agent in the FBI's Weapons of Mass Destruction Directorate, told members of Congress then that the bureau has concerns about Chinese government-backed efforts to gather massive amounts of data on Americans' health. [source]
Analysis: As you might expect, Wray's claims were widely politicized, with the U.S. media outlet reporting the story ensuring it contacted several 'Asian-American advocacy' groups for critical comments.
But Wray's dispassionate observations reflect legitimate concerns within the U.S. intelligence community about China's ongoing counterintelligence campaign to steal U.S. technology and secrets, which began in earnest in the 1990s during the Clinton administration. His observations are based on actual intelligence collection, not opinions tainted by negative ethnic characterizations and racist connotations. In terms of academic spies, both China and the U.S. have claimed successes — and failures [source]
The politicization of Wray's assessment is exactly why many of these congressional intelligence briefings take place behind closed doors, away from reporters and media cameras — so the intelligence professionals can give lawmakers the unfiltered truth about our enemies so they can make informed legislative decisions regarding the nation's national security and defense needs.
As for China, politicization aside, the country is our greatest challenge for the foreseeable future, and there is no spinning that.
Jon Dougherty
Jon E. Dougherty is a political, foreign policy and national security analyst and reporter with nearly 30 years of experience in both fields. A U.S. Army veteran of Operation Enduring Freedom, he holds BA in Political Science from Ashford University and an MA in National Security Studies/Intelligence Analysis from American Military University.
Shooting at entrance to NSA; several hospitalizedStrategic Intelligence Summary for 15 February 2018


text:
Quod erat demonstrandum (Q.E.D.) är en latinsk fras som ungefär kan översättas till svenska som "det som var menat att bli demonstrerat" eller "vilket skulle bevisas". Förkortningen används inom matematiken för att visa att ett bevis är slutfört (med önskat resultat).

Skrivsättet är en gammal tradition. Redan de gamla grekerna, inklusive Euklides och Archimedes, klargjorde på detta sätt, fast på grekiska , ὅπερ ἔδει δεῖξαι (hoper edei deixai; förkortat som ΟΕΔ), att ett bevis var slutfört.

Motsvarande svenska fraser är "vilket skulle bevisas" (förkortas V.S.B.) eller alternativt "vilket skulle visas" ("VSV", före stavningsreformen 1906 "HSB", 'Hvilket…').

Idag används även symbolen  (ifylld kvadrat) för att markera att ett bevis är avslutat, en notation som infördes av Paul Halmos.

Praktiskt skrivs förkortningen "Q.E.D." eller den svenska motsvarigheten "V.S.B." i slutet av bevis, efter svaret.

Exempel
Bevisa att:
 medför

Bevis:

Frasen följs ibland av Q.E.F.: "vilket skulle utföras".

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The airport of Skiathos "Alexandros Papadiamantis" is located 2 km from Town, on the north eastern side of the island. It receives flights from Athens and Thessaloniki and the flight time from both these cities of Greece is about 1 hour. In summer, this airport also receives charter flights from abroad.
From the airport of Skiathos island, there are taxis to transfer passengers to their destination around Skiathos island. Also many hotels provide transport to their guests from/to the airport.


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Browsing The Web During Work Makes You A Better Employee
Margaret Hartmann
It's nearly impossible for people to stay on task when placed in front of a computer with Internet access, and that may not be a bad thing. Researchers found that browsing the Web can make workers refreshed and more productive, and it's less disruptive than making personal calls, texting, or emailing.
Researchers from the National University of Singapore conducted two studies on the effect of taking web browsing breaks during work. The Wall Street Journal reports:
In the first, they assigned 96 undergraduate management students into one of three groups-a control group, a "rest-break" group and a Web-surfing group. All subjects spent 20 minutes highlighting as many letter e's as they could find in a sample text. For the next 10 minutes, the control group was assigned another simple task; members of the rest-break group could do whatever they pleased, except surf the Internet; and the third group could browse the Web. Afterward, all of the subjects spent another 10 minutes highlighting more letters.
Subjects who poked around online performed the tasks better and said they were more engaged and less mentally exhausted by the work.
The researchers say using the Internet is a better break activity because people only visit sites they enjoy reading. Tasks involving human interaction are "cognitively more demanding" and could wind up stressing people more. According to the WSJ, this means you shouldn't "feel guilty" about browsing the Web at work. If skimming through former classmates' Facebook photos all afternoon, much like pooping on company time, only fills you with a sense of triumph, then carry on.
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Web Surfing Helps at Work, Study Says [WSJ]
Image via Yuri Arcurs/Shutterstock.


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EnerOutlook 2019
Total CO2 emissions
CO2 intensity of electricity generation
CO2 intensity to GDP
CO2 intensity per capita
Achievement of NDCs may be accompanied by absolute emission growth in developing economies
Breakdown by region | EnerBlue scenario
Benchmark regions
Display World
EnerOutlook Presentation
Download the EnerOutlook 2019 presentation to have an overview of the main outcomes of our central scenario EnerBlue in various world regions.
The presentation includes details on the underlying assumptions of this scenario, along with insightful graphs and learnings on the future of energy systems through 2040.
EIA expects US crude oil production to rise by 9% in 2020
According to the Short-Term Energy Outlook released by the US Energy Information Administration, crude oil and gas production in the United States continued to increase in 2019 and should follow an upward trend until 2021.
EIA expects 32 GW of new wind and solar capacities in the US in 2020
The US Energy Information Administration (EIA) expects 42 GW of new power capacity to be installed and commissioned in 2020. Most of the new capacities would be renewable (76% of the total, i.e. nearly 32 GW), of which 18.5 GW would come from wind (44%) and 13.5 GW (32%) from solar. The remainder would consist of gas-fired power capacities (9.3 GW, i.e. 22%) and from other energy sources (hydropower and battery storage, 730 MW, 2%).
NPD forecast Norway's oil output to rise by 44% between 2019 and 2024
According to forecasts from the Norwegian Petroleum Directorate (NPD), Norway's crude oil production will rise from 1.41 mb/d in 2019 to 1.76 mb/d in 2020 and 2.02 mbd/d in 2024 (+44%), as major oilfields Sverdrup and Castberg will progressively enter production. Total liquids production should increase by more than 34% between 2019 (1.74 mboe/d) and 2024 (2.33 mb/d). Norway's natural gas output is expected to increase by 3% in 2020 and by 5% over the 2019-2024 period.
Kuwait plans to restart crude oil production in the Neutral Zone in 2020
Kuwait expects to resume crude oil production from the Neutral Zone shared with Saudi Arabia at the end of 2020 and to reach a production level of 250,000 bbl/d. In 2019, Kuwait and Saudi Arabia signed an agreement to end a 5-year dispute over shared resources, allowing a restart of production at the Khafji and Wafra fields, which used to produce 500,000 bbl/d before production was suspended. The agreement will also allow Kuwait to develop its share of the Dorra gas field.
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World Energy Scenarios 2040
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Campaigns of Knowledge: U.S. Pedagogies of Colonialism and Occupation in the Philippines and Japan (Asian American History & Cultu #204)
by Malini Johar Schueller
The creation of a new school system in the Philippines in 1898 and educational reforms in occupied Japan, both with stated goals of democratization, speaks to a singular vision of America as savior, following its politics of violence with benevolent recuperation. The pedagogy of recovery—in which sc... More
Exceptional State: Contemporary U.S. Culture and the New Imperialism
by Ashley Dawson • Malini Johar Schueller
Exceptional State analyzes the nexus of culture and contemporary manifestations of U. S. imperialism. The contributors, established and emerging cultural studies scholars, define culture broadly to include a range of media, literature, and political discourse. They do not posit September 11, 2001... More


The Primary phase school councillors will be hosting a cake sale on Wednesday 28th November.
The money raised will go towards an outdoor storage container and playground equipment. In order for our cake sale to go ahead please could we ask you to donate some cakes (either home baked or shop bought).
If you would like your child to buy a cake, please send your child into school with some money to do so; we will be charging 50p per cake.
The school councillors would like to thank you for your continued support.