text:
\section{Introduction} \label{sec:intro}
The Lyman-continuum (LyC, $\lambda<912$ \AA) photons escaping from star-forming galaxies into the neutral intergalactic medium (IGM) can account for the photon budget required to complete reionization only if a substantial fraction of them escape from the galaxies' interstellar and circumgalactic media (ISM and CGM). Given the number density of star-forming galaxies in the Epoch of Reionization (EoR), an average LyC escape fraction ($f_{esc}$) of $\sim 10\%$ across all galaxies would be required \citep[e.g.,][]{Finkelstein2019, Robertson2015} to both reionize the Universe by $z=6$ and match the Thomson optical depth of electron scattering observed in the cosmic microwave background \citep[CMB,][]{Planck2020}.

However, at $z \geq 4.5$ it is impossible to detect the LyC photons escaping from galaxies, since they are absorbed and scattered by the IGM along the line of sight \citep{inoue2014}. Therefore, efforts at low redshift, where LyC can be detected, have been focused on identifying other observable properties that trace physical conditions facilitating the escape of LyC photons. These  indirect indicators could then be used
in the EoR to identify the cosmic ionizers. Several indirect diagnostics have been proposed \citep[e.g.,][]{yamanaka2020,Izotov2018b,Marchi_2018,Verhamme2017}, but they are all characterized by a large scatter. One of the best indicators is the presence of a strong Ly$\alpha$ emission \citep[e.g.,][]{Pahl2021, Gazagnes2020}, often characterized by two emission peaks with a small velocity separation. However, at $z>6.5,$ this line is attenuated due to its resonant nature and by the increasingly neutral IGM as we approach the EoR \citep[][]{Pentericci_2018b,mason2019,jung2020,Ouchi_2020,bolan2021}.
Emission from the [\textrm{Mg}\textsc{ii}]\ensuremath{\lambda\lambda2796,2803}\ doublet has been proposed as a promising LyC proxy \citep{chisholm2020}, as the escape of this line is controlled by resonant scattering in the same low column-density gas as the \ifmmode {\rm Ly}\alpha \else Ly$\alpha$\fi\ \citep[see also][]{xu2022, izotov2022}.
\\
More recently, the nebular C \textsc{iv} emission line, requiring comparably high ionization energies to the He \textsc{ii} line (E $>$ 47.9\,eV and $>$ 54.4\,eV respectively), has attracted attention since its presence might be strongly linked to the escape of Lyman continuum photons from galaxies \citep[e.g.,][]{Schaerer_2022, Senchyna2022, Saxena2022, Mascia2023}, although this line is in general much fainter than \ifmmode {\rm Ly}\alpha \else Ly$\alpha$\fi.
Another very popular indicator is the  emission line ratio [\textrm{O}~\textsc{iii}]\ensuremath{\lambda\lambda4959,5007}/[\textrm{O}\textsc{ii}]\ensuremath{\lambda3727}\ (hereafter, $O32$), as  \cite{Nakajima2014} first found evidence for its correlation with $f_{esc}$: high values of $O32$ would reflect partially incomplete \textrm{H}\textsc{ii}\ regions, where some LyC photons could escape from \citep[][]{Marchi_2018}. Later on, it was found that this correlation is characterized by a substantial scatter, as highlighted by low-redshift studies \citep[e.g.,][]{Izotov2018b, Nakajima2020, Flury2022}. As a result, a high $O32$ flux ratio is still a necessary condition for a significant measurement of $f_{esc}$, although it is not sufficient by itself to define a LyC leaker, as viewing angles might play a role as well as variation in metallicity and ionization parameter \citep[e.g.,][]{Bassett2019, Katz2020}.
Further additional properties, such as low values of Balmer lines' rest-frame equivalent widths ($EW_0$), are thus required. As a matter of fact, measuring low values of EW in these lines could indicate lower optical depth in the \textrm{H}\textsc{ii}\ region \citep[e.g.,][]{bergvall2013}. However, many local LyC emitters exhibiting high values of Balmer emission line $EW_0s$ are present in the literature \citep{Izotov2016a, Izotov2016b, Izotov2018a, Izotov2018b}.
A possible explanation for this discrepancy lies in the fact that Balmer-line $EW_0s$ are sensitive not only to \textrm{H}\textsc{ii}\ region size, but also to starburst age and star formation history \citep[][]{Zackrisson2017, Binggeli2018, Alavi2020}. It is thus imperative to pair the EW diagnostic with another indicator in order to prevent degeneracy.
Finally, another diagnostic for a high $f_{esc}$ is the SFR surface density ($\Sigma_{SFR}$): feedback from star formation can blow bubbles or chimneys into the host galaxy's ISM, linking a high $\Sigma_{SFR}$ value to a high $f_{esc}$. This connection is supported by the detection of some compact LyC emitters \citep[LCEs, e.g.,][]{Izotov2018b, Marchi_2018}, even though compactness may not be a defining characteristic of all of them \citep[e.g.,][]{Marchi_2018}.

Recently, \cite{Flury2022} presented the first statistical test of many of the diagnostics just described on a large sample of low-redshift LCEs. Their conclusion is that indicators based on Ly$\alpha$ emission properties (such as peak velocity separation and equivalent width) perform well, and that diagnostics such as the [\textrm{O}\textsc{iii}]/[\textrm{O}\textsc{ii}]\ flux ratio and the SFR surface density, $\Sigma_{SFR}$, could also be used to determine if a galaxy is an LCE or not.

With the advent of \textit{JWST}, we now have the opportunity to constrain LyC diagnostics during the epoch of reionization with the first \textit{NIRSpec}\ observations of high-redshift galaxies. In this paper, we make use of \textit{NIRSpec}\ spectra obtained in the Abell 2744 cluster region for a sample of galaxies at $4.5 \leq z \leq 8$ observed as part of the \textit{JWST}\ Early Release Science program GLASS \citep[][]{TreuGlass2022} and the \textit{JWST}\ Director Discretionary Time program \citep[JWST-GO-2756; P.I. Chen;][]{Roberts-Borsani2022b}. With the wavelength coverage of $0.9 - 5.3\ \mu$m offered by the \textit{NIRSpec}\ observations, we can  confirm not only the redshifts of tens of photometrically selected candidates using intense emission lines, but we can also measure optical line ratios and rest-frame EWs with high precision. Our unique data set also includes deep \textit{JWST}/\textit{NIRCam}\ images, enabling us to better characterize those cosmic reionizer candidates based on their physical properties.

This paper is organized as follows. We present the data set in Sect.~\ref{sec:data}. We characterize the selected sample and compare the physical and spectroscopic proprieties with cosmological models and other samples at lower redshifts in Sect.~\ref{sec:analysis}. In Sect.~\ref{sec:predictions}, we indirectly infer $f_{esc}$ for the high-redshift sample and in Sect.~\ref{sec:results}, we summarize our key conclusions. Throughout this work, we assume a flat $\Lambda$CDM cosmology with $H_0$ = 67.7 km s$^{-1}$ Mpc$^{-1}$ and $\Omega_m$ = 0.307 \citep{Planck2020} and the \cite{Chabrier2003} initial mass function. All magnitudes are expressed in the AB system \citep{Oke1983}.

\section{Observations and method} \label{sec:data}

The final target list of the GLASS-JWST program and the way in which targets have been prioritized will be presented in a future paper. However, \cite{Morishita2022} have already described the observations and data reduction strategy. Here, we present a brief summary, highlighting the points that are most relevant for this work and describing the methods used to study the properties of the galaxies in our sample.

\subsection{JWST/NIRSpec MSA observations and data reduction}

\begin{figure*}[ht!]
\includegraphics[width=\textwidth]{images/footprintMUSEonUNCOVER}
\caption{Spatial location of the 29 selected sources, color coded by their spectroscopic redshift. They are superimposed on the RGB image of the UNCOVER program, made with NIRCam filters (blue = F115W + F150W, green = F200W + F277W, and red = F356W + F410M + F444W). The MUSE footprint is shown in white, the \textit{NIRSpec}\ GLASS-JWST pointing is shown in cyan, and the \textit{NIRSpec}\ DDT pointing is shown in red.
\label{fig:footprint}}
\end{figure*}

Our spectra were acquired through \textit{NIRSpec}\ MSA observations in two programs: the GLASS-JWST Early Release Science Program \citep[PID 1324, PI Treu;][]{TreuGlass2022} and a JWST DDT program \citep[PID 2756, PI. W. Chen;][]{Roberts-Borsani2022b}, which obtained \textit{NIRSpec}\ observations for a subset of targets residing over the central regions of the Frontier Field galaxy cluster Abell 2744.

The GLASS-JWST observations were carried out on November 10, 2022, with three spectral configurations (G140H/F100LP, G235H/F170LP, and G395H/F290LP). These configurations cover wavelengths between $1-5.14 \ \mu$m, at $R\sim2000-3000$. We exposed each of the three high-resolution gratings for a total of 4.9 hours. Specifically, in this work, we use the G235H/F170LP and G395H/F290LP observations, which contain the bright emission lines we will analyze.

DDT \textit{NIRSpec}\ observations were carried out on October 23 2022, using the CLEAR filter+PRISM configuration, which provides continuous wavelength coverage of $0.6-5.3 \ \mu$m at $R \sim 30-300$ spectral resolution. The on-source exposure time is 1.23 hours.

Data were reduced using the official STScI \textit{JWST}\ pipeline (ver.1.8.2)\footnote{\url{https://github.com/spacetelescope/jwst}} for Level 1 data products and the \texttt{msaexp}\footnote{\url{https://github.com/gbrammer/msaexp}} code for Level 2 and 3 data products, which is based on the STScI pipeline but also includes additional correction routines. In summary, we initially reduced the uncalibrated data using the \texttt{Detector1Pipeline} routine and the latest set of reference files (jwst\_1023.pmap) to correct for detector-level artifacts and convert them to count-rate images. Then, we applied custom preprocessing routines from \texttt{msaexp} to remove residual $1/f$ noise that is not corrected by the IRS2 readout, to identify and remove "snowballs", and to remove bias exposure by exposure before running STScI routines from \texttt{Spec2Pipeline} for the final 2D cutout images. To perform WCS registration, flat-fielding, path-loss corrections, and flux calibration, these routines include \texttt{AssignWcs}, \texttt{Extract2dStep}, \texttt{FlatFieldStep}, \texttt{PathLossStep}, and \texttt{PhotomStep}. Of note, our chosen reference files include an in-flight flux calibration, accounting for \textit{NIRSpec}'s better-than-expected throughput at blue wavelengths. Local background subtraction was performed using a three-shutter nod pattern before the resulting images are drizzled onto a common grid. We optimally extracted the spectra using an inverse-variance weighted kernel, which is derived by summing the 2D spectrum along the dispersion axis and fitting the signal along the spatial axis to a Gaussian profile. We visually inspected all kernels to make sure spurious events are not included. As a result, the kernel extracts the 1D spectrum along the dispersion axis. The final step was to verify the default wavelength calibration for the gratings, which is accurate within 1 \AA\ (Williams et al. in prep).

\subsection{Imaging data}

Deep \textit{NIRCam}\ images were acquired from the GO program UNCOVER (GO 2561; PI I. Labbe)\ and included observations in the F115W, F150W, F200W, F277W, F356W, F410M, and F444W filters. The imaging data were reduced using the STScI JWST pipeline and the latest versions of photometric zero points and reference files. A detailed description of all the reduction and calibration steps is presented in \cite{Merlin2022}. Of the 29 sources analyzed in this work (see next section), 27 were observed within the UNCOVER pointings. Their positions and the UNCOVER footprints are presented in Fig. \ref{fig:footprint}.

\subsection{Emission line and redshift identifications}
The focus of the study is on all sources at $z \geq 4.5$. Specifically, we analyzed the spectra of: 13 galaxies with a spectroscopic redshift larger than 4.5 previously confirmed by the MUSE observations \citep{mahler2018,richard2021}, all showing Ly$\alpha$ in emission in their optical spectra (the footprint of the MUSE observations is also shown in Fig. \ref{fig:footprint}); 29 galaxies with a photometric redshift in the range 4.5-8, of which 5 were selected as part of the $z \simeq 7.9$ candidate protocluster and whose confirmation has been recently presented by \cite{Morishita2022}.
Finally, 23 of the 42 galaxies were observed as part of GLASS-JWST, while 19 were part of the DDT program.

Spectra were visually examined for detectable optical lines using the spectroscopic or photometric redshift information. For photometric sources we determined the spectroscopic redshift when possible using the \ifmmode {\rm H}\beta \else H$\beta$\fi, [\textrm{O}~\textsc{iii}]\ensuremath{\lambda\lambda4959,5007},\ and (when present) \ifmmode {\rm H}\alpha \else H$\alpha$\fi\ lines.
In 29 cases, the [\textrm{O}\textsc{ii}]\ensuremath{\lambda3727}, [\textrm{O}~\textsc{iii}]\ensuremath{\lambda\lambda4959,5007}\ and \ifmmode {\rm H}\beta \else H$\beta$\fi\ were detected and their line fluxes were measured. We also measured the \ifmmode {\rm H}\alpha \else H$\alpha$\fi\ line in 17 out of 29 cases, since it falls within the observed spectrum (examples are shown in Fig. \ref{fig:GLASS_50038}). For this part of our analysis, we used the latest version of the \texttt{specutils}\footnote{\url{https://specutils.readthedocs.io/en/stable/index.html}} packages in \textsc{python}.

\begin{figure*}[ht!]
\centering
\includegraphics[width=0.9\textwidth]{images/grism_spectra.pdf}
\includegraphics[width=0.9\textwidth, trim = 0 0 0.8cm 0] {images/prism_spectra.pdf}
\caption{Example 2D and 1D spectra of two representative galaxies in our sample. Top: 2D (top) and 1D (bottom) \textit{NIRSpec}\ GLASS-JWST spectrum of 110000 at $z = 5.765$ (green for the G235H/F170LP and purple for the G395H/F290LP configuration) and 1$\sigma$ uncertainty (gray). Bottom:
2D (top) and 1D (bottom) \textit{NIRSpec}\ DDT spectrum of 150015 at $z = 5.041$ (black) and 1$\sigma$ uncertainty (gray). Vertical dashed lines mark the position of well-detected rest-optical emission lines. The continuum emission is also detected as seen in the 2D spectrum. On the X-axis in the bottom panel, the observed wavelength (\AA) is reported.
\label{fig:GLASS_50038}}
\end{figure*}

From our initial target list of 42 galaxies, there were eight sources with a spectroscopic redshift confirmed from previous MUSE observations, which were placed in the MSA, but for which we are unable to confirm any emission line from JWST data. Of these, five were observed as part of GLASS-JWST and three during the DDT. Most of these sources are extremely faint (fainter than 28 F150W), thus, their redshift confirmation was solely based on the presence of faint \ifmmode {\rm Ly}\alpha \else Ly$\alpha$\fi\ emission (flux on the order of $1-3 \times 10^{-19} \ \text{erg}/\text{s}/\text{cm}^2$) in the MUSE cubes.
We were also unable to detect any emission lines for five galaxies with a photometric redshift between 4.5 and 7: these galaxies are also faint ($m_{\text{F150W}} \simeq 27.2-28$). However, in these cases it is possible that the photometric redshift was incorrect and this is why we are unable to confirm any emission line in their spectra.

In Table \ref{tab:summary}, we report the GLASS-JWST IDs, the coordinates and the spectroscopic redshifts of all sources together with their $m_{\text{F150W}}$ magnitudes derived from the imaging data when present.

\subsection{Dust correction and flux measurements}
We measured the total flux of all detected lines (Balmer lines, [\textrm{O}\textsc{ii}],\ and of [\textrm{O}\textsc{iii}]) with a Gaussian fit of each line component. From the flux measurement we subtracted a constant continuum emission, which is estimated as the signal averaged over regions in which there are no lines near the one being measured. When the signal-to-noise ratio (S/N) of [\textrm{O}\textsc{ii}]\ or \ifmmode {\rm H}\beta \else H$\beta$\fi\  $\leq 2$, we set 2$\sigma$ as an upper limit.
Prior to carry out a quantitative analysis, it is necessary to consider corrections for dust reddening. For 22 galaxies, \ifmmode {\rm H}\alpha \else H$\alpha$\fi\ and \ifmmode {\rm H}\beta \else H$\beta$\fi\ are both available: for these, we calculated the correction for dust extinction on the basis of the Balmer decrement, assuming a \citet[][]{Calzetti2000} extinction law and an intrinsic ratio $\ifmmode {\rm H}\alpha \else H$\alpha$\fi/\ifmmode {\rm H}\beta \else H$\beta$\fi = 2.86$ \citep[see e.g.,][]{Dominguez2013, Kashino2013, Price2014}, which is valid for an electric temperature of 10000 K. For the other 7 sources where \ifmmode {\rm H}\alpha \else H$\alpha$\fi\ is not in the observed range, we applied the average correction $E(B-V)_{neb} \sim 0.1$ derived from all other sources.

With the dust corrected values, we calculated the $R23 = ([\textrm{O}\textsc{iii}] + [\textrm{O}\textsc{ii}])/\ifmmode {\rm H}\beta \else H$\beta$\fi$ and $O32$ line fluxes ratios and the \ifmmode {\rm H}\beta \else H$\beta$\fi\ rest-frame $EW_0$s. We list all these values in in Table \ref{tab:summary}. It is important to highlight that the $O32$ values slightly depend on the dust correction. The assumed temperature may be too low for high-z star-forming galaxies \citep[e.g.,][]{curti2023, nakajima2023}, however the \ifmmode {\rm H}\alpha \else H$\alpha$\fi/\ifmmode {\rm H}\beta \else H$\beta$\fi\ ratio varies by less than 5\% for a 20000 K temperature \citep{Dopita2003}
and therefore the $O32$ variation are well below the current uncertainties.

\begin{table*}
\caption{Sample and spectroscopic measurements.}\label{tab:summary}
$$
\begin{array}{llccccrrr}
\hline \hline
\noalign{\smallskip}
\text{PROGRAM} & \text{GLASS ID} & \text{RA} & \text{DEC} & z_{spec} & m_{\text{F150W}} & EW_0(\ifmmode {\rm H}\beta \else H$\beta$\fi) & R23 & O32 \\
 & & [\text{deg}] & [\text{deg}] & & [\text{mag}] & [$\AA$] & & \\
\noalign{\smallskip}
 \hline
 \noalign{\smallskip}
\textbf{DDT} &
 10025 & 3.59609 & -30.38581 & 7.875 & 26.7 & 139 \pm 30 & 8 \pm 3 & 6.6 \pm 1.4\\
 &40196 & 3.55803 & -30.38962 & 4.760 & 25.5 & 167 \pm 42 & > 11 & > 90 \\
 & 50017 &3.57006 &-30.40369 &5.550 & 26.3 & 89 \pm 17 & 8 \pm 3 & 9 \pm 2\\
 & 70002 & 3.60544 & -30.3966 & 5.771 & 27.0 & >210 & > 12 & > 8\\
& 80075 & 3.56755 & -30.40623 & 4.632 &26.9 & 173 \pm 38 & 3.4 \pm 1.5 & 9 \pm 2\\
& 100004 & 3.60657 & -30.38093 & 7.884 & 26.9 & > 130  & > 5 & > 5\\
& 110003 & 3.59069 & -30.39554 & 5.660 & 25.1 & 99 \pm 19 & > 4 & > 8\\
& 150015 & 3.55085 & -30.40590 & 5.041 & 25.7 & 268 \pm 53 & 4.1 \pm 1.8 & 7.2 \pm 1.9\\
& 150053 &3.58120 &-30.42853 &4.580 & 26.7 & 212 \pm 51 & > 5 & > 21\\
& 160170 & 3.56570 & -30.42613 & 4.895 & - & 190 \pm 43 & 5 \pm 2 & 8 \pm 2\\
& 160281 & 3.59015 & -30.42593 & 4.715 & 25.6 & 231 \pm 52 & 5 \pm 2 & 5.3 \pm 1.4\\
& 160284 & 3.58083 & -30.42526 & 4.700 & 24.8 & 130 \pm 27 & > 5 & > 8\\
& 160345 & 3.55293 & -30.40389 & 5.020 & 27.2 & 110 \pm 44 & > 4 & > 5\\
\noalign{\smallskip}
\hline
\noalign{\smallskip}
\textbf{GLASS-JWST} &
10000 & 3.60134 & -30.37923 & 7.884 & 25.5 & 76 \pm 13 & 7 \pm 2 & 8 \pm 3\\
& 10021 & 3.60851 & -30.41854 & 7.288 & 25.4 & 104 \pm 24 & 12 \pm 5 & 13 \pm 5\\
& 50002 & 3.57700 & -30.41552 & 5.135 & 27.8 & 69 \pm 23 & 12 \pm 6 & 19 \pm 7 \\
& 50038 & 3.56520 & -30.39426 &5.773 & 25.5 & 92 \pm 19 & 10 \pm 4 & 9 \pm 3\\
& 70018 & 3.58790 & -30.41159 & 5.284 & 27.1 & 155 \pm 32 & > 4 & > 12\\
& 80070 & 3.58232 & -30.38765 & 4.798 & 26.4 & 135 \pm 25 & 12 \pm 5 & 53 \pm 20\\
& 80085 & 3.57435 &-30.41253 & 4.728 & 28.1 ^a & 168 \pm 24 & 2.5 \pm 1.5 & 19 \pm 11\\
& 100001 & 3.60385 & -30.38223 & 7.875 & 26.5 & 39 \pm 8 & 10 \pm 4 & 3.2 \pm 1.0\\
& 100003 & 3.60451 & -30.38044 & 7.880& 26.2 & 85 \pm 18 &11 \pm 4 & 21 \pm 7\\
& 100005 & 3.60646 & -30.38099 & 7.883& 26.7 & 33 \pm 15 & 21 \pm 12 & 2.9 \pm 1.0\\
& 110000 & 3.57064 & -30.41464 & 5.765 & 25.8 & 57 \pm 13 & 9 \pm 4 & 6 \pm 2\\
& 150008 &3.60253& -30.41923& 6.230 & 25.8 & 141 \pm 30 & > 7 & > 20\\
& 150029 & 3.57717 & -30.42258 & 4.585 & 26.1 & 205 \pm 45 & 8 \pm 3 & 17 \pm 6\\
& 160122 & 3.5649 & -30.42496 & 5.333 & - & 149 \pm 25 & 5 \pm 2 & 18 \pm 7\\
& 160275 &3.58107 &-30.42830 &4.578 & 26.2 & 5 \pm 1 & - & - \\
& 400009 &3.60059 &-30.41027& 6.376 & 26.8 & 35 \pm 7 & - & -\\
\noalign{\smallskip}
\hline
\end{array}
$$
\begin{tablenotes}
 \small
 \item $^a$ from MUSE catalog, magnitude F140W HST. \\ Missing O32 and R23 values are due to [\textrm{O}\textsc{ii}]\ undetection because of its position in un-acquired part of the spectrum. \ifmmode {\rm H}\beta \else H$\beta$\fi\ and [\textrm{O}\textsc{iii}]\ are always detected.
 \end{tablenotes}
\end{table*}

\subsection{Measurements of physical parameters }\label{sec:SED_fitting}

Following \cite{Santini2022}, we measured the stellar masses $M_{\star, obs}$, the observed absolute UV magnitudes at 1500\AA\ ($M_{1500, obs}$), the star formation rates (SFRs), and dust reddening $E(B-V)$ by fitting synthetic stellar templates to the seven-band \textit{NIRCam}\ photometry and the released HST photometry \citep{Castellano2016} with \textsc{zphot} \citep{fontana00}. We adopted \cite{Bruzual2003} models and assumed delayed exponentially declining star formation histories -- SFH($t$)$\propto (t^2/\tau) \cdot \exp(-t/\tau)$ -- with $\tau$ ranging from 0.1 to 7 Gyr. The age ranges from 10 Myr to the age of the Universe at each galaxy redshift, while metallicity can assume values of 0.02, 0.2 or 1 times Solar metallicity. For the dust extinction, we used the \cite{Calzetti2000} law with $E(B-V)$ ranging from 0 to 1.1. We computed $1\sigma$ uncertainties on the physical parameters by retaining, for each object, the minimum and maximum fitted masses among all the solutions with a probability $P(\chi^2)>32\%$ of being correct, fixing the redshift to the best-fit value.

As a final step, we needed to adjust the stellar masses and $M_{1500}$ and the SFR values for the lensing amplification factor.
The magnification factor $\mu$ was derived by combining the LM-model \citep{Bergamini2022}, the model used by \cite{Roberts-Borsani2022c}, with a new spatially more extensive model that fully covers the JWST field of view (Bergamini et al. in prep). The $\mu$ values range from 1.6 to 12, with a median value of $\sim 2$.
The results on our sources' stellar masses, $M_{\star, true}$, their $M_{1500}$, and their lensing magnification factors $\mu$ are reported in Table \ref{tab:summary2}.

\subsection{Sizes and SFR surface density estimates}

The SFRs were derived from the \ifmmode {\rm H}\alpha \else H$\alpha$\fi\ emission line using the standard conversion by \cite{Kennicutt1998}, that is, $SFR(\ifmmode {\rm H}\alpha \else H$\alpha$\fi) [M_\odot \ \text{yr}^{-1}]= 7.9 \ 10^{42} \ L_{\ifmmode {\rm H}\alpha \else H$\alpha$\fi}$, and then corrected for the Chabrier IMF. For those few sources at $z \geq 6.6,$ where the \ifmmode {\rm H}\alpha \else H$\alpha$\fi\ line falls outside the observable window we used  dust-corrected \ifmmode {\rm H}\beta \else H$\beta$\fi\ fluxes instead. To correct for slit losses and possible residual uncertainties on flux calibration, we normalized the spectra to the F444W filter by integrating the spectrum under the F444W bandpass, the closest to the \ifmmode {\rm H}\alpha \else H$\alpha$\fi\ line in our sample.
Thanks to the high resolution of the GLASS-JWST spectra, no correction for [\textrm{N}\textsc{ii}]\ contamination is required for \ifmmode {\rm H}\alpha \else H$\alpha$\fi\ measurements. For galaxies observed by the DDT programs, \ifmmode {\rm H}\alpha \else H$\alpha$\fi\ is blended with the [\textrm{N}\textsc{ii}]\ doublet. However our sources are all very-low-mass galaxies and, based on low-redshift results, we expect contamination to be less than 10\% \citep[e.g.,][]{Faisst2018}. Therefore, we did not attempt to make any correction on the fluxes.

The results obtained on the SFR were also compared to the values determined by the SED fitting procedure described in Sect. \ref{sec:SED_fitting}, finding a reasonable agreement between the two data sets, indicating that there are no systematic issues. Obviously, the SED fitting SFR is heavily dependent on the choice of SFH, and also on the dust correction, while the value derived from the \ifmmode {\rm H}\alpha \else H$\alpha$\fi\ luminosity is sensitive to short timescales. That is to say that it only probes the presence of short-lived, massive stars, so their  ratio is actually an indication of the burstiness of the galaxy.

We measured the size of each galaxy $r_{e}$ in the F115W band, corresponding to the UV rest-frame of the galaxies.
Adopting forward-modeling technique, we assumed that galaxies are well represented by a Sersic profile \citep{sersicpaper} as \cite{Yang2022}. Then we modeled the appearance of the source in the image plane considering lensing and PSF effects.
The source reconstruction was performed via \texttt{python} software
\texttt{Lenstruction} \cite[see details in][]{Yang_2020}, which is built on \texttt{Lenstronomy} \citep{Birrer2021}.
In this way we obtained the intrinsic properties of galaxies in the source plane, hence, the intrinsic size. Finally, we calculated the SFR surface density using the relation $\Sigma_{SFR} = SFR/2\pi r_{e}^2$ \citep[e.g.,][]{Naidu2020, Flury2022}.
The SFR surface densities $\Sigma_{SFR}$ are listed in Table \ref{tab:summary2}.

\subsection{UV-$\beta$ slopes}
We measured the UV slope of our galaxies from the \textit{NIRCam}\ photometry and/or the previously available \textit{HST}\ photometry \citep{Castellano2016}, with the approach detailed in \cite{Calabro2021}.
In brief, we considered all the photometric bands whose entire bandwidths are  between a $1216$ and $3000$ \AA\ rest frame. The former limit is set to exclude the \ifmmode {\rm Ly}\alpha \else Ly$\alpha$\fi\ line and Ly-break, while the latter limit is slightly larger than that adopted in \cite{Calabro2021} to ensure a larger range.

Then, we fitted the selected photometry with a single power-law of the form f($\lambda$) $\propto \lambda^\beta$.
In practice, we fitted two or three photometric bands amongst \textit{HST}\ F814W and \textit{JWST}-\textit{NIRCam}\ F115W, F150W or F200W depending on the exact redshift of the sources. This choice allows us to  uniformly probe the spectral range between $1500$ and $3000$ \AA\ for most of the galaxies.
We measured the $\beta$ and associated uncertainty for each source using a bootstrap method. By using $n = 500$ Monte Carlo simulations, the fluxes in each band were varied according to their error. The results provided a resultant slope distribution from which we calculated the mean and standard deviation of $\beta$ for each galaxy.
The results on $\beta$ with associated errors are reported in Table \ref{tab:summary2}. We find a median $\beta$ of $-2.1$, with a $1\sigma$ dispersion of $0.4$. The UV magnitudes $M_{1600}$ that can be derived simultaneously with this approach are consistent with the values obtained from the SED fitting and described in the previous section.

\begin{table*}
\caption{Physical parameters derived from multi-band photometry. All measurements are corrected for magnification where needed.}\label{tab:summary2}
$$
\begin{array}{llcccccc}
\hline \hline
\noalign{\smallskip}
\text{PROGRAM} & \text{GLASS ID} & \mu^* & \log_{10}(M_\star) & r_e & \log_{10}(\Sigma_{SFR}) & M_{1500} & \beta \\
 & & & [\text{M}_\odot] & [\text{kpc}]& [\text{M}_\odot \ \text{yr}^{-1} \ \text{kpc}^{-2}] & [\text{mag}]\\
\noalign{\smallskip}
 \hline
 \noalign{\smallskip}
\textbf{DDT} &
 10025 & 2.60^{+0.08}_{-0.07} & 8.03 _{- 0.14 }^{+ 0.19 } & 0.40 & 0.4 \pm 0.2 & -19.00 _{- 0.03 }^{+ 0.01 } & -2.08 \pm 0.45 \\
 &40196 & 2.95^{+0.21}_{-0.72} & 7.87 _{- 0.13 }^{+ 0.13 } & 0.33 & 1.6 \pm 1.0 & -19.41 _{- 0.03 }^{+ 0.02 } & -2.03 \pm 0.48\\
 & 50017 & 2.27^{+0.07}_{-0.16} & 8.78 _{- 0.69 }^{+ 0.23 } & 0.43& 0.7 \pm 0.1 & -19.13 _{- 0.19 }^{+ 0.10 } & -1.77 \pm 0.25\\
 & 70002 & 2.19^{+0.05}_{-0.05} & 7.13 _{- 0.15 }^{+ 0.01 } & 0.12 & 2.0 \pm 1.3 & -18.44 _{- 0.01 }^{+ 0.01 } & -2.54 \pm 0.26\\
& 80075 & 2.02^{+0.06}_{-0.17} & 6.76 _{- 0.15 }^{+ 0.23 } & 0.07 & 2.3 \pm 1.7 & -17.37 _{- 0.03 }^{+ 0.01 } & -2.26 \pm 0.23\\
& 100004 & 1.92^{+0.06}_{-0.08} & 9.17 _{- 0.28 }^{+ 0.14 } & 0.40 & 0.2 \pm 0.3 & -19.76 _{- 0.10 }^{+ 0.11 } & -1.88 \pm 0.44 \\
& 110003 & 11.6^{+0.9}_{-1.0} & 7.92 _{- 0.06 }^{+ 0.71 } & 0.48 & 1.2 \pm 0.5 & -20.52 _{- 0.03 }^{+ 0.15 } & -2.51 \pm 0.24 \\
& 150015 & 1.79^{+0.05}_{-0.29} & 7.87 _{- 0.44 }^{+ 0.34 } & 0.38 & 1.2 \pm 0.7 & -19.52 _{- 0.15 }^{+ 0.09 } & -2.54 \pm 0.49 \\
& 150053 & 1.75^{+0.03}_{-0.14} & 7.85 _{- 0.45 }^{+ 0.48 } & 0.80 & -0.1 \pm 0.6 & -19.26 _{- 0.15 }^{+ 0.08 } & -1.25 \pm 0.21 \\
& 160170 & 1.58^{+0.04}_{-0.13} & - & - & - & - & -\\
& 160281 & 1.96^{+0.03}_{-0.15} & 7.93 _{- 0.08 }^{+ 0.24 } & 1.65 & -0.3 \pm 0.9 & -20.00 _{- 0.11 }^{+ 0.01 } & -2.26 \pm 0.51 \\
& 160284 & 1.85^{+0.03}_{-0.15} & 8.85 _{- 0.10 }^{+ 0.01 } & 0.53 & 1.2 \pm 0.6 & -20.16 _{- 0.01 }^{+ 0.02 } & -2.05 \pm 0.48 \\
& 160345 & 1.86^{+0.05}_{-0.30} & 7.95 _{- 0.81 }^{+ 0.09 } & 0.45& 0.5 \pm 0.1 & -18.67 _{- 0.12 }^{+ 0.06 } & -2.49 \pm 0.49 \\
\noalign{\smallskip}
\hline
\noalign{\smallskip}
\textbf{GLASS-JWST} &
10000 & 2.13^{+0.07}_{-0.11} & 8.11 _{- 0.01 }^{+ 0.27 } & 0.20 & 2.0 \pm 1.3 & -19.71 _{- 0.02 }^{+ 0.10 } & -2.27 \pm 0.46 \\
& 10021 & 2.17^{+0.08}_{-0.03} & 8.70 _{- 0.35 }^{+ 0.11 } & 0.68 &0.8 \pm 0.2 & -21.18 _{- 0.02 }^{+ 0.08 } & -2.25 \pm 0.48 \\
& 50002 & 2.15^{+0.06}_{-0.13} & 8.57 _{- 0.11 }^{+ 0.22 } & 0.70 & -1.4 \pm 2.0 & -18.78 _{- 0.11 }^{+ 0.06 } & -1.66 \pm 0.66 \\
& 50038 & 2.66^{+0.12}_{-0.32} & 9.23 _{- 0.39 }^{+ 0.03 } & 0.48 & -1.7 \pm 2.0 & -19.76 _{- 0.09 }^{+ 0.03 } & -1.79 \pm 0.25 \\
& 70018 & 6.89^{+0.21}_{-0.30} & 8.05 _{- 0.14 }^{+ 0.01 } & 0.19 & 1.9 \pm 1.3 & -18.00 _{- 0.04 }^{+ 0.04 } & -2.02 \pm 0.49 \\
& 80070 & 5.45^{+0.26}_{-0.27} & 7.42 _{- 0.06 }^{+ 0.21 } & 0.59 & 0.4 \pm 0.2 & -18.24 _{- 0.03 }^{+ 0.01 } & -1.92 \pm 0.49 \\
& 80085 & 2.11^{+0.05}_{-0.11} & - & - & - & - & -2.43^a \\
& 100001 & 1.99^{+0.06}_{-0.09} & 9.48 _{- 0.13 }^{+ 0.04 } & 0.50 & 0.34 \pm 0.3 & -20.45 _{- 0.02 }^{+ 0.04 } & -1.63 \pm 0.48 \\
& 100003 & 1.96^{+0.06}_{-0.09} & 8.29 _{- 0.15 }^{+ 0.31 } & 0.15 & 2.3 \pm 1.7 & -20.15 _{- 0.02 }^{+ 0.15 } & -2.51 \pm 0.48 \\
& 100005 & 1.92^{+0.06}_{-0.08} & 8.63 _{- 0.27 }^{+ 0.17 } & 0.25 & 1.5 \pm 1.2 & -19.85 _{- 0.07 }^{+ 0.11 } & -2.55 \pm 0.48 \\
& 110000 & 1.90^{+0.05}_{-0.14} & 9.10 _{- 0.62 }^{+ 0.05 } &0.54 & 0.5 \pm 0.2& -20.13 _{- 0.17 }^{+ 0.04 } & -1.70 \pm 0.23 \\
& 150008 & 2.60^{+0.03}_{-0.04} & 8.41 _{- 0.19 }^{+ 0.35 } & 0.40 & 1.5 \pm 0.7 & -19.33 _{- 0.06 }^{+ 0.14 } & -2.10 \pm 0.25 \\
& 150029 & 1.86^{+0.04}_{-0.14} & 8.55 _{- 0.01 }^{+ 0.07 } & 0.27 & 1.7 \pm 1.0 & -18.75 _{- 0.04 }^{+ 0.01 } & -1.85 \pm 0.20 \\
& 160122 & 1.59^{+0.04}_{-0.13} & - & - & - & - & -\\
& 160275 & 1.75^{+0.03}_{-0.14} & 7.73 _{- 0.14 }^{+ 0.11 } & 0.47 & -1.3 \pm 1.8 & -19.20 _{- 0.02 }^{+ 0.01 } & -2.55 \pm 0.20\\
& 400009 & 9.3^{+1.6}_{-0.6} & 6.77 _{- 0.26 }^{+ 0.54 } & 0.11 & 1.0 \pm 0.3 & -17.05 _{- 0.04 }^{+ 0.14 } & -2.17 \pm 0.25\\
\noalign{\smallskip}
\hline
\end{array}
$$
\begin{tablenotes}
 \small
 \item * Median magnification of the lens model by Bergamini (in prep.), calculated at the position of the source. Measurements are associated with 1 $\sigma$ uncertainties. $^a$ measured from HST photometry
\end{tablenotes}
\end{table*}

\section{Results}\label{sec:analysis}

\subsection{Possible AGN contamination}
Our sample was selected solely based on known spectroscopic redshift (via faint and narrow \ifmmode {\rm Ly}\alpha \else Ly$\alpha$\fi\ emission) or through photometric redshifts. It could therefore be affected by AGN contamination. Since we are interested in searching for candidate LyC emitters amongst the star-forming population, we first consider whether the primary source of ionization might not be star formation, but  AGN activity instead.

\begin{figure}[ht!]
\includegraphics[width=\linewidth]{images/O3hb_mass.pdf}
\caption{MEx diagram for the sample of galaxies analyzed in this paper:black dots and green squares are for the GLASS-JWST and DDT samples, respectively. For reference, we plot also the galaxies at $z = 0.3 - 0.4$ from \cite{Flury2022} (diamonds) and the LCE candidates from previous studies \citep[stars,][]{Izotov2016a, Izotov2016b, Izotov2018a, Izotov2018b, Izotov2021, Wang2019}. The two orange demarcation lines from \cite{Juneau2014} show the boundaries of the AGN-and-star-forming transition region. All objects above the upper line are AGN-dominated; all galaxies below or rightward of the lower line are presumptively dominated by star formation. We also show the separation from \cite{Coil2015} (dotted lines), which is the adaptation of the Juneau et al. model for galaxies and AGNs at $z\sim2.3$ from the MOSDEF survey.
\label{fig:AGN}}
\end{figure}

\begin{figure}[ht!]
\includegraphics[width=\linewidth]{images/O32_Hbeta.pdf}
\caption{$O32$ vs. rest-frame $EW_0(\ifmmode {\rm H}\beta \else H$\beta$\fi)$. Symbols are the same as in Figure \ref{fig:AGN}. For reference, we also plot  the galaxies at $z = 0.3 - 0.4$ from \cite{Flury2022} (diamonds) and the LCE from \cite{Izotov2016a, Izotov2016b, Izotov2018a, Izotov2018b, Izotov2021, Wang2019} (stars). Symbols are color coded as a function of their measured $f_{esc}$. The pink line ($O32 = 5$) indicates the threshold for LCEs as predicted by \cite{Flury2022}.
\label{fig:O32_Hbeta}}
\end{figure}

 We employed the mass-excitation (MEx) diagram, first proposed by \cite{Juneau2011} to  combine the measurements of the [\textrm{O}\textsc{iii}] $\lambda 5007$/\ifmmode {\rm H}\beta \else H$\beta$\fi\ emission line ratio with the stellar mass to discriminate between AGNs and star-forming galaxies. This diagram was proposed as an alternative to the
 classical BPT diagram that compares the [\textrm{O}\textsc{iii}] $\lambda 5007$/\ifmmode {\rm H}\beta \else H$\beta$\fi\ to the [\textrm{N}\textsc{ii}]/\ifmmode {\rm H}\alpha \else H$\alpha$\fi\ emission line ratios \citep[][]{BPT_1981}
 when these last two lines fall out of the visibility window and it is not possible to use them to characterize the ionization mechanism in the galaxies -- as is the case for our low-resolution DDT spectra where the [\textrm{N}\textsc{ii}]\ doublet is blended with \ifmmode {\rm H}\alpha \else H$\alpha$\fi.
Due to the high resolution of the GLASS-JWST spectra, for the galaxies with these observations, we used the dust-corrected flux measurement of the 5007 \AA\ component of the [\textrm{O}\textsc{iii}]\ doublet. Instead, for the galaxies observed as part of the DDT program for which the doublet cannot be resolved,
we determined the [\textrm{O}\textsc{iii}] $\lambda 5007$ flux, assuming the expected line ratio of 1:3 for the two components fixed by atomic physics. As shown in Fig. \ref{fig:AGN}, the position of our sources in the MEx diagram indicates that our sample contains essentially star forming galaxies, lying below or around the division line identified by \cite{Coil2015} for $z=2.3$ galaxies and AGN from the MOSDEF survey. For reference, we also plot  the galaxies at $z = 0.3 - 0.4$ from the Low-redshift Lyman Continuum Survey from \cite{Flury2022} and the compilation of low-z LCE also used by the same authors \citep[from][]{Izotov2016a, Izotov2016b, Izotov2018a, Izotov2018b, Izotov2021, Wang2019}.

\subsection{LyC indirect diagnostics}
As discussed above, \ifmmode {\rm Ly}\alpha \else Ly$\alpha$\fi\ is possibly the best indirect diagnostic of LyC escape, since the conditions that favour the escape of \ifmmode {\rm Ly}\alpha \else Ly$\alpha$\fi\ photons are often the same that allow for the escape of LyC photons. However, we cannot use this parameter for our sample, since the \textit{NIRSpec}\ data do not cover the 1216\AA\ region for most of our galaxies and only a small subset of our sources have been covered by previous MUSE observations (see also Fig. \ref{fig:footprint}). In addition, for the sources at $z \geq 7$, the IGM becomes significantly neutral, thus absorbing the emission even in sources where the line would be intrinsically bright \citep[e.g.,][]{Stark2010,Pentericci2011,Mason2018a}. Indeed,  \cite{Morishita2022} recently showed that none of the galaxies in the protocluster candidate at $z=7.89$ presents bright \ifmmode {\rm Ly}\alpha \else Ly$\alpha$\fi\ emission and estimate an average neutral hydrogen fraction of the IGM in the region to be $> 0.45$. Therefore in this work we concentrate on the other most promising diagnostics tested at low redshift by \cite{Flury2022} and available for our galaxies: these authors showed that $O32$, $\beta_{1200}$, $r_{50}$, and $\Sigma_{SFR}$ as well as $EW_0(\ifmmode {\rm H}\beta \else H$\beta$\fi)$ and $M_{1500}$ exhibit some of the strongest and most significant correlations with $f_{esc}$. This would indicate that certain characteristics, such as concentrated star formation, young stellar populations, and high ionization states, play an essential role in the escape of LyC photons.

We began by analyzing the $O32$ and the rest-frame $EW_0(\ifmmode {\rm H}\beta \else H$\beta$\fi)$ relation, as shown in Fig. \ref{fig:O32_Hbeta}. We plot the values for the \textit{JWST}\ high-redshift sample and compare them to the local galaxies with measured $f_{esc}$ from previous works \citep{Flury2022,Izotov2016a, Izotov2016b, Izotov2018a, Izotov2018b, Izotov2021, Malkan2021, Wang2019}. These values are color-coded as a function of their $f_{esc}$ (COS UV) measured values. We can see that the large majority of the high-redshift sources have values of $O32$ larger than 5, which has been indicated as a threshold for LyC leakers (LCEs from here onwards) by \cite{Flury2022}. We note that \cite{Flury2022} define leakers as galaxies with an $f_{esc} > 0.05$ measured with $S/N \geq 5$. Our sample indeed mostly lies in the region of the plot populated by low-redshift leakers. In Fig. \ref{fig:O32_mass}, we show  $O32$ as a function of total stellar mass, again comparing our sample to the low-z galaxies: our sample perfectly overlaps with the low-z galaxies at the low-mass end, where we find most of the LCEs.

\begin{figure}[ht!]
\includegraphics[width=\linewidth]{images/O32_mass.pdf}
\caption{$O32$ vs. $M_\star$. Symbols are as in Fig. \ref{fig:O32_Hbeta}.
\label{fig:O32_mass}}
\end{figure}

\cite{Zackrisson2013} suggested that galaxies ought to be identified with high $f_{esc}$ by combining the UV slope $\beta$ with the measurement of the EW of a Balmer line, such as \ifmmode {\rm H}\beta \else H$\beta$\fi, and that the predictions are almost independent of the model assumed (i.e., radiation or density bounded nebula).
We know that both $\beta$ and $EW_0(\ifmmode {\rm H}\beta \else H$\beta$\fi)$ are also good indirect indicators according to \cite{Flury2022}, although there does not seem to be a direct correlation between the two values: \cite{Flury2022} showed that their LCEs do not seem to follow the predictions provided by the models from \cite{Zackrisson2013}.

We show the properties of our sample in Fig. \ref{fig:beta_hb}. Specifically, at a given value of $EW_0(\ifmmode {\rm H}\beta \else H$\beta$\fi)$, the high-redshift galaxies are, on average, bluer than the majority of the low-z galaxies (consistent with the lower stellar mass probed by our sources); but their slopes are similar to the subset of the low-z sources with moderate-to-high values for $f_{esc}$. The $\beta$ slopes for our galaxies are perfectly consistent with the average values found for LBGs at z$\sim 6$ for galaxies with $M_{UV}$ in the same range \cite{Bouwens2014}.
 In the figure, we also show the models from \cite{Zackrisson2013} for various values of escape fraction, after correcting the intrinsic $\beta$ slopes of the models for dust attenuation and assuming the average reddening of our sample derived from the SED fitting, $E(B-V) = 0.097$ (solid line), and also the maximum and minimum $E(B-V)$ in our sample (shaded area). We note that our galaxies show more consistency with model predictions that assume moderate-to-low escape fractions $0.0 \leq f_{esc} \leq 0.5$.

Finally, we analyzed the sizes and star formation rate density for our galaxies. Several authors have postulated that concentrated star formation provides the feedback necessary to clear paths in the ISM that allow for the escape of LyC photons. In addition,  \cite{Marchi_2018} recently found that stacks of galaxies that are UV-compact ($r_{UV} \leq 0.30$ kpc) have much higher LyC flux than the average population
\citep[see also][]{Izotov2018b}.
We find that, with the exception of one galaxy (ID 160281, which has $r_e =1.65 \text{kpc}$), our targets are all extremely compact with typical $r_e$ in the rest-frame UV around $0.2-0.6$ kpc.
These values are similar or even lower than those found for the low-z galaxies and LCEs \citep{Flury2022}; thus, once again the high-redshift sources have equal properties to the low-z LCEs.
Since we know that sizes evolve with redshift and galaxies become progressively more compact, we also compared our sample to the general population of star-forming galaxies (LBGs selected) at $z\simeq 6$ analyzed by \cite{Shibuya2015}. Specifically, for $M_{UV} =-18 (-20)$, the average UV rest-frame sizes are $r_e \simeq 0.38(0.56)$ kpc, respectively. Thus, indeed our galaxies are, from this point of view, as compact as the general UV faint population at the same redshift.

As for the star formation rate densities,  the values of $\log_{10}(\Sigma_{SFR})$ for our galaxies span a very wide range, with an average $\Sigma_{SFR}$ that is slightly  higher than the average expected at their redshift, as measured by \cite{Shibuya2015}. We note that their values are inferred  from the UV and then dust corrected. LyC leakers at low and intermediate redshift, tend to show high  $\Sigma_{SFR}$  values, as discussed extensively by \cite{Naidu2020}, who actually proposed a physically motivated model in which $f_{esc}$ would scale as $\Sigma_{SFR}^{0.4}$. \cite{Flury2022} identify a threshold value of $\Sigma_{SFR} = 10 \ M_\odot \ \text{yr}^{-1} \ \text{kpc}^{-2}$ above which their LCE fraction changes from 10\% to 60\%, and where indeed we find half of our high-redshift galaxies.

\subsection{O32-R23 diagnostics}

The $O32$ vs $R23$ index diagram (Fig. \ref{fig:O32_R23}) is widely used to examine the gas-phase metallicity and ionization state both in the local universe \citep[e.g.,][]{Thomas2013, Izotov2016a, Izotov2016b, Izotov2018a, Izotov2018b} and at high redshift \citep[e.g.,][]{Flury2022, Nakajima2020, Reddy2022, Vanzella2019}, as both these indices are sensitive to combination of these quantities. \cite{Nakajima2020} showed that $z\sim 3$ LyC leakers tend to populate the upper right part of this diagram.
Recently \cite{Katz2020} used high-resolution cosmological radiation hydrodynamics simulations to examine the properties of LyC leakers deep into the epoch of reionization and found that simulated high-redshift galaxies populate the same regions of the $R23-O32$ plane, as the z$\sim$ 3 LyC leakers presented in \cite{Nakajima2020} that tend to have low metallicity.
Although they conclude that this plane is not the most useful to differentiate between leakers and non-leakers we note that the $z=3$ leakers by \cite{Nakajima2020}, with measured values and Ion2 occupy the same region as the $z=0.3$ low-redshift leakers. Our galaxies occupy a much broader region, which could reflect either a wider range of metallicity and ionization states or simply the fact that we have large measured uncertainties on the diagnostics.

\begin{figure}[ht!]
\includegraphics[width=\linewidth]{images/beta_hb.pdf}
\caption{$\beta$ vs. rest-frame $EW_0(\ifmmode {\rm H}\beta \else H$\beta$\fi)$. Models are from \cite{Zackrisson2013} and simulate the expected trend for galaxies with an exponential declining SFR ($Z = 0.02$, solid lines) and various values of escape fractions. Symbols are as in Fig. \ref{fig:O32_Hbeta}.
\label{fig:beta_hb}}
\end{figure}

\begin{figure*}[ht!]
\centering
\includegraphics[width=0.9\textwidth]{images/O32_R23.pdf}
\caption{$O32$ vs. $R23$ diagnostic diagram for our sample. Black dots and green squares show the GLASS-JWST and DDT samples, respectively. For reference, we plot also the SDSS galaxies from \cite{Thomas2013} as dark grey points. The LCEs from \cite{Nakajima2020}  are shown red dots. The Ion2 at $z = 3.2$ comes from \cite{Vanzella2016, deBarros2016} as a red x sign, the low-z LyC leakers from \cite{Izotov2016a, Izotov2016b, Izotov2018a, Izotov2018b, Wang2019} as stars, and the LCEs at $z = 0.3 - 0.4$ from the Low-redshift Lyman Continuum Survey \citep[as pink diamonds,][]{Flury2022}. We show also the locus of high-redshift LCEs predicted from cosmological simulations by \cite{Katz2020} as an orange dashed line and the threshold of $O32 > 5$ determined in \cite{Flury2022} as a pink dashed line.
\label{fig:O32_R23}}
\end{figure*}

\section{Predicting escape fractions of EoR galaxies}\label{sec:predictions}

In the sections above, we have shown that our high-redshift galaxies have properties that are largely overlapping with those of low-z LCEs. The next step is to try and give an indirect estimate of the $f_{esc}$ values for our galaxies, so as to understand if typical low-mass galaxies at $z \simeq 5-7$ could be really the drivers of reionization. We assume that the mechanisms that drive the escape of LyC photons are the same at all redshifts and depend only on the physical properties of the sources.

We proceeded as follows: we used the spectroscopic and physical properties of the 66 galaxies that are part of the \cite{Flury2022} sample, with the additional 22 LCEs from previous studies \citep{Izotov2016a, Izotov2016b, Izotov2018a, Izotov2018b, Izotov2021, Wang2019} to calibrate an empirical relation with the measured $f_{esc}$ values. Specifically, we focused on the following properties: $O32$, $EW_0(\ifmmode {\rm H}\beta \else H$\beta$\fi)$, $\beta$, $r_e$ (in kpc), $\Sigma_{SFR}$, and $M_{1500}$. For all 88 galaxies, these parameters are accurately measured and, of course, accurate measurements of $f_{esc}$ are available. To this end, we  specifically used the $f_{esc}$ derived by the COS UV spectral fits \citep[see definition in][]{Flury2022}.
Recently \cite{chisholm2022} followed a somewhat similar approach, also using the same set of low-redshift observations,  but limited to the UV-$\beta$ slope and an indirect proxy. They  provided  a scaling relation between $\beta$ and $f_{esc}$, although the relation has appreciable scatter that scales with $f_{esc}$.

 We first ran the Spearman rank correlation and found that $O32$, $r_e$, $EW_0(\ifmmode {\rm H}\beta \else H$\beta$\fi)$, and $\beta$ (in that order) are the properties that are best correlated with $f_{esc}$. We then identified one useful fitting linear relation to obtain an estimate of $\log_{10}(f_{esc})$ on the basis of the other four measured physical properties. A fully data-driven regression analysis was carried out by performing a regularized minimization of the root-mean-square error (MSE), computed between the values provided by the equation and the dataset, for several possible combinations of the above properties.
We tested both a scheme in which the error on the escape fraction, $f_{esc}$, is not considered and a scheme in which values are weighted by the error.
Since $O32$ and $EW_0(\ifmmode {\rm H}\beta \else H$\beta$\fi)$ exhibit a very tight correlation (Spearman correlation between them $> 0.9$, see also Fig. \ref{fig:O32_Hbeta}), the information they provide is redundant and therefore we decided to use only $O32$. We checked that the remaining three parameters are reasonably independent (Spearman correlation $<$ 0.5) and therefore provide complementary information. We finally found a best-fit relation of the form:
\begin{equation}
\log_{10}(f_{esc}) =A+B \log_{10}(O32)+ C r_e + D \beta.
\end{equation}
 After identifying the best type of equation, we repeated the minimization process 100 times, following a bootstrap approach every time a random number of sources (between 1 and 25, to avoid being left with too few sources) is randomly removed from the sample. In this way, we could constrain the confidence interval for the above best fit parameters. We find $A = -1.92 [-2.51, -1.71]$, $B = 0.48 [0.38, 0.69]$, $C = -0.96 [-1.20, -0.62]$, $D = -0.41 [-0.58, -0.31]$, where the values between the parentheses are in the 95th percentile distribution.

Testing the relation on the residuals, we find that it tends to slightly overestimates the $f_{esc}$ at very low values (much lower than 0.01), while it tends to underestimate the $f_{esc}$ at values that are higher than $\sim$0.1-0.2. This is due to the fact that in the sample used to fit the relation, there are very few galaxies with high $f_{esc}$ values and, in general, their measured $f_{esc}$ values have higher errors.

We finally applied the above relation to our sample of high-redshift galaxies: out of 29 sources, 3 galaxies do not have the $r_e$ measurement since they are outside the UNCOVER footprint; for another 2, we do not have an estimate for the $O32$ parameter. We therefore could apply the best-fitting relation only to 24 sources. In Fig. \ref{fig:fesc_re}, we show the predicted $f_{esc}$ for our sources as a function of $r_e$, as well as the low-redshift comparison sample (for which the $f_{esc}$ are measured values). Most of our galaxies have predicted $f_{esc}$ values larger than 0.05, meaning that they would be considered leakers. The average $f_{esc}$ is $\simeq 0.12$ with the bluest and most compact sources having $f_{esc}$ as large as $0.2-0.4$, which could be lower limits for the reasons discussed above.

\begin{figure}[ht!]
\includegraphics[width=\linewidth]{images/fesc_re.pdf}
\caption{Predicted $f_{esc}$ vs. size $r_e$ for our sample (blue and black symbols) and measured $f_{esc}$ vs. size $r_e$ from the literature. Symbols are as in Fig. \ref{fig:O32_Hbeta}.
\label{fig:fesc_re}}
\end{figure}

Clearly, the main limitations of the above analysis are the fact that the low-z sample used to calibrate the relation is small and, most importantly, it is not evenly populated as it contains mostly objects with rather low $f_{esc}$.
Also, it would be important to test these predictions at intermediate redshift ($z \sim 3-4$), that is, much closer to the EoR, where it is possible to both directly detect LyC emission and determine all other physical and spectroscopic properties.
However, at the moment, measurements of  $f_{esc}$ at intermediate redshift are still sparse and most samples lack near-infrared (NIR) spectroscopic follow-up results.
In spite of these limitations, a consistent picture emerges from our results, suggesting low-mass galaxies at $z\sim5-7$ have mostly properties which indicate moderate values of $f_{esc}$. Interestingly, the average $f_{esc}$ value inferred for our sample is equal to the one predicted by \cite{Naidu2020} for galaxies in the mass range $\log_{10}M_\star = 8-9$ at $z \sim 6$, according to their simple model, where $f_{esc}$ scales with $\Sigma_{SFR}$, which was constrained to reproduce the average observed values for the \cite{Steidel2018} sample at $z=3$.

\section{Summary and conclusions}\label{sec:results}

Thanks to the magnification power of the Abell 2744 cluster, in this paper, we present the first \textit{JWST}/\textit{NIRSpec}\ observations of 29 gravitationally lensed galaxies with photometric or spectroscopic redshift in the range $4.5 \leq z \leq 8$. From a combined \textit{NIRSpec}\ and \textit{NIRCam}\ analysis, we were able to derive accurate physical properties of the galaxies, including $M_{\star}$, SFR, $r_e$, UV-$\beta$ slopes, and measurements of the most prominent optical emission lines ([\textrm{O}\textsc{ii}], [\textrm{O}\textsc{iii}], \ifmmode {\rm H}\beta \else H$\beta$\fi, \ifmmode {\rm H}\alpha \else H$\alpha$\fi). We summarize our findings as follows:

\begin{itemize}

\item Our sample is composed of purely star-forming galaxies, as inferred from the MEx diagram that excludes the presence of any AGN.
\item The galaxies in our sample have blue UV slopes (median $\beta$ = -2.08) and are mostly very compact with $r_e \simeq 0.2-0.5$ kpc. These properties are consistent with those of the general population of LBGs at similar redshift and with similarly faint $M_{UV}$ \citep{Bouwens2014,Shibuya2015}.
 \item Compared to the low-z sample by \cite{Flury2022} as well as to the low-z LCEs from previous studies, our galaxies present properties (in terms of $O32$, $EW_0(\ifmmode {\rm H}\beta \else H$\beta$\fi)$, UV-$\beta$ slopes, $r_e$, and $\Sigma_{SFR}$) that are entirely consistent with those of low-z galaxies with measured $f_{esc}$ larger than 0.05 and which are considered to be LyC leakers.

\item Using a linear analysis that employs the minimization of MSE, we found a best fitting relation between $f_{esc}$ and the three most correlated and independent parameters ($O32$, UV-$\beta$, and $r_e$) for the low-redshift sample of 88 galaxies. Applying this relation to the 24 galaxies from our sample where these parameters are all measured, we find that 20/24 have predicted escape fractions larger than 0.05, that is, they would be considered leakers and the average $f_{esc}$ of our sample is 0.12.
\end{itemize}

In conclusion, our results show that indeed the average low-mass galaxies around the epoch of reionization have physical and spectroscopic properties consistent with moderate values of escaping ionizing photons ($f_{esc}= 0.1-0.2$).
With upcoming \textit{JWST}\ observations from GTO and GO programs, this analysis could be easily extended to larger samples of galaxies with higher masses and/or at higher redshift to determine if the bulk of the reionizing photons have been provided by even more massive and brighter galaxies \citep[as predicted, e.g., by][]{Sharma2016,Naidu2020} or if we need a more substantial contribution by the fainter and more numerous galaxies with $M_{UV} > -18,$ as predicted by most other popular models \citep[e.g.,][]{Trebitsch2022,Finkelstein2019, Atek2015}.

\begin{acknowledgements}

Support for program JWST-ERS-1324 was provided by NASA through a grant from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-03127.

This work is based on observations made with the NASA/ESA/CSA James Webb Space Telescope. The data were obtained from the Mikulski Archive for Space Telescopes at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-03127 for JWST. These observations are associated with programs GLASS-JWST \#1324, JWST DDT \#2756 and GO UNCOVER \#2561.

SM thanks the Department of Physics and Astronomy at the University of California, Los Angeles, for a productive and satisfying visit in which the majority of the work presented in this paper was done.

We acknowledge support from the INAF Large Grant 2022 "Extragalactic Surveys with JWST" (PI Pentericci).

This research is supported in part by the Australian Research Council Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), through project number CE170100013.

LY acknowledges support by JSPS KAKENHI Grant Number JP 21F21325. RAW acknowledges support from NASA JWST Interdisciplinary Scientist grants NAG5-12460, NNX14AN10G and 80NSSC18K0200 from GSFC.

MB acknowledges support from the Slovenian national research agency ARRS through grant N1-0238.

CM acknowledges support by the VILLUM FONDEN under grant 37459. The Cosmic Dawn Center (DAWN) is funded by the Danish National Research Foundation under grant DNRF140.
KG and TN acknowledge support from Australian Research Council Laureate Fellowship FL180100060.
\end{acknowledgements}

\bibliographystyle{aa}

redpajama_set_name: RedPajamaArXiv


Facing this annoying issue (YouTube Black Screen) on your computer while watching your favorite TV show, movies, song, or funny cat video?
Here are the reasons why are you facing this problem and the solutions for it.
1. Browsing YouTube on a weak Internet connection.
3. If you're using YouTube on browser then the browser's Cache and Settings may cause clogging up and YouTube black screen.
4. The video you're playing may have sensitive content.
If the black screen issue is from your end, then that can be usually solved by restarting your computer, restarting internet hardware device, upgrading your browser, disabling ad blocker, and other similar solutions. If the problem is with the video or YouTube or from your internet service provider, then the issue can't be fixed.
Use a better net connection: Bad or slow internet connection may prevent your video from playing smoothly. Poor internet causes the video to not load properly. This will result in clogging of video, and you'll see a black screen or hear audio without video.
• Check your internet network and connection, it should work well.
• Reload the YouTube page again.
• Close and reopen YouTube.
• Remove the older Adobe Flash Player version and install a newer version.
• Turn off hardware acceleration from the video.
Clear Cache from your Web Browser: If you see black screen suddenly while playing a video, then the problem may be because of browser's cache.
Adjust settings of your browser: if you're using YouTube on Chrome or Firefox and facing black screen issue, then the problem may be with your browser settings. Disable hardware acceleration feature to fix the issue then close and open the browser again.
Check the Content you're playing: if all the videos are playing smoothly while the problem occurs on some specific content then maybe you're playing the content against privacy and policies of YouTube. There is no practical solution to solve this issue, if you want to view the same content then try to use another website. These are the most common and effective solution that will surely fix the Black Screen error. Still, you're suffering from the problem, don't be disappointed because there will be various reasons for the error. Use another web browser, log out from your YouTube account, or disable extensions.
This entry was posted in News and tagged mcafee.com/activate, www.mcafee.com/activate, YouTube Black Screen. Bookmark the permalink.
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This fantastic new book from bestselling author Debbie Shore contains 24 projects: 12 bags and 12 matching purses. Choose from flowery patchwork totes, backpacks with faux leather detailing, clasp-top clutches, cute floral messenger bags, practical folder holders and a stylish business travel bag, all complete with a matching purse. Each purse is made in the same style and from the same fabric as its corresponding bag - mix and match the bags and purses or make yourself the pair.
Each item requires no more than half a yard of outer fabric, plus all the necessary hardware, trimmings and lining. All the instructions you need are provided in Debbie's clear, friendly style, along with inspiring, easy-to-follow photography, and any templates required are included at full size. There are also QR-coded video links, providing additional support and advice from Debbie.


Posted by Wendy Morton on Wednesday, January 23rd, 2019 at 10:46am.
The Sandestin Hotel is being constructed by Batson-Cook, a company that builds a wide range of commercial projects for multi-family residential, office and private development clients throughout the Southeast. Internationally recognized design firm, Cooper Carry, which specializes in the design of hospitality, residential and restaurant projects, is the architect for the hotel project.
"The hotel's architectural character blends seamlessly with the Grand and Baytowne developments while announcing a new level of quality," stated Pope Bullock, AIA, principal and vice president of Cooper Carry.
Highgate, a premier real estate investment and hospitality management company, has been selected to manage the newly developed hotel. Additionally, celebrity Chef Hugh Acheson will partner to develop the hotel's culinary offerings, including a 3-meal restaurant, a signature rooftop pool bar and in-room dining.
In addition to the food and beverage outlets, the full-service hotel will feature a luxurious spa and a fitness center appealing to both, leisure and business guests. The Sandestin Hotel will include 20,000+ square feet of meeting space including a 13,000-square foot ballroom, contiguous to the 30,000+ square feet of existing meeting space at Baytowne Conference Center. Additionally, guests of the hotel will have access to the many amenities offered by Sandestin Golf and Beach Resort including more than seven miles of beaches and bayfront, four championship golf courses, 15 world-class tennis courts and a 113-slip marina.
About Sandestin Golf and Beach Resort: Sandestin Golf and Beach Resort, named the #1 Resort on Florida's Emerald Coast, offers 65,000 square feet of function space from the gulf to the bay. The resort's 32,000-square-foot Baytowne Conference Center includes the largest ballroom on Northwest Florida's Gulf Coast with 13,500-square-feet. The newly renovated 15,000 square-foot Linkside Conference Center includes a 12,600-square-foot exhibit hall, two bayside conference rooms and four boardrooms. In 2018, Sandestin broke ground on the Sandestin Hotel, a 250-room full-service hotel and conference center located adjacent to the Baytowne Conference Center featuring 20,000+ square feet of meeting space and a 13,000-square foot ballroom. Additionally, Osprey Pointe at Sandestin has begun construction and will be the newest development of luxury property in Sandestin Golf and Beach Resort.
All venues are supported by Sandestin's on-site team of award-winning professional sales, conference services and culinary staff experts. As a member of Visit South Walton and Visit Florida, the resort features more than seven miles of beaches and pristine bayfront, four championship golf courses, 15 world-class tennis courts, 19 swimming pools, a 113-slip marina, a fitness center and spa, meeting space and The Village of Baytowne Wharf, a charming pedestrian village with events, shopping, dining and nightlife. For more information: Sandestin.com/Progress-Development.
About Batson-Cook Construction, Batson-Cook Construction, founded in 1915, builds a wide range of commercial projects for healthcare, multi-family, industrial, and private development clients throughout the Southeast. We have the heart of a family-owned general contractor with the reach of a global construction firm. We build with passion. We operate with integrity.


This holiday season WQAD News 8 and participating sponsors are bringing viewers 12 Days of Christmas. Find gift ideas for your loved ones and register to win a prize from each day's sponsor!
Friday, December 14th we featured Revell Jewelers in Bettendorf. You have until 11:59 a.m. on Saturday, December 15th to register to win a gold and silver necklace and earring set.


I was among strong women who endured suffering. They went on living and caring for those around them "while they grieved. They were aware of their need for help in the grieving process and had the courage to seek it. I listened to a woman openly cry while telling the story of her husband who died of a heart attack in her arms. I thought of how strong she was to recognize her need to grieve. She wanted to be healed. Another woman described how her husband of 54 years died unexpectedly this summer. A woman sitting next to me, Chris, showed me her ring finger with a tattoo of her deceased husband's name, Nick, on it. Even though a tattoo isn't something I would personally do, I empathized with her heartbreak. Terry, who sat two seats over to my right, still mourned the loss of her dad after four years. Her sadness was etched all over her face. Her loss, like mine, resided in the deep, dark places of her soul. Each woman spoke with honesty, searching for comfort amongst their deep losses. At times, they spoke of the physical suffering they were experiencing.
"At times it feels like I can't breathe my heart hurts so much," a woman named Janet shared.
For each of us, our suffering and pain manifested itself in similar and different ways. In the end, it led to the same place of grief. We hurt. We ached. We wondered if we would ever be happy.


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Animi-3 is a prescription vitamin supplement which includes vitamin B12, folic acid, vitamin B6, and omega-3 fatty acids. This product is used to help women maintain nutrient health during pregnancy or for patients who have a poor diet or certain illnesses. This and other drugs should be used under the direction of a doctor with a complete and current list of medications and medical history, including allergies. Patients who have had an allergic reaction to fish, soy, or inactive ingredients commonly found in medications may have a reaction to animi-3. Before using this product, tell your doctor if you have a personal medical history of certain blood disorders including anemias. At onset of treatment, this product can cause nausea, diarrhea, and flushing. Notify your doctor if these effects worsen or persist. Read all warnings from your pharmacist and doctor. Serious side effects should be reported to your doctor immediately, and include easy bruising or bleeding. Do not start, stop, or change the dosage of this drug without consulting your doctor. It's important to follow manufacturer, pharmacy, and doctor's instructions when using this and other medical products.
General Animi-3 Warning: The above information is for informational purposes only and is not meant to be a substitute for professional medical advice, diagnosis or treatment. Please seek professional medical advice before starting, changing or terminating any medical treatment. Pharmaquotes is not offering medical advice, pharmaceutical recommendations or endorsing any specific prescription drug, pharmacy or other information on the site. Pharmaquotes provides no warranty or guarantee for any of the discount data, medication, or other information.


text:
Cardi B Offers To Cover Funeral Costs For Victims Of Deadly Bronx Apartment Fire: 'I'm Extremely Proud To Be From The Bronx'
Derek J Involved in Hairstyle Debacle, Gunshots Fired
star Derek J was involved in a hair-raising argument this past Wednesday (March 14). According to police officials, Neffe (Keyshia Cole's sister) sought out Derek J's services at his <a href="https://www.vibe.com/t/atlanta/" id="auto-tag_atlanta_2"…
By Niki McGloster
Niki McGloster
More Stories by Niki
'WAGS' Stars Autumn Ajirotutu And Sasha Gates Talk Dating Hierarchy And Flipping Reality TV Fame Into Fortune
Vixen Chat: Taraji P. Henson Talks New Jergens Shea Butter Collection, Beauty Secrets and 'Poo-Pourri'
Serena Williams on Steubenville Rape Case: 'She Shouldn't Have Put Herself in That Position'
star Derek J was involved in a hair-raising argument this past Wednesday (March 14).
According to police officials, Neffe (Keyshia Cole's sister) sought out Derek J's services at his Atlanta salon when a previous stylist failed to do her hair any justice.
"Her (hair was) messed up to the point we didn't know what to do. So I was just like, reach out to the stylist and say 'Hey, what did you use, what did you do?" and it turned from a professional conversation to more of an argument but we thought it was done," Derek J recalls.
Once the first stylist heard the news that Derek was now fixing the hair fail, he made his way to the salon–gun included.
The salon owner, Lisa McCall says, "I asked [the stylist] to leave. Before turning away, he waved the gun in my face and said, 'You don't think I will?' And I backed up."
After letting off one shot into the floor, the crazed hairstylist fled and has since been seen. No one was harmed during the incident.
Hair is a very serious matter in the south's Peach State, but we didn't think gun play was necessary for solving hair-related issues!
Derek J

redpajama_set_name: RedPajamaCommonCrawl


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Customers face losing thousands of pounds after licence suspension closes Wembley restaurant
Hannah Mcgrath
Alisan restaurant owner Akbar Lakhani has apologised to angry customers - Credit: Archant
Customers who have booked events at a restaurant in Wembley could face a financial nightmare following the suspension of its licence.
Last week the Times revealed Alisan in Engineer's Way, closed their doors after Brent Council revoked their licence following a series of violent crimes on its premises including an attempted murder.
A decision on whether to strip it of its licence permanently will be made on April 27.
However, a number of customers including Vasile, who declined to give his surname, have contacted the Times to say they have been left stranded and out of pocket by its sudden closure.
Vasile said he has paid a £1,000 deposit to reserve the venue for his two-month-old daughter's christening party on April 25 and has been unable to contact the venue's owner in the last week.
He said: "I tried to speak with the manager, I've emailed and called but I haven't spoken to anyone. I have only one week to go and just really want my money back so I can book another place.
"There are a lot of people who are looking to speak to him."
The restaurant's sudden closure has also had an effect on Vasile's 80 relatives who have booked flights from Romania to attend the event.
So far the Times has learned that 10 events due to take place since March 30 have been cancelled without notice, and many more clients who put down deposits for more than 20 functions have voiced frustration at not being able to speak to the restaurant's management despite repeated calls, texts and emails.
The frustrated customers face losing up to £6,000 each on cancellation fees for DJ's, food and entertainment for wedding and birthday parties.
One customer, Ionut Brumia, 25, booked the venue for his wedding celebrations on July 11 with a £1,500 deposit and has been struggling to find an alternative venue to accommodate his one hundred guests.
Mr Brumia said: "I don't know what to do, I have everything booked, the music which costs £1000, special Romanian food, everything.We have invited a lot of people and it panics me."
Mr Brumia, a father of one, said he and his family were concerned about the safety of the venue following a string of violent incidents on the premises in the past month.
"I don't think it's a safe place any more, but what can I do? He says I will get my money back but I don't believe him. He should pick up the phone."
Businessman Akbar Lakhani, the venue's owner, blamed the closure on a dispute with his landlord and said he would try and help customers find a new location.
He added: "I am truly, truly, truly sorry.
It's been a really difficult time and very traumatic. I'm going to face this head on and ensure nobody suffers as a result. I will try to relocate events where possible.
"I am currently in discussion with my lawyers and I am hoping that I can repay all of the deposits but I can't guarantee anything at the moment. I will now contact as many people as I can directly and I really don't want anybody to be left out of pocket."


The Open Golf Club Trophy Edition 2019 organized by Premium Belgium Golf Courses will begin the forthcoming 20th of April.
The final will be held on the 13th and 14th October 2018 at Le Touquet Golf Course in France.
We offer 7 qualification opportunities for the final: a unique occasion to discover the most beautiful golf courses of Premium Belgium Golf Courses (PBGC)!
We want to thank our partners who will accompany us during the Trophy: Footjoy, Callaway, Tripel Karmeliet, Europ Assistance, Golf in Alsace, Golf At Home.


I pride myself of having introduced my family in Mexico to Quinoa as a Kosher for Passover food. The only way to top it would be to bring more innovative unleavened goods.
So I bought a case (not a can, but a full case) of Matzolah, Kosherfest's award for Best New Passover Product of 2012. It tastes really good, like granola, but without the pesky side effects of being good for you or helping your stomach digest food. We'll see what the reaction is.
Doesn't that look delicious? The challot look pretty good too.
I recently came back from a two week trip to Israel. People are asking me what I did over there. In one word: eat.
I even made a list of the things I wanted to eat, and got to all of them except for one. Highlights of what I ate in pictorial form follow. It's long so read more to see all. No explanation of what each thing is, so feel free to use Google.
For those who don't care about what I eat and instead want to see what I do, you can also check the trip album in The MKX® Photo Central at no additional cost.
Only once in the two weeks I was there I was able to eat schwarma, and only a few hours before flying.
I don't think I've mentioned this to anyone but I feel compelled to mention Trader Joe's, a local supermarket chain. They have a store across the street from the office and they sell very good, very cheap food. It's become my go-to place for quick, cheap, healthy meals.
For example, today I had a gigantic salad and some Indian food for a little over $5. And most of these things do not include chemical ingredients I cannot pronounce. This is perhaps the only thing so far that I've found to be cheaper than the Texan equivalent.
This one is a few weeks late, but I want to ensure readers that if you feed me something I like, you will get a mention.
Erika made machacado. Best machacado I've had in a while. Thank you Erika!


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Europejski challenge juniorów w curlingu – zawody curlingowe rozgrywane w latach 2005–2015. Stanowiły europejskie eliminacje do mistrzostw świata juniorów. Brały w nich udział te reprezentacje, które nie miały jeszcze zapewnionego miejsca w MŚJ. Challenge rozgrywany był w styczniu, 11 turniejów odbyło się w trzech miejscach: Tårnby, Pradze i Lohji. Od 2016 zostaną zastąpione, wraz z mistrzostwami Azji i strefy Pacyfiku, mistrzostwami świata juniorów grupy B.

Jeśli mistrzostwa świata rozgrywane były w Ameryce, awans uzyskiwały dwie czołowe drużyny. W przeciwnym wypadku prawo uczestnictwa w MŚ otrzymywał tylko zwycięzca challenge'u.

Najwyższym miejscem zajętym przez reprezentację Polski w challenge'u jest drugie. Drużyna Kamila Wachulaka przegrała finał challenge'u 2008 z Czechami i nie uzyskała awansu do mistrzostw świata.

Wyniki

Kobiety

Mężczyźni

redpajama_set_name: RedPajamaWikipedia


I am free to run. I am free to dance. I am free to live for You. Yes I am free.
Lately, God has been speaking a lot to me about freedom in Christ. You see by nature I am a "rule follower".
Some of us in particular really respond to rules and grades and times ect when they affirm us. We want to be affirmed because we are "worthy" of affirmation. God wants us to find affirmation in what He's done for us through Jesus as opposed to the "good" we've done.
One thing I often struggle finding freedom in is pleasure. Satan takes a little truth, like "we are not here for ourselves" and turns it into "therefore you can not enjoy anything for yourself". That is simply not true. God created pleasure and within the context of honoring him he wants us to enjoy life. This doesn't mean he wants us to enjoy the pleasures of sin, absolutely not. But he has created many things specifically for our pleasure. I won't get to deep into all that though, let me get to my point.
I enjoy running. I enjoy the time outside, the activity, the many moments I have with God or with a running buddy, the times I worship through music while I run, or the times that its just wonderful being by myself. Running is not only fun to me, its also a healthy outlet for me. Its also quite a metaphor to my Faith. Sometimes I do get sucked into the "performance" of running, and there are other moments that I feel guilty about enjoying it. I know that sounds silly and maybe even foreign to some. Guilt does not come from God though. Neither does performance based Faith. God recently used running as a tool to teach me more about freedom.
I was going into this race with a fresh attitude and a bit of experience. It's pretty typical of me to be an over achieving perfectionist and God is working in me to break free from that.
On Sunday January 12, 2014 I was running in the Disney Marathon.
You always have goals with races. My problem is I tend to bind myself to them allowing little room for adjustments if necessary. You commit, you plan, you train. Of course I tried to stick to my plan but I also cant allow my plan to rule life. This is all part of the freedom exercise. It can be a struggle for me to balance! 🙂 My training really got tossed to the side amidst the move and holidays and not to freak anyone out but I tested positive for strep the Tuesday before race day. I had the "go" from my doctor, don't worry. As with life, so with running. Training is good and planning is good. But you never know what is going to happen so when the curve ball comes you do your best to glorify God with where you are at.
Running for me is: to enjoy the abilities God has given me. He created me, he enables me to run, and he is pleased when I can run freely, unconcerned about expectations or affirmations, just embracing this gift that comes from Him and being content with His pleasure alone.
Letting go of my expectations was what made this race so incredible.
Disney blew me away with the phenomenal job they did organizing this event. I wish I could write the event planners, volunteers and every person who cheered thank you notes! They were awesome! There was elaborate sets with Disney characters all through out the race. Runners were stopping and getting pictures taken and riding rides even! We saw behind the scenes and went through the parks and resorts. It was so entertaining and exciting!
In some areas I did feel more prepared this time just having a general idea of "what to expect". It was fun having Mike, Jason's brother, around. This would be his first marathon. He was game for anything! Like getting up race day at 3am and going to Waffle House for breakfast.
The All Star breakfast, totally living up to its name! Oh meanwhile these guys photo bombing, they were just finishing up from the club. They were quite the crack ups!
We definitely were carbed up and I felt great through out the run in terms of nutrition.
We did have our moment of panic when, I kid you not, we got lost trying to get to Epcot. Don't ask me how this happened. We gave ourselves 70 minutes to get there. Our hotel was only 5 miles away. Somehow we made it to Animal Kingdom twice though haha! We literally parked and ran up to the check in just in time. It was not funny at that moment but I am sure we will laugh about it for years to come.
My mom always reminds me of this quote.
I really was focusing on Him. The thought that I bring him pleasure even when I am running, that thought was very freeing. With 1.2 to go I was listening to The Great I Am.
Because of you God, the Great I Am, I am free to run. I am free to live for you. I am free.
I got to the final stretch and unplug to see if I spot my family. There are so many people and they are all smiling and cheering! I hear Jason and my mommy in law and Jessica all screaming "KATIEEE!!!" And my girls with their homemade signs. I was so excited! I picked up my legs as much as I could and crossed the finish line smiling this time!
I finished hard and strong with my hands raised truly in awe over the One who brought me there. Because my strength, both physical and mental, is from Him.
Any runner will tell you that running is very freeing. A lot has happened over the last year and I think it's really beautiful that right now what God is speaking to me about is freedom.
I can't end this blog with out congratulating Mike on doing so well in his first marathon. Super proud of you brother!
I also have to put it out there that I am so totally grateful for my husband Jason. He encouraged me to run another, he signed me up for probably one of the best, most expensive races, (which y'all know that says A LOT about how much Mr. Frugal loves me hehehe 😉 $$$) and than he supported me through 18 weeks of training, watching 4 kids while I ran, running a business, moving, and everything else life brings. And he did it mostly with a fantastic attitude. 😉 I can't thank him enough. I feel loved and cherished by his sacrifice. God is working on both of us about letting go! Jason, you're not just "the" man, you are my man!


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Beating breast cancer with Artificial Intelligence
|BACK TO NEWS
BreastScreen Victoria is part of a ground-breaking Australian study using Artificial Intelligence (AI) to help improve and transform breast screening, set to benefit thousands of Australians.
The $2.26 million project aims to transform breast cancer screening in a way that improves detection, lowers harm, reduces cost, and causes less stress for those undergoing a mammogram.
Led by St Vincent's Hospital Melbourne and St Vincent's Institute of Medical Research, and supported by BreastScreen Victoria, the project is funded by the Commonwealth Government's Medical Research Future Fund.
A key component of the project is a series of studies where researchers will use an artificial intelligence algorithm they have trained to detect breast cancer in mammographic images.
The algorithm will be tested alongside scans that are done each day at St Vincent's Hospital Melbourne, home to Victoria's largest BreastScreen clinic.
Project lead, Dr Helen Frazer, Clinical Director at St Vincent's Hospital Melbourne's BreastScreen, says the project has a unique opportunity to play a leading role in Australia's battle against breast cancer.
"Breast cancer is the most common cancer affecting Australian women," says Dr Frazer.
"While screening is very effective in reducing deaths, reading mammograms is challenging. More women are recalled to assessment after a mammogram than those who end up with an eventual cancer diagnosis.
"By using AI screening models alongside our existing practices, we hope to transform Australia's breast screening program and help reduce the number of lives lost to breast cancer."
Computational biologist Dr Davis McCarthy from St Vincent's Institute of Medical Research says breast screen data is ideal for AI development.
"Working with BreastScreen Victoria allows us to draw on 20 years of high-quality data to inform our algorithm," says Dr McCarthy.
"Importantly, our algorithm is designed in an Australian setting – training with machines and images that are relevant to Australian women."
Dr Frazer says the project has the potential to not only tailor the program to meet each woman's individual needs, but also enhance the experience for women.
"A woman who has a mammogram today would expect to get her result of an all clear in about two weeks' time. With AI, this result could be instantaneous.
"By using AI we are confident we'll be able to deliver more accurate results more quickly, reducing the stressful time spent waiting for the result," says Dr Frazer.
The three-year research project also involves partners The University of Melbourne and The University of Adelaide.


POSCA PC-8K 8mm Paint Marker. New multipacks – See bottom of dropdown box. Broad 8mm tip Posca Paint Marker, each Posca Paint Marker pen contains non-toxic water based paint. Available in a full range of 33 colours – As a Premier Posca stockist we always stock the latest colours and have the full range available. Posca paint markers can be used on metal, wood, glass, plastic, plaster, canvas, fabric, pebbles, stones, rocks and much much more! Posca paint markers are non permanent and removable from non-porous, sealed surfaces like glass, plastic, acrylic, car bodywork, non-porous chalkboards with soapy water but for even better removal use easichalk Ultimate chalkboard cleaner. The opaque, water-based acrylic paint is non-toxic and acid-free, odourless, light-fast, Xylene-free, lead-free and waterproof when dry. Used by Professional and Amateur Artists all over the World these markers are also easy enough to be used by the most inexperienced beginner. Colours included in Packs. Mono Tones 4 Pack: White, Black, Gold and Silver. Fluorescent 4 Pack: Fluorescent Yellow, Fluorescent Red, Fluorescent Orange and Fluorescent Pink. Metallic 8 Pack: Gold, Silver, Bronze, Metallic Blue, Metallic Red, Metallic Green, Metallic Pink and Metallic Violet. 8 Piece Pack: Black, White, Red, Blue, Green, Yellow, Pink and Violet. Collection Box: All 33 current colours. The item "Posca Paint Marker PC-8K 8mm Pen Fabric Metal Glass Broad Nib 34 Colours" is in sale since Sunday, November 13, 2016. This item is in the category "Crafts\Art Supplies\Drawing & Lettering Supplies\Art Pens & Markers". The seller is "easichalk" and is located in Evesham. This item can be shipped worldwide.


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UEFA Distributes €754.1m To Participating Clubs
UEFA has announced that a total of €754.1m was distributed to clubs participating in the Champions League last season and that Barcelona and Manchester United received the largest amounts.
The €754.1m prize money allotted to the 32 teams who figured from the group stage onwards consisted of €413m in fixed amounts plus €341,100,000 from the market pool.
To put that number in perspective, UEFA announced that the 56 teams that participated in the Europa League last season received more than €150m in prize money. So playing in the Europa League is worth on average €3m, while playing in the Champions League is worth on average €23.5m.That is a huge difference.
All the Champions League clubs were entitled to a minimum €7.2m in accordance with the distribution system, which awarded a basic participation bonus of €3.9m, plus €3.3m from the six €550,000 match bonuses given per group game.
Additionally, performance bonuses were paid in the group stage: sides received €800,000 for every win and €400,000 for every draw. The 16 clubs that reached the round of 16 were each assigned an additional €3m, the eight quarter-finalists an extra €3.3m, and the four semi-finalists – including Real Madrid and Schalke – a bonus of €4.2m.
United's €53.197m was actually higher than what Barcelona received because the value of the national TV market in England is higher than in Spain. The United payment was comprised of more than €27m for their performances from the UEFA Champions League group stage onwards, and another €25.9m from the television market pool.
Barcelona' earned a total of €51.025m. The Spanish club's performance-related payments amounted to €30.7m and they also collected €20.3m from the TV market pool.
Barça netted €9m for winning the trophy, while United earned €5.6m as runners-up. The other major earners from the 2010/11 UEFA Champions League were Chelsea FC (€44,523,000), FC Schalke 04 (€39,750,000), Real Madrid CF (€39,288,000), FC Internazionale Milano (€37,982,000), FC Bayern München (€32,562,000) and Tottenham Hotspur FC (€31,133,000).