text:
\section{Introduction}
\hspace{12pt}In the last decade tens of quasars at $z \sim 6$ have been discovered through various different surveys, starting from the seminal work by Fan et al. (2001a, 2001b, 2001c, 2003, 2006a, 2006b), and then continued by Willott and collaborators (2005a, 2005b, 2009, 2010a, 2010b). Nowadays, new surveys as VIKING and PanSTARRS are discovering even more distant quasars (Venemans et al. 2013; Ba$\tilde{\text{n}}$ados et al. 2014). Follow-up observations of emission lines such as the MgII line have shown that these high-redshift quasars (with luminosities well in excess of $10^{47}$ erg $\text{s}^{-1}$) are powered by super-massive black holes (SMBHs) rapidly grown up to a mass $M_{\bullet} \sim (0.02-1.1)\times10^{10} M_{\odot}$ (Barth et al. 2003; Priddey et al. 2003; Willott et al. 2003; Willott et al. 2005a; Jiang et al. 2007; Wang et al. 2010; Mortlock 2011; Wu et al. 2015) in less than a billion years, depending on a still uncertain initial black hole seed (Haiman 2004; Shapiro 2005; Volonteri $\&$ Rees 2006; Tanaka $\&$ Haiman 2009; Treister 2013; Lupi et al. 2014; Tanaka 2014).

This evidence raises several problems about the formation process and growth of these compact objects (Rees 1978; Volonteri 2010; Latif et al. 2013). Several mechanisms are thought to produce SMBH ancestors, such as the collapse of the first generation of stars (PopIII stars) (Tegmark et al. 1997; Madau $\&$ Rees 2001; Palla et al. 2002; Shapiro 2005), gas dynamical instabilities (Haehnelt $\&$ Rees 1993; Loeb $\&$ Rasio 1994; Eisenstein $\&$ Loeb 1995; Bromm $\&$ Loeb 2003; Koushiappas et al. 2004; Begelman et al. 2006; Lodato $\&$ Natarajan 2006), stellar dynamical processes (Begelman $\&$ Rees 1978; Ebisuzaki et al. 2001; Miller $\&$ Hamilton 2002; Portegies Zwart $\&$ McMillan 2002; Portegies Zwart et al. 2004; G$\ddot{\text{u}}$rkan et al. 2004, 2006; Freitag et al. 2006a, 2006b) and even direct collapse from the gas phase (Haehnelt $\&$ Rees 1993; Begelman et al. 2006; Petri et al. 2012; Yue et al. 2013; Ferrara et al. 2014; Yue et al. 2014; Pallottini et al. 2015).

However, the processes responsible for the growth of initial black holes are still uncertain, also because the ancestors of SMBHs, namely sources with black hole masses of $10^{6-8} M_{\odot}$ at $z>7$, have never been detected so far in spite of the enormous progresses produced by deep X-ray and IR surveys. One possibility hinted by several studies (Yue et al. 2013), including the most recent one by Comastri et al. (2015), envisages that, before the quasar mode is on, accreting black holes are enshrouded by a thick cocoon of gas (and dust) heavily absorbing their optical/X-ray radiation. These sources would then escape detection by the standard X-ray surveys.

The transparency of gas and dust to radio, millimetre and submillimetre photons makes these kind of observations a promising tool for detecting obscured star formation, quasars in general, and, in particular, super massive black holes progenitors at very early epochs (e.g. Spaans \& Meijerink 2008; Gallerani et al. 2012; Gallerani et al. 2014). Here, we investigate the possibility to detect high-redshift ($z > 7$) quasars that might be completely obscured at optical to X-ray wavelengths by means of hydrogen Radio Recombination Lines (RRLs; for a comprehensive review, see Gordon \& Sorochenko 2002). In fact, one advantage of RRLs is that they are nearly always in the optically thin limit and therefore see all the gas. The other advantage of using hydrogen RRLs concerns with the fact that this method could work equally well for gas of primordial composition, as it relies only on the presence of hydrogen rather than lines from heavy elements.

Hydrogen RRLs represent a special class of spectral lines arising in HII regions from transitions between highly excited hydrogen levels (quantum numbers $n>27$) and appearing in the radio regime (rest frame frequencies $\nu_e<300$ GHz); H$n\alpha$ lines are the strongest hydrogen RRLs, i.e. those due to $n+1 \rightarrow n$ transitions. Also note that RRLs have the significant advantage that the principal quantum number of a line detectable at a fixed observed frequency decreases with increasing redshift. Given that the RRL flux density is proportional to $(1+z)(d_L(z))^{-2}n^{-2.72}$ (Rule et al. 2013, hereafter R13), this effect partially compensates the increase of the luminosity distance $d_L$ with redshift.

The search for RRLs from obscured quasars will become feasible in the near future with the SKA (Square Kilometre Array) telescope, thanks to its revolutionary capabilities in terms of frequency range, angular resolution and sensitivity (for SKA science and technical specifications, see: Morganti et al. 2014; SKA-‐SCI-‐LVL-‐001, 2015\footnote{http://astronomers.skatelescope.org/wp-content/uploads/2015/08/SKA-SCI-LVL-001W.pdf
}). In particular, the SKA-MID (0.35--14 GHz) frequency coverage will allow us to search for H$n\alpha$ ($35 < n < 210$) lines from sources at $1 < z < 10$. For all these reasons, in principle, the detectability of high-$z$ obscured quasars through RRLs could allow us to directly monitor the birth and growth of the earliest quasars during the first cosmic billion years.

The paper is organized as follows. In Sec. 2, we derive the RRL flux density expected from quasars, including secondary ionizations from X-ray photons. In Sec. 3, we test our model against available RRL observations. In Sec. 4, we analyse the contribution of the stimulated emission due to a nonthermal background source to the quasar RRL flux. In Sec. 5, we discuss the prospects for detecting obscured quasars through the SKA. In Sec. 6 we discuss the main conclusions of our work.

\begin{figure
\centering
\hspace{-0.8cm}
\includegraphics[width=0.5\textwidth]{nuobs_zSKAMID.eps}
\caption{Hydrogen RRL observed frequencies (in GHz) as a function of redshift. Blue curves correspond to quantum numbers from $n=34$ to $n=54$, and red lines correspond to $n=35$, $n=45$, $n=55$, $n=100$ and $n=150$. The lines with $n=56$ to $149$ are not shown for the sake of clarity. The grey region shows the frequency range covered by SKA-MID (0.35--14 GHz).}
\label{nuobs_z}
\end{figure}

\section{RRL\lowercase{s} from quasars}
\hspace{12pt}The observed frequencies of H$n\alpha$ lines are given by the following equation:
\begin{equation}
\nu_{\text{obs}}(z_e,n)=\frac{c\hspace{0.05cm}\text{R}_{\text{H}}}{1+z_e}\left[\frac{1}{n^2}-\frac{1}{(n+1)^2}\right],
\label{nu_obs}
\end{equation}
where $z_e$ is the redshift at which the line is emitted, $c$ is the speed of light, $\text{R}_{\text{H}}=1.0968 \times 10^5$ $\text{cm}^{-1}$ is the Rydberg number for hydrogen, and $n$ is the principal quantum number. In Fig. \ref{nuobs_z}, we show the observed line frequencies as a function of redshift for different values of $n$; the frequency range covered by SKA-MID is shown through a grey shaded region.

The flux density at the center of H$n\alpha$ lines ($f_{\text{H}n\alpha}$) can be written as (R13)
\begin{equation}
f_{\text{H}n\alpha}\approx 3.25\hspace{0.05cm}n^{-2.72}\dot{N}_{\gamma}\hspace{0.05cm}(1-f_{\text{esc}}^{912})\hspace{0.05cm}\frac{hc}{\delta v}\hspace{0.05cm}\frac{(1+z_e)}{4\pi d_L^2},
\label{main_formula}
\end{equation}
where $d_L$ is the luminosity distance of an emitting source at redshift $z_e$, $\delta v$ is the width of the line in velocity units, $h$ is the Planck constant, and $f_{\text{esc}}^{912}$ is the escape fraction of ionizing photons. Since we want to test the possibility of detecting optically obscured quasars through RRLs, we assume that all the ionizing photons remain trapped into a dense, fully neutral, surrounding medium, namely $f_{\text{esc}}^{912}=0$. We note that Eq. (\ref{main_formula}) is valid for $\alpha$-transitions within the interval $n=3-29$ (Hummer $\&$ Storey 1987), with an accuracy of a few percent for any value of the electron density $n_e$ (R13). We assume that this equation can be used even for higher values of $n$.

Finally, the production rate of ionizing photons $\dot{N}_{\gamma}$ is given by
\begin{equation}\label{ndot1}
\dot N_{\gamma}= \int _{\nu_{\text{LL}}}^{+\infty} \frac{L_\nu}{h\nu} d\nu ,
\end{equation}
where $\nu_{\text{LL}}$ is the Lyman limit frequency ($h\nu_{LL}=13.6$ eV) and $L_{\nu}$ is the luminosity per unit frequency. Substituting the usual relations:
\begin{equation}
L_{\nu}=4\pi d_L^2f_{\nu} ; \hspace{0.5cm}\lambda f_{\lambda}=\nu f_{\nu} ,
\end{equation}
we can rewrite eq. (\ref{ndot1}) as
\begin{equation}
\dot N_{\gamma}=\frac{4\pi}{hc}\int_0^{\lambda_{\text{LL}}}d_L^2(z)\lambda f_{\lambda} d\lambda ,
\label{Ndot}
\end{equation}
where $\lambda_{\text{LL}}=c/\nu_{\text{LL}}=911.8\hspace{0.1cm}\text{\AA}$. This equation clearly shows that $\dot N_{\gamma}$ (and therefore $f_{\text{H}n\alpha}$) depends on the Spectral Energy Distribution (SED) of the ionizing source.

\begin{figure
\centering
\hspace{-0.9cm}
\includegraphics[width=0.58\textwidth,height=0.285\textheight,keepaspectratio]{quasarSED_NGC1068.eps}
\caption{Schematic plot of the quasar SED, referring to our ``fiducial'' case with $\alpha_{\text{X,hard}}=-1.11, \alpha_{\text{X,soft}}=-0.7, \alpha_{\text{EUV}}=-0.7, \alpha_{\text{UV}}=-1.7$. Blue points represents measurements of the quasar NGC 1068. The upper $x$-axis shows the extreme energy values of each band.}
\label{SED_figure}
\end{figure}

\subsection{Quasar SED}\label{SED}
\hspace{12pt}
We parametrize the emitted quasar flux per unit wavelength as $f_{\lambda} \propto \lambda^{\alpha}$, where the spectral index $\alpha$ depends on the wavelength range. We adopt the following observationally constrained $\alpha$ values in different energy bands:
\begin{itemize}
\item $\alpha_{\text{X,hard}}=-1.11 \pm 0.11$ for the hard X-ray band (2500--12000 eV, Piconcelli et al. 2005);
\item $-0.7 < \alpha_{\text{X,soft}} < 0.3$ for the soft X-ray band (250--2000 eV, Fiore et al. 1994);
\item $\alpha_{\text{EUV}}=-0.7^{+0.8}_{-0.6}$ for the EUV band (12--200 eV, Wyithe \& Bolton 2011);
\item $\alpha_{\text{UV}}=-1.7^{+1.5}_{-0.9}$ for the UV band (5.5--11.8 eV, Reichard et al. 2003).
\end{itemize}
Fig. \ref{SED_figure} presents the quasar SED obtained in our ``fiducial'' case, given by the following combinations of slopes: $\alpha_{\text{X,hard}}=-1.11, \alpha_{\text{X,soft}}=-0.7, \alpha_{\text{EUV}}=-0.7, \alpha_{\text{UV}}=-1.7$. The blue points represent the photometric data of the quasar NGC 1068 (from NASA/IPAC Extragalactic Database (NED)). This example show how our adopted spectral indices, once compared with the observations, well reproduce real measurements of AGN spectra. Afterwards, we will also consider the case in which $\alpha_{\text{X,hard}}=-1.11, \alpha_{\text{X,soft}}=-0.7, \alpha_{\text{EUV}}=-1.3, \alpha_{\text{UV}}=-1.7$, which we call ``extreme'' model.

\begin{figure
\vspace{-1.1cm}
\centering
 \begin{tabular}{@{}cc@{}}
        \hspace{-0.5cm}\subfigure{\includegraphics[width=0.5\textwidth]{Ndot57_alphaEUV_E.eps}}
        \vspace{-1cm}\\
        \hspace{-0.58cm}\subfigure{\includegraphics[width=0.5\textwidth]{contour_boost_E.eps}}
\end{tabular}
\vspace{-0.5cm}
\caption{Upper: ionization rate in units of $10^{57}$ s$^{-1}$ versus $\alpha_{\text{EUV}}$, with fixed values $\alpha_{\text{X,hard}}=-1.11$, $\alpha_{\text{X,soft}}=-0.7$, $\alpha_{\text{UV}}=-1.7$, for a quasar magnitude $M_{\text{AB}}^{1500}=-27$. The vertical lines indicate the best value (solid) and the 2$\sigma$ C.L. values (dotted) of $\alpha_{\text{EUV}}$. Lower: contour plot of the boost due to secondary ionizations as a function of $\alpha_{\text{X,soft}}$ and $\alpha_{\text{EUV}}$, with $\alpha_{\text{X,hard}}=-1.11$ and $\alpha_{\text{UV}}=-1.7$. Contours correspond to $\dot{N}_{\text{Q}}^{\text{sec}}/\dot{N}_{\text{Q}}=1, 2, 3, 4, 5$. In both panels, the `excluded' regions (in grey) are the ones in which the constraint $-2<\alpha_{ox}<-0.5$ does not hold.}
\label{contours}
\end{figure}

We compute the production rate of ionizing photons in quasars ($\dot{N}_{Q}$) by substituting the SED in eq. (\ref{Ndot}):
\begin{align}
\dot N_{Q} &=\frac{4\pi d_L^2(z)}{hc}f_{1500} \bigg[f_{\text{X,hard}}\int_{\lambda_{\text{min}}}^{\lambda_{2\text{ keV}}}\lambda\left(\frac{\lambda}{\lambda_{2\text{ keV}}}\right)^{\alpha_{\text{X,hard}}} d\lambda \nonumber\\
&+ f_{\text{X,soft}}\int_{\lambda_{2\text{ keV}}}^{\lambda_{0.25\text{ keV}}}\lambda\left(\frac{\lambda}{\lambda_{0.25\text{ keV}}}\right)^{\alpha_{\text{X,soft}}} d\lambda \nonumber\\
&+ f_{\text{EUV}}\int_{\lambda_{0.25\text{keV}}}^{\lambda_{\text{LL}}}\lambda\left(\frac{\lambda}{1050\hspace{0.1cm}\text{\AA}}\right)^{\alpha_{\text{EUV}}} d\lambda \bigg].
\label{Ndot-final}
\end{align}
Here $\lambda_{\text{min}}=hc/E_{\text{max}}$ ($E_{\text{max}}=10$ keV), $f_{\text{X,hard}}$, $f_{\text{X,soft}}$ and $f_{\text{EUV}}$ are normalization factors required to match the flux densities between different bands of the spectrum and $f_{1500}$ is the flux density at 1500 $\text{\AA}$, related to the AB magnitude ($M_{\text{AB}}^{1500}$) through the following relation (R13)
\begin{equation}
f_{1500}=\frac{c}{\lambda^2}10^{-(M_{\text{AB}}^{1500}+5\log_{10}d_L(z)+43.6)/2.5}.
\label{norm1500}
\end{equation}
The UV spectral index, $\alpha_{\text{UV}}$, enters in eq. (\ref{Ndot-final}) through the normalization $f_{\text{EUV}}$.

While varying the spectral indices in the different energy bands in the allowed intervals, we compute the spectral hardness between the UV and X-ray bands (Tananbaum et al. 1979) defined as
\begin{equation}
\alpha_{ox}=0.3838\log[L_{2\hspace{0.05cm}\text{keV}}/L_{2500\hspace{0.05cm}\text{\AA}}],
\end{equation}
where $L_{2\hspace{0.05cm}\text{keV}}$ and $L_{2500\hspace{0.05cm}\text{\AA}}$ are the monochromatic luminosities at 2 keV and 2500 $\text{\AA}$, respectively. Observations allow us to constrain this parameter in the range $-2<\alpha_{ox}<-0.5$ (Wu et al. 2012).

We find that $\dot N_{Q}$ strongly depends on the assumed value of $\alpha_{\text{EUV}}$ (while being completely independent on $\alpha_{\text{X}}$ and $\alpha_{\text{UV}}$), varying between $10^{57}<\dot N_{Q}/\hspace{0.1cm}\text{s}^{-1}<14\times10^{57}$ for $1>\alpha_{\text{EUV}}>-2$, as shown in the top panel of Fig. \ref{contours}, where we fix $M_{\text{AB}}^{1500}=-27$. The grey region represents the $\alpha_{\text{EUV}}$ values excluded by the $\alpha_{\text{OX}}$ constraints. The vertical lines shown in the figure correspond to the $\alpha_{\text{EUV}}$ best value (solid) and to the 2$\sigma$ confidence level (C.L.) values (dotted).
\subsection{Secondary ionizations}
\label{sec_ion}
\hspace{12pt}
Since quasars are particularly bright in the X-ray wavelength range, the contribution of secondary ionizations from fast electrons should be taken into account in the estimate of $\dot N_{Q}$. In fact, a non negligible fraction $f_i$ of the energy of these electrons ($E_e = h (\nu -\nu_{\text{LL}})$) released by photo-ionization, is expected to cause additional (i.e. secondary) ionizations from collisions on the neutral component. The efficiency of the secondaries is then a function of both the electron energy and the ionized fraction of the gas $x_e$.
According to the model presented by Vald\'{e}s \& Ferrara (2008) (see also Furlanetto \& Stoever 2010; Evoli et al. 2012), in a cosmological pristine gas, the relation between $f_i$ and $x_e$ can be written as\footnote{We assume an initial energy of the primary electron in the range 3-10 keV.}
\begin{equation}\label{sec_ion}
f_i=0.3846(1.0-x_e^{0.5420})^{1.1952}.
\end{equation}

We compute the production rate of ionizing photons including secondary ionizations ($\dot{N}_{\text{Q}}^{\text{sec}}$) by replacing each factor $\lambda f_{\lambda}$ in eq. (\ref{Ndot}) with $\lambda f_{\lambda}\left(1+\frac{hc}{13.6 \mathrm{eV}\lambda}f_i\right)$. In particular, since we want to compute the effect of secondary ionizations in the fully neutral medium surrounding the H{\small II} region, we assume $x_e\sim 0$. As the secondaries deriving from photo-ionization have a spectral energy distribution, we account for the dependence $f_i(E_e)$ by considering the relation $f_i=4.94\arctan{E_e}-7.37$ for $x_e\sim 0$, obtained by fitting the corresponding curve in Fig. 2 from Furlanetto \& Stoever (2010).

\begin{figure
\centering
\hspace{-0.5cm}
\includegraphics[width=0.49\textwidth]{fHnalpha_MAB_E.eps}
\caption{Logarithm of $[f_{\text{H}n\alpha} n^{2.72} d_L^{2} \delta v/(1+z)]$ as a function of $M_{\text{AB}}^{1500}$. The observational data of RRL flux densities from extragalactic sources at $0.000811<z<0.158$ with the relative error bars (see Table \ref{table_extragalSources})
are plotted with different colors and symbols: magenta circles represent Seyfert galaxies, red diamonds denote starburst galaxies and purple squares are AGNs (filled and empty are respectively H90$\alpha$/H92$\alpha$ and H53$\alpha$ line observations). The arrow indicates that 3C 273 has an upper limit flux only. For comparison, the lines representing the theoretical fluxes predicted for galaxies from R13 (cyan dotted) and for quasars without (dot-dashed blue, for the ``fiducial'' case) and with the inclusion of secondary ionizations with $x_e=0$ (solid and dashed blue lines, corresponding to our ``fiducial'' and ``extreme'' model respectively) are also shown.}
\label{flux_densities}
\end{figure}

\begin{table*
\caption{Local extragalactic sources with the observed line parameters and relative references.}
\centering
\begin{tabular}{@{}lccccccl}
\hline\hline
source & $z$ & $m_{\text{AB}}^{1500}$ & $n$ & FWHM (km s$^{-1}$) & $F_{\text{peak}}$ (mJy) & source type & references\\
\hline
ARP 220    &    0.0018   &  18.57  & 92 &   $363\pm 45$  &          $0.6\pm 0.1$      &    2 merging AGNs               & (a) \\
ARP 220    &    0.0018   &  18.57  & 53 &   $230\pm 20$  &          $16\pm 2$         &                                 & (b) \\
NGC 3628   &    0.002812 &  14.23  & 92 &   $170\pm 70$  &          $1.4\pm 0.09$     &    starburst                    & (c),(d) \\
IC 694     &    0.013200 &  15.28  & 92 &   $350\pm 110$ &          $0.47\pm 0.10$    &    starburst                    & (c),(d) \\
NGC 1365   &    0.005457 &  11.99  & 92 &   $310\pm 110$ &          $0.99\pm 0.10$    &    Seyfert                      & (c) \\
NGC 5253   &    0.001358 &  12.64  & 92 &   $95\pm 10$   &          $0.53$            &    starburst                    & (e) \\
NGC 660    &    0.002835 &  15.20  & 92 &   $377$        &          $0.5$             &    starburst                    & (f) \\
NGC 3256   &    0.009354 &  16.44  & 92 &   $114\pm 60$  &          $0.56\pm 0.32$    &    starburst                    & (g) \\
NGC 1808   &    0.003319 &  14.68  & 92 &   $339\pm 75$  &          $0.47\pm 0.08$    &    Seyfert                      & (h) \\
M 83       &    0.001711 &  10.62  & 92 &   $95\pm 30$   &          $0.8\pm 0.15$     &    starburst                    & (i) \\
NGC 2146   &    0.002979 &  15.58  & 92 &   $200\pm 95$  &          $0.36\pm 0.09$    &    starburst                    & (i) \\
NGC 253    &    0.000811 &  11.47  & 92 &   $190\pm 10$  &          $9.0\pm 0.5$      &    starburst                    & (j) \\
NGC 1068   &    0.003793 &  12.79  & 53 &   $200\pm 100$ &          $37.3\pm 12.9$    &    AGN                          & (k) \\
3C 273     &    0.158    &  13.85  & 90 &   --           &          $< 200$           &    AGN                          & (l) \\
\hline
\hline
\end{tabular}\\
\begin{flushleft}
(a) Anantharamaiah et al. 2000; (b) Rodr\'{i}guez-Rico et al. 2005; (c) Anantharamaiah et al. 1993; (d) Zhao et al. 1997; (e) Mohan et al. 2001; (f) Phookun et al. 1998; (g) Roy et al. 2005; (h) Roy et al. 2008; (i) Zhao et al. 1996; (j) Anantharamaiah $\&$ Goss 1996, 1997; Das et al. 2001; Kepley et al. 2011; Mohan et al.  2002; Mohan et al. 2005; (k) Puxley et al. 1991; (l) Allen et al. 1968
\end{flushleft}
\label{table_extragalSources}
\end{table*}

We quantify the boost of the H$n\alpha$ line flux density due to secondary ionizations through the ratio $\dot{N}_{\text{Q}}^{\text{sec}}/\dot{N}_{\text{Q}}$. In the bottom panel of Fig. \ref{contours}, we plot this quantity as a function of $\alpha_{\text{X,soft}}$ and $\alpha_{\text{EUV}}$. Since $\dot{N}_{\text{Q}}^{\text{sec}}/\dot{N}_{\text{Q}}$ is only slightly dependent on $\alpha_{\text{X,hard}}$ and $\alpha_{\text{UV}}$, we fix these slopes to their best-values ($\alpha_{\text{X,hard}}=-1.11$, $\alpha_{\text{UV}}=-1.7$). As in the top panel, the grey areas represent regions of the parameter space that are excluded by the $\alpha_{\text{OX}}$ constraints.

We find that $\dot{N}_{\text{Q}}^{\text{sec}}/\dot{N}_{\text{Q}}=2.2$ in the ``fiducial'' case and $\dot{N}_{\text{Q}}^{\text{sec}}/\dot{N}_{\text{Q}}=3.7$ in the ``extreme'' one. Once compared with the production rate of ionizing photons for galaxies, it turns out that $\dot{N}_{\text{Q}}$ ($\dot{N}_{\text{Q}}^{\text{sec}}$) is greater than $\dot{N}_{\text{G}}$ by a factor of 2 (4) to 4 (13), in our ``fiducial'' and ``extreme'' model respectively. For $M_{\text{AB}}^{1500}=-25$, we find $\log \dot{N}_{\text{G}}=56.33$ for galaxies, while for quasars we have $\log \dot{N}_{\text{Q}}=56.60$ and $\log \dot{N}_{\text{Q}}=56.88$ in the ``fiducial'' and ``extreme'' case respectively.

\section{Test with local sources}
\label{tests}
\hspace{12pt}To test the model described above, we compare its predictions with observations of radio recombination lines from a sample of extragalactic sources (starburst galaxies, Seyfert galaxies and AGNs, listed in Table \ref{table_extragalSources}) at $z\sim 0$ (Allen et al. 1968; Anantharamaiah et al. 1993, 1996, 1997, 2000; Das et al. 2001; Kepley et al. 2011; Mohan et al. 2001, 2002, 2005; Phookun et al. 1998; Puxley et al. 1991; Rodr\'{i}guez-Rico et al. 2005; Roy et al. 2005, 2008; Zhao et al. 1996, 1997). In this sample there are two AGNs, NGC 1068 and 3C 273 (the latter has an upper limit flux only). In addition, recent results (Paggi et al. 2013) strongly suggest that Arp 220 also hosts two merging, deeply buried AGNs, whose bolometric luminosity is likely in the range $2\times 10^{42}$ erg $\text{s}^{-1}$ and $5.2\times 10^{43}$ erg $\text{s}^{-1}$ for the eastern and western nuclei, respectively. Finally note that NGC 1068 and Arp 220 are radio-quiet quasars (RQQs) while 3C 273 is a radio-loud source (RLQ).

In this context, the distinction between RQQs and RLQs is important due to the fact that in radio-loud quasars, the presence of a strong radio continuum emission makes possible the detection of RRLs out to greater distances with respect to RQQs, thanks to the stimulation of their line flux densities (see Section 4 for the details).

For each source of the previous sample but NGC 1068 and 3C 273 we extract the observed line parameters of the H92$\alpha$ line ($\nu_{\text{rest}}=8309.383$ MHz). In the case of Arp 220 (besides the H92$\alpha$ detection) and NGC 1068 we have observations of the H53$\alpha$ line ($\nu_{\text{rest}}=42951.97$ MHz) and we use the observed values. Furthermore, a search for the H90$\alpha$ line ($\nu_{\text{rest}}=8872.569$ MHz) in the emission spectrum of 3C 273 has led to an upper limit only in the detected signal. More specifically, we collect the data relative to the quantum number ($n=92$ for all the sources except NGC 1068 and 3C 273, $n=53$ for NGC 1068, both for Arp 220, and $n=90$ for 3C 273), the line width in $\text{km}$ $\text{s}^{-1}$ and the peak line flux density in mJy.
The redshift $z$ (thus the luminosity distance) and the apparent magnitude $m_{\text{AB}}$ at 1500 $\text{\AA}$ of each source are taken instead from the NED website.

\begin{figure*
\centering
 \begin{tabular}{@{}cc@{}}
       \subfigure{\includegraphics[width=0.5\textwidth]{contour_frac_n265-77_S10_eq1_inverse.eps}}
       \subfigure{\includegraphics[width=0.5\textwidth]{contour_frac_n139-40_S001_eq1_inverse.eps}}
\\
${\bf z=0}$; ${\bf S_0=10}$ {\bf mJy}.  \hspace{5.5cm} ${\bf z=6}$; ${\bf S_0=0.01}$ {\bf mJy}.
\end{tabular}
\vspace{0.4cm}
\caption{Contour plots of the logarithm of the ratio X between stimulated and spontaneous emission as a function of the temperature $T_e$ and the density $n_e$ of the H{\small II} region, for RRLs of quantum numbers observable at $z=0$ (left panel) and $z=6$ (right panel), with a continuum flux density $S_0=10$ mJy and $S_0=0.01$ mJy respectively. Black solid contours are traced for the minimum SKA-MID frequency, $\nu_{\text{min}}=0.35$ GHz, and correspond to quantum numbers $n=265$ (left) and $n=139$ (right), while red dashed contours are for RRLs detectable in correspondence of the maximum SKA-MID frequency, $\nu_{\text{max}}=14$ GHz, with quantum numbers $n=77$ (left) and $n=40$ (right). The model adopted is our ``fiducial'' case with the inclusion of secondary ionizations, for quasars with magnitude $M_{\text{AB}}^{1500}=-26$.}
\label{contours_z0_z6}
\end{figure*}

Fig. \ref{flux_densities} shows, for this compilation of data, the logarithm of $[f_{\text{H}n\alpha} n^{2.72} d_L^2 \delta v/(1+z)]$ versus $M_{\text{AB}}^{1500}$, with different colors and symbols according to the different class of sources (the downward arrow indicates that the line flux density of 3C 273 is an upper limit). In this figure, we also plot our theoretical predictions: the blue solid line indicates our ``fiducial'' case, the blue dashed line the ``extreme'', and the blue dot-dashed line the ``fiducial'' case without taking into account secondary ionizations. The cyan dotted line represents predictions for the case of low-metallicity ($Z < 10^{-5}$) galaxies without AGN. For these sources, we compute $f_{\text{H}n\alpha}$ according to the R13 formalism:
\begin{align}
f_{\text{H}n\alpha} &\approx 1.2\times 10^{-7}n^{-2.72}10^{-0.4M_{\text{AB}}^{1500}}(1+z) \nonumber\\
&\times \left(\frac{d_L}{10^5 \hspace{0.1cm}\text{Mpc}}\right)^{-2} \left(\frac{\delta v}{100 \hspace{0.1cm}\text{km s$^{-1}$}}\right)^{-1}(1-f_{\text{esc}}^{912}) \hspace{0.1cm}\mu \text{Jy}.
\label{fHnalpha}
\end{align}
In this case, $\dot{N}_{\text{G}}=(2.2\times10^{-11})\times 10^{-0.4M_{\text{AB}}^{1500}}$. Eq. (\ref{fHnalpha}) is obtained from eq. (\ref{main_formula}) by using empirical relations between the star formation rate (SFR) and the 1500 $\text{\AA}$ luminosity (Mu\~{n}oz $\&$ Loeb 2011), and between the SFR and $\dot{N}_{912}$ (Table 4 from Schaerer 2003).

While the R13 model is better suited for comparison with starburst galaxies (red filled diamonds), our predictions should be compared with Seyfert and AGN data (magenta circles and purple squares). We note that the R13 model underpredicts by more than one order of magnitude the observed flux for most of the sources (all but two). Although the $f_{\text{H}n\alpha}$ values predicted by us are $\sim 10$ times higher than the R13 ones, we still can not reproduce the observations of local AGNs. This means that very likely we are neglecting further important contributions to the RRL emission.

\section{Radio stimulated emission}
\hspace{12pt}
Up to now, we have considered only spontaneous emission in radio-quiet quasars. However, radio recombination lines may arise from a combination of spontaneous and stimulated emission (e.g. Bell \& Seaquist 1977). In fact, in radio-loud quasars, the strong radio continuum radiation may stimulate the RRL emission thus boosting their flux (Shaver 1978; Shaver et al. 1978). Therefore, in RLQs the RRL flux density is expected to be higher than what we found through our calculations. For this reason, RLQs are in principle detectable out to greater distances with respect to RQQs.

In this section, we quantify the relative contribution of the stimulated emission due to a nonthermal background source with respect to the spontaneous emission, in order to understand what are the conditions under which such mechanism can become significant in boosting the quasar RRL flux.

To this purpose, we take advantage of the formalism introduced by Shaver (1978). According to equation (1) of this work, the ratio $X$ between the stimulated $f_{\text{H}n\alpha}^{\text{stim}}$ and spontaneous emission $f_{\text{H}n\alpha}^{\text{spont}}$ can be written as follows:
\begin{equation}
X=\frac{f_{\text{H}n\alpha}^{\text{stim}}}{f_{\text{H}n\alpha}^{\text{spont}}}=\frac{c^2S_0}{2k_B\nu_{\text{obs}}^2\Omega T_e}\times {\cal F},
\label{xfac}
\end{equation}
where $k_B=1.38\times 10^{-16}$ erg/K is the Boltzmann constant, $\nu_{\text{obs}}=\nu/(1+z)$ is the observed frequency of the transition, $T_e$ is the electron temperature, $\Omega=(l/d)^2$ is the solid angle subtended by the H{\small II} region, $l$ is the total path length through the ionized gas and $d$ is the proper distance to the source, related to the luminosity distance $d_L$ through $d=d_L/(1+z)^2$, $S_0$ is the continuum flux density of the background radio source, and ${\cal F}$ is
\begin{equation}
{\cal F}=\Bigg[\frac{e^{-\tau_C}|e^{-\tau_L}-1|}{\Big(\frac{b_{m}\tau_L^*+\tau_C}{\tau_L+\tau_C}\Big)(1-e^{-(\tau_L+\tau_C)})-(1-e^{-\tau_C})}\Bigg].
\label{F}
\end{equation}
In eq. (\ref{F}), $b_m$ is the departure coefficient which relates the population of the atomic energy level $m=n+1$ (for $\alpha$-lines) to its value in local thermodynamic equilibrium (LTE), $\tau_C$ is the continuum optical depth and $\tau_L=b_n\beta_n\tau_L^*$ is the central line optical depth, where:
\begin{equation}
\beta_n\equiv 1-\frac{kT_e}{h\nu}\frac{\Delta b}{b_n}.
\end{equation}
The optical depths $\tau_C$ and $\tau_L^*$ can be written as
\begin{equation}
\tau_C=\frac{0.03014n_e^2lf}{\nu_{\text{obs}}^2T_e^{3/2}}[1.5\ln T_e-\ln (20.2\nu_{\text{obs}})]
\end{equation}
and\footnote{The expression for $\tau_L^*$ assumes that the profile width is due to pure Doppler broadening.}
\begin{equation}
\tau_L^*=\frac{575n_e^2lf}{\nu_{\text{obs}} \Delta V_{\text{obs}}T_e^{5/2}}x_{\text{HII}}e^{\frac{1.58\times10^5}{n^2T_e}}.
\end{equation}
Here $\Delta V_{\text{obs}}$ (km/s) is the observed FWHM of the line ($\Delta V_{\text{obs}}=\Delta V/(1+z)$), $n_e$ (cm$^{-3}$) is the electron density, $f(=V_{\text{gas}}/V_{\text{total}})$ is the volume filling factor, $x_{\text{HII}}$ is the ionized fraction of the gas and $n$ is the principal quantum number. Now, since $l=2R_{\text{HII}}$, where $R_{\text{HII}}^3=3\dot N_{\gamma}/(4\pi\alpha(T)n_e^2)$ is the Stromgren radius, eq. (\ref{xfac}) becomes:
\begin{equation}
X=\frac{3.10\times10^{-34}c^2\alpha(T)^{2/3}}{k_B\nu^2\dot N_{57}^{2/3}}\bigg(\frac{n_e^{4/3}S_0}{T_e}\bigg)\frac{d_L(z)^2}{(1+z)^2}\times \cal{F},
\label{xfac_final}
\end{equation}
where $\alpha$ (cm$^3$ s$^{-1}$) is the recombination rate, $\dot N_{57}$ (s$^{-1}$) is the rate of production of ionizing photons in units of $10^{57}$, and the units of $\nu$, $d_L$ and $S_0$ are GHz, Mpc and mJy respectively\footnote{Here $k_B$ is in units of erg/K and $c$ is in cm/s.}.\\

Following the formalism presented by Shaver (1975), the interstellar medium can be classified according to three main categories: HII regions ($10<n_e/\text{cm}^{-3}<10^4$; $2.5\times 10^3<T_e/\text{K}<10^4$), diffuse intercloud components ($n_e \sim 5\times 10^{-2}$ cm$^{-3}$; $T_e\sim 10^3$~K) and cold cloud components ($n_e \sim 5\times 10^{-2}$cm$^{-3}$; $T_e\sim 20$~K). With the aim of bracketing the physical properties of the ISM, in this work, we consider only two extreme cases: ($n_e>10^3$ cm$^{-3}$; $T_e\approx 10^4$ K) and ($10^{-2} < n_e/\text{cm}^{-3} < 1$; $10^2<T_e/\text{K}<10^3$), hereafter referred to as H{\small II} regions and diffuse interclouds, respectively.\\
In the case of H{\small II} regions, we assume LTE ($b_n=1$, $\beta_n=1$) and we compute the X factor for RRLs of quantum numbers detectable at $z=0$ and $z=6$ in correspondence of two reference SKA frequencies, i.e. the minimum and maximum observable with SKA-MID, as shown in Table \ref{table_SKA}. We can verify that in the LTE case, $\cal{F}$$=1$.

\begin{table
\caption{Quantum numbers of radio recombination lines detectable at $z=0$ and $z=6$ in correspondence of the two extreme SKA-MID frequencies.}
\centering
\begin{tabular}{lcc}
\hline
\hline
$\nu_{\text{obs}}$(GHz) & $n(z=0)$ & $n(z=6)$\\
\hline
\hspace{0.4cm}$0.35$ & $265$ & $139$\\
\hspace{0.4cm}$14$ & $77$ & $40$\\
\hline
\hline
\end{tabular}
\label{table_SKA}
\end{table}

In Figure \ref{contours_z0_z6} we show, at $z=0$ (left panel) and $z=6$ (right panel), contour plots of the logarithm of the X factor for these particular RRLs as a function of $T_e$ and $n_e$ in the intervals ($10^3<T_e/\text{K}<10^5$) and ($10^3<n_e/\text{cm}^{-3}<10^5$), for a radio continuum flux density\footnote{Radio-quiet quasars at $z\sim 6$ have typical radio fluxes of the order of $\lesssim$ tens of $\mu$Jy (Wang et al. 2008).} $S_0=10$ mJy and $S_0=0.01$ mJy respectively. Black solid contours are for RRLs detectable in correspondence of $\nu_{\text{min}}=0.35$ GHz, while red dashed contours correspond to $\nu_{\text{max}}=14$ GHz. We consider our ``fiducial'' case for quasars including secondary ionizations from $X$-ray photons, in which $\dot N_{57}=(8.76\times 10^{-11})\times10^{-0.4M_{\text{AB}}^{1500}}$, and we assume sources with $M_{\text{AB}}^{1500}=-26$.

\begin{figure
\centering
\hspace{-0.7cm}
\includegraphics[width=0.51\textwidth]{frac_NLTE_eq1_inverse.eps}
\caption{Logarithm of the X factor for radio recombination lines of quantum numbers $n$ detectable at $z=0$ (triangles) and $z=6$ (squares) in correspondence of two SKA frequencies, $\nu=0.4$ GHz and $\nu=7.3$ GHz. The curves are plotted for two values of electron temperature: $T_e=10^2$ K (blue) and $T_e=10^3$ K (black), and two values of electron density: $n_e=10^{-2}$ cm$^{-3}$ (dashed) and $n_e=1$ cm$^{-3}$ (solid), both at $z=0$ and $z=6$. Our calculations assume $S_0=10^3$ mJy, $\Delta V=100$ km s$^{-1}$ and our ``fiducial'' case with secondary ionizations for a quasar magnitude $M_{\text{AB}}^{1500}=-26$.}
\label{frac_NLTE}
\end{figure}

We find that, at $z=0$ the logarithm of the X factor is in the interval $[-6,1]$, being greater than zero in the cases of very high-$n$ (i.e. $n=265$). This means that, except for these cases, the spontaneous emission dominates over the stimulated one for local sources. At $z=6$ instead, we find $-4 < \log X < 3$, being negative for very small quantum numbers. Thus, in all the situations but these, the stimulated radio flux due to the nonthermal continuum radiation can give a significant contribution to the total RRL flux density of the quasar at $z=6$. As a further comment, we notice that the X factor is linearly proportional to $S_0$, thus if $S_0$ reduces by a certain factor the stimulated contribution with respect to the spontaneous emission
also reduces by the same amount.

In the case of diffuse interclouds, we cannot assume LTE. In this case, we use the $b_n$ and $\beta_n$ tabulated values as computed by Salem \& Brocklehurst (1979) for a nonthermal background source.\\
Furthermore, assuming the cloud is spherically symmetric ($f=1$) and the gas inside this region is fully ionized ($x_{\text{HII}}=1$), we rewrite $\tau_C$ and $\tau_L^*$ as follows:
\begin{equation}
\tau_C=\frac{0.12n_e^{4/3}\dot N_{57}^{1/3}}{\nu^2T_e^{3/2}\alpha(T)^{1/3}}\bigg[1.5\ln T_e-\ln\bigg(\frac{20.2\nu}{1+z}\bigg)\bigg](1+z)^2
\end{equation}
and
\begin{equation}
\tau_L^*=\frac{2.31\times10^{3}n_e^{4/3}\dot N_{57}^{1/3}}{\nu \Delta V T_e^{5/2}\alpha(T)^{1/3}}e^{\frac{1.58\times10^5}{n^2T_e}}(1+z)^2.
\end{equation}

In Figure \ref{frac_NLTE} we show the logarithm of the X factor for non-LTE cases for H$n\alpha$ lines as a function of the quantum numbers $n=95, 260$ at $z=0$ and $n=50, 135$ at $z=6$. We make the calculation in the case of quasars with $M_{\text{AB}}^{1500}=-26$ in our ``fiducial'' case including secondary ionizations, and assuming $S_0=10^3$ mJy and $\Delta V=100$ km s$^{-1}$. We plot the results for two values of electron temperature: $T_e=10^2$ K (blue curves) and $T_e=10^3$ K (black curves), and two values of electron density: $n_e=10^{-2}$ cm$^{-3}$ (dashed) and $n_e=1$ cm$^{-3}$ (solid) , both at $z=0$ and $z=6$.

We note that at $z=0$, log($X$) is between 4 and 5 orders of magnitude lower than the corresponding ratio (with the same $T_e$ and $n_e$) at $z=0$. Also, at a fixed density, log($X$) takes greater values for lower temperatures, while, at fixed $T_e$, it increases with increasing $n_e$; in all the cases, the ratio between the stimulated and spontaneous flux density increases with increasing $n$, more rapidly at $z=6$ with respect to $z=0$. We can conclude that, in the situation with low densities and low temperatures, the nonthermal stimulated emission dominates over the spontaneous emission only at $z=6$ and with $n_e\gtrsim 1$ cm$^{-3}$, for RRLs of quantum numbers $n\gtrsim 70$. Indeed, the contribution of the nonthermal radiation field becomes more important at the higher energy levels (or lower frequencies), with a more rapid increasing of log($X$) for $T_e=10^2$ K ($\log(X)\approx 3.5$ for $n=135$) with respect to the case of $T_e=10^3$ K ($\log(X)\approx 1.5$ for $n=135$).

\begin{figure
\centering
\hspace{-1.03cm}
 \includegraphics[width=0.53\textwidth,height=0.33\textheight]{sensitivitySKAMID_E_14GHz-stim.eps}
\caption{Logarithm of the 5$\sigma$ sensitivity (in $\mu\text{Jy}$) as a function of redshift ($1 \leq z \leq 10$) for different values of the quasar absolute magnitude ($-27 \leq M_{\text{AB}}^{1500} \leq -23$). The calculations are done for the maximum frequency observable with SKA-MID, $\nu_{\text{max}}=14$ GHz. The solid and dashed curves correspond to our ``fiducial'' and ``extreme'' model respectively, with the inclusion of the stimulated contribution from a nonthermal radio source, using the mean value of $\log(X)$ obtained for $S_0=10$ $\mu$Jy at this frequency. The horizontal black lines represent the 5$\sigma$ ``threshold'' sensitivities reached by SKA-MID at the corresponding frequency, with an integration time of 10, 100 and 1000 hours. In addition, the upper $x$-axis indicates the values of the quantum numbers $n$ of the lines detectable at each $z$, corresponding to $\nu_{\text{max}}$. The H$n\alpha$ line intensity decreases with decreasing frequency.}
   \label{sigma_z}
\end{figure}

\section{Detecting (obscured) quasars}
\hspace{12pt}
Given the model outlined in Sec. 2 and taking into account the stimulated emission due to a nonthermal background source, we estimate the expected H$n\alpha$ line flux density arising from quasars of different AB magnitudes ($-27 \leq M_{\text{AB}}^{1500} \leq -23$) and redshifts ($1 \leq z \leq 10$), both in the ``fiducial'' and ``extreme'' case\footnote{We assume $\delta v=100$ km $\text{s}^{-1}$ in these calculations.}, and we compute the sensitivity ($\sigma=f_{\text{H}n\alpha}/5$) required to detect H$n\alpha$ lines with 5$\sigma$ significance at all considered redshifts and AB magnitudes. The total (spontaneous + stimulated) RRL flux density is
\begin{equation}
f_{\text{H}n\alpha}^{\text{tot}}=f_{\text{H}n\alpha}(1+X),
\label{fHnalpha_TOT}
\end{equation}
where $f_{\text{H}n\alpha}$ includes only the spontaneous emission from quasars, and $X$ is the ratio between stimulated and spontaneous flux density from eq. (\ref{xfac_final}). In our calculations, we use the mean value of $\log X$ obtained for RRLs observable in correspondence of the maximum frequency observable with SKA-MID, $\nu_{\text{max}}=14$ GHz, for a radio continnum flux\footnote{The assumption $S_0=10$ $\mu$Jy underestimates the contribution of the stimulated emission in low-redshift quasars, whose observed radio fluxes are typically higher.} $S_0=10$ $\mu$Jy.

The results are shown in Fig. \ref{sigma_z}, for the concerned ranges of magnitude and redshift, in the ``fiducial'' (solid curves) and ``extreme'' (dashed curves) case.\\
In this figure we also plot, through horizontal black lines, the 5$\sigma$ SKA sensitivity (5$\sigma_{\text{SKA}}$) that is expected to be reached in $t=10$, $100$ and $1000$ hours of SKA-MID observing time at the corresponding frequency. We adopt the usual formula:
\begin{equation}
\sigma_{\text{SKA}}=\sigma_{0}\sqrt{\frac{t_{0}}{t}\frac{\Delta v_{0}}{\Delta v}},
\end{equation}
where $\sigma_{0}=63\hspace{0.1cm}\mu\text{Jy}$ is the sensitivity obtained over a channel $\Delta \nu_{0}=100$ kHz in $t_{0}=1$ hr of SKA-MID integration time (SKA-‐SCI-‐LVL-‐001, 2015), $\Delta v_{0}=c\Delta \nu_{0}/\nu _{0}$, $\Delta v=100$ km $\text{s}^{-1}$ and $\nu_{0}=\nu_{\text{max}}$.

Considering that: a) $f_{\text{H}n\alpha}$ increases with increasing frequency, and b) the stimulated contribution increases (i.e. $X$ increases) with decreasing frequency, at $\nu=\nu_{\text{max}}$ we are maximizing the expected H$n\alpha$ flux but we are minimizing the stimulated emission.

From the figure, we can see that at $\nu_{\text{max}}=14$ GHz, and according to our ``fiducial'' model, SKA-MID could detect sources with $M_{\text{AB}} < -26$ ($M_{\text{AB}} < -25$) at all redshifts (at $z\lesssim 3$) in 1000 hrs of integration time. In the ``extreme'' case, quasars up to $M_{\text{AB}}=-25$ ($M_{\text{AB}}=-24$) at all redshifts (at $z\lesssim 4$) would be detected in the same (large) amount of observing time. In 100 hrs of observing time, SKA-MID would detect sources with $M_{\text{AB}}<-27$ ($M_{\text{AB}}<-26$) at $z\lesssim 8$ ($z\lesssim 2.5$) in our ``fiducial'' case, and sources with $M_{\text{AB}}<-26$ ($M_{\text{AB}}<-25$) at all redshifts (at $z\lesssim 3$) in the ``extreme'' case.\\
As stated in Sec. 3, our predicted flux densities are $\sim 2$ orders of magnitude below the observed fluxes of local AGNs (Figure \ref{flux_densities}).
This means that, if some relevant contribution to the RRL emission is still missing, then the integration time would go down by a factor $>10$, making RRLs from quasars much more detectable.

Furthermore, Fig. \ref{sigma_z} shows that moving from $z\sim 1$ to $z\sim 10$, the sensitivity required for detecting quasars through RRLs changes only by a factor of 10. To understand this trend in $z$, and since $f_{\text{H}n\alpha} \propto (1+z)d_L^{-2} n^{-2.72}$ we also express $n$ and $d_L$ as a function of redshift. For a flat universe ($1-\Omega_m-\Omega_\Lambda=0$), $d_L$ is
\begin{equation}
d_L(z)=\frac{c}{H_0}(1+z)\int_0^z\frac{dz'}{[\Omega_m(1+z')^3+\Omega_\Lambda]^{1/2}},
\label{dL}
\end{equation}
where $H_0$ is the Hubble parameter, and $\Omega_m$ and $\Omega_\Lambda$ are the total matter density and the dark energy density in the units of critical density, respectively. At high redshift, by neglecting $\Omega_{\Lambda}$, we obtain that $d_L \propto (1+z)$. The quantum number $n$ can be written in terms of $z$ by using eq. (\ref{nu_obs}) and making some approximations for high $n$: the resulting relation is
\begin{equation}
n \approx \left(\frac{2c\hspace{0.05cm}\text{R}_{\text{H}}}{\nu_{\text{obs}}(1+z)}\right)^{1/3}.
\label{n}
\end{equation}
We finally get $f_{\text{H}n\alpha} \propto (1+z)^{-0.1}$, an expression that reproduces the slow decrease of $\sigma$ with increasing redshift.

The optimal strategy to detect RRLs from quasars depends on the nature of the source itself. As discussed above, the two factors which play a role in determining the total flux $f_{\text{H}n\alpha}^{\text{tot}}$ are the spontaneous term ($f_{\text{H}n\alpha}^{\text{spont}}\propto \nu_{\text{obs}}^{0.9}$) and the stimulated one ($f_{\text{H}n\alpha}^{\text{stim}}\propto \nu_{\text {obs}}^{-1}$). This means that, in the case of a radio-quiet source ($f_{\text{H}n\alpha}^{\text{stim}}<<f_{\text{H}n\alpha}^{\text{spont}}$), high frequencies (e.g. $\nu_{\text{obs}}\sim 14$~GHz in the case of SKA-MID) optimize the chance of RRLs detection. Viceversa, in the case of a radio-loud source it is better to look for RRLs by means of low-frequency receivers (e.g. $\nu_{\text{obs}}\sim 1$~GHz in the case of SKA-MID).
\section{Summary and discussion}
\hspace{12pt}We have examined the feasibility of detecting obscured quasars at radio frequencies, through their hydrogen RRL emission. To this purpose, we have developed a model for estimating the expected flux densities of H$n\alpha$ lines from quasars, including secondary ionizations from X-ray photons.

By comparing our results with observations of RRLs in local quasars, we have found that our predictions are in good agreement with the observed RRLs strengths. Our predicted fluxes are, however, still below the observed line fluxes for local AGNs by a factor of a few orders of magnitude, suggesting that some additional mechanism is at work to amplify line fluxes. We have shown that, under some specific conditions, the contribution of stimulated emission due to a nonthermal radio source may be relevant in boosting the flux densities from quasars, thus making possible the detection of RRLs out to very large distances. Additionally, we have explored the potential of the SKA in detecting quasars at very high redshift ($z>7$). We have found that, taking into account the stimulated contribution, at a frequency $\nu=14$ GHz, the SKA-MID telescope would be able to detect sources with $M_{\text{AB}}\lesssim-27$ ($M_{\text{AB}}\lesssim-26$) at $z\lesssim 8$ ($z\lesssim 3$) in less than 100 hrs of integration time.

We point out that, if we study the possible detectability of radio recombination lines based on the observed flux densities in local AGNs, which are brighter than our predictions by $\sim 2$ orders of magnitudes, then the required observing time would reduce by a factor $>10$, thus making RRLs from quasars more easily detectable.

Given our predictions, the proposed survey could be carried out as a piggyback of proposed deep HI surveys with SKA-MID (Blyth et al. 2015).

It must be noticed that we are maximizing the expected H$n\alpha$ flux through our assumptions $f_{\text{esc}}^{912}=0$ in eq. (\ref{main_formula}) and $x_e=0$ in eq. (\ref{sec_ion}). By assuming that ionizing photons can not escape from the galaxy, being trapped into the dense ISM of the quasar host galaxy, we are maximizing the number of ionizations (and consequent recombinations) in HII regions. Moreover, by considering the case of an almost complete neutral gas, we are maximizing the amount of free-electrons energy that can be used to produce secondary ionizations.

We remark here that the possibility of detecting RRLs even at high redshift is due to an important property of these lines, concerning with the fact that their principal quantum number decreases with increasing redshift (see Section 1 and Figure \ref{nuobs_z}).

Furthermore, we have obtained a relation between the quantum number of a RRL detectable at a given $z$ in correspondence of some observed frequency: $n \approx (2c\hspace{0.05cm}\text{R}_{\text{H}}/[\nu_{\text{obs}}(1+z)])^{1/3}$, valid for high $n$. This explains the slow decrease of the H$n\alpha$ line flux density with increasing redshift ($f_{\text{H}n\alpha} \propto (1+z)^{-0.1}$).

Also, it is worthwhile to mention a recent result from Ba$\tilde{\text{n}}$ados et al. (2015), showing that the fraction of radio-loud quasars (i.e. RLF $= 6\%-19\%$) does not vary with redshift, in contrast to what previously found by some studies at lower redshifts (e.g. Jiang et al. 2007; Kratzer \& Richards 2014).

Our results for the line flux densities must be still considered as preliminary. More detailed radiative transfer computations of UV/Xray photons performed on realistic density field are necessary to draw firmer conclusions. We aim at presenting these improved results in a future work, where we plan to use the state-of-the-art RT code \texttt{CRASH} in its latest version (\texttt{CRASH4}, Graziani et al. in prep). The ratio between the intensity of the $\text{He}^{++}$ and $\text{H}^{+}$ lines is expected to be a good diagnostic of the hardness of the ionizing spectrum, thus providing a clear discriminant between AGN and starburst activity. The advantage of this technique is that both lines can be detected contemporarily with a bandwidth of 10 GHz (Scoville $\&$ Murchikova 2013). We will investigate how this ratio varies for different slopes of the quasar spectrum and for different values of the ionization fraction of the gas. Since this technique can be applied also in the millimetre domain, the proposed scientific case can be, on longer time scales, a driver for the synergy between the SKA and ALMA.

Finally, we also plan to study the redshift evolution of the UV luminosity function, by fitting the most updated observational data at $0<z<7$, and theoretically extending it beyond $z=7$. This will allow to make detailed predictions of the expected QSO number counts for a single observation with SKA-MID (FoV = 0.49 $\text{deg}^2$) in 1000 hrs of integration time, taking into account the full frequency coverage of this instrument (0.35-14 GHz).

\section*{Aknowledgements}
\hspace{12pt}This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.

This work is based on research supported by the National Research Foundation under grant 92725. Any opinion, finding and conclusion or recommendation expressed in this material is that of the author(s) and the NRF does not accept any liability in this regard.

redpajama_set_name: RedPajamaArXiv


text:
GamersGate Holiday Gift Guide
All available from GamersGate, coincidentally.
Published on Dec. 10, 2008
New York, December 10, 2008 - GamersGate today announced its Holiday Gift Guide, with discounts for individual games as well as combinations of titles.
The Holiday gift guide presents more than 97 titles and a total of 39 offerings, including the 1C super pack with King's Bounty and eight other premium titles for $99.99/€99.99 and discounts on individual games such as Supreme Ruler 2020 and Dark Horizon of up to 66%.
The Holiday sales start immediately on GamersGate and ends after the Holiday Season.
Follow the link below to go to the complete Holiday Gift Guide:
www.gamersgate.com/giftguide
About GamersGate
GamersGate is a leading digital distribution platform, providing ready gaming experiences for gamers worldwide – anytime, anywhere. Viewed as a strong contender in the digital download arena, GamersGate continues to redefine the download industry. Future strategies include the launch of several additional services, and the further aggressive expansion of its product portfolio, from a wide range of internationally recognized publishers. http://www.gamersgate.com
Xbox and Bethesda Developer Direct Showcase reveals Tango Gameworks' Hi-Fi Rush

redpajama_set_name: RedPajamaCommonCrawl


A great start – the gift bag. Give gift bags for your destination wedding with little goodies that they will need during their beach getaway. Maybe with several miniature things they can keep in their purse that come handy during their trip – like a mini nail file, a Tide Stick, chapstick, sunscreen, a small mirror, flip flops, and necessities like aspirin and band-aids! Make the bag, itself, even more special by adding a monogram of their name.
On Trend: Your girls are will be there by your side getting ready (almost) all day! A comfortable and stylish way to help them feel special (and look great in photos) is to give them each a silk robe to wear as they prepare for the wedding. Embroider cute messages on the back like: "Maid of Honor", or "Team Bride"!
We know that nothing is more important when you are away from home than a small bag with life-saving touch-up items like a small lipstick, eyeliner, mascara and more inside to "freshen up" – especially on the wedding day. This is definitely a gift that will come handy for a destination wedding. Pro Tip: Go online and order cute makeup bags from a major cosmetic company with samples of the top selling seasonal items and colors already inside the bag!
Nothing says "everlasting" and "luxury" like a gorgeous bracelet, earrings, or a personalized necklace. If it is in your budget, give a gift of matching jewelry to wear on the wedding day. It's fun to wear a common detail at the wedding that you can also cherish forever. Customize it with an engraved message or initials!
There are moments in our lives when we simply need to take the time for relaxation and pampering! Encourage some pre-wedding relaxation with a gift of aromatic sea salts, exfoliating creams and a scrubby brush. There are so many options – add in an organic face peel and essential oils and top it off with comfy house slippers (also pairs nicely with the silk robe!). Give this gift at your rehearsal dinner so they can pamper themselves the night before and show up fresh, relaxed and ready for your big day!
TELL US: What is the best bridesmaid gift you have received?


Andrew Maxin and his boyfriend Mark Waier were gearing up for a cruise in 2012 when the former had a bright idea: to craft some new swimwear for his partner to don on deck.
Vanwolff, his subsequent swimwear brand, continues to thrive today, with multiple lines of briefs, trunks, shorts and underwear. Surprisingly, the bestseller is the briefs, aka the Speedo cut, Maxin tells me. It's also the most popular cut for fashion features in magazines, despite the fact that the cultural milieu in the U.S. still views the Speedo as a punchline, whether it be in TV and film (often to signify an exotic man who can steal your girl), parody internet videos, rude BuzzFeed listicles and beyond. Often, the Speedo is depicted as a deeply uncomfortable thing for men to dare to try. You think you're brave, huh?, such depictions seem to ask. Are you brave and weird enough for a Speedo?
The origin story of tiny briefs suggests they were always meant to be equal parts practicality and flash. The original nylon Speedo brief was a larger cut that debuted in 1955 and caught attention in the 1956 Melbourne Olympics, where the Aussie swim team dominated in their Speedos and won eight gold medals.
Since then, the tiny nylon swim brief has become ubiquitous around the world. What's strange is America's deep disconnect with a number of other Western nations, notably in Europe, where Speedos are a common sight on all sorts of male bodies of varying ages. Wearing the cut isn't just tolerated there, but encouraged. Many public pools in France, for instance, ban boardshorts in favor of Speedos for "hygienic reasons," claiming baggy shorts can drag dirt and objects into the water. Tiny briefs speckle the beaches of the French Riviera, too, where a man wearing baggy shorts is more likely to get odd looks than a man who's comfortable in his briefs.
Yet there's clearly some daring that goes into rocking a Speedo in public spaces. Waier tried his first pair when he was around 20, and caught some jokes from his friends and acquaintances about the skimpy swimwear (my greatest fear, of course). Even today, he picks and chooses the occasions to bust out the briefs: "When I'm at a resort with a nice private pool, my mood is to wear a brief. My mood at a big pool party with 300 people in Vegas is to wear a mid-thigh trunk. That comfort level is still a big factor," he says.
Since the majority of people don't wear brief-cut swimwear, anyone who does is automatically subject to greater scrutiny, which can be challenging even to those who are comfortable with their bodies. As 32-year-old redditor JustRandomOne, who lives in Southeast Asia, says, it's a mental obstacle that has to be overcome, similar to venturing out in public in any sort of unconventional outfit. "Now I just wear it and don't think much. I'd still admit that occasional jokes or glances from others do make me uncomfortable from time to time, though," he explains.
In JustRandomOne's mind, there's a double standard in American culture, where women are generally encouraged through imagery and media messaging that skimpy swimwear is ideal, but where men are mocked for trying a Speedo unless he's shredded, with abs and a tight upper body worth showing off.
Maxin adds that another way to start wearing brief-cut swimwear is to layer them with board shorts, so that you can bust out the Speedo look when "optimum sun hits and get rid of the tan lines," which provides a more concrete justification for trying the look.


Connecticut College Student Center, Mohegan Ave.
The Quilt Guild will be exhibiting over 250 quilts as well as an exhibit of Hoffman Challenge quilts. The featured speaker is Gyleen Fitzgerald who will be teaching a workshop and presenting a trunk show. There will also be vendors, demonstrations, large boutique area, basket drawings, and a quilt raffle.


text:
Video courtesy Hawaii County Council / edited by BIVN, voice of Sherry Bracken
VIDEO: Council Gets East Hawaii Organics Facility Update
HILO, Hawaii - Officials reveal the three new sites under consideration for the future East Hawaii Organics Facility. The studies will take a year to complete.
Courtesy EHOF draft EA
(BIVN) – Hawaii County Councilmembers were given an update on the organic waste program during a recent committee meeting.
The issue goes back to early 2017. As the new year began, the East Hawaii Organics Facility planned for Panaewa had the community concerned. When newly elected mayor Harry Kim said he was going to take a second look at the project – which was spearheaded by the previous administration – it came to the attention of the Council, which had previously approved the facility. The debate that followed exposed a rift between the county's legislative and executive branches.
Video by David Corrigan, voice of Sherry Bracken, published Dec. 31, 2017.
One year later: On February 7, Environmental Management Committee chair Eileen O'Hara summarized the events leading up to today.
"On February 16th, our mayor canceled a contract that had been let by the previous administration," O'Hara said. "It was a ten year contract. After considerable back-and-forth between the council, the administration,
and the company, it was resolved by rescinding the cancellation notice in April. At that time, because negotiations were taking place between the company (Hawaiian Earth Recycling) and the County, a change-to-contract or a supplemental contract needed to be fashioned."
Corporation Counsel Joe Kamelamela then gave an update on the county's supplemental contract with Hawaiian Earth Recycling, or HER.
"This thick contract that you see before me," Kamelamela said, turning to a thick binder of paper, "really takes a lot of work. As you can see by my two-page letter, there's a lot of time that is spent to ensure that both parties – both HER and at the county – work together to make sure that we get the best contract term for both parties."
Hilo councilmember Aaron Chung was alarmed by the need to put the project out to bid.
"Whose idea was that?" Chung demanded.
"It was an issue that was brought up because of the procurement code," Kamelamela responded. "So it was important that the county does that. So, that is a substantial change."
If Hawaiian Earth Recycling is going to operate the facility, then "why don't they build it?" Chung asked.
"The issue of the construction of the facility modified, once we went in and we were changing the location," the Director of the Department of Environmental Management, Bill Kucharski, tried to explain. "My understanding of when the original RFP went out, there were no funds available to pay for the facility. It was only after the original contract was signed that we have a cost the $10 million, plus or minus. Then, once we went in and we moved the facility – and we had the rescission and we returned – we had already allocated that money, county monies, that $10 million dollars, because we couldn't sign the contract without having the allocation, and certifying funds are available for that contract."
"Once those funds were certified," Kucharski continued, "We are now in a position of not having put out for bid a design-build, and so now we have to do a design-bid-build, because we're building this with county funds. Originally, it was the contractors' funds that were going to be used and we were going to repay. At this point, we're now in a design-bid-build. So, that was the primary reason for the change."
"To me a design-build is more efficient," Chung said. "We had a contract with these guys."
"I'm gonna blow my mind if the price goes up, now, because we are coming in to build this thing," Chung said.
Kucharski also revealed that the site for the East Hawaii facility will be somewhere in the Kea'au area of Puna.
"We currently have a contract with AECOM, who is looking at three separate sites," Kucharski said. "Two of them in the Shipman Industrial Park, another one by the Keaau Transfer Station. They're being examined for engineering suitability of these sites."
"They will then grade those three sites to find a preferred site from the perspective of engineering," Kucharski continued. "We have a second contract with SSFM to do an (Environmental Assessment) that is being routed for a
signature, and we should commence within the month. That EA will then take a look at all of the cultural, traffic, noise, all of the things that you're required to do for all three of the sites as is required by the environmental statutes, by HR 343. We expect to have that decision done, and the report done, by the end of this year. Once we go through the process, if everything works as we hope it will – and nothing is certain with an EA – by January of next year we should have a site selected and the full EA process completed."
"That then leaves 18 months for design and construction," Kucharski said. "Design, bidding, and construction of the
facility in East Hawaii. And so that is the schedule."
The larger environmental waste project looming over East Hawaii is the closure of the South Hilo Sanitary Landfill. On February 8, the final environmental assessment for the landfill closure was published. The document has come up with a Finding of No Significant Impact resulting from the project.
Filed Under: Video Report Tagged With: Aaron Chung, Bill Kucharski, East Hawaii Organics Facility, Eileen O'Hara, Gregory Goodell, Hawaii County Council


text:
Ebben a szócikkben a Manchester City nemzetközi kupaszereplései találhatóak. A Manchester City története során 15 szezonban 16 európai kupasorozatban vett részt, ezek közül egyet meg is nyert, az 1970-es kupagyőztesek Európa-kupája-döntőt.

1968–69

Bajnokcsapatok Európa-kupája

1. kör

Továbbjutott a Fenerbahçe 2–1-es összesítéssel.

1969–70

Kupagyőztesek Európa-kupája

1. kör

Továbbjutott a Manchester City 6–3-as összesítéssel.

2. kör

Továbbjutott a Manchester City 8–0-s összesítéssel.

3. kör

Továbbjutott a Manchester City 1–0-s összesítéssel.

Elődöntő

Továbbjutott a Manchester City 5–2-es összesítéssel.

Döntő

1970–71

Kupagyőztesek Európa-kupája

1. kör

Továbbjutott a Manchester City 2–2-es összesítéssel, idegenben lőtt több góllal.

2. kör

Továbbjutott a Manchester City 3–0-s összesítéssel.

3. kör

Újrajátszott mérkőzésen továbbjutott a Manchester City 2–2-s összesítéssel.

Elődöntő

Továbbjutott a Chelsea 2–0-s összesítéssel.

1972–73

UEFA-kupa

1. kör

Továbbjutott a Valencia 4–2-es összesítéssel.

1976–77

UEFA-kupa

1. kör

Továbbjutott a Juventus 2–1-es összesítéssel.

1977–78

UEFA-kupa

1. kör

Továbbjutott a Widzew Łódź 2–2-es összesítéssel, idegenben lőtt több góllal.

1978–79

UEFA-kupa

1. kör

Továbbjutott a Manchester City 4–3-as összesítéssel.

2. kör

Továbbjutott a Manchester City 4–2-es összesítéssel.

3. kör

Továbbjutott a Manchester City 5–2-es összesítéssel.

Negyeddöntő

Továbbjutott a Mönchengladbach 4–2-es összesítéssel.

2003–04

UEFA-kupa

Selejtezőkör

Továbbjutott a Manchester City 7–0-s összesítéssel.

1. kör

Továbbjutott a Manchester City 4–2-es összesítéssel.

2. kör

Továbbjutott a Dyskobolia Grodzisk Wielkopolski 1–1-es összesítéssel, idegenben lőtt több góllal.

2008–09

UEFA-kupa

Első selejtezőkör

Továbbjutott a Manchester City 4–0-s összesítéssel.

Második selejtezőkör

Továbbjutott a Manchester City 1–1-s összesítéssel, büntetőkkel.

1. kör

Továbbjutott a Manchester City 4–2-es összesítéssel.

Csoportkör

Csoportjából a Manchester City 1. helyen jutott tovább.

A legjobb 16 közé jutásért

Nyolcaddöntő

Továbbjutott a Manchester City 2–2-es összesítéssel, büntetőkkel.

Negyeddöntő

Továbbjutott a Hamburg 4–3-as összesítéssel.

2010–11

Európa-liga

Rájátszás

Továbbjutott a Manchester City 3–0-s összesítéssel.

Csoportkör

Csoportjából a Manchester City 1. helyen jutott tovább.

A legjobb 16 közé jutásért

Továbbjutott a Manchester City 3–0-s összesítéssel.

Nyolcaddöntő

Továbbjutott a Dinamo Kijev 2–1-es összesítéssel.

2011–12

Bajnokok Ligája

Csoportkör

A Manchester City a 3. helyen végzett csoportjában, így az Európa-ligában folytatta.

Európa-liga

A legjobb 16 közé jutásért

Továbbjutott a Manchester City 6–1-es összesítéssel.

Nyolcaddöntő

Továbbjutott a Sporting 3–3-as összesítéssel, idegenben lőtt több góllal.

2012–13

Bajnokok Ligája

Csoportkör

A Manchester City a 4. helyen végzett csoportjában, így kiesett.

2013–14

Bajnokok Ligája

Csoportkör

A Manchester City a 2. helyen végzett csoportjában és továbbjutott.

Nyolcaddöntő

Továbbjutott a Barcelona 4–1-es összesítéssel.

2014–15

Bajnokok Ligája

Csoportkör

A Manchester City a 2. helyen végzett csoportjában és továbbjutott.

Nyolcaddöntő

Továbbjutott a Barcelona 3–1-es összesítéssel.

2015–16

Bajnokok Ligája

Csoportkör

A Manchester City az 1. helyen végzett csoportjában és továbbjutott.

Nyolcaddöntő

Továbbjutott a Manchester City 3–1-es összesítéssel.

Negyeddöntő

Továbbjutott a Manchester City 3–2-es összesítéssel.

Elődöntő

Továbbjutott a Real Madrid 1–0-s összesítéssel.

2016–17

Bajnokok Ligája

Rájátszás

Továbbjutott a Manchester City 6–0-s összesítéssel.

Csoportkör

A Manchester City a 2. helyen végzett csoportjában és továbbjutott.

Nyolcaddöntő

Továbbjutott a Monaco 6–6-os összesítéssel, idegenben lőtt több góllal.

2017–18

Bajnokok Ligája

Csoportkör

A Manchester City az 1. helyen végzett csoportjában és továbbjutott.

Nyolcaddöntő

Továbbjutott a Manchester City 5–2-es összesítéssel.

Negyeddöntő

Továbbjutott a Liverpool 5–1-es összesítéssel.

2018–19

Bajnokok Ligája

Csoportkör

A Manchester City az 1. helyen végzett csoportjában és továbbjutott.

Nyolcaddöntő

Továbbjutott a Manchester City 10–2-es összesítéssel.

Negyeddöntő

Továbbjutott a Tottenham Hotspur 4–4-es gólkülönbséggel, idegenben lőtt több góllal.

Statisztika

Versenyenként
{| class="wikitable plainrowheaders unsortable" style="text-align:center"
|-
!scope=col|Sorozat
!scope=col|Szezon
!scope=col|
!scope=col|
!scope=col|
!scope=col|
!scope=col|
!scope=col|
!scope=col|
|-
!colspan="9"|UEFA-versenyek
|-
!scope=row|BEK / BL
|9||72||34||14||24||136||89||+47
|-
!scope=row|Kupagyőztesek Európa-kupája
|2||18||11||2||5||32||13||+19
|-
!scope=row|UEFA-kupa / Európa-liga
|7||52||28||13||11||86||58||+28
|-
!scope=row|Összesen
|18||142||73||29||40||254||160||+94
|}

Országonként

Kapcsolódó szócikkek

Források

 uefa.com

Manchester City FC

redpajama_set_name: RedPajamaWikipedia


Why Small Molecule Crystal Structure Validation ? Ton Spek, National Single Crystal Facility, Utrecht University, Utrecht, The Netherlands Sevilla, 14 -Dec-2010.
1964 Nobel Lecture Dorothy Hodgkin …. [The] great advantage of X-ray analysis as a method of chemical structure analysis is its power to show some totally unexpected and surprising structure with, at the same time, complete certainty. . .
With "Complete Certainty" ? Yes, in most cases, in particular in the hands of experienced investigators. No, when proper scientific procedures have been ignored. This presentation will address a number of obvious cases where proper procedures were ignored, resulting in erroneous science. Automated Structure Validation is offered as a tool to add a qualifier Good (Correct), Bad(False) or Ugly(Poor) to a structural study.
HOT STRUCTURE – FAST LANE PUBLICATION Cp*(+) !!. ?
Strange Bond Pattern and Ring pucker D o D PACKING EFFECTS ? ? Double Bond ?
Where did it go Wrong ? First impression/interpretation of the structure was likely based on a preliminary result (plot) without H-atoms. Rushed as a short communication into the prestigious high impact journal Angewandte Chemie. Ignoring all counter evidence. No experienced crystallographer as referee ? No unbiased automated CIF-validation to ALERT.
Has any Referee Looked at this Recent Paper ? Ce(III), Ce(II) or Something else ?
Consult CSD/VISTA for Expected X-Ow Distances Ce-Ow Distances Cd-Ow Distances Conclusion: This is a Cd complex and not a Ce complex ? The authors claim the use of Ce(NO 3) in the synthesis !? We need the (absent) reflection data for an absolute proof !
Three Examples of Erroneous entries archived in the CSD • The CSD is a rich source of chemical information. • However: An analysis of the > 500000 structures in the CSD learns that a not insignificant number of the entries has undetected serious errors. • Nearly all searches in the CSD for statistical info show (e. g. with VISTA) outliers that, when inspected closely, can be shown to be erroneous. • The following three problem cases were detected as part of a search for short S…S contacts.
Huge Geometry Differences !? EXAMPLE 1 There is obviously a problem with 3 e: Where were the referees of this paper ?
But with Space Group Symmetry EXAMPLE 2 => Different structure with S-S Bond !
EXAMPLE 3 DIMER: S-S Bridge !
Moral • 'Molecules' in a crystal are not always identical with what is found in the asymmetric unit – look at the crystalline environment. • Similarly: Hydrogen atoms on O-H generally point to an acceptor and not somewhere in space.
WHAT ARE THE VALIDATION QUESTIONS ? Single Crystal Structure Validation addresses three simple but important questions: 1 – Is the reported information complete? 2 – What is the quality of the analysis? 3 – Is the Structure Correct?
Implementation Problems of Structure Validation Before 1990 • • • Multiple Data Storage Types (often hard-copy listings ). No Standard Computer Readable Format for data exchange. Data entry for publication via retyping in the manuscript. Thus: multiple typo's in Published Data. CSD Database Archival by Retyping from the published paper. • Published data often incomplete. • No easy numerical checking by referees etc.
VALIDATION ALERT TYPES 1 - CIF Construction/Syntax errors, Missing or Inconsistent Data. 2 - Indicators that the Structure Model may be Wrong or Deficient. 3 - Indicators that the quality of the results may be low. 4 – Info, Cosmetic Improvements, Queries and Suggestions.
Problems Addressed by PLATON Too Many Hydrogen Atoms on an Atom Missing or misplaced Hydrogen Atoms Valence & Hybridization Short Intra/Inter-Molecular Contacts O-H without Acceptor Unusual Bond Length/Angle CH 3 Moiety Geometry To be extended with tests for new problems 'invented' by authors.
Simple Validation Issues • Many data sets are apparently collected at either 293(2) or 273 K • Improper program defaults or values from previous papers are retained (e. g. sealed tube in combination with synchrotron data) • Data collected with a CCD system and corrected for absorption with Psi-scans ! ?
Examples of Correctable Issues • Following are some examples of the type of problems addressed. 1 – Refinement in the Wrong Space group. 2 – Wrong Atom Type Assignment. 3 – Misplaced H-Atoms. 4 – Missing H-Atoms.
Searching for structures with a Methyl Moiety bridging two metals … Structure of a strange CH 3 Bridged Zr Dimer Paper has been cited 47 times ! So can we believe this structure? The Referees did …! But … H. . H = 1. 32 Ang. !
Evaluation and Performance • The validation scheme has been very successful for Acta Cryst. C & E in setting standards for quality and reliability. • The missed symmetry problem has been solved for the IUCr journals (unfortunately not generally yet: There are still numerous 'Marshable' structures). • Most major chemical journals currently have now some form of a validation scheme implemented. • But, has it solved all problems … ?
Problems to be Addressed • Synthetic Chemist View: 'Addressing Crystallographic Details holds up the Publication of Important Chemistry' (but see previous example in Angew. Chemie !) • Interesting Author Question in response to referee issue: What does it mean "Space group Incorrect" • Crystallographic Education (beyond Pushbutton training and Black Box operation) is getting scarce nowadays. • Sadly: Referees who do not understand or do not know how to respond adequately to ALERTS • Recently: The need to Detect Fraud and Fraudulous manipulation ….
Note on Editing the CIF • The Idea of editing the CIF is to add missing (experimental) information to the CIF. • However: Some authors have now been found to polish away less nice numerical values. • This leaves traces and is generally detected sooner or later by the validation software and is not good for the scientific career of the culprit… • The recently implemented FCF-Checking now addresses this issue in even more detail.
FCF-VALIDATION - Check of CIF & FCF data Consistency - Check of completeness of the reflection data set. - Automatic Detection of ignored twinning - Detection of Applied Twinning Correction without having been Reported in the paper. - Validity check of the reported Flack parameter value against the Hooft parameter value. - Analysis of the details of the Difference Density Fourier Map for unreported features.
Sloppy, Novice or Fraudulent ? • Errors are easily made and unfortunately not always discernable from fraud. • Wrong element type assignments can be caused as part of an incorrect analysis of an unintended reaction product. • Alternative element types can be (and have been) substituted deliberately to create a 'new publishable' structure.
The need of serious validation by knowledgeable Referees • The validation issues and tools are probably best illustrated with an analysis of a few fraudulous papers that reached the recent literature and (unfortunately) the CSD. • Early warning signs are generally: troublesome displacement parameters and unusual short inter-molecular contacts.
Comparison of the Observed data for two 'isomorphous' compounds. The Only Difference Is the SCALE ! Same Data ! SLOPPY Or FRAUD ?
References www. cryst. chem. uu. nl/platon www. cryst. chem. uu. nl/xraysoft www. cryst. chem. uu. nl/platon/CIF-VALIDATION. pdf www. cryst. chem. uu. nl/platon/FCF-VALIDATION. pdf • Papers on structure validation: • A. L. Spek (2003). J. Appl. Cryst. 36, 7 -13. • A. L. Spek (2009). Acta Cryst. D 65, 148 -155.


text:
Siasat.com/UAPA
UAPA
UAPA Tribunal issues notice to Zakir Naik's Islamic Research Foundation
New Delhi: A tribunal, which is examining the validity of the five-year extension of the ban on Zakir Naik's Islamic Research Foundation (IRF) by the Centre as an unlawful association under the UAPA,…
Exclusive interview: Justice Chandru on why our Constitution matters
Hyderabad: On December 18, Justice K Chandru – the high court judge popularized by the movie Jai Bhim—was supposed to attend the movie screening followed by a Q and A at the…
Centre forms UAPA Tribunal to probe ban on Zakir Naik's IRF
New Delhi: The Centre has constituted an Unlawful Activities (Prevention) Tribunal headed by Delhi High Court Chief Justice D.N. Patel under the Unlawful Activities (Prevention) Act, 1967 (UAPA) provisions to adjudicate whether there…
Activist Sudha Bharadwaj released from jail after 3 years
Mumbai: Activist Sudha Bharadwaj, an accused in the Elgar Parishad-Maoist links case, was on Thursday released from a prison here on bail, after spending over three years in jail. Bharadwaj (60), who…
Sudha Bharadwaj to be released; NIA imposes tough bail terms
Mumbai: A special NIA court on Wednesday held that jailed lawyer-activist Sudha Bharadwaj, who has been granted default bail by the Bombay High Court in the Elgar Parishad-Maoist links case, to be released…
Sedition, UAPA being distributed like Prasad: Swara to Mamta Banerjee
Mumbai: Artists are finding it difficult to "tell stories" and the government is using sedition law and UAPA provisions indiscriminately, actor Swara Bhaskar said during an interaction with West Bengal Chief Minister…
Sharjeel Imam granted bail in one of the cases, to remain in jail
Hyderabad: Jawaharlal Nehru University (JNU) scholar and activist Sharjeel Imam has been granted bail in one of the cases registered by the Uttar Pradesh police against him. Sharjeel will however continue to…
Tripura police to review UAPA cases against journalists, lawyers
Agartala: Tripura Chief Minister Biplab Kumar Deb on Saturday directed Director General of Police (DGP) V.S. Yadav to review the UAPA (Unlawful Activities Prevention Act) cases lodged against journalists and lawyers, after some…
Malegaon blast case: Pragya Thakur appears before Mumbai court
Mumbai: BJP's Bhopal MP Pragya Singh Thakur, an accused in the 2008 Malegaon blast case, appeared before a special NIA court here on Wednesday. She appeared before special judge P R Sitre, hearing…
NIA arrests Kashmiri human rights activist Khurram Parvez
New Delhi: The National Investigation Agency (NIA) on Monday arrested prominent human rights activist Khurram Parvez from Jammu and Kashmir in connection with its ongoing probe in a terror funding case. The…
Vir Das's 'I come from 2 Indias' performance stirs row in India
Indian stand-up comedian Vir Das has become the centre of discussion on social media after he posted the video of his show filmed at the John F Kennedy Center for the Performing…
SC grants protection to lawyers, journalist booked with UAPA in Tripura
New Delhi: The Supreme Court on Wednesday issued notice to the Tripura government on a plea against its decision to invoke the Unlawful Activities (Prevention) Act (UAPA) against two lawyers, and a…
Central govt extends bans on Zakir Naik's NGO IRF for 5 years
New Delhi: The ban imposed on the Islamic Research Foundation (IRF), set up by Zakir Naik who was accused of inspiring Muslim youths in India and abroad to commit terror acts, has…
Tripura violence: SC agrees to hear plea by journalist, others booked under UAPA
New Delhi: The Supreme Court on Thursday agreed to hear a plea challenging the Tripura Police's decision to invoke the Unlawful Activities (Prevention) Act (UAPA) against several lawyers, activists and journalist Shyam…
Penguin postpones Varavara Rao's book amidst UAPA charges
Hyderabad: Unlawful Activities Prevention Act's (UAPA) victim, Telugu poet Varavara Rao's book of poetry is not likely to be published anytime soon. The poet's collection of poems has been put on hold…


text:
Sessions 25COM
Year Year 202320222021202020192018201720162015201420132012201120102009200820072006200520042003200220012000199919981997199619951994199319921991199019891988198719861985198419831982198119801979197819771976
25th session of the World Heritage Committee
Helsinki, Finland 11- 16 December 2001
Bureau Members
Chairperson: Mr. Henrik Lilius (Finland)
Rapporteur: Francisco Javier Lopez Morales (Mexico)
Vice-Chairpersons: Egypt, Greece, Hungary, South Africa, Thailand
Argentina, Belgium, China, Colombia, Egypt, Finland, Greece, Hungary, India, Lebanon, Mexico, Nigeria, Oman, Portugal, Republic of Korea, Russian Federation, Saint Lucia, South Africa, Thailand, United Kingdom of Great Britain and Northern Ireland, Zimbabwe
End of
Argentina 2001-2005 2005
Belgium 1999-2003 2003
China 1999-2005 2005
Colombia 1999-2005 2005
Egypt 1999-2005 2005
Finland 1997-2003 2003
Greece 1997-2003 2003
Hungary 1997-2003 2003
India 2001-2007 2007
Lebanon 2001-2005 2005
Mexico 1997-2003 2003
Nigeria 2001-2005 2005
Oman 2001-2005 2005
Portugal 1999-2005 2005
Republic of Korea 1997-2003 2003
Russian Federation 2001-2005 2005
Saint Lucia 2001-2005 2005
South Africa 1999-2005 2005
Thailand 1997-2003 2003
United Kingdom of Great Britain and Northern Ireland 2001-2005 2005
Zimbabwe 1997-2003 2003
Report of the Rapporteur on the twenty-fifth extraordinary session of the Bureau, Helsinki, Finland, 7-8 December 2001
Report of the twenty-fifth session of the World Heritage Committee (Helsinki, Finland, 11 - 16 December 2001)
Working and Information Documents Nominations
States Parties Meeting towards a joint nomination of areas of the Alpine Arc for the World Heritage List (Turin, Italy 5-8 July 2001)
Information Meeting for States Parties


The SVG Generator example shows how to add SVG file export to applications.
Scalable Vector Graphics (SVG) is an XML-based language for describing two-dimensional vector graphics. Qt provides classes for rendering and generating SVG drawings. This example allows the user to create a simple picture and save it to an SVG file.
The example consists of two classes: Window and DisplayWidget.
The Window class contains the application logic and constructs the user interface from a Qt Designer UI file as described in the Qt Designer manual. It also contains the code to write an SVG file.
The DisplayWidget class performs all the work of painting a picture on screen. Since we want the SVG to resemble this picture as closely as possible, we make this code available to the Window class so that it can be used to generate SVG files.
Much of this class is used to configure the appearance of the drawing. The paintEvent() and paint() functions are most relevant to the purpose of this example, so we will describe these here and leave the reader to look at the source code for the example to see how shapes and colors are handled.
Here, we only construct a QPainter object, begin painting on the device and set a render hint for improved output quality before calling the paint() function to perform the painting itself. When this returns, we close the painter and return.
As with the DisplayWidget class, we concentrate on the parts of the code which are concerned with painting and SVG generation. In the Window class, the saveSvg() function is called whenever the Save As... button is clicked; this connection was defined in the window.ui file using Qt Designer.
The start of the saveSvg() function performs the task of showing a file dialog so that the user can specify a SVG file to save the drawing to.
In the rest of the function, we set up the generator and configure it to generate output with the appropriate dimensions and write to the user-specified file. We paint on the QSvgGenerator object in the same way that we paint on a widget, calling the DisplayWidget::paint() function so that we use exactly the same code that we used to display the drawing.
The generation process itself begins with the call to the painter's begin() function and ends with call to its end() function. The QSvgGenerator paint device relies on the explicit use of these functions to ensure that output is written to the file.
The SVG Viewer Example shows how to display SVG drawings in an application, and can be used to show the contents of SVG files created by this example.
See the Qt SVG module documentation for more information about SVG and Qt's SVG classes.


text:
Гладсаксе () — датская коммуна в составе области Ховедстаден. Площадь — 25 км², что составляет 0,06 % от площади Дании без Гренландии и Фарерских островов. Численность населения на 1 января 2008 года — 62562 чел. (мужчины — 30477, женщины — 32085; иностранные граждане — 4257).

В состав коммуны входят Сёборг (Søborg), Буддинге (Buddinge), Багсвер (Bagsværd), Мёркхёй (Mørkhøj).

Железнодорожные станции
 Багсвер (Bagsværd)
 Буддинге (Buddinge)
 Киллебакке (Kildebakke)
 Скоубрюнет (Skovbrynet)
 Стенгорден (Stengården)

Изображения

Ссылки
 Гладсаксе на borger.dk
 Официальный сайт

Коммуны Дании


This study tests whether individuals who grow up with parents on welfare benefits are themselves more (or less) likely to be welfare recipients as young adults, compared to individuals who grow up in non-welfare households. We use the sibling difference method to identify causal effects separately from the effects of correlated factors. While a descriptive analysis reveals a fairly high positive intergenerational correlation, especially in the late teens and conditional on a large set of household level factors, the sibling analysis provides no support for a causal effect of parents' welfare benefit receipt on children's future welfare use.


text:
Student on Leave After Claiming She Jabbed Patient Over Pronoun Pin
Roni Robbins
A student at Wake Forest University School of Medicine is on leave after apologizing for a tweet in which she bragged about unnecessarily sticking a patient twice while drawing blood.
In the post, which has since been deleted, the student said she did so to make a point about transgender rights. After a backlash on social media, the school told Medscape Medical News it followed all protocols and the student has apologized for the misleading tweet.
Kychelle Del Rosario, a fourth-year student at the North Carolina medical school, tweeted that she responded to a male patient joking about the "she/her" pronoun pin she was wearing by double jabbing his arm.
https://twitter.com/InspirationName/status/1508848629888569357
"I had a patient I was doing a blood draw on see my pronoun pin and loudly laugh to the staff 'She/Her? Well of course it is! What other pronouns even are there? It?' I missed his vein so he had to get stuck twice'," Del Rosario tweeted in the post that has since been removed. It was captured, though, by others on Twitter reacting harshly to the tweet.
When Del Rosario's controversial post was first brought to its attention, the medical school responded on Twitter: "This student's tweet does not reflect how Wake Forest University School of Medicine treats patients and provides patient care. We are taking measures to address this with the student."
Late Thursday, the medical school told Medscape Medical News its review of the social media post "revealed that the description of the patient encounter on social media does not reflect what actually occurred. We also determined that all of our procedures were followed while caring for this patient."
The school explained that all student actions are documented while treating patients and if students have an initial unsuccessful blood draw, a certified medical professional steps in. That's what happened in this case, the med school stated. "The student did not attempt to draw blood again."
In addition, the student apologized to the school "for her misguided post," and the school shared that apology, with her permission.
"I am writing this as an apology for a very irresponsible tweet that I sent on Twitter that I highly regret. For the event mentioned in the tweet, I was performing a blood draw on a patient, and during our conversation they had shown dismay at my pronoun pin. I calmly shared my thoughts about pronouns and did not escalate the situation further."
The student chalked up her unsuccessful blood draw to "my inexperience as a student," but explained that her supervisor performed the second successful draw. "During this encounter, I never intended to harm the patient. I understand how my misguided tweet read that I did intend to harm them as retribution."
She said the tweet was the result of "an emotional moment" in which she didn't consider the consequences. "I am truly sorry for poorly representing our school and our health system. I will reflect on responsible social media use as a professional and my duty to care for all patients, regardless of any differences in beliefs."
The med school concluded, "As a result of the inappropriate and misleading post, the student has been placed on a leave of absence."
The comments by Del Rosario, who is a trans rights activist, were in response to a post by illustrator and author Shirlene Obuobi, MD, about transphobia. Oboubi, who identifies as a cisgender woman, posted that she has worn a "she/her" badge for a year. "I wear it to help my patients & colleagues who fall under the trans umbrella feel a little more comfy. In the last few weeks, several cis patients have berated me for it."
Among the responses to Del Rosario's post, one tweeter commented: "This is offensive and disturbing. I am a nurse practitioner and this is a form of patient abuse."
Another tweeter posted: "It's concerning that a doctor feels that patients [whose] political stance they don't agree with deserve what they deem to be 'karma.'"
Still more tweets included: "We have all done things we regret, but being proud of them is frightening for future patients." Or as one tweeter opined: "Unprofessional, unethical & negligent."
According to Del Rosario's LinkedIn account, she is a graduate of the University of Virginia Class of 2017 in cognitive science with a neuroscience concentration and biology, is working in several general pediatrics clinics, and is "aspiring to become a medical doctor."
Last year, Del Rosario published an essay that appeared in the Winston-Salem Journal urging the US Senate to pass the Equality Act prohibiting discrimination based on sex, gender identity, and sexual orientation.
She stated in the essay, which also appeared on The Albert Schweitzer Fellowship website, that she was a leader in Safe Zone in Medicine, which is "run by healthcare trainees whose goal is to educate health professionals about the needs and disparities in LGBTQ+ healthcare."
Del Rosario further stated that the role prepares her "to become a trustworthy doctor and advocate for the transgender community — a population which the medical field has harmed greatly in the past. It also allows me to train other healthcare professionals who aim to improve their practice to be more welcoming and gender-affirming."
For more news, follow Medscape on Facebook, Twitter, Instagram, and YouTube.
Lead Image: Getty Images
Medscape Medical News © 2022
Cite this: Roni Robbins. Student on Leave After Claiming She Jabbed Patient Over Pronoun Pin - Medscape - Mar 31, 2022.
A Gender Imbalance Emerges Among Trans Teens Seeking Treatment
As More Transgender Children Seek Medical Care, Families Confront Many Unknowns
What Trump and Biden Should Debate at the Cleveland Clinic: Why the Hospital's Private Police Mostly Arrest Black People
Gender-Inclusive Language Is Key to Transgender Patient Care
Nurses' Questions Answered: Bedside Manner When Training
Med Student's App Links Trans Patients, Gender-Affirming Docs


Beowulf @Beowulf77 replied to this post.
Beowulf @Beowulf77 liked @DD-DD's drawing.
Beowulf commented on this post.
"Moonstar:*Turns into A red skinned creature with no eyes* Everyone aim for the throat!"
"Moonstar: All leaders Use your Abilities!"
From a show Called Wakfu Im still a child!
"*Five more Windigos charge into the cave*"
"*Knocks the Windigo into the wall* ////Smokeheart: *bites its throat.*"
"Windigo:*runs into the camp runing to the biggest crowd*////moonstar: * jumps on its back*Lionstar roar!"
"Moonstar: Thank you My friend* Everyone get to the sides of the cave*Windigos starts screeching and howling* and dont let them get to you."
"Moonstar: Ok, how ever We need all othose who do not want to fight go to the back of the cave."


text:
Hear Darius Rucker, Luke Bryan, Jason Aldean + Charles Kelley Go 'Straight to Hell'
Darius Rucker is going "Straight to Hell" in one of the coolest songs on his new album, When Was the Last Time, and Luke Bryan, Jason Aldean and Lady Antebellum singer Charles Kelley are along for the ride.
"Straight to Hell" is a song originally written by Drivin' N Cryin' singer Kevn Kinney and released on the Atlanta-based group's Mystery Road album in 1989. Rucker says he's wanted to cover it for a long time, but he never got around to it until he got a random phone call from Kelley.
"Charles calls me out of the blue and says, 'Hey man, I just listened to this Drivin' N Cryin' song, you should cut that 'Straight to Hell,'" Rucker tells Taste of Country Nights. "I thought that was the universe telling me to cut the song."
Nope, There's No Way These Country Singers Are 50!
Kelley also told Rucker he'd love to join him on the track, and Rucker ended up inviting Bryan and Aldean aboard for an all-star collaboration that he says he'd like to release as a single. The new recording trades the pathos and driving power-chord rock of Drivin' N Cryin's original with a more easygoing countrified, contemporary feel that has all of the hallmarks of an early contender for next year's Musical Event of the Year, and Rucker hopes he might find an opportunity to give the song even more exposure.
"I hope some awards show or something gives us an opportunity to come out and play that," he says.
Rucker released When Was the Last Time on Oct. 20. He's already scored a No. 1 hit with its lead single, "If I Told You," and the second single from the album, "For the First Time," is currently at country radio.
See Artists Who've Unexpectedly Gone Country
Next: Darius Rucker + More Tell Dad Jokes
Filed Under: Charles Kelley, Darius Rucker, Jason Aldean, Luke Bryan
Categories: Country Music News, Country Songs


text:
import bouncebox.core.api as bb
import pandas as pd

class TestEventComponent(bb.Component):
    listeners = [(bb.Event, "handle_event")]

    def __init__(self):
        super(TestEventComponent, self).__init__()

        self.sum = 0

    def handle_event(self, event):
        print event

    def end(self, _event):
        print 'THE END'

ind = pd.date_range(start="2000-01-01", freq="D", periods=10)
# create events
events = (bb.Event(ts) for ts in ind)
box = bb.BounceBox()

# add source, EventBroadcaster will broadcast an iterable
source = bb.EventBroadcaster(events)
box.add_source(source)

comp = TestEventComponent()
box.add_component(comp)

box.start_box()

redpajama_set_name: RedPajamaGithub


text:
Q: Print array diagonally I want to print diagonals from the following matrix
XVSOKG
WTPLHD
UQMIEB
RNJFCA

starting from bottom right corner so output should be A, B, C, D etc..
I wrote down elements and following indices like this
A [3,5], B[2,5], C[3,4], D[1,5], E[2,4], F[3,3] and so on but I cannot find out any pattern from this. How am I suppose to do this?

A: The pattern in fact is quite simple, the problem is that you need to be aware of the borders. I made a function that does what you are looking for (if i didn't misunderstand, for the matrix you posted you wanted the alphabet to be printed).
Unfortunaly I don't have any setup to do this in C# so I did it in Java, I hope you can simplify it and port it easily.
I tested with diferent sizes of matrices but... you know. Test it if you can.
With the following matrix:
String[][] matrix = new String[][]{
            {"X","V","S","O","K","G"},
            {"W","T","P","L","H","D"},
            {"U","Q","M","I","E","B"},
            {"R","N","J","F","C","A"}
        };

the result is:
3 - 5 = A
2 - 5 = B
3 - 4 = C
1 - 5 = D
2 - 4 = E
3 - 3 = F
0 - 5 = G
1 - 4 = H
2 - 3 = I
3 - 2 = J
0 - 4 = K
1 - 3 = L
2 - 2 = M
3 - 1 = N
0 - 3 = O
1 - 2 = P
2 - 1 = Q
3 - 0 = R
0 - 2 = S
1 - 1 = T
2 - 0 = U
0 - 1 = V
1 - 0 = W
0 - 0 = X

The code is the following:
(this looks long, but its mostly comments)
/**
 * Prints the diagonals of a matrix from bottom right to top left.
 *
 * @param matrix the matrix to print
 */
public static void printDiagonals(String[][] matrix){
    // extract the width and the height of the matrix
    int width = matrix[0].length;
    int height = matrix.length;

    /**
     * these are the pointers that go through the matrix, we inicialize it
     * in the bottom right corner
     */
    int xIndex = width - 1;
    int yIndex = height - 1;
    /**
     * these are auxiliar pointers to let me trace in what diagonal is the
     * next, they are optional but help making the code more clear; I
     * initialize it with the position above the bottom right corner
     */
    int startingX = xIndex;
    int startingY = yIndex - 1;

    //while we have not reach the top left corner
    while (xIndex >= 0 && yIndex >= 0){
        // print the current index and the value, here change it with watever you need
        System.out.println(yIndex + " - " + xIndex + " = " + matrix[yIndex][xIndex]);
        /**
         * as we are moving diagonally to the bottom left we achieve this by
         * decreasing the x index and increasing the Y index
         */
        xIndex--;
        yIndex++;
        //if we hit one of the borders
        if (yIndex == height || xIndex < 0){
            //move the indices to the next diagonal
            yIndex = startingY;
            xIndex = startingX;
            //then we adjust the next diagonal
            if (startingY > 0){
                startingY--;
            } else {
                startingX--;
            }
        }
    }
}

redpajama_set_name: RedPajamaStackExchange


If you were waiting for Telltale's Batman: The Enemy Within adventure game to fully finish before picking it up, now would be the time to do so as the final "Same Stitch" episode has just made its way to PC and consoles. There are very few details available, for obvious spoiler-related reasons, but what I can tell you is that the focus of the season finale will be on the Joker and the decisions you've made so far.
What would you choose: a friend whose unhinged approach to justice turns your allies against you, or a sworn enemy who will stop at nothing to see you suffer as your city burns," reads the fairly brief announcement. "Based on the relationship you've built with John Doe, you'll see one of two very different stories play out. So what'll it be, Bruce: friend…or foe?"
I can't tell you much more without potential ruining things, but if you're a fan of Batman I would highly recommend you check out The Enemy Within by heading over to Steam.


Sociological Methods & Research is a peer-reviewed academic journal that covers research in the field of sociology. The journal's editor-in-chief is Christopher Winship (Harvard University). It was established in 1972 and is currently published by SAGE Publications.
Sociological Methods & Research is abstracted and indexed in Scopus and the Social Sciences Citation Index. According to the Journal Citation Reports, its 2017 impact factor is 3.625, ranking it 5 out of 146 journals in the category "Sociology" and 3 out of 49 journals in the category "Social Sciences, Mathematical Methods".
^ "Journals Ranked by Impact: Sociology". 2013 Journal Citation Reports. Web of Science (Social Sciences ed.). Thomson Reuters. 2017.
^ "Journals Ranked by Impact: Social Sciences, Mathematical Methods". 2017 Journal Citation Reports. Web of Science (Social Sciences ed.). Thomson Reuters. 2017.
This page was last edited on 17 January 2019, at 14:52 (UTC).