text:
\section{#1}}
\newcommand{\addtocounter{section}{1} \setcounter{equation}{0}{\addtocounter{section}{1} \setcounter{equation}{0}
                         \section*{Appendix \Alph{section}}}
\renewcommand{\theequation}{\arabic{equation}}
\newcommand{\begin{equation}}{\begin{equation}}
\newcommand{\end{equation}}{\end{equation}}
\def\buildrel < \over {_{\sim}}{\buildrel < \over {_{\sim}}}
\def\buildrel > \over {_{\sim}}{\buildrel > \over {_{\sim}}}
\renewcommand{\today}{}
\title{\textbf{Investigating Sterile Neutrino Flux in the Solar Neutrino Data}}
\author{\small{Ankush
\footnote{ankush.bbau@gmail.com}}}
\author{\small{Rishu Verma
\footnote{rishuvrm274@gmail.com}}}
\author{\small{Gazal
Sharma\footnote{gazzal.sharma555@gmail.com}}}
\author{\small{B. C. Chauhan\footnote{chauhan@associates.iucaa.in}}}
\affil{\textit{Department of Physics \& Astronomical Science, }\\
\textit{ School of Physical \& Material Sciences,}\\
\textit{ Central University of Himachal Pradesh (CUHP),
Dharamshala, Kangra (HP),
India 176215}}
\date{}
\begin{document}

\maketitle

\begin{abstract}
There are compelling evidences for the existence of a fourth degree of freedom of neutrinos i.e. sterile neutrino. In the recent studies the role of sterile component of neutrinos has been found to be crucial, not only in particle physics, but also in astrophysics and cosmology. This has been proposed to be one of the potential candidates of dark matter. In this work we investigate the updated solar neutrino data available from all the relevant experiments including Borexino and KamLAND solar phase in a model independent way, and obtain bounds on the sterile neutrino component present in the solar neutrino flux. The mystery of the missing neutrinos is further deepening as subsequent experiments are coming up with their results. The energy spectrum of solar neutrinos, as predicted by Standard Solar Models (SSM), is seen by neutrino experiments at different parts as they are sensitive to various neutrino energy ranges. It is interesting to note that more than 98\% of the calculated standard model solar neutrino flux lies below 1 MeV. Therefore, the study of low energy neutrinos can give us better understanding and the possibility to know about the presence of antineutrino and sterile neutrino components in solar neutrino flux. As such, this work becomes interesting as we include the data from medium energy ($\sim$1 MeV) experiments i.e. Borexino and KamLAND solar phase. In our study we retrieve the bounds existing in literature, and rather provide more stringent limits on sterile neutrino ($\nu_{s}$) flux available in solar neutrino data.

\end{abstract}

\section{Introduction}
H. Bethe proposed that the thermonuclear reactions are responsible for energy generation inside the stars, and it was subsequently established too. Sun, being the closest star to us, glows due to these thermonuclear fusion reactions, which also produce a huge amount of neutrinos leaving the solar core without any hinderance. To look for these neutrinos, the era of the solar neutrino experiments began in the late 1960\textquotesingle s with the Homestake solar neutrino detector, which was headed by astrophysicists Raymond Davis, Jr. and his theoretician friend John N. Bahcall. This experiment was designed to understand the mechanism of fusion reactions taking place inside the sun, instead it discovered a significant shortfall of neutrino flux as compared to SSM. This is known  as the Solar Neutrino Problem (SNP) \cite{{Davis:1968cp},{Cleve:1998}}.  After a journey of about four decades a leading solution for the SNP was identified with the help of reactor experiment KamLAND \cite{Eguchi:2002dm} in Japan, which independently verified neutrino oscillations through Large Mixing Angle (LMA) \cite{LMA,LMA1,LMA2,LMA3,LMA4,LMA5,LMA6,LMA7}\bibliographystyle{unsrtnat}
as the dominant solution using neutrinos from nearby reactors. Motivated by peculiar nature of neutrinos, a number of subsequent experiments were performed, which rather than solving the mystery of the missing neutrinos, deepened it further. It came to the light that more than 98\% of the solar neutrino flux lies below 1MeV. The rare $^{8}$B neutrino flux is the high energy tail of solar neutrinos for which statistically significant measurements have been made so far. As such, the explored part of the flux is just a tip of an iceberg, there could be more mysteries hidden deep inside the water. Along with LMA there might be some sub-dominant effect (s) also affecting the nature and dynamics of these so called ghost particles. Therefore, the study of low energy neutrino data can give us better understanding and the possibility to explore the presence of sterile neutrinos and other components in solar neutrino flux.

Neutrinos are special and have a unique status in the Standard Model (SM) in the sense that they are massless and interact solely through the weak interaction. They are left handed only, i.e. active and partner of a corresponding charged lepton in a weak isospin doublet. As such, there is no place for the right-handed neutrinos in the SM. Right-handed neutrinos, if they exist, would be weak isospin singlets, i.e. not sensitive to even weak interaction. They would communicate with the other SM member neutrinos (left-handed active neutrinos) through mixing only. That is the reason, the right-handed neutrinos are called as inactive i.e. sterile.
There are mounting evidences for existence of additional degrees of freedom ( >3) of neutrinos, which indicate the existence of a new class of heavy and light sterile neutrinos, and possibility of their mixing with active ones \cite{sterile,sterile1,sterile2,sterile3,sterile4}\bibliographystyle{unsrtnat}.

The Stanford group has done analysis of the available solar neutrino data \cite{Sturrock:2004hx,Sturrock:2003kv,Caldwell:2003dw,Sturrock:2001qn}\bibliographystyle{unsrtnat} that provided increasing evidence that the neutrino flux from the sun is not constant but varies with well-known solar rotation periods. If such findings are confirmed ever in future, the need for an addition to the LMA solution will be obvious and will most likely rely on an interaction of the solar magnetic field with the neutrino  magnetic moment. Since an SFP (Spin Flavour Precession) conversion to active antineutrinos is unlikely, this interaction is expected to produce a significant and time varying flux of sterile neutrinos \cite{sterile}, \cite{Berezinsky:2002fa} and \cite{deHolanda:2002ma}.
It has become evident that the mechanism of SFP to active antineutrinos in the sun is either absent or plays a subdominant role.
In fact these active neutrinos would originate a sizeable $\bar\nu_e$ flux \cite{Eguchi:2003gg}, whose upper bound has become stricter and corresponds to 0.028\% of the $^8$B neutrino flux.

In the light of latest data available from various solar neutrino experiments, like the Neutral Current Detectors (NCDs) phase of Sudbury Neutrino Observatory (SNO), SuperK-III, SuperK-IV, Borexino and KamLAND solar phase \citep{sno,ncd,sk,BorII,Bor,kl} for neutrinos of energy range $\sim$1 MeV, we derive, in a model independent way, bounds on the sterile neutrino component present in the solar neutrino flux. We update the limits on the sterile neutrinos $(\nu_s)$ flux and compare them with the previous results obtained using various SNO phase data and data from SuperKamiokande experiments. Various such analysis \cite{Barger:2001pf,Barger:2001zs,Barger:2002iv,Balantekin:2004hi,bmw,Band,kang,bcc,skumar,lalsingh1} have been done in the past, but our results include all the experimental data, in a way it is a global data analysis and we obtain more constrained limits on the sterile neutrino flux as compared to the bounds existing in literature. The degeneracy of SSM normalisation factor (f$_B$)  and active neutrinos (sin$^2 \alpha$) is updated and best fit values for various cases using $\chi^{2}$ analysis are obtained.

In section ({\bf\ref{sec:2}}) we present the experimental details and the data available from all the solar neutrino experiments. In section ({\bf\ref{sec:3}}) we discuss the entire theory of model independent analysis starting from the master equations. Section ({\bf\ref{sec:4}}) presents results and discussion of our work including the $\chi^{2}$-analysis for different combination cases of various experiments, and the conclusions are finally summarised in section ({\bf\ref{sec:6}}).

\section{Data from various Solar Neutrino Experiments} \label{sec:2}

Kamiokande, a large water Cerenkov detector, was primarily designed to do search for proton decay. It was diverted to take data of solar neutrinos in the second phase i.e. Kamiokande-II in 1985, and provided a directional information of solar neutrinos demonstrating directly for the first time that the sun is a source of neutrinos. Via elastic scattering (ES) experiment this also discovered the atmospheric neutrinos anomaly and observed neutrino signals from the supernova 1987A.
Super-Kamiokande (SK) was designed after overhauling the Kamiokande to do search for proton decay, studied solar and atmospheric neutrinos, and watched the supernovae in the Milky Way Galaxy.
SK is a cylindrical 50kt water Cerenkov detector which observes high energy solar neutrinos via ES of electrons. The SK experiment started taking data in April 1996 and continued the observation for five years till July 2001, the running period referred as SK-I. The SK detector was rebuilt after an accident met with the half of the original PMT density in the inner detector and resumed observation from October 2002, which is referred as the beginning of SK-II running period.
The SK-II continued the measurements for three years and finished in October 2005 for the reconstruction work to put the PMT density back to the SK-I level. The detector restarted observation in June 2006, which is referred as the SK-III period.
The fourth phase of SK (SK-IV) started of in September of 2008, with new front-end electronics, QBEE (QTC Based Electronics with Ethernet)\cite{sk4,Yamada} for new data acquisition system.

The data obtained SNO consists also of high energy end part of $^{8}$B solar neutrinos. The SNO, based in Canada, detects neutrinos via three reaction channels 1) charged-current interactions (CC) on deuterons, in which only electron neutrinos participate; 2) neutrino-electron ES, which are dominated by contributions from electron neutrinos and 3) neutral-current (NC) disintegration of the deuteron by neutrinos, which has equal sensitivity to all active neutrino flavours. So far, the SNO has three stages/phases of running. The first phase was with pure D$_{2}$O (heavy water), ran from November 1999 to May 2001. In the second phase, to increase the neutron detection efficiency, 2000 kg of NaCl salt was added to the target material D$_{2}$O. This SNO-II (Salt phase) ran from June 2001 to October 2003. The third and final stage of SNO phase used NCDs, which was achieved by the removal of the salt and addition of 36 strings of $^{3}$He proportional counters  to provide an independent detection of neutrons. This SNO-III (NCDs)  phase ran from November 2004 to November 2006. As these three stages have very different systematic uncertainties for the detection of neutrons, the stages of the SNO (Phase -I, II, III) can be considered as three independent experiments in measuring the flux of $^{8}$B solar neutrino flux with the NC reaction. It is further added that in the second SNO phase of running a data set of 254.2 days with a 5.5 MeV energy threshold, and in the third phase of running for 385.2 days of data with a 5 MeV energy threshold are taken.

Kamioka Liquid Scintillating Anti-Neutrino Detector (KamLAND) is located in the Kamioka Mine near the city of Kamioka in the Gifu prefecture
of Japan. The reactor experiment KamLAND is exactly located in the old Kamiokande site within the mine. KamLAND started data collection in January 2002 and the results were reported using only 145 days of data. The detector consists of a 1000 metric tons (1 kilo-ton or 1 kt) of liquid scintillator as both the target and detection medium for low energy nuclear/particle physics processes like neutrino ES and inverse beta decay. The liquid scintillator molecules give off light when charged particles move through the detector. As such, the KamLAND is designed and instrumented to detect this light and reconstruct the physics processes that produce the light. In the solar phase, KamLAND is focussed to detect medium energy solar neutrinos ($\sim$1 MeV). We take the latest data for $^{8}$B solar neutrinos based
on a 123 kton-day exposure of KamLAND \cite {kl}. KamLAND also reported measurement of the neutrino-electron ES rate 862 keV $^7$Be solar neutrino based on a 165.4 kton-days exposure of KamLAND for 616 days between April 7, 2009 and June 21, 2011 \cite{bekam}.

Borexino is an ultra-high radio purity detector located in the underground laboratory at Gran Sasso, Italy. It is a low threshold liquid scintillator detector, which detects solar neutrinos of medium energy range ($^{7}$Be, CNO, pep) via ES of electrons. This detector is the first experiment able to do a real-time analysis of low energy sector solar neutrinos.
The modelling of the detector response has been steadily improved since the beginning of data taking in 2007, and invaluable information has been provided by an extensive calibration campaign in 2009. As a target, 300 ton of liquid scintillator is contained in a spherical nylon vessel. To provide a passive shielding, a non-scintillating buffer liquid is used outside. More than 2200 PMTs are mounted on the inner surface of a stainless steel sphere to register the scintillation light.  The water volume shield the detector against external gamma and neutron radiations, which acts as an active muon veto.

Borexino reports the interaction rate of the 0.862 MeV $^{7}$Be solar neutrinos  for 192 live days data in the period from May 16, 2007 to April 12, 2008 (Borexino Phase-I). The first simultaneous measurement of the interaction rates of pp, $^{7}$Be, and pep solar neutrinos was taken in an extended energy range (0.19-2.93) MeV. This result pertains to the span of 1291.51 days, i.e. Borexino Phase-II data, which was collected between December 2011 and May 2016 after an extensive scintillator purification campaign. Borexino is the first experiment to succeed in suppressing all major backgrounds, above the 2.614 MeV photon ($\gamma$) from the decay of $^{208}$Tl, to a rate below that of electron scatterings from solar neutrinos. This allows to reduce the energy threshold for scattered electrons by $^8$B solar neutrinos to 3 MeV (Borexino (3 MeV)). Borexino also reported the $^8$B interaction rate with 5 MeV threshold (Borexino (5 MeV)).

The summary of SNO-I, II, III, SK-I, II, III, IV, SK-combined, KamLAND Solar Phase, Borexino (3 MeV) and Borexino (5 MeV) data are shown in the Table {\ref{Table:1}}. In Table {\ref{Table:medium}}, survival probabilities of $^7$Be solar neutrinos from KamLAND, Borexino Phase-I, Borexino Phase-II are given.  In Table {\ref{Table:2}} we present the data in terms of the corresponding rates with reference to the SSM flux \cite{SSM}.

\begin{table}[h]
\caption{Solar Neutrino Flux measured by various experiments in units of $10^6$ cm$^{-2}$s$^{-1}$.}
\label{Table:1}
\centering
	\begin{tabular}{|c|c|c|c|c|}
		\hline
	\bf {Data} & \boldmath${\phi^{CC}}$ &  \boldmath${\phi^{NC}}$ & \boldmath$\phi^{ES}$ & \bf{Reference} \\
		\hline
		SNO-I& 1.76 $\pm$ 0.11 & 5.09 $\pm$ 0.45 & 2.39 $\pm$ 0.27 & \cite{sno} \\
		\hline
		SNO-II& 1.68 $\pm$ 0.10 &4.94 $\pm$ 0.41 &2.35 $\pm$ 0.27 & \cite{sno}\\
		\hline
		SNO-III& 1.67 $\pm$ 0.09 &5.54 $\pm$ 0.47 &1.77 $\pm$ 0.24 & \cite{sno}\\
		\hline
		SK-I& - & - &2.38 $\pm$ 0.08 & \cite{sk}\\
		\hline
		SK-II& - & - &2.41 $\pm$ 0.17 & \cite{sk}\\
		\hline
		SK-III& - &-  &2.40 $\pm$ 0.07 & \cite{sk}\\
		\hline
		SK-IV& - & - &2.308 $\pm$ 0.044 & \cite{sk}\\
		\hline
		SK Combined& - & - &2.345 $\pm$ 0.04 & \cite{sk}\\
		\hline
		KamLAND&-  & - &2.77 $\pm$ 0.41 & \cite{kl}\\
		\hline
		Borexino (3 MeV) &-  &-  &2.55 $\pm$ 0.20 & \cite{BorII}\\
		\hline
		Borexino (5 MeV) &-  &-  &2.70 $\pm$ 0.45 & \cite{Bor}\\
		\hline
	\end{tabular}
	\end{table}

\begin{table}[H]
		\centering
	\begin{tabular}{|c|c|c|}
		\hline
	\bf {Experiment} & \bf{P}\boldmath{$_{ee}$} & \bf{Reference} \\
		\hline
		KamLAND  & 0.66 $\pm$ 0.15 & \cite{bekam}\\
		\hline
		Borexino Phase-I & 0.51 $\pm$ 0.07 & \cite{Bor}\\
		\hline
		Borexino Phase-II & 0.53 $\pm$ 0.05 & \cite{bebor2}\\
		\hline
	\end{tabular}
\caption{Solar electronic neutrino survival probability measured by various experiments for $^7$Be neutrinos.}
\label{Table:medium}
\end{table}

\begin{table}[H]
\centering
\begin{tabular}{|c|c|c|c|}
	\hline
	\bf{Experiment}  & \bf{R}\boldmath {$^{CC}$} & \bf{R}\boldmath{$^{NC}$} & \bf{R}\boldmath{$^{ES}$}  \\
	\hline
	SNO I & 0.32 $\pm$ 0.04 & 0.93 $\pm$ 0.14 & 0.44 $\pm$ 0.07\\
	\hline
	SNO II & 0.31 $\pm$ 0.04 & 0.90 $\pm$ 0.13 & 0.43 $\pm$ 0.07\\
	\hline
	SNO III& 0.30 $\pm$ 0.04 & 1.01 $\pm$ 0.15 & 0.32 $\pm$ 0.05\\
	\hline
	SK I&- & -  & 0.43 $\pm$ 0.05 \\
	\hline
	SK II& - & - & 0.44 $\pm$ 0.06\\
	\hline
	SK III& - &- & 0.44 $\pm$ 0.05 \\
	\hline
	SK IV&- &   -& 0.42 $\pm$ 0.05\\
	\hline
	SK Combined &  - & -& 0.42 $\pm$ 0.05\\
	\hline
	KamLAND&- &   - & 0.51 $\pm$ 0.09\\
	\hline
	Borexino (3 MeV)& -  & - & 0.46 $\pm$ 0.06\\
	\hline
	Borexino (5 MeV)& - &   -& 0.49 $\pm$ 0.10\\
	\hline
\end{tabular}
\caption{Different rates with errors for the SNO, SK, KamLAND and Borexino experiments.}
\label{Table:2}
\end{table}

\section{Model Independent Analysis Theory} \label{sec:3}
 In the master equations \cite{skumar,lalsingh1} of the model independent analysis given below we neglect electronic antineutrino component as evident from KamLAND results \cite{Eguchi:2003gg}
 \vspace{-1cm}
\begin{center}
\begin{eqnarray}
\phi^{CC}=\phi_{\nu_{e}} ,\label{eq:1}\\
\phi^{NC}=\phi_{\nu_{e}}+\phi_{\nu_{x}}+\bar{r}_{d} \phi_{\bar{\nu}_{x}},\label{eq:2}\\
\phi^{ES}=\phi_{\nu_{e}}+r\phi_{\nu_{x}}+\bar{r_{x}}\phi_{\bar{\nu}_{x}}.\label{eq:3}
\end{eqnarray}
\end{center}
From these equations we can see that the NC is sensitive equally for all neutrino components, the ES is more sensitive to electronic neutrino component than the non-electronic ones, and the CC is only due to the electronic component of the neutrinos.

 The quantities $r$, $\bar{r}_{x}$ used are the ratios of the NC neutrino and non-electronic antineutrino event rates to the NC + CC neutrino event rate, respectively. The remaining $\bar{r}_{d}$ is the ratio of the antineutrino deuteron fission to neutrino deuteron fission event rate.
We calculate them using the following forms of expressions
\begin{eqnarray}
r=\frac{\int dE_{\nu}\phi(E_{\nu})\int dE_{e}\int dE^{'}_{e}\frac{d\sigma_{NC}}
{dE_e}f(E^{'}_e,E_{e})}{\sigma_{NC}\rightarrow \sigma_{NC+CC}},\label{eq:4}
\end{eqnarray}
\begin{eqnarray}
\bar{r}_{x}=\frac{\int dE_{\nu}\phi(E_{\nu})\int dE_{e}\int dE^{'}_{e}\frac{d\bar\sigma_{NC}}
{dE_e}f(E^{'}_e,E_{e})}{\sigma_{NC}\rightarrow \bar\sigma_{NC+CC}},\label{eq:5}
\end{eqnarray}
\begin{eqnarray}
\bar r_{d}=\frac{\int dE_{\nu}\phi(E_{\nu})\bar\sigma_{NC}(E_{\nu})}
{\bar\sigma_{NC}\rightarrow \sigma_{NC}}.\label{eq:6}
\end{eqnarray}
Here the energy resolution function is $f(E^{'}_e,E_{e})$ and $\sigma$'s are the cross sections.
 The subscript $x$ in $\nu_{x}$ and $\bar{\nu_{x}}$ stands for the non-electronic ($\mu/ \tau$) components. One can extract the expression for ES flux from the master equations \eqref{eq:1} - \eqref{eq:3} as
\begin{eqnarray}
\phi^{ES} = r\phi
^{NC}+(1-r)\phi^{CC}-(r \bar{r}_{d}-\bar{r}_{x})\phi_{\bar{\nu}_{x}}.\label{eq:7}
\end{eqnarray}

If we neglect the antineutrino component, as there are stringent limits from KamLAND, the expression for ES flux is obtained as
\begin{eqnarray}
\phi_{no \bar{\nu_{x}}}^{ES}=r\phi^{NC}+(1-r)\phi^{CC}. \label{eq:8}
\end{eqnarray}

 Since we are specifically interested in estimating the flux of sterile neutrinos, therefore we derive an expressions for the active neutrino ($\nu_{e}+\nu_{x}+ \bar{\nu}_{x}$), non-electronic neutrino component ($\nu_{x}$) and thereafter the sterile neutrino ($\nu_{sterile}$) fluxes can be estimated as
\begin{eqnarray}
\phi_{active}=\frac{[(r-\bar{r}_{x})\phi^{NC}+(1-\bar{r}_{d})((1-r)\phi^{CC}-\phi^{ES})]}{r\bar{r}_{d}-\bar{r}_{x}},\label{eq:9}\\
\phi_{\nu_{x}}^{NC}=\phi^{NC}-\phi^{CC}, \label{eq:10}\\
\phi_{\nu_{x}}^{ES}=\frac{\phi^{ES}_{SK}-\phi^{CC}}{r}.\label{eq:11}
\end{eqnarray}

We can get the expression for the sterile neutrino flux if we subtract the active neutrino flux from the SSM predictions as
\begin{eqnarray}
\phi_{sterile}=\phi_{SSM}^{B}-\phi_{active}.\label{eq:12}
\end{eqnarray}

The active-sterile admixture can also be estimated as the mixing angle $\alpha$ between the active and sterile neutrinos, such that sin$^{2} \alpha$ will denote the fraction of all the active neutrinos. Therefore the component of the sterile neutrinos is proportional to cos$^2{\alpha}$. Excluding the electronic component the fraction of active neutrino flux, as measured by CC flux, present in the solar neutrino flux can be calculated by the following relation

\begin{eqnarray}
 \sin^{2}\alpha = \frac{\phi_{active}-\phi^{CC}}{\phi_{SSM}-\phi^{CC}}.\label{eq:13}
\end{eqnarray}

The degeneracy between the sterile neutrino component and the parameter designated as f$_{B}$, the  normalisation to the SSM $^8$B neutrino flux, can be clearly seen if we rewrite the model independent flux equations in terms of the expressions for the CC, NC and ES rates \cite{bcc}
\begin{eqnarray}
R^{CC}=f_{B}P_{ee}, \label{eq:14}\\
R^{NC}=f_{B}P_{ee}+f_{B}(1-P_{ee})[\sin^{2}\alpha\sin^{2}\psi+\bar
{r}_{d}\sin^{2}\alpha\cos^{2}\psi],\label{eq:15} \\
R^{ES}=f_{B}P_{ee}+f_{B}(1-P_{ee})[r\sin^{2}\alpha\sin^{2}\psi+\bar{
r_{x}}\sin^{2}\alpha\cos^{2}\psi].\label{eq:16}
\end{eqnarray}
As evident from above equations, these are reduced rates.
Here we exploit the near energy independence in the range of interest and factorize the electron neutrino survival probability P$_{ee}$ out of these integrals as in equations \eqref{eq:14} - \eqref{eq:16}.
The above equations clearly show that the conversion of electron neutrinos into the other flavours are directly proportional to 1-P$_{ee}$. Here sin$^{2}\psi$ gives the measure of antineutrino components. Since we assume negligible antineutrino components, it is safer to take sin$^{2}\psi = 1$.
Re-arranging the rate equations we get sin$^{2}\alpha$ and f$_{B}$ degeneracy equation as
\begin{eqnarray}
\sin^{2}\alpha=\frac{R^{ES}-R^{CC}}{(f_{B}-R^{CC}){r}}.\label{eq:19}
\end{eqnarray}

Using ES rate equation and the survival probability P$^{M}_{ee}$ for intermediate energy neutrinos, we obtain
\begin{eqnarray}
R^{ES}=P^{M}_{ee}+(1-P^{M}_{ee})[r\sin^{2}\alpha\sin^{2}\psi+\bar{r}_{x}\sin^{2}\alpha\cos^{2}\psi],\label{eq:20}
\end{eqnarray}
where $r$ and $\bar{r}_{x}$ are cross-sectional ratios as defined above. From the above equation, rate for no antineutrino component (sin$^{2}\psi=1$) and a sterile admixture with the active neutrinos is given as
\begin{eqnarray}
R^{ES}_{BOR/KL}=P_{ee}^{M}+ (1-P_{ee}^{M})r\sin^{2}\alpha. \label{eq:21}
\end{eqnarray}

In both cases, the value of cross-sectional ratios $r$ will be different.
As of today we know the corresponding ES rates ( R$^{ES}_{BOR}$ and  R$^{ES}_{KL}$) and the survival probabilities for medium energy neutrinos (P$^{M}_{ ee}$) from the experiments, therefore using these, we estimate the sterile neutrino flux component present in the observed data.

\section{ Results and Discussions} \label{sec:4}
The SSM predictions \cite{SSM} for $^{8}$B solar neutrino flux to be observed at all experiments is taken to be $\phi_{SSM}=5.46 \pm 0.65 \times 10^{6}$ cm$^{-2}$s$^{-1}$. One has a number of possible combinations for doing  analysis, we use only the ones, which are giving us the most constrained limits on the unknown parameters under investigation. So, for first three analysis we choose the Sets in which we use fluxes $\phi^{NC},~\phi^{CC}$ from SNO-III with $\phi^{ES}$ from SNO-III, SK Combined, KamLAND, Borexino (3 MeV), Borexino (5 MeV), and flux of $\phi^{ES}$ common to all experiments as shown in Fig. {\ref{figure:overlapflux}}. We take all experiments one by one and derive constraints on f$_{B}$, active and sterile neutrinos. These Sets are shown in Table {\ref{Table:cases}}.\\

\begin{figure}[H]
\centering
\includegraphics[scale=.50]{flxovr.png}
\caption{$\phi^{ES}$ Overlap region (shaded) from all experiments.}
\label{figure:overlapflux}
\end{figure}

\begin{table}[H]
\centering
\begin{tabular}{|c|c|c|c|}
\hline
\bf{Set} & \boldmath$\phi^{CC}$ & \boldmath$\phi^{NC}$ & \boldmath$\phi^{ES}$ \\
\hline
1. & SNO-III & SNO-III & SNO-III \\
\hline
2. & SNO-III & SNO-III & SK Combined \\
\hline
3. & SNO-III & SNO-III & KamLAND \\
\hline
4. & SNO-III & SNO-III & Borexino (3 MeV) \\
\hline
5. & SNO-III & SNO-III & Borexino (5 MeV) \\
\hline
6. & SNO-III & SNO-III & $\phi^{ES}$ Overlap \\
\hline
\end{tabular}
\caption{ Grouping of data in different sets.}
\label{Table:cases}
\end{table}

The values of r, $\bar{r}_{x}$, $\bar{r}_{d}$ used are shown in Table {\ref{Table:r}}:
\begin{table}[H]
\centering
\begin{tabular}{|c|c|c|c|}
\hline
\bf{Experiment} & \bf{r} & \boldmath{$\bar{r}_{x}$} & \boldmath{$\bar{r}_{d}$} \\
\hline
SNO-I & 0.150 & 0.115 & 0.954 \\
\hline
SNO-II & 0.150 & 0.115 & 0.954 \\
\hline
SNO-III & 0.151 & 0.116 & 0.955 \\
\hline
SK-I & 0.149 & 0.114 & - \\
\hline
SK-II & 0.151 & 0.116 & - \\
\hline
SK-III & 0.151 & 0.116 & -\\
\hline
SK-IV & 0.151 & 0.116 & - \\
\hline
SK-Combined & 0.151 & 0.116 & - \\
\hline
KamLAND & 0.210 & - & - \\
\hline
Borexino (3 MeV) & 0.213 & 0.181 & - \\
\hline
Borexino (5 MeV) & 0.213 & 0.181 & - \\
\hline
\end{tabular}
\caption{Cross-sectional ratios for various experiments .}
\label{Table:r}
\end{table}

\subsection{The sin$^{2}\alpha$ - f$_{B}$ Degeneracy}
 Using the equation which relates the f$_{B}$ and sin$^{2}\alpha$ i.e. equation \eqref{eq:19}, we obtain sin$^{2}\alpha$ - f$_{B}$ degeneracy plots for all the chosen Sets. Since we know from experiments that R$^{ES}_{i} >$ R$^{CC}_{SNO}$ (where i = SNO, SK, KamLAND and Borexino), possibility of sin$^2 \alpha = 0$ i.e. total conversion to sterile neutrinos, is rejected. However sin$^2 \alpha$ can approach to zero if f$_B$ is very large, which is unlikely. To make sin$^2 \alpha$ - f$_{B}$ plots, we vary f$_{B}$ from 0 to 1.2 and obtain a common parameter space. From this we get constraints on sterile neutrino percentage and the lower value of f$_{B}$.
The variation of f$_{B}$ with sin$^2 \alpha$ for the fixed value of sin$^{2}{\psi}$ i.e. 1, obtained from the analysis is shown in the Fig. {\ref{figure:1}} for different Sets. Just to have reference, the dotted vertical line in the plots corresponds to the central value of f$_B = 1 \pm 0.12$\cite{SSM}.
\begin{figure}[H]
\begin{subfigure}[b]{0.4\textwidth}
\includegraphics[scale=0.6]{SNO-III.pdf}
\caption{sin$^2 \alpha$ vs f$_{B}$ plot for SNO-III.}
\end{subfigure}
\hspace{1cm}
\begin{subfigure}[b]{0.4\textwidth}
\includegraphics[scale=0.6]{SK-Combined.pdf}
\caption{sin$^2 \alpha$ vs f$_{B}$ plot for SK Comb.}
\end{subfigure}

\vspace{1cm}
\begin{subfigure}[b]{0.4\textwidth}
\includegraphics[scale=0.6]{KamLAND.pdf}
\caption{sin$^2 \alpha$ vs f$_{B}$ plot for KamLAND.}
\end{subfigure}
\hspace{1cm}
\begin{subfigure}[b]{0.4\textwidth}
\includegraphics[scale=0.6]{3Borexino.pdf}
\caption{sin$^2 \alpha$ vs f$_{B}$ plot for Borexino (3 MeV).}
\end{subfigure}

\vspace{1cm}
\begin{subfigure}[b]{0.4\textwidth}
\includegraphics[scale=0.6]{5Borexino.pdf}
\caption{sin$^2 \alpha$ vs f$_{B}$ plot for Borexino (5 MeV).}
\end{subfigure}
\hspace{1cm}
\begin{subfigure}[b]{0.4\textwidth}
\includegraphics[scale=0.6]{Overlap.pdf}
\caption{sin$^2 \alpha$ vs f$_{B}$ plot for R$^{ES}$ Overlap.}
\end{subfigure}
\caption{sin$^2 \alpha$ vs f$_{B}$ common parameter space plots for all six Sets.}
\label{figure:1}
\end{figure}

 From these plots we calculate bounds on active neutrinos (sin$^2 \alpha $) and hence the sterile neutrino percentage as shown in Table \ref{Table:fb}.
 \begin{table}[H]
\centering
\begin{tabular}{|c|c|c|c|c|}
 \hline
\bf {Set} & \bf {Data} & \bf {Bounds on f}\boldmath ${_B}$ & \bf {Bounds on sin}\boldmath ${^2 \alpha}$ & \bf {Sterile}\boldmath${\%}$ \\
 \hline
1. & SNO-III & \boldmath {$0.85 \leq$ f$_B \leq 1.2$} & $0.613 \leq$ sin$^2 \alpha \leq 1$ & \boldmath{$0 - 38.7$} \\
 \hline
 2. & SK Combined &  $0.71 \leq$ f$_B \leq  1.2$ & $0.434 \leq$ sin$^2 \alpha \leq 1$ & 0 - 56.6 \\
 \hline
 3. & KamLAND &  \boldmath{$0.85 \leq$ f$_B \leq  1.2$} & $0.607 \leq$ sin$^2 \alpha \leq 1$ & \boldmath{$0 - 39.3$} \\
 \hline
 4. & Borexino (3 MeV) &  $0.74 \leq$ f$_B \leq  1.2$ & $0.470 \leq$ sin$^2 \alpha \leq 1$ & 0 - 53.0 \\
 \hline
 5. & Borexino (5 MeV) &  $0.71 \leq$ f$_B \leq  1.2$ & $0.443 \leq$ sin$^2 \alpha \leq 1$ & 0 - 55.7\\
 \hline
 6. & R$^{ES}$ Overlap  &  $0.77 \leq$ f$_B \leq  1.2$ & $0.500 \leq$ sin$^2 \alpha \leq 1$ &0 - 50.0\\
 \hline
 \end{tabular}
 \caption{Results from sin$^2 \alpha$ - f$_{B}$ degeneracy plots.}
 \label{Table:fb}
 \end{table}

 We find the most constrained results in case of SNO-III ($0-38.7\%$) and KamLAND ($0-39.3\%$) with 0.85 $\leq$ f$_B \leq 1.2 $, which is close to f$_B = 0.88$ i.e. the lower side of f$_B = 1 \pm$ 0.12\cite{SSM}.

\subsection{ The $\phi$ - Active Flux}
We use the equations \eqref{eq:9}, \eqref{eq:12} and \eqref{eq:13} and obtain the results via two different analysis techniques - 1) sterile neutrino flux ($\phi_{sterile}$) and 2) sterile neutrino component percentage calculated as [(1-sin$^2 \alpha$)*100], i.e. depicted in column 6 of Table { \ref{Table:3}}. It is noted that, for no-sterile neutrinos, the CC/NC flux ratio in SNO is a direct measure of the average survival probability of $^{8}$B solar neutrinos that were detected through experiment as P$_{ee}=\phi^{CC}/\phi^{NC}$. Solving it with errors, we will have P$_{ee}$= 0.306 $\pm$ 0.04 with SSM and P$_{ee}$= 0.301 $\pm$ 0.03 with NC for high energy neutrinos. The difference in above two results for NC and SSM flux indicates the possibility for sterile neutrino flux present in the solar neutrino flux.

\begin{table}[H]
\centering
\begin{tabular}{|c|c|c|c|c|c|}
	\hline
	\bf{Set} & \bf{Data Set} &\boldmath${\phi_{active}}$  & \boldmath$\phi_{sterile}$ & \bf {sin}\boldmath$^{2} \alpha $ & \bf{Sterile $\%$} \\
	\hline
1. &	SNO-III & 6.313 $\pm$ 0.708 & -0.853 $\pm$ 0.961 & 1.225 $\pm$ 0.281 & \boldmath{$0 - 05.6$} \\
	\hline
2. &	SK Combined & 5.395 $\pm$ 0.599  & 0.065 $\pm$ 0.884 & 0.983  $\pm$ 0.231 & 0 - 24.8   \\
	\hline
3. &	KamLAND & 4.879 $\pm$ 1.185  & 0.581 $\pm$ 1.352  & 0.847 $\pm$ 0.345 & 0 - 49.8  \\
	\hline
4. &	Borexino (3 MeV) & 5.428 $\pm$ 0.794   & 0.032 $\pm$ 1.026 & 0.991 $\pm$ 0.269 & 0 - 27.8 \\
	\hline
5. &	Borexino (5 MeV)  & 5.127 $\pm$ 1.134  & 0.333 $\pm$ 1.307 & 0.912 $\pm$ 0.338 & 0 - 42.6 \\
	\hline
6. &	$\phi^{ES}$ Overlap & 5.789 $\pm$ 0.686 & -0.329 $\pm$ 0.945 &   1.086 $\pm$ 0.259  & 0 - 27.3     \\
	\hline

\end{tabular}
    \caption{Constraints on active and  sterile neutrino fluxes in units of $10^6$ cm$^{-2}$s$^{-1}$.}
 \label{Table:3}
\end{table}
The constraints for active and sterile neutrino fluxes are depicted in columns 3 and 4 of Table {\ref{Table:3}}.
We calculate the upper bound on the  $\phi_{sterile}$ present in the solar neutrinos  for the all the Sets as:

\hspace{5cm} $\phi_{sterile} \leq 0.11 \times 10^6$ cm$^{-2}$s$^{-1}$ ( SNO-III)

\hspace{5cm} $\phi_{sterile} \leq 0.95 \times 10^6$ cm$^{-2}$s$^{-1}$ ( SK Combined )

\hspace{5cm} $\phi_{sterile} \leq 1.93 \times 10^6$ cm$^{-2}$s$^{-1}$ ( KamLAND)

\hspace{5cm} $\phi_{sterile} \leq 1.06 \times 10^6$ cm$^{-2}$s$^{-1}$ ( Borexino (3 MeV))

\hspace{5cm} $\phi_{sterile} \leq 1.64 \times 10^6$ cm$^{-2}$s$^{-1}$ ( Borexino (5 MeV))

\hspace{5cm} $\phi_{sterile} \leq 0.62 \times 10^6$ cm$^{-2}$s$^{-1}$ ($\phi^{ES}$ Overlap)

\vspace{.5cm}
 Column 5 of Table {\ref{Table:3}} represent the fraction of active neutrinos present in the solar neutrino flux using equation \eqref{eq:13}. The 1$\sigma$ range of sin$^{2}\alpha$ for KamLAND  indicates strong possibility, i.e. up to $49.8\%$, of sterile neutrino  (which is proportional to cos$^{2}\alpha$) percentage given in column 6 at 1$\sigma$ range. However, in the SK Combined case there is a possibility upto $24.8\%$  for sterile fraction at  1$\sigma$. The 1$\sigma$ range of sin$^{2}\alpha$ for Borexino (3 MeV) and Borexino (5 MeV) indicates much less possibility up to $27.8\%$ and $42.6\%$ respectively. However, in the Set-1 there is much less possibility for sterile fraction, which is $5.6\%$ at 1$\sigma$.

\subsection{The Medium Energy Neutrino Data}
Here, we use equation \eqref{eq:21}, which relates sin$^2 \alpha $ and R$^{ES}_{BOR/KL}$, and obtain sin$^2 \alpha $ vs R$^{ES}_{BOR/KL}$ plots for different values of P$_{ee}$ from different experiments. The values of P$_{ee}$ for different experiments is taken from Table {\ref{Table:medium}}. In Fig. {\ref{figure:plot}} we show a plot of sin$^2 \alpha $ vs R$^{ES}$ for KamLAND (dotted lines), Borexino Phase-I (red lines) and Borexino Phase-II (blue lines).

\begin{figure}[H]

\centering
\includegraphics[scale=.8]{7be.png}
\caption{1$\sigma $ plot of sin$^2 \alpha $ vs R$^{ES}$ for KamLAND (dotted lines), Borexino Phase-I (red lines) and Borexino Phase-II (blue lines). The shaded region corresponds to the overlapping region of all three experiments.}
\label{figure:plot}
\end{figure}
\begin{figure}[H]
\centering
\includegraphics[scale=.6]{overlap.png}
\caption{$1\sigma $ plot of sin$^2 \alpha $ vs R$^{ES}$ zoomed for overlapping region of  KamLAND, Borexino Phase-I and Borexino Phase-II. Vertical dotted lines corresponds to R$^{ES}$ equal to $0.57$ , $0.58$ and $0.66$.}
\label{figure:20}
\end{figure}

We zoom in the overlapped shaded region in Fig. \ref{figure:20} and project the three lines (dotted) vertically on it corresponding to three different arbitrary values of R$^{ES}$ to have some useful results. The fraction of sterile neutrinos is computed as 1 - sin$^2 \alpha$ (in the overlap region). It is clear from Fig. {\ref{figure:20}} that there is $14.03\%$ sterile neutrino component in the solar neutrino flux corresponding to R$^{ES}$ = 0.57 at $1\sigma$ and $15\%$ sterile neutrino component corresponding to R$^{ES}$ = 0.58 at $1\sigma$. Here R$^{ES} = 0.66$ corresponds to no sterile component.

 \subsection{\texorpdfstring{The $\chi^2$}{\chi\^{2}}-Analysis} \label{sec:5}
In order to perform $\chi^2$-analysis, we focus on the reduced rates (henceforth to be called 'rates') of various experiments as shown in Table \ref{Table:2}. Therefore, the available data need to re-classified in various best possible cases to obtain useful results. In this exercise we arrange the data in various five cases as the most meaningful combinations. In Case-I we use R$^{NC}$, R$^{CC}$ and R$^{ES}$ from all the experiments. Then in Case-II we consider just the experimental results having best precision measurements. So we use R$^{NC}$ from SNO-II, R$^{CC}$ from SNO-I, SNO-II, SNO-III and R$^{ES}$ from SK-I, SK-III, SK-IV and SK Combined. In Case-III we use R$^{NC}$ and R$^{CC}$ from all the SNO-I, SNO-II, SNO-III experiments and R$^{ES}$ from all experiments except SNO-III as it has quite  different rate as compared to other experiments as shown in Fig. \ref{figure:2}. We consider the R$^{ES}$ of SNO-III as an independent case i.e. Case-IV, where we take R$^{NC}$ and R$^{CC}$ from all the SNO-I, SNO-II, SNO-III experiments and R$^{ES}$ from SNO-III only. In Case-V we use R$^{NC}$ and R$^{CC}$ from all the SNO-I, SNO-II, SNO-III experiments and R$^{ES}$ from the overlapping region of all the experiments for R$^{ES}$ as shown in Fig. {\ref{figure:2}}. All these different cases with various combinations of rates are shown in Table {\ref{Table:cases2}}.

\begin{figure}[H]
\centering
\includegraphics[scale=.65]{rateovr.png}
\caption{ R$^{ES}$ Overlap region (shaded) from all experiments.}
\label{figure:2}
\end{figure}

Here, we perform the $\chi^{2}$-fitting for various cases with all the possible degrees of freedom using the $\chi^{2}$ formula given by the equation below:
\begin{equation}
\chi^{2}=\Sigma_{i}\frac{(R_{i}-R_{i}^{th})^{2}}{\delta R_{i}^{2}}.
\end{equation}

The sum extends over all the experimental data points (i $=$ ES$_{SK}$, ES$_{SNO}$, ES$_{KL}$, ES$_{Bor}$, NC, CC, etc.) as depicted in Table {\ref{Table:2}}.  Here R$_i$ and $\delta$R$_{i}$ denote the experimental rates and the corresponding errors, and R$^{th}_{i}$ are the theoretical values given by equations \eqref{eq:14}, \eqref{eq:15} and \eqref{eq:16}. $ \chi^2_{min} / n $  in column 5 of all the tables below is reduced $\chi ^2$-minimum, where $'n'$ represents the number of degrees of freedom (dof). We fix the value of sin$^2 \psi=1$, i.e no antineutrino component possibility as taken in the entire investigation.

Here, the maximum number of experimental data points is 17 (3R$^{NC}$+3R$^{CC}$+11R$^{ES}$) as can be seen from Table {\ref{Table:2}. However the maximum number of free parameters are three as shown in all the tables given below. As such, we get the number of dof accordingly for all the cases discussed.

\begin{table}[H]
\centering
\def\arraystretch{1.5} \small

\begin{tabular}{|p{2cm}|p{2cm}|p{2cm}|p{7cm}|}

\hline
\bf{Case} & \centering $\bf{R^{CC}}$ & \centering $\bf{R^{NC}}$ & $\bf{R^{ES}}$  \\
\hline
I & SNO-I, SNO-II, SNO-III. & SNO-I, SNO-II, SNO-III. & SNO-I, SNO-II, SNO-III, SK-I, SK-II, SK-III, SK-IV, SK Combined,
KamLAND, Borexino (3 MeV) and Borexino (5 MeV). \\

\hline
II & SNO-I, SNO-II, SNO-III. & SNO-II & SK-I, SK-III, SK-IV and SK Combined. \\
\hline
III & SNO-I, SNO-II, SNO-III. & SNO-I, SNO-II, SNO-III. &  SNO-I, SNO-II, SK-I, SK-II, SK-III, SK-IV, SK Combined,
KamLAND, Borexino (3 MeV) and Borexino (5 MeV). \\
\hline
IV & SNO-I, SNO-II, SNO-III. & SNO-I, SNO-II, SNO-III. & SNO-III \\
\hline
V & SNO-I, SNO-II, SNO-III. & SNO-I, SNO-II, SNO-III. &  R$^{ES}$ Overlap \\
\hline
\end{tabular}
\caption{Different Cases for $\chi ^2$-analysis.}
\label{Table:cases2}
\end{table}

\begin{table}[H]
\begin{center}
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
 \bf{Case} & \bf{No. of dof} & $\bf{f_{B}}$ & $\bf{P_{ee}}$ & \bf{sin}\boldmath{$^2 \alpha$} & \boldmath$\frac {\chi^2_{min}}{n}\ $ & \bf{ Sterile} \boldmath $\%$ ($1\sigma$)\\
\hline
& 16  & $0.974$ & $0.327$ & $0.970$ & $0.363$ & 0 - 31.5 \\
I & 15  & $0.975$ & $0.327$ & $0.970$ & $0.387$ & 0 - 31.5 \\
& 14  & $0.975$ & $0.327$ & $0.970$ & $0.415$ & 0 - 31.5 \\
\hline
\hline
& 7  & $0.962$ & $0.332$ & $0.970$ & $0.138$ & 0 - 22.5 \\
II & 6  & $0.965$ & $0.332$ & $0.970$ & $0.161$ & 0 - 22.5 \\
& 5  & $0.965$ & $0.332$ & $0.970$ & $0.194$ & 0 - 22.5 \\
\hline
\hline
& 15 & $0.982$ & $0.330$ & $0.970$ & $0.127$ & 0 - 26.8 \\
III & 14  & $0.985$ & $0.330$ & $0.970$ & $0.136$ & 0 - 26.8 \\
& 13  & $0.985$ & $0.330$ & $0.970$ & $0.146$ & 0 - 26.8 \\
\hline
\hline
& 6  & $0.921$ & $0.322$ & $0.970$ & $0.441$ & 0 - 19.4 \\
IV & 5  & $0.924$ & $0.322$ & $0.970$ & $0.530$ & 0 - 19.4 \\
& 4  & $0.924$ & $0.322$ & $0.970$ & $0.662$ & 0 - 19.4 \\
\hline
\hline
& 6  & $0.956$ & $0.328$ & $0.970$ & $0.118$ & 0 - 18.4 \\
V & 5  & $0.957$ & $0.328$ & $0.970$ & $0.141$ & 0 - 18.4 \\
& 4  & $0.957$ & $0.328$ & $0.970$ & $0.177$ & 0 - 18.4 \\
\hline

\end{tabular}
\end{center}
\caption{Results of $\chi^2$-analysis for all cases.}
\label{Table:6}
\end{table}

\begin{figure}[H]

\begin{subfigure}[b]{0.45\textwidth}
\includegraphics[width=8cm, height=6cm]{contour1.pdf}
\caption{1$\sigma$, 2$\sigma$ contour plots in the f$_B$, sin$^2{\alpha}$ plane for Case-I.            }
\end{subfigure}
~\qquad
\hspace{.4cm}
\begin{subfigure}[b]{0.45\textwidth}
\includegraphics[width=8cm, height=6cm]{contour2.pdf}
\caption{1$\sigma$, 2$\sigma$ contour plots in the f$_B$, sin$^2{\alpha}$ plane for Case-II.}
\end{subfigure}
~\qquad

\vspace{0.3cm}
\begin{subfigure}[b]{0.45\textwidth}
\includegraphics[width=8cm, height=6cm]{contour3.pdf}
\caption{1$\sigma$, 2$\sigma$ contour plots in the f$_B$, sin$^2{\alpha}$ plane for Case-III.}
\end{subfigure}
~\qquad
\hspace{.4cm}
\begin{subfigure}[b]{0.45\textwidth}
\includegraphics[width=8cm, height=6cm]{contour4.pdf}
\caption{1$\sigma$, 2$\sigma$ contour plots in the f$_B$, sin$^2{\alpha}$ plane for Case-IV.}
\end{subfigure}
~\qquad

\vspace{0.3cm}
\centering
\begin{subfigure}[b]{0.6\textwidth}
\centering
\includegraphics[width=8cm, height=6cm]{contour5.pdf}
\caption{1$\sigma$, 2$\sigma$ contour plots in the f$_B$, sin$^2{\alpha}$ plane for Case-V.}

\end{subfigure}
\caption{1$\sigma$, 2$\sigma$ contour plots for all five Cases. The dot represents the best fit point.}
\label{figure:3}
\end{figure}

From all these plots and $\chi^2$-fitting tables, it is interesting to note that the best fit point for active neutrino fraction gives incidentally the same value for all the cases as shown in the tables above, and i.e. sin$^2 \alpha = 0.970$. This leads to just $3\%$ sterile neutrino fraction given by all the cases irrespective of the data combinations taken.

 As can be seen from Fig. {\ref{figure:3}}, the most constrained results correspond to Case-V. In this case, there is the least fraction of sterile neutrino  component which is $18.4\%$ at $1\sigma$, as shown in the last row of Table {\ref{Table:6}}. In the same Table {\ref{Table:6}}, the sterile neutrino fractions for all other cases at  $1\sigma$ are also shown. For Case-I, a possibility of $31.5\%$, for Case-II $22.5\%$ and, $26.8\%$ and $19.4\%$ sterile neutrino fractions are shown for Case-III and Case-IV, respectively.

In all the above four subsections, we discuss five different model independent analysis techniques to constrain the percentage and flux of sterile neutrinos. From  the results of the four analysis techniques, we get sterile neutrino percentages summarized in Table \ref{Table:comparision}.
\begin{table}[h]
\begin{tabular}{|c|c|c|c|c|}
\hline
\bf{S.No.} &  \bf{sin}\boldmath{$^2 \alpha$ }\bf{- f}\boldmath{$_B$} \bf Degeneracy & \bf{sin}\boldmath{$^2 \alpha$} & \bf{Medium Energy Analysis} & \boldmath$ {\chi^2}$ \bf {- Analysis} \\
\hline
1 &  \boldmath{$0 - 38.7 \%$} & \boldmath{$0 - 05.6 \%$} & \boldmath{$0 - 14.03 \%$} & $0 - 31.5 \%$ \\
\hline
2 & $0 - 56.6 \%$ & $0 - 24.8 \%$ & $0 -  15 \%$ & $0 - 22.5 \%$ \\
\hline
3 & \boldmath{$0 - 39.3 \%$} & $0 - 49.8 \%$ & - & $0 - 26.8 \%$ \\
\hline
4 & $0 - 53.0 \%$ & $0 - 27.8 \%$ & - & $0 - 19.4 \%$ \\
\hline
5 & $0 - 55.7 \%$ & $0 - 42.6 \%$ & - & \boldmath{$0 - 18.4 \%$} \\
\hline
6 & $0 - 50.0 \%$ & $0 - 27.3 \%$ & - & - \\
\hline
\end{tabular}
\caption{Sterile neutrino percentage obtained from various model independent ways.}
\label{Table:comparision}
\end{table}

 We can see that from sin$^2 \alpha$ - f$_B$ degeneracy, most constrained limits on sterile neutrino component at $1\sigma $ are obtained in Set-1 ($38.7 \%$) and Set-3 ($39.3 \%$), where we use SNO-III and KamLAND data respectively. From sin$^2 \alpha $, we see that in the Set-1, there is much less possibility for sterile fraction, which is $5.6\%$ at $1\sigma$. In these two techniques shown in columns 2 and 3 in Table \ref{Table:comparision}, we  use same Sets which are described earlier. Medium energy analysis gives a sterile neutrino percentage of $0-15 \% $. From  $\chi^2 $ analysis we obtain most constrained limit as $18.4 \% $ in Case-V as shown in Table \ref{Table:comparision}.
However, the fifth technique puts constraints on the fluxes of sterile neutrinos as shown in subsection 4.2. It is clear that more constrained upper bounds on $\phi_{sterile}$ are obtained in Set-1 (SNO-III). It has been noted that the Set-6, in which we use $\phi^{ES}$ Overlap is also giving quite constrained bounds on sterile neutrino flux.

\section{Conclusions} \label{sec:6}
The constraints on the flux of sterile neutrinos present in solar neutrino data would reveal many riddles still hidden in the solar neutrino physics, as well as in the neutrino astrophysics as a whole. In this work, we derive such constraints in a model independent way i.e. on the flux of sterile neutrinos $\nu_s$, which are more stringent as compared to the existing in literature. The global and comprehensive analysis of the solar neutrino data available from all the solar neutrino experiments including KamLAND solar phase and Borexino (3 MeV), Borexino (5 MeV) have been done. This kind of updated analysis has been done for the first time, and thereby appearing in literature. Therefore, it becomes interesting to present the bounds obtained by such investigation.

From sin$^2 \alpha$ - f$_{B}$ degeneracy plots, it is clear that most constrained limits on sterile component are obtained in Set-1 (38.7 $\%$) and Set-3 ($39.3 \%$), where we use SNO-III and KamLAND data respectively. It is clear that more constrained upper bounds on $\phi_{sterile}$ are obtained in Set-1 (SNO-III). Set-6 in which we are using $\phi^{ES}$ Overlap is also giving very constrained bounds on sterile neutrino flux. It may be noted that these bounds are more constrained as compared to the ones obtained earlier in literature \cite{Barger:2001pf}, \cite{bmw}, \cite{kang}, \cite{bcc}, \cite{skumar} and \cite{lalsingh1}. In Table {\ref{Table:3}}, we observe that in Set-1, there is much less possibility for sterile neutrino fraction, which is $5.6\%$ at $1\sigma$. From medium energy data analysis, we see that there is a possibility of no sterile component corresponding to reduced R$^{ES} = 0.66$. Also from $\chi^2 $ analysis we obtain that there is a posssibility of $31.5\%$, $22.5\%$, $26.8\%$, $19.4\%$ and $18.4\%$ sterile component for Case-I, II, III, IV and V respectively as shown in Table {\ref{Table:6}}.

The indication for the existence of sterile neutrinos has emerged from Wilkinson Microwave Anisotropy Probe (WMAP), data as well, which suggested that the number of neutrino families in the early universe was more than three \cite{WMAP}. There are several models suggested in literature, which fit the sterile neutrinos in the scheme like a 3+1 model i.e. the three ordinary neutrinos and a sterile one. From the present work it is clear that there is a substantial number of sterile neutrinos and active-sterile mixing in solar neutrino flux. Such additional mass eigen states are light and could be of $\sim$1 eV scale as assumed in 3+1 and other particle physics and cosmological models including light sterile neutrinos and their mixing.

The Liquid Scintillator Neutrino Detector (LSND) anomaly indicated the signal of light sterile neutrinos of mass scale $\sim$1 eV. The data from Mini Booster Neutrino Experiment (MiniBooNE) are consistent in energy and magnitude with the excess of events reported by the LSND, and this excess is significant at 6.0$\sigma$, when the results of both experiments are combined together \cite{LSND}. On the other hand, the joint analysis of Main Injector Neutrino Oscillation Search (MINOS) and MINOS+ (continuation of MINOS) experiments sets stringent limits on active-sterile mixing (in 3+1 model) for values of $\Delta$m$^2_{41}$ >  10$^{-2}$ eV$^2$. However, the final year of MINOS+ data with ongoing analysis improvements will increase the senstivity for future limits on sterile neutrinos even further \cite{MINOS}. As such, more statistics and analysis techniques are awaited to conclude about the issue. Sterile neutrinos are well motivated extensions of the SM, and symmetry protected seesaw scenarios allow for  electroweak scale sterile neutrino masses and active-sterile mixings. This work strongly indicates the existence of sterile neutrinos and therefore, such a study is quite promising for the future searches of this class of neutrinos.

\vspace{.6cm}
\begin{large}
\textbf{Acknowledgements}
\end{large} \\
 We acknowledge the financial support provided by the UGC, Govt. of India under the project grant MRP-MAJOR-PHYS-2013-12281. One of the authors BCC thanks
IUCAA for the providing hospitality during the preparation of the work. The earlier version of this manuscript has been presented as conference abstract in "International Conference on Sciences : Emerging Scenario and Future Challenges (SESFC-2016)"\cite{gazal}. We thank Lal Singh for useful discussion.

redpajama_set_name: RedPajamaArXiv


If you have registered a domain name through PRHL, thank you! You may find the answers to some of your questions below — as always, though, feel free to contact us if anything isn't covered. You may also wish to read our terms and conditions.
How long does a domain registration last?
Most registrations are for two years, though some names are only registered for one. Depending on the name, other periods may be possible — let us know if that's of interest to you.
What happens when the name is due for renewal?
We will contact you (by E-mail) a month or so before the registration expires, to let you know that the renewal is due, and how much it will cost to renew the registration. If you want to renew though us, simply let us know and we'll bill you once the renewal date is passed. If you don't want to renew the name, you can just ignore the reminder (though if you let us know you definitely don't want it any more, we can stop bothering you about it!). If you'd like to renew the name, but not with us, that's no problem, though of course we'd be sorry to see you go — please see the questions about transfers, below.
What do domain names cost?
It depends on the domain — in general, .uk domains are slightly cheaper than generic domains such as .com; more obscure ones, .tv for example, are often far more expensive. As ever, we'd be happy to give you a price for a particular domain, just ask us.
How can I find out who owns a particular domain name?
You can try our WHOIS tool, but in general personal information for domain owners isn't available.
How do I update the registration information for my domain name?
We can make most changes for you — just tell us what you need done. For .uk names, you can make some changes directly with Nominet's Online Services (you'll need the "welcome" E-mail they sent when you first registered the domain to log in).
How can I set up E-mail addresses, or a web site, with my domain name?
We can provide whatever Internet-based services you need. Note, though, that the fee for the domain name only covers the registration of the name itself, services like mailboxes or web space are charged separately. Since we pride ourselves on providing a solution specific to your needs, there's no set list of possible services and prices — please let us know what you need.
I have a domain name registered elsewhere, which I'd like PRHL to look after.
For a .uk domain, the simplest thing is usually to tell the present ISP to "change the tag for domain name to PRHL". That should be a quick process (a few minutes), and is likely to be free (ISPs may make a charge, but most don't). Or you can log on to Nominet's Online Services and change the tag yourself, though note that there is a charge for that, so going through the current ISP is usually a better bet.
For most other domains, the process is more complicated. First of all the domain needs to be "unlocked" to allow a transfer — that's normally done by the current ISP. They should also give you an authorisation code, which you'll need to pass to us. You also need to make sure that the contact E-mail address(es) associated with the domain are correct — again, the present ISP should be able to amend them if necessary. We then make a transfer request, which is usually passed to the listed contact addresses for approval. A transfer of most generic domains (.com, .net, etc) usually takes a few days, though some can complete in a few minutes, and some can take longer. The transfer itself is usually free of charge, though transferring some domains (eg .com) automatically extends their registration by a year, and there is a charge for that extra registration.
I would like someone other than PRHL to look after my domain names.
The process is more-or-less the reverse of that listed above — for a .uk domain, you need to tell us the tag of the new ISP, and we'll make the transfer. That takes a few minutes, and is free of charge. For other domains, we'll unlock the domain, and provide you with the authorisation code; you'll need to pass those to your new ISP to effect the transfer. We don't make any charge for that, but the new ISP probably will.
I would like to sell (or give) my domain name to someone else.
Again, the process to follow depends on the domain name in question. For a .uk domain, you must make the transfer yourself, through the "Registrant Transfer" service at Nominet's Online Services. For most other domains, we can make the change in owner details for you, we simply need to know the details of the new owner.
Transferring domain names can be a confusing process, and is an area where our personal approach can be very helpful — please feel free to contact us if you feel there's anything we can do for you.
I have a complaint about abuse from a domain name registered through PRHL.
We take all abuse complaints very seriously. Please let us know the details of the problem, either by E-mail to Abuse@PRHL.net, by phone to 020 8868 4719, (from outside the UK, +44 20 8668 4719), or by filling in our contact form here. We will respond to any complaint within 4 working hours.


This badge would be one of four badges that you could get from the "Deep Blue Theme Park", a theme park based upon the computer that beat Kasperov at chess in 1997. You would be able to play Deep Blue at a variety of games such as Tic-Tac-Toe & BattleShips. The Badges would retail at around £1 per badge £3 for the complete set.
These slogans would be also be available on Mugs, T-shirts, hats, socks, stickers, posters and bath mats.


text:
Peristyle
The Toledo Museum of Art
Skinner Opus 603, 1926
The Peristyle Organ at the Toledo Museum of Art
Skinner Organ Company, Opus 603, 1926
RESTORED BY A. THOMPSON ALLEN COMPANY
Before restoration
Built in 1926 for the Museum's Hemicycle auditorium, this four-manual organ was the gift of the Libbey family, and was installed in two chambers on either side of the stage. The console was located in a small and shallow pit on the main floor of the room, confined by the seating around it. Renowned American organist Lynnwood Farnam acted as consultant and designer of the stoplist for the instrument. The organ contained fifty-nine speaking stops derived from forty-eight ranks and 3,201 pipes. Opus 603 was to be the largest Skinner organ furnished with the firm's sophisticated multiplex roll-player, although records indicate that very few rolls were ever owned by the Museum.
Download Stoplist
In the 1920s it was not uncommon for art museums to own pipe organs. Skinner organs could be found in Cleveland's Museum of Art (Opus 333, 1920); San Francisco's California Palace of the Legion of Honor (Opus 455, 1924); Dayton (OH) Art Institute (Opus 749, 1929); and the Brooklyn Art Museum (Opus 758, 1929). Having a fine pipe organ was considered a natural addition to an organization dedicated to the arts.
In 1931 the organ was removed from the Hemicycle auditorium and relocated by the Skinner Organ Company to the newly-built and much larger Peristyle auditorium. The new "atmospheric style" venue has two chambers that were constructed to duplicate the instrument's original situation. The console was made movable and furnished with its own integral dolly so that it could be conveniently placed among the other instruments on the stage.
Unfortunately over the years the instrument suffered from water damage to its mechanism in the left (Solo and Choir) chamber and basement relay room, where the player de-multiplexing equipment and other electro-pneumatic switching apparatus is located. By the late 1970s some of the organ's stops had to be shut off, and water damage in the relay room soaked and damaged several crucial electrical cables. A new stage apron elevator occasioned the removal of the cable conduit and wind line to the chamber containing the Great and Swell divisions, permanently rendering the instrument completely unplayable for more than fifteen years.
In 2001, through a generous grant from the Joseph Bradley Foundation and several gifts from the Museum's patrons and supporters, a contract was signed for the complete restoration of Opus 603. This restoration included a complete rebuilding of the console, the equipment in the basement relay room, and the chassis and pipework of the two organ chambers. Working with Suzanne Hargrove, the Museum's Conservator, the restorers developed a plan to return the instrument to its original condition, preserving not only its musical qualities but also its technological details.
All of the damaged and perished materials were painstakingly replaced with identical new materials installed to original Skinner standards. At the request of the client, the original cone-tuning of the treble pipes, the original tuning sleeves for the pipework, and the original protective finishes on the metal flue pipes were retained. The restoration was carried out in 2003 and 2004, and the completed instrument was dedicated in April 2005.
AFTER RESTORATION

redpajama_set_name: RedPajamaCommonCrawl


Art Panels - Antique Wallpaper is a photograph by Andrea Kollo which was uploaded on November 11th, 2018.
I personally find this one intriguing and a perfect blend of textures and color, offset for added drama. A collection of antique and vintage wallpapers created this art panel and fine art photograph.
There are no comments for Art Panels - Antique Wallpaper . Click here to post the first comment.


text:
Q: Create a column based on the name of the element list that contain the data frame in R I have a list of data frames and the names of the element list contains information about each data frame.
Here is a reproducible example,
list_df <- list(jan_2013 = data.frame(id = 1:10, x = rnorm(10), y = runif(10)),
                feb_2013 = data.frame(id = 1:10, x = rnorm(10), y = runif(10)))

How can create a column in each data frame with the information contained in the element names?
I'm working with purrr operations over the list, so how can use purrr::map to iterate over each data frame and have access to the element name on which is store in the list?
$jan_2013
  id    x    y   meta_information
   1    0.2  2.3      jan_2013
   2    0.3  2.1      jan_2013

$feb_2013
  id    x    y   meta_information
   1    0.1  2.4      feb_2013
   2    1.4  2.1      feb_2013

A: An alternate approach is to collapse your list into a single data frame and use the name of the list as an additional column.
dplyr::bind_rows(list_df, .id = "meta_information")

# # A tibble: 20 x 4
#   meta_information    id       x      y
#   <chr>            <int>   <dbl>  <dbl>
# 1 jan_2013             1 -1.09   0.877
# 2 jan_2013             2  0.136  0.828
# 3 jan_2013             3 -0.376  0.0376
# 4 jan_2013             4 -0.793  0.780
# 5 jan_2013             5  0.259  0.179
# 6 jan_2013             6  0.971  0.556
# 7 jan_2013             7 -0.787  0.579
# 8 jan_2013             8 -0.294  0.563
# 9 jan_2013             9  0.331  0.896
# 10 jan_2013           10 -0.392  0.577
# 11 feb_2013            1  0.0139 0.0381
# 12 feb_2013            2  0.640  0.0744
# 13 feb_2013            3  0.813  0.270
# 14 feb_2013            4 -0.748  0.305
# 15 feb_2013            5  0.528  0.380
# 16 feb_2013            6 -0.627  0.832
# 17 feb_2013            7 -1.21   0.0529
# 18 feb_2013            8  1.45   0.494
# 19 feb_2013            9  0.490  0.402
# 20 feb_2013           10 -0.765  0.531

If it is really necessary to keep the lists separate, we can use an indexed map from purrr
purrr::imap(list_df, ~mutate(.x, meta_information = .y))

# $jan_2013
#    id          x          y meta_information
# 1   1 -1.0867168 0.87674573         jan_2013
# 2   2  0.1357794 0.82798892         jan_2013
# 3   3 -0.3763973 0.03761698         jan_2013
# 4   4 -0.7934503 0.77968454         jan_2013
# 5   5  0.2586395 0.17917052         jan_2013
# 6   6  0.9707220 0.55617247         jan_2013
# 7   7 -0.7871748 0.57870521         jan_2013
# 8   8 -0.2939041 0.56255010         jan_2013
# 9   9  0.3307507 0.89646137         jan_2013
# 10 10 -0.3917830 0.57723403         jan_2013
#
# $feb_2013
#    id           x          y meta_information
# 1   1  0.01386418 0.03814336         feb_2013
# 2   2  0.64030914 0.07435783         feb_2013
# 3   3  0.81281978 0.26987216         feb_2013
# 4   4 -0.74768467 0.30482967         feb_2013
# 5   5  0.52820991 0.38045027         feb_2013
# 6   6 -0.62720336 0.83191998         feb_2013
# 7   7 -1.20532079 0.05291640         feb_2013
# 8   8  1.45277032 0.49355127         feb_2013
# 9   9  0.48985425 0.40229656         feb_2013
# 10 10 -0.76508432 0.53114667         feb_2013

A: I found a way to do the task with purrr::map2 iterating over two arguments in parallel: list_df and the names(list_df). Then an anonymous function used these two arguments, taking a data frame (df) and creating a constant column based on the name of the element (name_elem_contain_df) that contain the data frame (df)
purrr::map2(list_df, names(list_df),
    function(df, name_elem_contain_df) mutate(df, meta_information = name_elem_contain_df))

redpajama_set_name: RedPajamaStackExchange


text:
Shell Sells its Appalachian Shale Gas Assets; Remains Committed to Cracker Plant
Royal Dutch Shell announced it is selling its Appalachian shale gas holdings in northwestern Pennsylvania, but remains committed to its petrochemical plant under construction in Beaver County.
Shell's affiliate Swepi reached an agreement with National Fuel Gas Company to sell its shale assets for $541 million. National Fuel, through its Seneca Resources subsidiary, has gas drilling operations in the Allegheny National Forest.
National Fuel said the "opportunistic acquisition" will allow the company to acquire "upstream and midstream assets that are geographically contiguous and highly synergistic to existing Tioga County operations, and firm transportation capacity on the company's Empire pipeline system."
Shell will sell about 450,000 acres and 350 wells in the Marcellus and Utica plays, along with 142 miles of gathering pipelines, compression, and related facilities. The wells produce about 250 million cubic feet of dry gas per day. Dry gas does not contain ethane, a gas liquid that is used as feedstock for petrochemical plants that turn the component into polyethylene pellets for plastic products.
Shell announced in May that it planned to restructure its shale assets. It entered the Appalachian market when it purchased East Resources for $4.7 billion in 2010. Chevron, which has almost 900,000 acres in the tri-state area, also announced in May that it was trying to divest itself of those assets, eight years after entering the market in another multi-billion dollar acquisition.
Shell will be paid in cash for the holdings, a statement said, but National Fuel could instead provide up to $150 million in common stock at a predetermined price. National Fuel expects the addition of the Shell assets to provide increased efficiencies in and reduce operating expenses by 5 to 8 cents per Mcfe.
In its statement, Shell said it "remains committed to Pennsylvania, for example through our Pennsylvania Petrochemicals Complex, which brings new growth and jobs to the region, with up to 6,000 construction workers involved in building the new facility and an expected 600 permanent employees when completed."
While divesting itself of its Appalachian position, Shell noted that it "continues to have attractive opportunities in its shales portfolio both inside and outside the United States, which we operate with a focus on driving down costs while increasing efficiency in all areas of our business."
As natural gas producers continue to seek more efficiency and lower costs to free up cash during the current low-price environment and fallout from the COVID-19 pandemic, more moves within the industry could occur.


text:
Pantherodes arizonensis är en fjärilsart som beskrevs av Capps 1950. Pantherodes arizonensis ingår i släktet Pantherodes och familjen mätare. Inga underarter finns listade i Catalogue of Life.

Källor

Mätare
arizonensis

redpajama_set_name: RedPajamaWikipedia


A boy who must undergo surgery every eight weeks has given a cash boost to the hospital that treats him.
Marley Gill and his family raised a whopping £4,543 for the Leeds children's liver unit.
Mum Rachel said, after giving the money, the kindhearted four-year- old was keen to know what he could do next.
He is thrilled the cash raised in his name will pay for laptops, iPads and sensory equipment for poorly children in the unit.
"He got up the next day and asked, 'when's my next charity night?'," said the proud mum from Berwick Hills, Middlesbrough.
But his generosity came as no surprise to mum and dad. Marley has bravely faced all that life has thrown at him.
As reported in the Gazette earlier this year he was diagnosed with congenital hepatic fibrosis, polycystic kidney disease and Caroli disease - genetic conditions affecting his liver and kidneys.
In February he suffered a massive internal bleed and was rushed to James Cook University Hospital and then transferred to the liver unit at Leeds General Infirmary.
He was diagnosed with portal hypertension, an increase in pressure that had caused the blood to develop large swollen veins (varices) which were wrapped around the gullet.
These fragile veins can rupture leading to the major bleed.
Marley went into surgery to have the bleeding varices banded - an operation he now must have on a regular basis.
The diagnosis of the liver and kidney diseases followed. He may eventually need a transplant.
As the conditions are hereditary, mum Rachel, 29, and, dad, Mark, 37, a steel worker, feared their youngest son, Theo, 21 months, could also be affected, but he has just been given the all clear. The family organised a sponsored Zumba-thon and a charity night to raise money for the children's unit, inspired by Marley.
She thanked Kathryn Bruce, who ran the zumba-thon, and the new management team at Teesside Bridge Social Club in North Ormesby for providing the room for the charity night.


What's all this faffery and poppycock about Green not being able to kill creatures? This Wurm will best any creature in combat regardless of power or toughness before the combat damage is even dealt, and gain you life in the process. True, indestructibility and regeneration will thwart the engulfing, but regeneration removes a creature from combat, and an indestructible creature may yet shrug off the seven damage that the Wurm will deal, but will still have to deal a full seven damage in kind to slay this Wurm. If this is untapped on the other side of the board, sending any non-evasive creature to attack is tantamount to throwing fuel on your opponent's fire-- a fool's errand indeed. And if you're lucky enough to have it on your side? You need fear no blockers, no deathtouch, no pump spell. Condemn could kill it, but in 99 games out of 100, no creature will.
Some cards become famous because of their power. Some cards become famous because of their popularity. Still others, like Engulfing Slagwurm, become famous for being different. I for one have never known why green didn't get more effects that kill creatures; animals fight all the time, and have you ever had a tree fall on you? It hurts. Even if Wizards of the Coast ends up seeing things the same way I do and makes more cards like this in the future, Engulfing Slagwurm will always be famous - for eating Titans in one bite, for working on creatures with protection from green, and most of all, for being here first.
Welcome back readers as we continue to count down our top cards of 2010, today we review Engulfing Slagwurm. In standard there is a plethora of more powerful creatures readily available if you can get the mana for the wurm you are better off playing a titan or eldrazi, Engulfing Slagwurm is a decent budget option for players who don't want to break the bank to play standard. In extended and eternal the availability of even more powerful cards means this card wont and should not see play. In casual and multiplayer this card is a lot better, being able to gain life and have a huge board presence and a creature that's powerful on offense and defense is a great thing for players staring down multiple opponents. In limited its a commitment to green but a big creature that can help end the game quickly, just watch out for the removal. Overall a casual and multiplayer oriented card that just doesn't cut it for competitive decks.
Michael "Maikeruu" Pierno Today's is card number eight of 2010 is Engulfing Slagwurm which is a seven mana 7/7 with effects similar to First Strike, Deathtouch, and Lifelink that all trigger when it blocks or is blocked before damage is actually dealt. This is a fairly impressive set of effects, but requires Green's mana acceleration to see play in a reasonable period of time.
Without Trample an opponent can use tokens or other small creatures to stall, so support effects can help. Overall this is a powerful card that can be used as a threat in a deck that can afford it, but the high cost will limit it from being played anywhere else.
For Limited this is a bomb card that is very difficult for an opponent to deal with outside of Indestructible creatures. It gets around Infect and is a huge problem if left unblocked which makes an obvious first choice in Booster and worth playing whenever possible in Sealed. Echo Circlet is a nice card to have with this defensively, but preferably you'd be on the attack whenever possible.
Today's Card of the Day Top 10 of 2010 is Engulfing Slagwurm. This card is one of personal favorites. Seven mana, two green, five generic, gets you a 7/7. Back in the early days, that made for a decent trade off. But this guy takes getting what you pay for to the next level. Not only do you get a 7/7 for seven, but whenever this guy blocks a creature, or becomes blocked by a creature, destroy it. Seems like a great deal, huh? Sounds like the Sylvan Basilisk of old. But it STILL gets better. It gets better because you also gain life equal to the toughness of the creature you destroy. I honestly cannot say enough good stuff about this card, except I wish it had placed higher on the list.
In standard and limited formats, this guy is definitely held back. While there are certain cards that can exploit forced blocks, Irresistible Prey, one mana to force it to be blocked, or Feral Contest, four mana for a counter and a forced block. Perhaps it thrives best as that hold off card. No one would dare send a large creature to attack you, knowing that in the end it only benefits you.
ridiculous. A simple Lure, or Bloodscent, or channeled Shinen of Life's Roar, and he wipes the field, ala the aforementioned Sylvan Basilisk, except with the perk of life gain. Exterminate your opponents defenses and gain tons of life AND waltz threw with everything else you have, yes please! Vintage decks certainly gained one major trump card here.


text:
Basingstoke News
North Hampshire News
Home > News > Local News > Police release facial reconstruction in a bid to identify mystery Micheldever man
You are viewing content from The Breeze Basingstoke & North Hampshire.
Police release facial reconstruction in a bid to identify mystery Micheldever man
More from Local News
Thursday, May 16th, 2019 5:59am
Facial reconstruction of mystery Micheldever man
Detectives have released a facial reconstruction image of a man whose body was found in a farm building in Micheldever in 2017.
Officers searched the disused barn off Bazeley Copse Lane on Friday 1st December 2017 as part of enquiries into an unrelated burglary.
Inside, they found human remains along with items including a sleeping bag, a rucksack, a Sony Walkman, a Martina Cole novel and a Winchester street atlas.
Despite extensive forensic and DNA examinations, detectives have been unable to identify this man, and they are now appealing for hlep from the public.
Officers say following a Home Office post mortem, and various scientific tests, they believe the man was:
Middle aged or older (age range from 30s to 60s)
Around 5ft 6ins tall
Short, fair brown hair
Narrow face with an overbite
Police say they believe the remains had been in the barn for at least a year.
The cause of death was unascertained, but there were no signs that the man had been attacked or restrained.
Detectives are treating the death as unexplained but not suspicious.
A number of lines of enquiry have been followed in an attempt to identify the man including: DNA testing, dental examinations, fingerprint analysis from items left in the barn, and checking people reported missing in the Hampshire Constabulary area and other forces.
Officers have also liaised with the National Crime Agency's UK Missing Persons Unit.
So far, the man has not been identified.
The facial reconstruction has been produced by Dr Christopher Rynn at the Centre for Anatomy and Human Identification at the University of Dundee.
Detectives have also released images of the clothing the man was wearing, and items that were found in the barn.
Items include a black Karrimor backpack, a Blacks olive green sleeping bag, yellow protective gloves, a Sony Walkman, a Winchester street atlas and the Martina Close novel, 'Close'.
Clothing included a pair of pale Fruit of the Loom tracksuit bottoms, a navy blue zipped Outdoor Scene fleece jacket, dark coloured black wooly hat, size 10 Wellington boots, and a pale Marks and Spencers long-sleeved shirt.
Detective Constable Clare Hughes told us they want to hear from anyone who may be able to help identify this man:
CCTV image released of man following Basingstoke assault
Hampshire Police have released a CCTV image of a man in connection with an assault outside the Chick Mex shop on Church Street, Basingstoke on Sunday 12 January, 2020.
Reading Borough Council agree £43 million leisure contract
A 25-year contract, worth £43 million, to design, build, operate and run leisure services in Reading has been awarded by the Borough Council's Policy Committee.
Mural displayed at Basingstoke shopping centre on 'Blue Monday'
An 'underwater-themed' mural has been unveiled in Festival Place in Basingstoke on 'Blue Monday' (20 January, 2020) which is the third Monday of January and regarded as the 'most depressing day of the year'.
Murder investigation launched in Southampton after teenager's death
A murder investigation has been launched in Southampton in connection with the death of a 17-year-old boy, who has been named as James Laurie, of Montague Avenue.
SWR and Samaritans team up to launch 'Brew Monday'
South Western Railway (SWR) is working alongside Samaritans to promote 'Brew Monday' across their network, spreading the message that it's okay not to be okay.
Pup power project given green light
A pilot project to help Hampshire's vulnerable and disadvantaged children through canine assisted learning has been given the green light thanks to £30,000 of Hampshire County Council funding.


text:
namespace tensorflow {

namespace internal {

void AppendProtoDebugString(
    ::tensorflow::strings::ProtoTextOutput* o,
    const ::tensorflow::GPUOptions_Experimental_VirtualDevices& msg);
bool ProtoParseFromScanner(
    ::tensorflow::strings::Scanner* scanner, bool nested, bool close_curly,
    ::tensorflow::GPUOptions_Experimental_VirtualDevices* msg);

void AppendProtoDebugString(
    ::tensorflow::strings::ProtoTextOutput* o,
    const ::tensorflow::GPUOptions_Experimental& msg);
bool ProtoParseFromScanner(
    ::tensorflow::strings::Scanner* scanner, bool nested, bool close_curly,
    ::tensorflow::GPUOptions_Experimental* msg);

void AppendProtoDebugString(
    ::tensorflow::strings::ProtoTextOutput* o,
    const ::tensorflow::GPUOptions& msg);
bool ProtoParseFromScanner(
    ::tensorflow::strings::Scanner* scanner, bool nested, bool close_curly,
    ::tensorflow::GPUOptions* msg);

void AppendProtoDebugString(
    ::tensorflow::strings::ProtoTextOutput* o,
    const ::tensorflow::OptimizerOptions& msg);
bool ProtoParseFromScanner(
    ::tensorflow::strings::Scanner* scanner, bool nested, bool close_curly,
    ::tensorflow::OptimizerOptions* msg);

void AppendProtoDebugString(
    ::tensorflow::strings::ProtoTextOutput* o,
    const ::tensorflow::GraphOptions& msg);
bool ProtoParseFromScanner(
    ::tensorflow::strings::Scanner* scanner, bool nested, bool close_curly,
    ::tensorflow::GraphOptions* msg);

void AppendProtoDebugString(
    ::tensorflow::strings::ProtoTextOutput* o,
    const ::tensorflow::ThreadPoolOptionProto& msg);
bool ProtoParseFromScanner(
    ::tensorflow::strings::Scanner* scanner, bool nested, bool close_curly,
    ::tensorflow::ThreadPoolOptionProto* msg);

void AppendProtoDebugString(
    ::tensorflow::strings::ProtoTextOutput* o,
    const ::tensorflow::RPCOptions& msg);
bool ProtoParseFromScanner(
    ::tensorflow::strings::Scanner* scanner, bool nested, bool close_curly,
    ::tensorflow::RPCOptions* msg);

void AppendProtoDebugString(
    ::tensorflow::strings::ProtoTextOutput* o,
    const ::tensorflow::ConfigProto& msg);
bool ProtoParseFromScanner(
    ::tensorflow::strings::Scanner* scanner, bool nested, bool close_curly,
    ::tensorflow::ConfigProto* msg);

void AppendProtoDebugString(
    ::tensorflow::strings::ProtoTextOutput* o,
    const ::tensorflow::RunOptions& msg);
bool ProtoParseFromScanner(
    ::tensorflow::strings::Scanner* scanner, bool nested, bool close_curly,
    ::tensorflow::RunOptions* msg);

void AppendProtoDebugString(
    ::tensorflow::strings::ProtoTextOutput* o,
    const ::tensorflow::RunMetadata& msg);
bool ProtoParseFromScanner(
    ::tensorflow::strings::Scanner* scanner, bool nested, bool close_curly,
    ::tensorflow::RunMetadata* msg);

void AppendProtoDebugString(
    ::tensorflow::strings::ProtoTextOutput* o,
    const ::tensorflow::TensorConnection& msg);
bool ProtoParseFromScanner(
    ::tensorflow::strings::Scanner* scanner, bool nested, bool close_curly,
    ::tensorflow::TensorConnection* msg);

void AppendProtoDebugString(
    ::tensorflow::strings::ProtoTextOutput* o,
    const ::tensorflow::CallableOptions& msg);
bool ProtoParseFromScanner(
    ::tensorflow::strings::Scanner* scanner, bool nested, bool close_curly,
    ::tensorflow::CallableOptions* msg);

}  // namespace internal

}  // namespace tensorflow

#endif  // tensorflow_core_protobuf_config_proto_IMPL_H_

redpajama_set_name: RedPajamaGithub


text:
The ITAM Review
News, reviews and resources for worldwide ITAM, SAM and Licensing professionals.
Software Ownership: Who should 'Own' software licenses within an organisation?
'It is important to remember that no single person, department or organisation actually 'owns' any piece of software'
Software license ownership is a common talking point within organisations. Who owns the license, or who has taken responsibility for 'ownership'? It may be the case that nobody has been made responsible, or that there isn't a dedicated and well communicated software license 'owner'. So who should take ownerships of software and their licenses?
There are positives and negatives for the various options, and experience shows that it all depends on how the organisation is structured and run. Technically there is no wrong or right answer, but we will highlight the 'recommended' method of identifying ownership.
Assigning ownership
It is important to remember that no single person, department or organisation actually 'owns' any piece of software (apart from internally developed applications). Software publishers own all of the rights to the software; they are selling a license to use their product. However, it is important to assign 'ownership' of the software and software licenses within an organisation to ensure that all users, departments and senior staff members are aware of what software licenses they have, and where they should in theory be used. Assigning ownership is another key component towards being 'audit ready' and having a sophisticated ITAM estate.
Organisations may identify software license owners differently, based on how the organisation is structured and how it is run on a daily basis. It also depends on existing procurement and financial processes that are already in place, but the common 'ownership' areas are:
The organisation as a whole
Individual departments or cost centres
Individuals (such as Software / License Champions)
In essence, it does not really matter where the ownership of the licenses lies, as what works for one organisation may not work for another. What is important is that clear responsibility and ownership for licenses is communicated and assigned so that users and the business knows where they stand and who to contact about the software or software license for a specific vendor.
The case for cost centre/department ownership
This is one of the most common options for organisations wishing to assign software license ownership. Organisations assign cost centres or departments as the owners responsible for certain software vendors. This is usually the department or cost centre with the biggest investment or most amounts of users of the software. The department or cost centre is then in charge of managing the licenses and ensuring compliancy, and also in charge of help with any software license additions or a renewal of the contract or software maintenance.
Departments or cost centres can get very protective over their licenses as the cost usually comes out of their individual budgets. Whilst this may be the case it is important to remember that the license is still the organisations license, it does not belong to the cost centre or department. The department or cost centres budget was given to them by the organisation anyway, so anything they purchase with that money is an asset to the organisation as a whole.
Having a department or cost centre as the owner of a specific vendors software licenses can result in under-used software, or other departments wasting money on licenses because the ownership department will not allow them any of their free licenses. This results in the organisation being over compliant, not using their licenses effectively and also over-spending on software unnecessarily.
However, there are positives to assigning ownership to a department or individual. The department or cost centre are responsible for the compliancy, procurement and overall management of the licenses which helps take some of the strain and pressure off of a SAM or ITAM team. This also allows a department or collection of users to become experts in licensing for that vendor, allowing them to provide support for the business and its users.
1. Assigns a department to manage licenses and finances, taking the pressure off the ITAM/SAM team Can be protective over 'their' software licenses
2. Helps develop internal knowledge of software vendor and their licenses Can result in over-spending and not using licenses effectively
3. Should be heavy users of the software, so know how to provide support to other users and the business Can result in internal bickering if licenses are not 'lent' out to other departments
The case for individual ownership
Out of the three options, this is the option that is used the least. Organisations may assign a specialist or heavy user of a certain piece of software to be the 'Software/License Champion'. What that effectively means is that the user is responsible for managing any renewals for the license or maintenance, is the point of contact for any licensing issues around the software, and in some cases they may also be a part of the approval process for any new requests.
Assigning ownership to an individual is a risky option. There are a number of issues to consider. What happens when the software champion leaves? Do they take of their knowledge about the software and its licenses with them? There is also the risk that the software champion will make emotional decisions. This can range from rejecting license requests for users that they may not like, or not assigning licenses to users because they want to save their department money.
However, the software champion is only focusing on one vendor, and should be a heavy user of the software. That means that, whilst in the role of software champion, they should be an expert, both technically and licensing wise, which takes off a bit of the pressure and strain on the ITAM or SAM teams. This is also a big asset to the organisation, as through the software champion's expertise they may be able to save money on their maintenance costs as they have the knowledge internally to support their users.
1. Expert knowledge and understanding of the software and licensing Internal resource, if that person leaves the knowledge will leave with them
2. Only focuses on one vendor/application, minimal time taken out of their daily job Can make emotional decisions and prevent certain users or departments from having a license
3. Knowledge can support other users and the business with the software and licenses May not be financially savvy, negotiating a good deal on future agreements may be up to someone else
4. Internal knowledge and resource. Cheap! May be resistant if the organisation wishes to remove or cut-back on the amount of installs for the application
5. Heavy user of the software, so is in a good position to assist the business with future renewals/license purchases A lot of responsibility on one person. If they are absent from work, who can help with any questions or requests?
The case for organisation ownership
At the end of the day, the organisation will own the license. Any software licenses purchased should be in the organisations name, or in the name of one of the entities within the organisation. To allow all users to use the software, and allow for greater flexibility, some organisations assign software license ownership to the organisation as a whole. The organisation pays for the software (event departmental budgets still come out of the organisations banks!), so they assign license ownership to the business. This means that all the licenses can be used by anyone (within the T&C's) regardless of what department they are in.
Assigning ownership to the business takes out all of the arguments around who owns what software, and what department is using another departments software license. If there is a central pool and a central procurement method, then organisations can be flexible and more responsive with software license requests. This allows for better software asset management and will help the organisation manage their software licenses correctly and effectively via an ITAM or SAM team.
Personally, I would assign license ownership to the business so that a centralised ITAM or SAM team can manage all of the licenses and make the most out of the organisations investment. With no departmental restrictions (there may still be entity restrictions or regional restrictions) the ITAM or SAM team are free to try and utilise all of the available licenses and have a central pool for future requests and distribution.
1. More flexibility when allocating licenses There still may be entity or regional restrictions to licenses
2. Can be managed centrally Managed by one team to may not have individual expertise on all software vendors
3. Helps reduce SLA's and waiting times for new software requests
4. Assists with being 'audit ready' and knowing compliancy
5. Allows the organisation to utilise existing/ software license before acquiring more licenses
Top Tips for assigning ownership
We have arranged a number of top tips for assigning software license ownership within your organisation:
Ensure ownership is clearly defined and understood
It is important to clearly set define who has ownership for what software licenses, and who the point of contact is for certain vendors. This can be done via an internal document on SharePoint, or via an ITAM/SAM solution.
Ensure ownership is communicated throughout the business
Make sure end users know who to contact regarding any enquires about software or software licenses. Communicate the department/software champion/ITAM team's name or contract details, and have the information stored somewhere that all users can access.
Ensure the owner is capable and has the knowledge to manage software licenses (If assigned to a software champion)
If assigning ownership to a single person, it is important that they have the time, and knowledge to effectively manage the software and its licenses. They should be a heavy user and an expert in using the software, and have some understanding of how it is licensed.
Ensure the department understands what licenses they have, and that they understand use rights (if assigned to a department)
Before handing ownership of licenses to a particular department or cost centre, it is important they understand exactly what licenses they have and can use. They also need to know what the terms and conditions of the license are and whether they are entitled to any internal charge back if another department wishes to use one of their licenses.
No matter what, ensure that the ITAM/SAM/Licensing team are fully aware of all licenses purchased and owned by the organisation
Assigned ownership or not, the ITAM or SAM team still need to be told of any new software licenses or any existing ones to manage the organisations software assets effectively. All new license requests and purchases should still be done via the official channels.
If you have any questions about this article or would like to know more about software license ownership, then please get in touch with us. We love hearing your views and opinions on our content so have your voice heard!
SAM Tool vendors should focus on retention over new business
Cloud accounting changes on the horizon
Windows 8 Licensing Quick Guide
Pros and Cons of Adobe Creative Cloud
The reverse click-through EULA to cancel software audits
Self Service Portals can add a new dimension to the SAM offering
Tags: Department ownership · Individual ownership · ITAM · License champion · Organisation ownership · Ownership · SAM · Software champion · software licenses
About David Foxen
David Foxen is a Software Asset Management expert and enthusiast. He had a vast experience of successfully implementing SAM, SAM tools and also made huge cost savings. A member of the ISO Standards WG21, David is a massive ITAM geek, so uses any opportunity to talk about the subject to who-ever will listen. He believes that the industry needs to share its knowledge and success stories to help the SAM industry mature and become more effective. Always willing to help, his primary goal is to make a difference to organisations and the SAM industry so everyone will know how epic SAM is!
Paul DeGroot says:
May 24, 2015 at 5:36 am /
The most interesting ownership structure I've seen centered around one individual in a company with about 90,000 PCs who developed (and exhaustively documented) a complex system that provided fine-grained control of licenses and regular harvesting of unused or retired software. It even included a tiered charge-back system in which business units who needed software such as SQL Server had multiple choices. If they wanted the latest product, they were charged nearly full price. If they wanted the previous version, they would pay less, all the way back to older versions that might be available for 10% the cost of a new license. This encouraged people to use older and already-paid-for licenses before purchasing new ones.
The guy who ran this system had enormous control, which was not always welcome. If he didn't think you needed a product, you didn't get an activation key for it. (And since he kept meticulous track of what was actually running, woe to those who tried to get around it.)
But, with something like 10,000 servers running at any given time, the company always knew exactly where it stood and it ran a lean, clean software infrastructure.
Receive free monthly updates about the SAM, ITAM, and Software Licensing market, upcoming events & link to resources you won't find anywhere else!
© Copyright 2008-2023 Enterprise Opinions Ltd. All rights reserved.


text:
Gingrich Courts Christian Leaders; Viability Still Questioned
CP Politics | Thursday, December 08, 2011
By Paul Stanley, Christian Post Reporter | Thursday, December 08, 2011
Republican Presidential candidate and former Speaker of the House Newt Gingrich met with 63 of the nation's most prominent conservative leaders – most of whom are uncommitted in the presidential election – at an Arlington, Va., hotel on Wednesday to outline his plan for winning the GOP nomination. All listened intently, but some are still expressing concerns over Gingrich's "viability."
Republican presidential candidate Newt Gingrich walks into Trump Towers for a meeting with real estate investor Donald Trump on 5th Avenue in New York December 5, 2011. | (Photo: REUTERS/Andrew Burton)
Dr. Richard Land: An Open Letter to Newt Gingrich
Gingrich Eyes Cain Supporters as Romney Gets Bad News
Does the Public Have a Right to Know About a Candidate's Personal Life?
Could Rick Santorum Become the Next Anti-Romney?
Pelosi Threat To Expose Gingrich Will Backfire, Say Conservatives
Richard Viguerie of ConservativeHQ.com hosted the meeting. "This will not be a typical meet and greet," the invitation read. From all indications, it wasn't.
"Speaker Gingrich called me over Thanksgiving and suggested we get a good group of conservative leaders in the same room for a frank discussion," Viguerie told The Christian Post. "Over the years I've been disappointed with some conservative leaders because they've caved into the Republican Party's platform as opposed to their own. Now I believe conservatives are willing to stand up for their own issues."
"We had a good, frank discussion of the issues and we talked about a number of issues, both personally and politically. Everyone listened closely to what Newt had to say and he was well received."
The gathering could well prove to be a decisive moment for the former history teacher and Speaker of the House as he hopes to convince evangelicals that his ideas and candidacy are now grounded enough to take on President Obama next November.
In addition to Viguerie, some of those in attendance were former GOP presidential candidate Gary Bauer, publisher Al Regnery, Mike Farris, head of the Home School Legal Defense Fund, Charmaine Yoest, head of Americans United for Life, and Penny Nance of Concerned Women for America.
Gingrich, who requested the meeting, began his remarks by providing a brief commentary on the state of the economy, reminding those in the room that "if Obama is re-elected, America will be a very, very different country from the one we grew up in."
Gingrich Woos Conservative Leaders
Claiming a convincing victory in the Iowa caucuses could send him into New Hampshire with enough momentum to take on former Massachusetts Gov. Mitt Romney in his own backyard prior to heading to the southern primaries.
However, Gingrich also needs to convince grassroots conservatives – especially in Iowa and several southern states – that any prior personal shortcomings should not be a factor as he has expressed sorrow and repentance for those he has hurt, including his two former spouses.
Asked directly if he could handle attacks on his personal life, Gingrich said he expected both his GOP primary opponents and eventually "Obama's attack dogs" to engage in negative campaigning.
Others in the room wanted to know if a Gingrich administration would fight for conservative values. "Mine is going to be a conservative administration … this is very tough work that I will be asking people to undertake," responded Gingrich. "I'm only going to appoint people who are willing to come in to implement our agenda."
How did such a demanding group receive Gingrich?
"I would say that the crowd was extremely interested in what Speaker Gingrich had to say," said one of the attendees who asked not to be identified.
"This is a critical election and it's real important who the Republican nominee will be. I would say one of the overriding issues is those gathered in the room do not want to have mud on their faces in a general election. We want to make sure that whoever takes us to the dance can drive us home safely. A few still had some doubts about his viability."
Interrupted numerous times by applause, Gingrich made a direct appeal to the conservative leaders in the room – most of whom could collectively influence several hundred thousand prized, evangelical primary voters.
So, how did Gingrich fair with the group? "He didn't do himself any harm," another attendee who asked to not be identified stated. "No doubt about it – Newt's smart. Everyone wants to be smart and strategic from this point forward."


Our Arizona Collection Agency collects commercial bad debt and consumer account receivables in Arizona with an emphasis on the collection of judgments. We apply conventional collection methods and utilize a network of bonded Arizona collection law firms whenever necessary.
Call our Arizona office today toll free at (888) 378-8100 to customize a collection plan which meets your specific needs. We recognize that each and every client is important to our success. We treat each and every Arizona client, big and small, as if they were our only client.
Arizona Settlements are accepted only with your authorization. Legal actions are initiated only with your authorization. All funds recovered by us are placed into our trust account.