text:
\section{Introduction}

A common technique to reduce the impact of systematic uncertainties, in particular in precision measurements in high energy physics,  is to constrain the range of their variations by the data. A simultaneous fit of these variations and the parameters to be measured can be performed based on prior knowledge of the uncertainties and suitable distributions to constrain them. This technique can reduce the total uncertainty in many cases significantly, as in Refs.~\cite{Khachatryan:2137231,Sirunyan:2017uhy,Khachatryan:2016yzq}, and can be used to measure several parameters simultaneously (see e.g. Refs.~\cite{Kieseler:2015jzh,Aad:2014jra}).
However, it leads to non-negligible correlations between all fitted parameters. These are particularly important when at least one measurement that uses this technique contributes to a combination.

The most consistent approach to such combination would be to define a \textit{combined likelihood} based on the original models, including all systematic variations, and the original data the models were fit to.
Also other commonly used combination techniques and the corresponding software tools would require this information~\cite{LYONS1988110,Nisius1,Nisius2,Alekhin:2014irh}, which is publicly available only in very rare cases and often unrecoverable. This poses a serious problem for a consistent combination involving measurements obtained with simultaneous nuisance parameter fits.

The method described here provides a solution for this problem, since it is based on the central results and their covariance or Hessians, only.
It allows separating constraints and correlations imposed by the previously fitted data from those that stem from prior knowledge of the systematic variations.

Therefore, the combination can be performed accounting for correlations between the measurements as well as for correlations and constraints within each individual measurement.

The dedicated software tool ``Convino'' is also presented in this article. It is specifically developed to perform combinations based on the method described here and provides a simple text-based user interface that can be used without knowledge of any programming language.
Assumptions on  correlations can be varied in an automated way.
Moreover, partially correlated measurements of different quantities (e.g. bins of a differential distribution) can be combined simultaneously accounting for all correlations.
In addition to the text-based interface, a C\kern-0.1em\raisebox{.2ex}+\kern-0.1em\raisebox{.2ex}+{} interface is provided to define the input to the combination. This interface can either read basic C\kern-0.1em\raisebox{.2ex}+\kern-0.1em\raisebox{.2ex}+{} standard library data types or  ROOT~\cite{Brun:1997pa} histogram and graph classes, which are commonly used in high-energy-physics analyses.

The combination method is described in Section~\ref{sec:math}.  It is validated against the combined likelihood approach in Section~\ref{sec:valid}. The effect of neglecting correlations within the same measurement is studied in Section~\ref{sec:negcorr}.
The installation and the user interface of the Convino program is described in Section~\ref{sec:install}.

\section{Combination method}
\label{sec:math}

The combination is performed using a $\chi^2$ minimisation. The $\chi^2$ is defined as
\begin{equation}
\label{eq:fullchi}
\chi^2 =  \sum_{\alpha} \left(\chi^2_{s,\alpha} + \chi^2_{u,\alpha} \right) + \chi^2_p
\end{equation}
It is composed of three terms: the term $\chi^2_{s,\alpha}$ represents the results of each measurement $\alpha$ and its statistical uncertainties. It follows a Neyman or Pearson $\chi^2$ definition, with the statistical uncertainty being fixed for each measurement or being scaled with the combined value, respectively. A measurement can aim to determine a set of quantities, e.g. bins of a differential cross section, where the Pearson definition is more applicable. Alternatively a single quantity can be measured, e.g. the mass of a particle from a fit of an invariant mass peak position, where the Neyman definition is presumably better suited to describe the measurement.
In both cases, the measured quantities are referred to as estimates in the following.
The additional term  $\chi^2_{u,\alpha}$ describes the correlations between the systematic uncertainties and constraints on them from the data for each measurement $\alpha$. The last term, $\chi^2_p$, incorporates prior knowledge of the systematic uncertainties and correlation assumptions between uncertainties of the measurements to be combined.

\

In a typical measurement that exploits simultaneous constraints on the uncertainties from the data, the sources of uncertainties are uncorrelated prior to the fit to the data and the knowledge about their variations is modelled by independent penalty terms in the original likelihood.
The goal of the {me-thod} described here is to find an approximation for this likelihood that allows disentangling the independent penalty terms from the constraints and correlations between them, which are typically introduced by the data\footnote{The same procedure can be applied if correlations are present prior to the fit to the data}.
Therefore, the first central assumption is that the original likelihood for a measurement $\alpha$ can be approximated by:
\begin{equation}
\label{eq:evchi2}
\chi^2_\alpha  =  (\chi^2_{s,\alpha} + \chi^2_{u,\alpha}) + \sum_i (P_i^\alpha(\lambda_i) )^2 \text{,}
\end{equation}
where $(P_i^\alpha(\lambda_i) )^2$ represents the penalty term for a systematic uncertainty $i$ parametrised by a continuous parameter $\lambda_i$, such that $\lambda_i=1$ corresponds to a $1\sigma$ variation.
The terms $\chi^2_{s,\alpha}$ and $\chi^2_{u,\alpha}$ are defined as:
\begin{eqnarray}
\chi^2_{s,\alpha} & = &  \sum_{\mu\nu} {M}_{\mu\nu}^\alpha \frac{\xi_{\mu}^\alpha \xi_{\nu}^\alpha} { \tau_{\mu}^\alpha \tau_{\nu}^\alpha}  \text{ and} \\
\chi^2_{u,\alpha} & = &  \sum_{ij} \lambda_i  D_{ij}^\alpha \lambda_j   \text{, with}
\end{eqnarray}
\begin{equation}
\xi_{\mu}^\alpha  =  x_{\mu}^\alpha -  \bar{X}_\mu \text{ and}
\end{equation}
\begin{equation}
\bar{X}_\mu  =   \bar{x}_\mu \prod_i (\lambda_i K_{\mu i}^\alpha /x_{\mu}^\alpha +1 ) + \sum_i \lambda_i  k_{\mu i}^\alpha
\text{.}
\end{equation}
Here, $x_{\mu}^\alpha$ is the estimate $\mu$ obtained in measurement $\alpha$ and $\bar{x}_\mu$ the combined value to be determined. The relation between both is given by $\tau_{\mu}^\alpha = ({\bar{X}_\mu/x_{\mu}^\alpha})^{0.5}$ for the Pearson $\chi^2$ definition. In case of the Neyman $\chi^2$, all $\tau_{\mu}^\alpha = 1$. The matrix $M$ represents the inverted statistical covariance of the estimates.
The parameters $k_{\mu i}^\alpha$ and $K_{\mu i}^\alpha$ model the effect of the systematic variations on the estimates for absolute or relative uncertainties, respectively. Here, a relative uncertainty is an uncertainty that scales with the measured value such as e.g. the luminosity uncertainty in a cross-section measurement, while absolute uncertainties have a constant value irrespective of the central result.
In principle, also other classes of dependencies can be incorporated through additional terms in $\xi^\alpha_\mu$.
The correlations between the uncertainties and the constraints that stem from the fit to the data are described by the matrix $D^\alpha$.  Throughout this paper, indices $\mu$ and $\nu$ are used for estimates, while systematic uncertainties are denoted with indices $i$ and $j$.

The procedure to obtain the parameters of $\chi^2_\alpha$ from the measurements to be combined are discussed in the following - firstly for results obtained through a simultaneous nuisance parameter fit and secondly for the specific case of orthogonal uncertainties.

\subsection{Measurements obtained with simultaneous fits}

The second central assumption of the method is that the parameters of $\chi^2_\alpha$ can be determined from the Hessian of measurement $\alpha$ evaluated at the best-fit values, $\tilde{H}^\alpha_\text{in}$.
The entries of the Hessian can be ordered such that the matrix can be split in the following sub-matrices:
\begin{equation}
\tilde{H}^\alpha_\text{in} = \begin{pmatrix}
\tilde{D} & {\kappa}^T \\
{\kappa} & \tilde{M}
\end{pmatrix}^\alpha \text{,}
\end{equation}
where $\tilde{M}$ describes the relation between the estimates $x_\mu^\alpha$ and $x_\nu^\alpha$. The relation between systematic variations and the estimates is described by $\kappa$. The matrix $\tilde{D}$ quantifies the relation between the systematic variations.

All parameters of $ \chi^2_\alpha$ are determined by calculating analytically the Hessian of  $\chi^2_\alpha$, ${H}^\alpha (\vec{0})$, and identifying the resulting terms with their counterparts of the input $\tilde{H}^\alpha_\text{in}$. Here $\vec{0}$ means $\lambda_i =0$ and $x_\mu^\alpha - \bar{x}_\mu = 0\ \forall\ i,\ \mu$.
The components are calculated as follows:
\begin{equation}
 {H}^\alpha_{\mu\nu} (\vec{0}) = \frac{1}{2} \left(\frac{\partial^2 }{ \partial \Delta x_\mu^\alpha \partial \Delta x_\nu^\alpha}   \chi^2_\alpha \right)\biggr\rvert_{\vec{0}}
 =  {M}_{\mu\nu}  \text{,}
\end{equation}
\begin{equation}
{H}^\alpha_{\mu i} (\vec{0}) = \frac{1}{2} \left( \frac{\partial^2 }{ \partial \Delta x_\mu^\alpha \partial \lambda_i}   \chi^2_\alpha \right)\biggr\rvert_{\vec{0}}
 =  \sum_\nu {M}_{\mu\nu} ( - \hat{k}_{\nu i}^\alpha) \text{,}
\end{equation}
with $\hat{k}_{\nu i}^\alpha = K_{\nu i}^\alpha + k_{\nu i}^\alpha$.
The matrix ${M}$ can be directly identified with $\tilde{M}$.
Since $\tilde{M}$ stems from a measurement of a physics quantity, $\tilde{M}$ is positive definite and therefore invertible. Thus, the parameters $\hat{k}_{\nu i}^\alpha$ can be determined as:
\begin{equation}
\hat{k}_{\nu i}^\alpha = - \sum_\mu ((M^\alpha)^{-1})_{\mu\nu}\ \kappa_{\mu i}^\alpha \text{.}
\end{equation}
Since a variation $i$ is either relative or absolute, $\hat{k}_{\nu i}^\alpha$ equals either $K_{\nu i}^\alpha$ or $k_{\nu i}^\alpha$, with the other parameter being 0.
The terms describing the analytic relations between the systematic uncertainties are calculated as:
\begin{equation}
\begin{aligned}
{H}^\alpha_{i j} (\vec{0}) = & \frac{1}{2} \left( \frac{\partial^2 }{ \partial \lambda_i \partial \lambda_j}   \chi^2_\alpha \right)\biggr\rvert_{\vec{0}} \\
 =   &
D_{ij}^\alpha + \delta_{ij} \frac{1}{2} \frac{\partial^2 }{ \partial \lambda_i ^2}(P^\alpha_i)^2\biggr\rvert_{\lambda_i =0}  + \sum_{\mu \nu} M_{\mu \nu}^\alpha  \hat k_{\nu i}^\alpha\hat k_{\mu j}^\alpha \text{.} \\
\end{aligned}
\end{equation}
Only Gaussian penalty terms describing the prior knowledge of the uncertainties
are considered\footnote{In principle also other penalty terms (e.g. log-normal priors) can be accounted for. However, these lead to a non-constant $D^\alpha$.} ($P_i^\alpha(\lambda_i) = \lambda_i$), which simplify the equations, since in this case
\begin{equation}
\frac{1}{2}\frac{\partial^2 }{ \partial \lambda_i ^2}(P^\alpha_i)^2 \biggr\rvert_{\lambda_i =0} = 1 \text{.}
\end{equation}
In consequence $D^\alpha$ becomes:
\begin{equation}
D_{ij}^\alpha = \tilde{D}_{ij}^\alpha  -  \delta_{ij} -  \sum_{\mu \nu} M_{\mu \nu}^\alpha \hat k_{\nu i}^\alpha\hat k_{\mu j}^\alpha \text{,}
\end{equation}
such that all parameters of Eq.~\ref{eq:evchi2} are defined.

\subsection{Measurements with orthogonal uncertainties}
\label{sec:orthunc}

For orthogonal uncertainties, the same initial $\chi^2$ described in Eq.~\ref{eq:evchi2} is used. However, the calculation of its parameters does not necessarily require the full Hessian. Instead, the calculation of the parameters simplifies to:
\begin{equation}
\hat{k}_{\mu i}^\alpha = \frac{\sigma_{\mu i}^\alpha}{\sigma_{\mu \text{ total}}^\alpha} \text{,}
\end{equation}
with $\sigma_{\mu i}^\alpha$ being the contribution of uncertainty $i$ to the total uncertainty $\sigma_{\mu \text{ total}}^\alpha$ of estimate $x_\mu^\alpha$. The matrix $D^\alpha$ is 0, the terms of $M$ are calculated as:
\begin{equation}
M_{\mu \nu} = \frac{ \rho_{\mu\nu} }{\sigma_\mu \sigma_\nu} \text{.}
\end{equation}
Here, $\rho_{\mu\nu}$ is the statistical correlation between estimate $\mu$ and $\nu$, and $\sigma_\mu$ and $\sigma_\nu$  are the corresponding statistical uncertainties.

\

For the orthogonal uncertainties as well as for measurements obtained by simultaneous fits, the constraints from the prior knowledge of the uncertainties are implemented in Eq.~\ref{eq:fullchi} through the term:
\begin{equation}
\label{eq:globalConstr}
\chi^2_{p} = \sum_{ij} P_i(\lambda_i) (C^{-1})_{ij} P_i(\lambda_j) \text{,}
\end{equation}
with $C$ being the matrix describing the correlation assumptions between the systematic uncertainties. In case no correlations are assumed, the term simplifies to:
\begin{equation}
\chi^2_{p}(\text{no corr}) = \sum_{i} P^2_i(\lambda_i)  \text{.}
\end{equation}
Only Gaussian penalty terms are considered in the following, such that $P_i(\lambda_i) = \lambda_i$.
For a combination, $C$ will be of the structure
\begin{equation}
C = \begin{pmatrix}
\mathds{1} & A & \cdots \\
A & \mathds{1} &  \cdots \\
\vdots & \vdots & \ddots \\
\end{pmatrix}\text{,}
\end{equation}
with matrices $A$ describing the correlation assumptions, and $\mathds{1} $ being the identity matrix.

\subsection{Technical implementation}
\label{sec:tech}

The final minimisation of Eq.~\ref{eq:fullchi} is performed using the Minuit algorithms~\cite{James:1975dr}. The total uncertainty on each combined value is determined by scanning $\chi^2 = \chi^2_\text{min} +1$ using the Minos algorithm.
These algorithms as implemented in ROOT~6 as ``TMinuit2'' are employed.

The correlations that are assumed between systematic uncertainties can vary between -1 and 1. These extremes are special cases for which the correlation matrix $C$ becomes non-invertible. In practice, a correlation of $C_{ij}=\pm1$ means that  parameters $i$ and $j$ describe the same variation.
In such cases, an entry $C_{ij}=\pm1$ is replaced by $C_{ij}=\pm(1-10^{-3})$.
The difference to $\pm1$ is almost negligible.

For illustration, $2\times 2$ parameters are chosen with $C_{ij}\approx \pm1$. The affected part of the $\chi^2$, $\chi^2_{F}$, can be simplified to
\begin{eqnarray}
\chi^2_{F} & = & \frac{1}{1-C_{ij}^2} (\lambda_i^2 + \lambda_j^2  \mp 2 C_{ij} \lambda_i \lambda_j)  \\
 & \approx & \frac{1}{1-C_{ij}^2} ( \lambda_i \mp \lambda_j)^2
\end{eqnarray}
and corresponds to $( \lambda_i \mp \lambda_j)^2 \cdot 10^6$ for  $C_{ij} = \pm (1- 10^{-3})$. Given that a variation of $\lambda = \pm 1$ corresponds to only a fraction of the total uncertainty on each estimate, the effect of the approximation $C_{ij} = \pm (1- 10^{-3})$ is negligible.

\section{Validation}
\label{sec:valid}

The validation is based on \textit{{pseu\-do-\-mea\-su\-re\-me\-nt}s}. Each {pseu\-do-\-mea\-su\-re\-me\-nt} is a binned likelihood fit with steerable central value and bin-wise uncertainties.
This has the advantage, that the full likelihood of each {pseu\-do-\-mea\-su\-re\-me\-nt} is known and can be adjusted to different scenarios. Therefore, it is possible to compare the results obtained with the method proposed here to the ones obtained using the combined likelihood as reference. Since the latter in principle contains arbitrarily more parameters, small deviations are expected.

The validation is first performed with respect to the statistical bias, only. Secondly, the modelling of systematic uncertainties is tested with respect to correlations between the uncertainties of the {pseu\-do-\-mea\-su\-re\-me\-nt}s, and the modelling of relative uncertainties.

For each {pseu\-do-\-mea\-su\-re\-me\-nt} a Poisson likelihood is chosen to determine the central result $\bar{x}_\mu$. The bin-wise uncertainties are randomly generated and modelled by the parameters $\lambda_i$.
In the case that an uncertainty corresponds to an absolute variation, its effect on each bin is generated independently.
For more than one bin ($N_\text{bins}>1$) this results in correlations between the uncertainties after the fit, as well as in constraints on their variations.

The likelihood for {pseu\-do-\-mea\-su\-re\-me\-nt} $\alpha$ is defined as:
\begin{equation}
\label{eq:pseudoLH}
 L^\alpha = \prod_\mu  \prod_i^{N_\text{bins}^\alpha}  \mathcal{P}\left( X_\mu^\alpha, \bar{X}_{\mu i}^\alpha \right)
 \cdot \prod_i \tilde{P}^\alpha_i(\lambda_i)  \text{,}
\end{equation}
with $\mathcal{P}$ being the Poisson likelihood and $\tilde{P}^\alpha_i(\lambda_i)$ the Gaussian penalty terms modelling the prior knowledge of each uncertainty. The parameters $X_\mu^\alpha$ and $\bar{X}^\alpha_{\mu i}$ are given as:
\begin{eqnarray}
X_\mu^\alpha & = &  \frac{x_\mu^\alpha}{N_\text{bins}^\alpha} \text{ and} \\
\bar{X}_{\mu i}^\alpha  & = &  \frac{\bar{x}_\nu}{N_\text{bins}^\alpha}\prod_j \left( \frac{K_{\nu j}^\alpha \lambda_j}{x_\nu}^\alpha + 1 \right) + \sum_j k_{\nu ij}^\alpha \lambda_j  \text{,}
\end{eqnarray}
where $K_{\nu j}^\alpha$ describes the magnitude of global relative variations and $k_{\nu ij}^\alpha$ absolute shape variations, different for each bin $i$. The value of $x_\mu^\alpha$ is the input to each {pseu\-do-\-mea\-su\-re\-me\-nt} and corresponds to the number of events that would be observed in a real measurement. The elements of the matrices $K^\alpha$ and $k_i^\alpha$ are chosen to describe different validation scenarios. Finally, the fit to determine $\bar{x}_\mu^\alpha$ is performed and the resulting Hessian is recorded.

The combined likelihood for several {pseu\-do-\-mea\-su\-re\-me\-nt}s is given by:
\begin{equation}
L_\text{comb} = \left( \prod_\alpha \frac{L^\alpha}{\prod_i \tilde{P}_i^\alpha} \right) \cdot \phi (\lambda_0, ..., \lambda_N) \text{,}
\end{equation}
where $\phi$ models the prior knowledge of $N$ systematic uncertainties and the correlation assumptions between them,  analogue to $\chi^2_p$ in Eq.~\ref{eq:globalConstr}. For every validation step, the difference $\Delta \bar{x}$ between the result obtained with the method proposed in this document and using the combined likelihood  is recorded.
The compatibility of both approaches is is quantified by $\Delta \bar{x}/ \sigma_{\bar{x}}$, which is the difference between their central results normalised to the total uncertainty of the combined-likelihood combination.

\subsection{Statistical bias}
\label{sec:statbias}

To evaluate the statistical bias, the impact of systematic uncertainties on each {pseu\-do-\-mea\-su\-re\-me\-nt} is set to 0, corresponding to $K=0$ and $k=0$. Only one quantity, $\bar{x}$, is determined from two estimates $x^a$ and $x^b$, chosen as:
\begin{eqnarray}
x^a & = & s \cdot 100 \text{,} \\
x^b & = & x^a + \gamma \sqrt{x^a} \text{,}
\end{eqnarray}
with $s$ being a scaling factor and $\gamma$ describing the compatibility between the estimates. The latter is chosen to be either $\gamma=10$ to describe two very incompatible measurements or $\gamma=3$ for a more realistic scenario where both estimates still agree well enough to enter a combination.
Two {pseu\-do-\-mea\-su\-re\-me\-nt}s are generated for each choice of $s$ and $\gamma$ and are combined either using a Pearson or Neyman $\chi^2$ definition.
For both choices, the uncertainties on the combined results agree very well with the ones obtained using the direct combination based on $L_\text{comb}$. The bias of the central value is shown in Figure~\ref{fig:chibias} relative to the uncertainty of the combined value. It behaves as expected: it is smaller but of opposite sign for the Pearson $\chi^2$ definition and is reduced with smaller statistical uncertainties and better compatibility between the results.

\begin{figure}[htbp]
  \begin{center}
\includegraphics[width=0.4\textwidth]{Convino_p_ney.pdf}
\caption{Difference between the combined values using a direct Poisson-likelihood combination and the method proposed here with Neyman and Pearson $\chi^2$ definition relative to the total uncertainty. The estimates to be combined differ by about $\gamma\sigma$  and are displayed as a function of the first estimate's relative statistical uncertainty. The second estimate's statistical uncertainty scales accordingly. \label{fig:chibias}}
\end{center}
\end{figure}

\subsection{Systematic uncertainties}
\label{sec:sysunc}

The effect of absolute systematic uncertainties is evaluated by combining two {pseu\-do-\-mea\-su\-re\-me\-nt}s, with randomly chosen elements of the matrices  $k_\nu^\alpha$. An upper threshold $t$ is defined, such that for each element $i,\ j$:
\begin{equation}
| k_{\nu i j}^\alpha | \leq t \cdot X_{\mu}^\alpha \text{,}
\end{equation}
limiting the contribution of systematic uncertainties.
Two bins, two systematic uncertainties, and one $x_\mu^\alpha$ per {pseu\-do-\-mea\-su\-re\-me\-nt} are considered. The sign of $k_{\nu i j}^\alpha$ is chosen to be constant for each systematic uncertainty.
The estimates $x^a$ and $x^b$ for measurement $a$ and $b$ are set to:
\begin{eqnarray}
x^a & = & 30000 \text{ and}\\
x^b & = & 30600
\end{eqnarray}
to reduce the effect of statistical uncertainties. The resulting statistical uncertainty of 0.6\% does not account for the difference of 2\% between both values, such that the modelling of the systematic uncertainties will affect the combination significantly.

For large systematic variations the maximisation of Eq.~\ref{eq:pseudoLH} with Minuit can become numerically unstable. This is the case when the variation becomes as large as the nominal entry, $X_\mu^\alpha$,  in at least one of the bins. Therefore, the Poisson likelihood is approximated with a Gaussian form, which is valid for low statistical uncertainties such as in this test. Thus, $L^\alpha$ becomes:\\
\begin{equation}
\label{eq:npseudoLH}
 L^\alpha = \prod_{\mu\nu}  \prod_i^{N_\text{bins}^\alpha}
\exp\left[
-  S^\alpha_{\mu\nu} \frac{(\bar{X}_{\mu i}^\alpha - X_\mu^\alpha)(\bar{X}_{\nu i}^\alpha - X_\nu^\alpha)}{2 (\bar{X}_{\mu i}\bar{X}_{\nu i})^{1/2} }
\right] \text{.}
\end{equation}
The matrix $S^\alpha$ allows modelling direct statistical correlations between $\bar{X}_{\mu i}^\alpha$ and $\bar{X}_{\nu i}^\alpha$. Here, $S$ is set to $\mathds{1}$.

In total $2 \times 20,000$ {pseu\-do-\-mea\-su\-re\-me\-nt}s are generated, each with a different random choice of the uncertainties.
The total relative uncertainty, $\sigma_x/x$, on the estimate of {pseu\-do-\-mea\-su\-re\-me\-nt} $a$ is shown in Figure~\ref{fig:errb} for different values of the threshold $t$. Depending on $t$, the uncertainty varies from moderate values to more than 100\%. The same applies to {pseu\-do-\-mea\-su\-re\-me\-nt} $b$ (not displayed). The average constraints on the systematic uncertainties reach from about 90\% ($t=0.01$) to 50\% ($t=1.0$) with respect to their initial $1\sigma$ variation.
\begin{figure}[h]
  \begin{center}
\includegraphics[width=0.4\textwidth]{sys_contr.pdf}
\caption{Relative total uncertainty of the {pseu\-do-\-mea\-su\-re\-me\-nt} $a$ for different values of the threshold $t$.  \label{fig:errb}}
\end{center}
\end{figure}

In a first validation step, each uncertainty of one {pseu\-do-\-mea\-su\-re\-me\-nt} is assumed to be highly correlated with exactly one uncertainty of the other {pseu\-do-\-mea\-su\-re\-me\-nt} by assigning a correlation factor $c=0.99$. A total of 20,000 combinations are performed.
\begin{figure}[h]
  \begin{center}
\includegraphics[width=0.4\textwidth]{err_dev.pdf}
\caption{Ratio of the uncertainties on the combined value obtained using the method proposed here and the direct likelihood combination, shown for different values of the upper threshold for systematic uncertainties $t$.  \label{fig:errb2}}
\end{center}
\end{figure}
The ratio $\Delta^r \sigma$ between the uncertainty on the combined value obtained with the method proposed here and by maximising $L_\text{comb}$ is shown in Figure~\ref{fig:errb2} as a function of $t$. Asymmetric uncertainties on the combined value are accounted for and are equally well described.
With an increasing contribution of the systematic uncertainties, the $\Delta^r \sigma$-distribution becomes slightly broader, but does not indicate any numerically relevant mismodelling.
The resulting values for $\Delta \bar{x}/ \sigma_{\bar{x}}$ are illustrated in Figure~\ref{fig:deltaxbarrel}.
For $t=0.01$, the statistical uncertainties are non negligible. This leads to a small bias towards lower values introduced by the choice of Eq.~\ref{eq:npseudoLH} and discussed in the Section~\ref{sec:statbias}. However, for all choices of $t$ and all pseudo experiments, the differences between the direct likelihood approach and the method described here are well below 5\% of the total uncertainty and can therefore be considered negligible.
 %
\begin{figure}[h!]
  \begin{center}
\includegraphics[width=0.4\textwidth]{reldev.pdf}
\caption{
Difference between the combined result $\bar{x}$ obtained with the method proposed here and using a direct likelihood combination relative to the total uncertainty on $\bar{x}$, shown for different values of the upper threshold for systematic uncertainties $t$.\label{fig:deltaxbarrel}}
\end{center}
\end{figure}

Moreover, the dependence on the assumed correlation between the uncertainties of both {pseu\-do-\-mea\-su\-re\-me\-nt}s is studied, as well as possible biases with respect to the number of bins in each {pseu\-do-\-mea\-su\-re\-me\-nt}.
Figure~\ref{fig:syscorr} shows the dependence of $\Delta \bar{x}/ \sigma_{\bar{x}}$ on the choice for the correlation coefficients $c$ for $t=1$.
The modelling worsens slightly when $|c|$ decreases, but is below about 3\% with respect to the total uncertainty on the combined value for all 20,000 pseudo experiments.
\begin{figure}[h!]
  \begin{center}
\includegraphics[width=0.4\textwidth]{reldev_syscorr.pdf}
\caption{
 Difference between the combined results $\bar{x}$ from the method proposed here and using a direct likelihood combination relative to the total uncertainty on $\bar{x}$. The distribution is shown for different values of the correlation $c$ between the systematic uncertainties of both {pseu\-do-\-mea\-su\-re\-me\-nt}s.
\label{fig:syscorr}}
\end{center}
\end{figure}
Also, the total uncertainty remains well modeled with only a very moderate increase of combinations with $|\Delta^r \sigma |$ slightly different from 1, as shown in Figure~\ref{fig:syscorr2}. The same conclusion can be drawn when the procedure described here is repeated for a different number of bins in each {pseu\-do-\-mea\-su\-re\-me\-nt} (not shown here). All results for 2, 4, 20, and 100 bins show a good modelling of the combined likelihood approach with respect to the central values and the total uncertainties.
\begin{figure}[htbp]
  \begin{center}
\includegraphics[width=0.4\textwidth]{errdev_syscorr.pdf}
\caption{
Ratio of the uncertainties on the combined value obtained using the method proposed here and the direct likelihood combination. The distribution is shown for different values of the correlation $c$ between the systematic uncertainties of both {pseu\-do-\-mea\-su\-re\-me\-nt}s.
\label{fig:syscorr2}}
\end{center}
\end{figure}

In general, the central result and its uncertainty are very well modelled for a large range of relative contributions from systematic uncertainties, correlations among them, and the chosen number of bins in each {pseu\-do-\-mea\-su\-re\-me\-nt}.
Very small deviations of the order of a few per-cent with respect to the total uncertainty are observed.
These are expected as a result of reducing the binned information of the initial measurement likelihood to one or many estimates and a corresponding Hessian.
The method described here shows a similar stability for different choices of $x^a$ and $x^b$, and of the number of uncertainties. Moreover, it is also valid for multiple estimates within one {pseu\-do-\-mea\-su\-re\-me\-nt} without statistical correlations between them. The case of statistical correlations is discussed separately in Section~\ref{sec:dircorr}.

\subsection{Modeling of statistical correlations}
\label{sec:dircorr}

The correct modelling of statistical correlations between the estimates within a measurement is tested by generating two {pseu\-do-\-mea\-su\-re\-me\-nt}s $a$ and $b$ similar to Section~\ref{sec:sysunc}, each with two estimates $x^a_1$ and $x^a_2$ or $x^b_1$ and $x^b_2$, respectively. The corresponding correlation matrices $S^a$ and $S^b$ are randomly chosen to have off-diagonal elements with an absolute value of $d\pm 0.1$. In total, 10000 combinations are performed for each choice of $d=\{0,\ 0.3,\ 0.9\}$, $t=\{0.01,\ 0.50\}$, and $c=\{0.00, 0.99\}$. The values for $x^\alpha_\mu$ are chosen to be $x^a_1  =  30000 $, $x^b_1 =  30600$, $x^a_2  =  20000$, and $x^b_2  =  20500$.
The resulting values for $\Delta \bar{x}_1/ \sigma_{\bar{x},1}$ and $\Delta^r\sigma_1$ are illustrated in Figure~\ref{fig:dircorr} and~\ref{fig:dircorr1a} for $c=0$.
\begin{figure}[htbp]
  \begin{center}
\includegraphics[width=0.4\textwidth]{reldev_dtscan.pdf}
\caption{
Difference between the combined value of $\bar{x}_1$ obtained with the method described here and using a direct likelihood combination relative to the total uncertainty of $\bar{x}_1$. The distribution is shown for different values of the scale $t$ for systematic uncertainties and the statistical correlation between the estimates $d$.
The combination assumes no correlation between the uncertainties of both {pseu\-do-\-mea\-su\-re\-me\-nt}s.
 \label{fig:dircorr}}
\end{center}
\end{figure}
\begin{figure}[htbp]
  \begin{center}
\includegraphics[width=0.4\textwidth]{errdev_dtscan.pdf}
\caption{
Ratio of the uncertainties on $\bar{x}_1$ obtained with the method proposed in this document and using a direct likelihood combination.  The distribution is shown for different values of the scale for systematic uncertainties $t$ and the statistical correlation between the estimates $d$. The combination assumes no correlation between the uncertainties of both {pseu\-do-\-mea\-su\-re\-me\-nt}s.
 \label{fig:dircorr1a}}
\end{center}
\end{figure}

No significant mismodelling of the statistical correlation between estimates of the same measurement can be observed.
The dependence on  $c$ is similar to the one discussed in Section~\ref{sec:sysunc} and not shown here. Also the result of the combination of $x_2$ shows identical behaviour and is therefore not depicted either.  Different choices for $x^\alpha_\mu$ were tested and confirm a good modelling with respect to $d$.

\subsection{Relative uncertainties}

The modelling of relative uncertainties is studied by generating two {pseu\-do-\-mea\-su\-re\-me\-nt}s, each of them with one parameter to be combined, one relative uncertainty, and two absolute uncertainties. The relative uncertainty applies to all bins in the same way and will therefore not receive constraints. In consequence, it will be dominant. Thus, the total uncertainty of each {pseu\-do-\-mea\-su\-re\-me\-nt} will differ from the dependence on $t$ previously illustrated in Figure~\ref{fig:deltaxbarrel}. A total of $2 \times 5000$ {pseu\-do-\-mea\-su\-re\-me\-nt}s are generated.
Figure~\ref{fig:relerrrelunc} shows the relative uncertainty of {pseu\-do-\-mea\-su\-re\-me\-nt} $a$, including one relative uncertainty, as a function of $t$. For $t$ larger than 0.15, the direct likelihood combination shows instabilities in some cases, likely related to the Gaussian penalty terms, while log-normal terms would be more suitable for large relative uncertainties.
\begin{figure}[h]
  \begin{center}
\includegraphics[width=0.4\textwidth]{errcontr_relunc.pdf}
\caption{Relative total uncertainty of the {pseu\-do-\-mea\-su\-re\-me\-nt} $a$ for different values of the threshold $t$ for systematic uncertainties.  All {pseu\-do-\-mea\-su\-re\-me\-nt}s comprise one relative and two absolute uncertainties.
 \label{fig:relerrrelunc}}
\end{center}
\end{figure}
As shown in Figures~\ref{fig:relerrrelunc2} and~\ref{fig:relerrrelunc3}, also when combining {pseu\-do-\-mea\-su\-re\-me\-nt}s with contributions from relative uncertainties, central values and uncertainties are well modelled, assuming the uncertainties of one {pseu\-do-\-mea\-su\-re\-me\-nt} to be uncorrelated with the uncertainties of the other. The same holds true for high correlations between the {pseu\-do-\-mea\-su\-re\-me\-nt}s.
\begin{figure}[h]
  \begin{center}
\includegraphics[width=0.4\textwidth]{reldev_relunc.pdf}
\caption{Difference between the combined value of $\bar{x}$ obtained with the method proposed here and using a direct likelihood combination relative to the total uncertainty of $\bar{x}$, shown for different values of the threshold $t$ for systematic uncertainties.  All {pseu\-do-\-mea\-su\-re\-me\-nt}s comprise one relative and two absolute uncertainties.
 \label{fig:relerrrelunc2}}
\end{center}
\end{figure}

\begin{figure}[h]
  \begin{center}
\includegraphics[width=0.4\textwidth]{errdev_relunc.pdf}
\caption{Ratio of the uncertainties on $\bar{x}$ obtained with the method described in this document and using a direct likelihood combination, shown for different values of the threshold $t$ for systematic uncertainties.  All {pseu\-do-\-mea\-su\-re\-me\-nt}s comprise one relative and two absolute uncertainties.
 \label{fig:relerrrelunc3}}
\end{center}
\end{figure}
Additionally, the method is validated using exactly one estimate per {pseu\-do-\-mea\-su\-re\-me\-nt} and one large relative uncertainty of +15\%. The input estimates are set to $30000 + \beta$, where $\beta$ is a randomly generated value between 0 and 750.
The uncertainty is assumed to be fully correlated between the {pseu\-do-\-mea\-su\-re\-me\-nt}s. This results in asymmetric uncertainties on each {pseu\-do-\-mea\-su\-re\-me\-nt} and the combined value. Moreover, for this particular choice of uncertainties, the combined value can be larger than the highest input estimate.
When comparing the direct likelihood combination to the method proposed here, also in this case no bias with respect to the central value or its uncertainties can be observed.

In summary, the combination method described here does not require the original data and the full fit model, but sufficiently describes the initial measurement for a large variety of possible central values, binning choices and uncertainties. In consequence, the combination results are numerically equivalent to a using the full likelihood information, in particular in case of dominant systematic uncertainties.

\

\section{Neglecting correlations}
\label{sec:negcorr}

For comparison, two {pseu\-do-\-mea\-su\-re\-me\-nt}s $a$ and $b$ with two bins, two systematic uncertainties, and the same parameters described in Section~\ref{sec:sysunc} are combined neglecting correlations between uncertainties within the same {pseu\-do-\-mea\-su\-re\-me\-nt}, but still considering strong correlations between {pseu\-do-\-mea\-su\-re\-me\-nt}s $a$ and $b$. This approximates the situation in which the BLUE method~\cite{LYONS1988110,Nisius1,Nisius2} can be used  for the combination.
The correlations within one {pseu\-do-\-mea\-su\-re\-me\-nt} are removed by inverting $(D^\alpha + \mathds{1})$ in Eq.~\ref{eq:evchi2}, removing the off-diagonal elements of the resulting covariance matrix, and replacing $D^\alpha$ by the inverse of this covariance matrix minus $\mathds{1}$. By choosing the Neyman $\chi^2$ definition in addition, this makes this test equivalent to the BLUE method.
As shown in Figure~\ref{fig:nocorr}, this approximation can lead to wrong individual combination results with respect to the central value when the contribution of systematic uncertainties becomes non-negligible.
\begin{figure}[hbtp]
  \begin{center}
\includegraphics[width=0.4\textwidth]{reldev_nocorr.pdf}
\caption{
 Difference between the combined results neglecting correlations between uncertainties within a measurement and using a direct likelihood combination relative to the total uncertainty on $\bar{x}$.
The distribution is shown for different values of the upper threshold for systematic uncertainties $t$. For comparison with the method proposed here, see Figs.~\ref{fig:errb2} and~\ref{fig:deltaxbarrel}.
\label{fig:nocorr}}
\end{center}
\end{figure}
Also, the uncertainty on the combined value can be severely mismodelled if the correlations within one measurement are neglected, as displayed in Figure~\ref{fig:nocorr2}. The total uncertainty can be underestimated or strongly overestimated, in particular if it is dominated by systematic uncertainties.
Therefore, it is crucial to model these correlations consistently when performing a combination of results obtained in simultaneous fits of systematic uncertainties and the quantity to be determined.
\begin{figure}[hbtp]
  \begin{center}
\includegraphics[width=0.4\textwidth]{err_dev_nocorr.pdf}
\caption{
 Ratio of the uncertainties on the combined value obtained neglecting correlations between uncertainties within a measurement and using a direct likelihood combination. The distribution is shown for different values of the upper threshold for systematic uncertainties $t$. For comparison with the method proposed here, see Figs.~\ref{fig:errb2} and~\ref{fig:deltaxbarrel}.
\label{fig:nocorr2}}
\end{center}
\end{figure}

\

\input{software_man.tex}

\section{Summary}
\label{sec:summary}

The combination method presented in this document allows combining measurements obtained with simultaneous nuisance parameter fits consistently, taking into account the constraints from the data as well as correlations between systematic uncertainties within each measurement.
In contrast to the optimal case of a direct likelihood combination, based on the product of the individual likelihoods of each measurement, the method does not require the full knowledge of the original data and the fit models. This information would also be required by other commonly used combination methods, however, it is publicly available only in rare cases. It is shown that not accounting for correlations between uncertainties within the same measurement can lead to non-negligible deviations from the combined likelihood approach with respect to the combined value and its uncertainty.

The method described here does not introduce such deviations and relies on the central results and their covariances or Hessians, only, which makes it applicable to a significantly larger variety of combinations.
An extensive validation is performed using {pseu\-do-\-mea\-su\-re\-me\-nt} with varying contributions of statistical and systematic uncertainties, correlation assumptions, binning choices, and {pri-or} statistical correlations. All obtained results and uncertainties are numerically equivalent to a direct likelihood combination. Only for measurements strongly limited by statistical precision, the same known caveats as in other $\chi^2$ or least-squares-based approaches (e.g. the BLUE method) apply.
In addition, the Convino program is presented. It is developed to perform combinations using the method described here and provides a text-based and a C\kern-0.1em\raisebox{.2ex}+\kern-0.1em\raisebox{.2ex}+{} user interface. The text-based user interface provides an automatic scan of correlation assumptions and creates the corresponding figures for graphical representation.

\section*{Acknowledgements}
I would like to thank O. Behnke for fruitful discussions and comments alongside M. Aldaya Martin, C. Diez Pardos, M. Mulders, and A. Giammanco for editorial suggestions.

\bibliographystyle{ieeetr}

\section{Program Installation and User Interface}
\label{sec:install}

The method described in Section~\ref{sec:math} is implemented in the dedicated Convino program for the combination of experimental results.
The source code can be found at \path{https://github.com/jkiesele/Convino/releases}.  It can be compiled using \texttt{make} with gcc version~$4.9$ or newer, or clang~8.0.0 or newer (OSX) and ROOT~6 installed on the system. Other versions might be sufficient but are not tested.

The measurements and the configuration for the combination are contained in human-readable text files.
Alternatively, a C\kern-0.1em\raisebox{.2ex}+\kern-0.1em\raisebox{.2ex}+{} library is provided with the software package, providing an interface to {C\kern-0.1em\raisebox{.2ex}+\kern-0.1em\raisebox{.2ex}+{}} standard-library or ROOT classes, the latter commonly used in high-energy physics.
Both interfaces are described in the following, starting with the text-based interface. The discussion of the text-based interface serves as reference for the description of the C\kern-0.1em\raisebox{.2ex}+\kern-0.1em\raisebox{.2ex}+{} interface.

\subsection{Text-based Interface}
\label{sec:tbui}

The ``convino" executable can be found in the base directory after compiling. It prints usage information and a list of options if the \verb+-h+ option is specified. Other options are:
\begin{itemize}
\item[] \verb+-s+ perform correlation scan
\item[] \verb+-p+ save scan plots as .pdf in addition to a .root file
\item[] \verb+-d+ switch on debug printout
\item[] \verb+--neyman+ uses a Neyman $\chi^2$ instead of the Pearson $\chi^2$
\item[] \verb+--prefix+  defines a prefix for all output files and directories
\end{itemize}
In addition to the options, a text file is passed to the executable. It is referred to as \textit{base file} in the following and is described in Section~\ref{sec:basefile}.
Each measurement comprising one or a set of estimates is described in a \textit{measurement file}. Well documented examples for both types of files are provided in the \texttt{examples} directory and should be consulted alongside this manual.

\subsubsection{Measurement File}

Each measurement file consists of blocks. Each block describes estimates or uncertainties. They are defined by a Hessian, a correlation matrix together with constraints, or a set of orthogonal uncertainties. The latter should be provided in the following format:
\begin{verbatim}
[not fitted]
                  sys_a1  sys_b1  sys_c1    stat
  estimate_a1     5       6.1     2         6
  estimate_b1     3       1       4         2
[end not fitted]
\end{verbatim}
The uncertainties \texttt{sys\_XX} on the estimates \texttt{esti\-mate\_XX} are given in absolute values. The keyword \texttt{stat} is reserved for the statistical uncertainty.
The uncertainties and their effect on the estimates in a measurement using a simultaneous nuisance parameter fit technique are described either by a Hessian or a correlation matrix. The Hessian must be written in the following form:
\begin{verbatim}
[hessian]
  sys_a3       1944.6
  sys_b3      -1349. 1154.4
  estimate_a3 -0.525 0.5398   3.25e-4
  estimate_b3 -0.708 0.2706   0       4.89e-4
[end hessian]
\end{verbatim}
while the correlation matrix has to include additional information about the constraints on the parameters. These constraints are given in units of $1\sigma$ variations for the systematic uncertainties, such that a value of 1 corresponds to no reduction and lower values indicate a constraint from the fit to the data. For estimates, the constraints are given in absolute units and correspond to the total uncertainties. In both cases, they are defined in parentheses, such that the correlation matrix is of the format:
\begin{verbatim}
[correlation matrix]
  sys_a2       (1)     1
  sys_b2       (1)     -0.2         1
  estimate_a2  (10.6)  0.547945 0.1059  1
  estimate_b2  (12.8)  0.147945 0.4305  0 1
[end correlation matrix]
\end{verbatim}
If uncertainties have been described in form of a Hessian or correlation matrix, additional contributions from orthogonal uncertainties can be provided in the \texttt{[not fitted]} block. These uncertainties must not have any correlation with the uncertainties defined in the Hessian or the correlation matrix.
The next block of the measurement file describes the type of each uncertainty.
\begin{verbatim}
[systematics]
    sys_a2 = absolute
    sys_b2 = relative
[end systematics]
\end{verbatim}
The type can be either \texttt{ab\-so\-lute} or \texttt{re\-la\-tive}. The default is \texttt{ab\-so\-lute} and does not need to be specified explicitly.
The last block defines which of the parameters are estimates, and their nominal values:%
\begin{verbatim}
[estimates]
    n_estimates = 2
    name_0     = estimate_a2
    value_0    = 780
    name_1     = estimate_b2
    value_1    = 280
[end measurements]
\end{verbatim}
Here, \texttt{n\_es\-ti\-mates} gives the number of estimates.

\subsubsection{Base File}
\label{sec:basefile}
The first block of the base file defines the number of measurement files (\texttt{nFiles}) to be considered for the combination and the corresponding file names. An example is given below:
\begin{verbatim}
[input]
    nFiles = 2
    file0   = exampleMeasurement1.txt
    file1   = exampleMeasurement2.txt
[end input]
\end{verbatim}
The files must be in the same directory as the base file.
The second block defines the observables, the estimates should be combined to:
\begin{verbatim}
[observables]
    combined_a = estimate_a1 + estimate_a2
    combined_b = estimate_b1 + estimate_b2
[end observables]
\end{verbatim}
Here, \texttt{es\-ti\-mate\_a1} and \texttt{es\-ti\-mate\_a2} should be combined to \texttt{com\-bined\_a}, and similarly for   \texttt{es\-ti\-mate\_b1} and \texttt{es\-ti\-mate\_b2}. The number of estimates that should be combined to a single quantity is not limited, as well as the number of combined values. This makes it possible to combine simultaneously e.g. a large amount of bins from differential cross sections from various channels and experiments. However, in this case, the C\kern-0.1em\raisebox{.2ex}+\kern-0.1em\raisebox{.2ex}+{} interface is probably more practical.

The last block describes the correlations that should be assigned using the following syntax.
\begin{verbatim}
[correlations]
    sys_b1 = (0.2) sys_c2
    sys_c1 = (-0.3) sys_d2
[end correlations]
\end{verbatim}
Here, a correlation coefficient of 0.2 is assigned between \texttt{s\-ys\_b1} and \texttt{s\-ys\_c2} and  -0.3 between \texttt{s\-ys\_c1} and \texttt{s\-ys\_d2}.
The correlation assumptions between the parameters can be scanned in an automated way. In this case, the following syntax is used to define the scan ranges:
\begin{verbatim}
[correlations]
    sys_b1 = (0.2 & -0.1 : 0.4) sys_c2
[end correlations]
\end{verbatim}
Here,  \texttt{s\-ys\_b1}  has a nominal correlation of 0.2 to  \texttt{s\-ys\_c2} . The correlation is scanned from -0.1 to 0.4.
If several correlation coefficients should be scanned simultaneously, they have to be specified in a single line:
\begin{verbatim}
[correlations]
sys_b1=(0.2&-0.1:0.4)sys_c2+(-0.3&0.2:-0.3)sys_d2
[end correlations]
\end{verbatim}
In this case, the scan range for a single coefficient can start from positive values to negative values to allow accounting for anti-correlations between the parameters that are scanned simultaneously.

Correlation matrices are positive definite by definition, a correlation matrix $C$ with large off-diagonal entries might lose this property if ill-posed assumptions are made, such as:
\begin{equation}
\label{eq:wrongcorr}
C = \begin{pmatrix}
1 & .99 & 0  \\
.99 & 1 & 0.5 \\
0 & 0.5 & 1 \\
\end{pmatrix}\text{.}
\end{equation}
In this case, the program exits and it is strongly advised to revise the plausibility of the correlation assumptions.

The results of the combination are saved in the output file \path{result.txt}, or \path{<prefix>_result.txt} in case a prefix is specified.
The output file contains the original input correlations, the combination results, the minimum $\chi^2$, and pulls and constraints on all parameters.
The output of the scan, including all correlation matrices, is saved in the file \path{scan_result.txt}. The corresponding figures are saved as \texttt{TGraph\-Asymm\-Errors} classes in the file \path{scanPlots.root}. If pdf-file output was enabled, the resulting Figures can be found in the directory \path{scan_results}.
Examples of such Figures obtained with the example configuration are shown in Figure~\ref{fig:scan} and~\ref{fig:scan2}.
\begin{figure}[h]
  \begin{center}

\includegraphics[width=0.4\textwidth]{combined_a_sys_a1_sys_b2.pdf}
\end{center}
\caption{Combined value for \texttt{com\-bined\_a}
for a scan of the correlation coefficient for \texttt{sys\_a1}
and \texttt{sys\_b2}.
The open marker shows the result obtained with the nominal assumption and its uncertainty.The shaded area represents the uncertainty associated to the scanned dependence, indicated by a continuous line. All values are obtained with the example configuration. \label{fig:scan}
}
\end{figure}
\begin{figure}[h]
  \begin{center}

\includegraphics[width=0.4\textwidth]{combined_b_sys_a1_sys_b2_detailed.pdf}
\end{center}
\caption{Combined values for \texttt{com\-bined\_b}
 (upper panel), and minimum $\chi^2$ (lower panel)  for a scan of the correlation coefficient for \texttt{s\-ys\_a1}
and \texttt{s\-ys\_b2}.
The open marker shows the result obtained with the nominal assumption and its uncertainty. The shaded area represents the uncertainty associated to the scanned dependence, indicated by a continuous line. All values are obtained with the example configuration. \label{fig:scan2}
}
\end{figure}

\subsection{C++ Interface}

The C\kern-0.1em\raisebox{.2ex}+\kern-0.1em\raisebox{.2ex}+{} interface is optimized for the combination of differential distributions and provides three basic classes which will be described in the following: the class \texttt{meas\-ure\-ment}, which is analogous to a measurement file discussed in the previous Section, the class \texttt{com\-bi\-ner} to perform the combination, and a class \texttt{com\-bi\-na\-tion\-Re\-sult} that collects the output of the combination. The \texttt{meas\-ure\-ment} class and the \texttt{com\-bi\-na\-tion\-Re\-sult} class provide interfaces to C\kern-0.1em\raisebox{.2ex}+\kern-0.1em\raisebox{.2ex}+{} standard library \texttt{std::vec\-tor\-<dou\-ble>} or alternatively to ROOT histograms and graphs.
An example of the usage is provided in \texttt{bin/\-differ\-ential\-Ex\-ample.cpp}. Any cpp file that will be placed in the \path{bin} directory will be compiled automatically when running \path{make}.
Alternatively, the compilation of the Convino{} package will create the library \path{libconvino.so} that can be linked against. The header files can be found in the \path{include} directory.

Each class is documented in the corresponding header file. Therefore, the documentation here is limited to the general usage.

\subsubsection{Measurement class}

The measurement class provides the possibility to define a set of estimates, their statistical correlations and systematic uncertainties.
Each object can only contain one set of estimates at once. In case the information is read from a ROOT \texttt{TH1} histogram, each measurement class object can contain only one nominal histogram.

For a measurement with orthogonal uncertainties, the following procedure should be applied:
the nominal values are set using the function \texttt{set\-Meas\-ured}.
Systematic uncertainties can be added in a second step to the measurement object with \texttt{add\-Sys\-te\-matics}.
The type of each uncertainty is defined using the function using \texttt{set\-Para\-meter\-Type} after all uncertainties have been added. Here, it is recommended to use the parameter name to identify the correct uncertainty.
In a last step, statistical correlations between the estimates can be set using the method \texttt{set\-Es\-ti\-mate\-Cor\-re\-lation}.

If a measurement comprises correlated uncertainties, the corresponding measurement object should be configured using the function \texttt{set\-Hes\-sian}, which defines the uncertainties and estimates at once. Additional orthogonal uncertainties can be added in a subsequent step using \texttt{add\-Sys\-te\-ma\-tics}.

\subsubsection{Combiner class}

Once the individual \texttt{meas\-ure\-ment} objects are defined, they are added to a \texttt{com\-bi\-ner} object using the function \texttt{add\-Mea\-sure\-ment}.
For the following combination, it is assumed that the entries of each measurement in the same bin or with the same vector index should be combined. It is not possible to combine a number of estimates from one measurement object with a different number of estimates from another.
The correlation assumptions are defined with \texttt{set\-Syst\-Cor\-rel\-ation}. It is advised to use the uncertainties names  as input for unambiguous identification.

The combination is initiated by calling the method \texttt{com\-bi\-ne}, which returns a \texttt{com\-bi\-na\-tion\-Re\-sult}  class object.

\subsubsection{CombinationResult class}

The \texttt{com\-bi\-na\-tion\-Re\-sult} class is a container for all information regarding the inputs to the combination, the correlation matrices, and the combined values as well as the post-combination correlation matrices, pulls and constraints.
If differential distributions are combined, the result can be fed back to a ROOT \texttt{TH1} object or a \texttt{TGraph\-Asymm\-Errors} using the functions \texttt{fill\-TH1} or \texttt{fill\-TGraph\-Asymm\-Errors}.

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As to whether he can beat Obama, opinions vary. But many feel that a Gingrich victory might be scarier than a GOP defeat. Gingrich's defenders say such fear is a compliment because it shows that he's a "change agent" threatening the status quo.
#ad#They have a point. Inside D.C., it sounds very strange to say that Gingrich is an "outsider." Gingrich has eaten from just about every trough imaginable inside the Beltway. And yet, he's always been very clear that he wants to ("fundamentally," "historically," "categorically," and "radically") overturn the existing order. Some critics always thought, plausibly, that such pronouncements were part of his act or a sign of his megalomania.
But there's another possibility: It's true. Moreover, the times may be ripe for precisely the sort of vexing, vainglorious, and all-too-human revolutionary Gingrich claims to be. That's the argument a few people have been wrestling with (most notably John Ellis for RealClearPolitics.com and Steven Hayward for National Review Online). Gingrich, after all, is the only candidate to actually move the government rightward. While getting wealthy off the old order, he's been plotting for decades how to get rid of it. To paraphrase Lenin, perhaps the K Streeters paid Gingrich to build the gallows he will hang them on?
That remains a stretch. Mitt Romney is still the sensible choice if you believe these are rough, but generally sensible, times. If, however, you think these are crazy and extraordinary times, then perhaps they call for a crazy, extraordinary — very high-risk, very high-reward — figure like Gingrich.
This helps explain why Newtzilla is so formidable. In order to stop him, you need to explain to very anxious GOP voters that the times don't require him.
— Jonah Goldberg is editor-at-large of National Review Online and a visiting fellow at the American Enterprise Institute. You can reach him by e-mail at JonahsColumn@aol.com, or via Twitter: @JonahNRO. © 2011 Tribune Media Services, Inc.
Jonah Goldberg is a National Review contributing editor. @JonahDispatch

redpajama_set_name: RedPajamaCommonCrawl


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Q: VHDL: variable and process I am studying VHDL and I found one thing particularly difficult to understand, since VHDL is a HDL, in my humble opinion, everything it describe should be able to be converted into a circuit. But how could this happen to variable and process? Is there any circuit that can realize variable and process? Can you give me an example of this? Thanks

A: Processes containing variables certainly can be converted into circuits.
Here are a couple of simple examples.
Process(clk)
Variable Q : std_logic_vector(7 downto 0);
begin
  if rising_edge(clk) then
     if En = '0' then
        Q := D;
     end if;
  end if;
  Output <= Q;
end process;

In every clock cycle, if the En (Enable) input is low, the input data D is stored in the variable Q; otherwise nothing happens (and the variable keeps its old value). This is a very specific circuit; an 8-bit register with enable; look up the 74LS377 in an old data book to see the same circuit in TTL.
Notice that the clock "if" statement is kept separate from the En statement, and surrounds it. Synthesis tools look for specific patterns that they know how to translate, and this is one of them. If you have any software experience you might be tempted to combine them :  if rising_edge(Clk) and En = '0' then ... - and in simulation you would get exactly the same behaviour.
However some synthesis tools may not recognise this pattern, and may report errors instead of generating hardware. (Synthesis tools are continually improving, so you might be lucky nowadays). The tool's documentation (e.g. Xilinx "synthesis and simulation design guide") ought to describe what is and isn't possible. [edit:] unfortunately it is stuck around 1995 practices and contains some truly horrible examples of VHDL.
Process(clk)
Variable Count : Integer range 0 .. 255 := 0;    -- set to 0 when process first starts
begin
  if rising_edge(clk) then
     Count := Count + 1 mod 256;
  end if;
  Output := Count;
end process;

Notice that variables, like signals, do not need to be logic types; integers, arrays and records (with some restrictions) are synthesisable; floats usually are not (though this is changing as tools improve). Notice that I limited the range of the integer, to get an 8-bit counter.
With integers, you also need to explicitly specify what happens when they overflow (as I did here) - otherwise you will get errors in simulation. However, specifying the obvious behaviour (as here) should not cost any additional hardware. And using other numeric types like numeric_std.unsigned, the tools are not so fussy.
I have simplified a little; usually there is a Reset clause in a typical process to let you control startup behaviour, but these examples are real and ought to work.

A: Variables can be very handy - they change immediately, but can also keep their value from one tick to the next.  This avoid replicating code when you want to access a previously calculated value which is normally an "output" of your process.
As to creating circuits, variables and signals merely transfer values from one place to another within the design.  Variables are limited to within a process, signals can flow all over the design.  Either way the synthesiser's job is to figure out what behaviour you have described and implement logic to match.  If you increment a variable, or a signal, the same set of "gates" (or look-up tables, etc) results.

redpajama_set_name: RedPajamaStackExchange


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Sri Lanka > Sri Lanka, weather in March: Climate and travel budget
Sri Lanka in January
Sri Lanka in February
Sri Lanka in March
Sri Lanka in April
Sri Lanka in May
Sri Lanka in June
Sri Lanka in July
Sri Lanka in August
Sri Lanka in September
Sri Lanka in October
Sri Lanka in November
Sri Lanka in December
< February
Sri Lanka in March : Travel budget & tourist seasons.
In March, here's what you can expect on average:
• Round-trip flight: 620 €
• Tourist season: low
Climate in March, picked destinations
In March, weather conditions in Sri Lanka make it a medium trip destination. Among our chosen destinations (see below), the average temperatures you'll face in March would be between 24.0°C and 32.0°C, with exceptional possible peaks as low as 18°C and high as 35°C as observed in previous years.
The average amount of rain observed during March in Sri Lanka is 146 mm and you would typically have 8 rainy days.
Colombo 8 24 32 18 35 146 8
Sri Lanka: Climate & Weather
The climate in Sri Lanka is tropical, with an alternation between the monsoon and dry season that gradually sweeps through all regions of the island; however, this means that one part of the country is always enjoying great weather.
The season of Yala, from May to August, brings heavy rains to the south, west and centre. Maha season takes in its turn the monsoon from October to January to the northern and eastern parts. It would therefore be more pleasant to visit the west and south from December to March, and the east from May to September to take advantage of the dry season.
The temperature is constant at around 27 ° C on the coast, both the air and the water!
Sri Lanka: Map
Not the best weather? Look for other destinations: Where to go in March


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Have I been sexually abused as a child?
More than any other question, people ask me 'Have I been sexually abused?' People are desperate for answers. Have you been abused? Well, unless you have memories of the actual abuse, there's no easy way to tell. Most symptoms are not exclusive to childhood sexual abuse. There are a large number of symptoms and conditions that point to childhood sexual abuse, but there isn't a bloodtest or urine sample that you can have analyzed. Unless you happen to remember, you may never be sure.
There are tell tale signs, symptoms that point in the direction and they tend to be cumulative. Having one or more symptoms of the Self Test doesn't mean for sure you have been abused. There could be other causes for each of those symptoms. However, the more statements from the Self Test you check, the more likely it is that you have been sexually abused as a child.
The test doesn't give you the answer to the question 'Have I been sexually abused as a child?' It does tell you some of the multitude of symptoms are known to have a possible connection to childhood sexual abuse. Just reading the list can give you more insight into how childhood sexual abuse affects people. It can also give you more clarity on where you stand with this issue. Whether you are at the start of your healing or at the tail end of it, this test will give you an idea about the terrain and how far along you've come.
If you checked many symptoms, it's probably a good idea to seek help. Life is too beautiful to be suffering from so many symptoms, regardless of whether childhood sexual abuse is the cause. You deserve better. Part two of my book outlines some of the help that is available and gives you an idea of how these different types of therapy work.


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Sainsbury upbeat on outlook. Photo: Reuters/Stefan Wermuth.
Supermarkets continue to be weak on competition from discounters and the prospects of a severe price war, and this week's fall in food prices as reported by the British Retail Consortium has not helped.
Sainsbury's remains one of the most shorted stocks in Europe at present with concerns over its ability to compete and the strength of its balance sheet. The message we had from this session was of a company not burying its head in the sand, it understands the issues at hand but has a clear, consistent strategy and plenty of insight into the path ahead.
There was little sign of Sainsbury's burying their heads in the sand over what is happening in the UK. They spoke openly of how they see negative like for likes for the next couple of years and expect the discounters to keep on growing, reaching a market share of 15% (in line with the UK in the early 90s and in line with many European countries).
However there was clarity what needed to be achieved (1% outperformance of other supermarkets will see them retain market share) and how they will do this. Continued focus on quality but focussed price investment. Although not specifically targeting the discounters their price investment, it will help people who have a value/time arbitrage to answer (i.e. if they get cheap enough, people won't split their shop between Sainsbury's and Lidl). They measure the discounters to be 15% cheaper today, and [a] 10% cut on...1,000 [products] gets them ball park where they want to be.
Recent commentary on Sainsbury's has suggested that Sainsbury's has led a charmed life of late and is destined to suffer as soon as Tesco wakes up.
They fully expect that Tesco will improve and it is likely this will involve some action on price. However the remaining issue is that Tesco does not have the resources to do everything: It can't kill its margins and retain its investment grade status and it cannot be all things to all people; if they go hard on price then (1) Sainsbury's will do all that is necessary to remain price competitive but (2) this will create opportunities to further differentiate at the quality end of the market.
They don't see Tesco simply cutting prices by 5% as the immediate likely scenario (if it does happen then "all bets are off", and consolidation in the industry become likely); this would only address one issue (price), but Tesco have issues on quality and service as well. Going so nuclear on price would mean heavy cost savings and no spare resources to improve on other aspects. The current trajectory by [Tesco chief executive] Dave Lewis (adding more staff hours) is more adding costs than cutting them out. We however would argue this is simply a temporary measure to stop Christmas being a disaster.
[Concerning the balance sheet] a rights issue next year is simply not something they can imagine. They have plenty of measures already in place to deal with the balance sheet strength under a lot of scenarios. Even if it get substantially worse than their own scenarios, there are substantially more measures they can take as well.
However Sainsbury shares are now down 7p at 233.5p.
[We] stick to our current forecast of (an announcement of) a first intermediate quantitative easing in the first quarter, followed by sovereign QE in the second quarter, unless the eurozone economy stages an unexpected growth revival.
The ECB cutting its forecasts for both growth and inflation also unsettled investors.
Among the risers, Sage is up 27.5p at 449.6p as analysts issued positive notes after Wednesday's better than expected full year figures.
Tui Travel has climbed 16.3p to 445p as it unveiled an 11% rise in underlying profits, just weeks before it completes its merger with parent company Tui AG.
Royal Mail has risen 6.6p to 404.6p as Goldman Sachs lifted its target price from 575p to 580p with a buy rating.
But mining shares have come under pressure again, with Anglo American down 37p at £12.83 after Bank of America Merrill Lynch moved from buy to underperform.
WH Smith is up 5p to £12.80 amid reports it had bought Supanews in Australia.
Having flagged that Phil Harris has sold even more shares in Carpetright, we have been asked who on earth has been buying them. And the answer is that an 11.5% stake in Carpetright has been built up by Neptune Investment Management, the fund management group based in Hammersmith.


text:
Q: What would you substitute for { and } in Mathematica code so it will display in YouTube comments? Curly braces are not allowed in YouTube comments, so it would be good to find another character that Mathematica doesn't use and YouTube will allow so a global find and replace will put back the braces.

A: Conversion of @Michael E2's comment to a community wiki answer:
@Michael E2:
Would List[..] work? Then no change is needed when pasting into Mma.


text:
Thaksin 'will wait for right moment' to return to Thailand
BANGKOK - Exiled former Thai prime minister Thaksin Shinawatra, whose sister appears to have won a landslide in the general election on Sunday, said he would wait for the right moment to return to Thailand from Dubai.
"I want to go back to Thailand but I will wait for the right moment" he said.
Thaksin, a billionaire ousted in a 2006 coup, lives in Dubai to avoid jail for graft charges he says were politically motivated.


Would you like to get more information about the honours track Science & Society? Come and visit the information meeting. You will hear everything about the programme, the admission requirements and the apllication procedure. Of course there will be plenty of opportunities to ask questions.


LAS VEGAS (August 15, 2018) – Putting customers first is a mantra at Aristocrat, and the company underscored that commitment at its recently held "Insight to Innovation Customer Advisory Forum." The two-day event was held in Chicago and drew slot and systems leaders from across the industry spectrum.
Nationally recognized author and co-founder of Age Wage Maddy Dychtwalt opened the event with a keynote address that set the stage for the next two days of discussions.
In addition to sessions specifically dedicated to customer feedback, the Forum consisted of several breakout presentations covering a broad range of topics such as game design philosophy, floor performance management, loyalty, and mobile solutions.
Listening to customers and striving to support their success has underpinned Aristocrat's progress. For example, customers recently voted Aristocrat the number one slot provider, and nominated the business as having the most anticipated portfolio of games in the industry, in the 2018 Goldman Sachs Slot Survey.
Additionally, the Q2 Eilers Fantini Quarterly Slot Survey highlighted Aristocrat's Lightning Link™, Dragon Link™, and Buffalo Grand™ as the top premium games in the industry. Further, Buffalo Gold™ was ranked the top casino-owned game.
"We can't succeed unless our customers succeed – it's that simple. We are extremely grateful to our customers for attending this year's forum and for providing us with the insights and engagement that will help us better support their success in future," Wilson said.
For more information about Aristocrat's industry-leading games, cabinets, and system solutions, contact your Aristocrat representative or visit www.aristocrat-us.com. Join Aristocrat on Facebook, LinkedIn, and Twitter.


Hello from Barbour County! It's hard to believe that the first month of the year is almost over.
It just seems like a week ago that we were celebrating Christmas. Maybe this means that I'm getting old? I hope not.
Today, Jan. 26, there will be a Wild Game Feed at the Belington Fire Hall from 3 – 6 p.m. This will feature a buffet of all you can eat items including, wild game, vegetables, salad, desserts, and non wild meat will also be available.
The cost is $10 for adults and $5 for children under the age of 13.
All proceeds will got to benefit the Nestorville United Methodist Charge.
There will be a Food Service Worker Permit Class on Feb. 7 at the Market Place in Philippi. Registration begins at 5:15 p.m., with the class starting at 6 p.m.
The cost for a statewide card is $20, and the cost for a Barbour County card is $10.
Cards are valid for two years.
For more information, call Sanitarian Bill Nestor, at the Barbour County Health Dept. at (304) 457-1670.
In addition to the monthly classes, the Barbour County Health Department has a weekly Food Service Worker test that will be given every Tuesday from 9 a.m. – 10 a.m. at the health department.
It's coming up sooner than we think….Keep in mind that the Barbour County Winter Fair will take place March 8 and 9 at the Belington Fire Department. Craft tables are $15 per space and can be reserved by calling (304) 669-6833.
If you have any Barbour County news that you would like to see in the Inter-Mountain, give me a call at (304) 614-7782.
You can also send me an email to sharris@theintermountain.com. I love hearing from you!


Last night iHeartRadio and 103.5 KISS FM brought the Jingle Ball Tour to Chicago's Allstate Arena in Rosemont, IL. With the sold-out Windy City crowd watching, some of the biggest names in music brought a memorable night of live music to the Allstate. Artists like Ariana Grande, the Backstreet Boys, Ellie Goulding, Daya and Hailee Steinfeld (just to name a few) were there to give the packed arena a night that they will not soon forget.
First up for the night was the lovely and diversely talented, Hailee Steinfeld, who kicked things off with her track 'You're Such A'. Also performing tracks like her DNCE collaboration 'Rock Bottom', 'Love Myself' and 'Starving', which went platinum early this week, Steinfeld put on a great opening set for her Chicago fans, dubbing 2016 one of the best years of her entire life. And with a platinum single and a critical acclaimed film in theaters now, with "The Edge of Seventeen", can you blame her?
Next up, emerging singer Daya greeted the Jingle Ball crowd, calling her recent Jingle Ball performances as "such a dream". Daya performed songs like 'Sit Still, Look Pretty', 'Words', 'Don't Let Me Down' and of course the track that changed her life, 'Hide Away'.
After Daya thanked the sold-out arena, it was time for Lukas Graham to hit the stage. Perhaps one of the top performances of the entire night, Lukas Graham exceeded the expectations of many. Like so many artists on the Jingle Ball lineup, Lukas Graham also have a lot to celebrate. Fresh of their three Grammy nominations, jumping from a spring Chicago performance of about 700 people to performing for a sold-out arena in Rosemont, and getting the crowd engaged with their tracks 'You're Not There', 'Mama Says', 'Strip No More', 'Drunk In The Morning' and their big single '7 Years', it's a great time to be in Lukas Graham.
After fans finished singing along to '7 Years', One Direction's Niall Horan blessed the stage with a performance of his new solo track, 'This Town'. Horan called Chicago his favorite city in the United States, a place where he would spend a lot of time while touring. Unfortunately for Niall though, he told the fans "it makes me upset that I only have one song to perform." Don't worry Niall, we are sure you'll be back very soon with a debut solo album to perform.
Next on the Jingle Ball stage was Tove Lo, who not only played her biggest singles like 'Habit (Stay High)' and 'Talking Body', but also gave fans some awesome performances from her new LP, Lady Wood, including 'Cool Girl' and 'True Disaster'.
And then it was time for probably the biggest performance of the night. That's right, the Backstreet Boys are back, and they made a huge stop in Chicago before their forthcoming Las Vegas residency. Whether you were a mom who brought your daughter and her best friends or a '90s baby (but birth certificate or just at heart), you probably lost your voice or hearing from all the screams. Opening with their mega-hit 'Everybody', which was the perfect opening track to set the tone for the rest of their performance, and later ending with their equally huge, 'Larger Than Life', BSB gave us years of hits and still was able to leave us wanting more. If you missed out on the Jingle Ball or if you were there and just a half hour of the Backstreet Boys left you feeling "incomplete", well make your way to Planet Hollywood in Vegas from March to June and see what the Backstreet Boys "got going on".
Met with the very difficult task of following one of the best selling groups of all-time, Ellie Goulding met the challenge head on and surely delivered. Goulding opened with her big hit single, 'On My Mind', and whether or not the track was inspired by Ed Sheeran's displeasure of her rumored fling with fellow Jingle Ball artist Niall Horan, Ellie killed it. Goulding also performed tracks like 'Anything Could Happen', 'Love Me Like You Do' and busted out the guitar for her hit single 'Burn'. Ellie hasn't been around as long as BSB, but still her entire set was hit after hit. Ellie Goulding live will never disappoint.
While the Backstreet Boys were certainly the highlight for the moms in the audience, the night's headliner was all about the daughters, as Ariana Grande closed out the Chicago stop on the Jingle Ball Tour. Ariana of course got things going with her huge 2016 single, 'Side To Side', and although she wasn't joined by Nicki Minaj for the performance, Ariana didn't need it. Grande kept the fans screaming and ended the night on a high note, and who can hit those high notes better than Ari? From top to bottom, everyone delivered for Chicago last night.
Check out our photos from the Jingle Ball last night in Chicago below, and peep the remaining dates on the Jingle Ball Tour here!


As expected the interim budget of 2019 is full of populism. With general election just months away the BJP government has announced series of sops especially targeting the middle class and farmers. PM Modi's administration has unleashed full of populist goodies for farmers, the middle class and small-and-medium-sized businesses. Regardless of whether the government implements any of this with the election due by May, the announcements could still hurt the prospect of opposition parties. It looks advantage Modi for now but much will depend whether govt can implement these budget announcement in the next two months before the model code of conduct sets in.
For the North East region the budgetary allocation has seen 21% rise to Rs 58,166 crore. The finance minister Piyush Goyal also announced that government will introduce container cargo movement in the region by improving the navigation capacity of the Brahmaputra River. This is a good move. Brahmaputra River has massive potential for the cargo movement. It flows through heart of the region. Especially Arunachal Pradesh stands to gain as most of the rivers of state are tributaries of Brahmaputra. The interim budget presented today is likely to boost the government's popularity ahead of polls. It has given huge advantage to ruling BJP. But in politics things can change very quickly.


This is the second year I've been at our friends' charity race. This year I had a more official role as photographer/videographer. They have done an amazing job raising money for Rady Children's Hospital.
Even more amazing was that due to a police incident which happened over night, they had to move the entire race to a different location the morning of the race! I was amazed at how well they handled the unexpected move.
And for those of you from San Diego, yes that's Derek Togerson from NBC San Diego 7/39 who emceed the event and did an incredible job.
I expect to see all of you there for next year's race!
Click here to view/order prints.
Paula Cook posted the following on March 3, 2010 at 1:00 pm.
Great video footage and pictures! You really captured the event. Thanks so much!


Figure 1. Yeast life cycle. Most lab strains form ascospores containing spores of opposite mating types, a and a. These spores can mate, hybridize, and form diploidal cells capable of budding or sporulating. In contrast, brewing yeasts generally only reproduce by budding.
chain reaction (PCR), restriction fragment length polymorphism (RFLP), amplified fragment length polymorphism (AFLP), pulsed field gel electophoresis (PFGE), and karyotyping all provide unique genetic fingerprints that distinguish not only between ale and lager yeasts, but also between strains of the same group.
Table 2. Characteristics of Saccharomyces species used in brewing1.
Dufour, J.-P, K. Verstrepen, and G. Derdelinckx. 2003. Brewing yeast, p. 347—388. In T. Boekhout and V Robert (ed.), Yeasts in food.Woodhead Publishing Limited, Cambridge, England and CRC Press, Boca Raton, Florida.
Hammond,J.R.M., 2003.Yeast genetics,p.67—112. In F.G.Priest and I.Campbell (ed.), Brewing Microbiology, 3rd ed. Kluwer Academic/Plenum Publishers. New York.
Kurtzman, C.P., and J.W. Fell. 1998. Definition, classification and nomenclature of the yeasts. P. 3—5.In C.P. Kutrzman and J.W. Fell (ed.), The Yeast: A Taxonomic Study, 4th Edition. Elsevier Science B.V. The Netherlands.
Vaughan-Martini,A., and A. Martini. 1998. Saccharomyces Meyen ex Reess, 358-371. In C.I? Kurtzman and J.W. Fell (ed.), The Yeast:A taxonomic study, 4th Edition. Elsevier Science B.V.The Netherlands.
Table 9.4. Differences between ale and lager yeasts.
previous fermentation to pitch the next batch. Only when the fermentation appears slow or sluggish or when quality attributes suffer will a new culture be prepared.
How does the ascospores germinate in yeast?


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Seminary administrator to lead Global Ministries unit
Mary Lou Greenwood Boice, a longtime United Methodist theological school administrator, will serve as interim executive director of the United Methodist mission agency's unit responsible for communications, marketing, fundraising and connectional relations.
Her appointment, effective May 10, was announced by Thomas Kemper, chief executive of the General Board of Global Ministries, which includes the United Methodist Committee on Relief (UMCOR). She will lead the Mission Engagement Unit, which incorporates relations with annual (regional) conferences and the Advance, the designated mission giving channel of the denomination.
"Mary Lou brings experience in fund-development, organizational relations and communications and, after a combined 37 years at Emory University's Candler School of Theology in Atlanta and Boston University School of Theology, knows The United Methodist Church extremely well," Kemper said. "Familiarity with the church and its people, along with administrative talent, is basic to mission interpretation and outreach at this point in our denominational journey."
Boice retired at the end of 2017 as associate dean of admissions and financial aid at Candler, a post she held for seven years, having earlier been associate dean of development and external relations. She came to Emory in 1992 after serving on the administrative staff at Boston School of Theology for a decade. Originally from Massachusetts, she holds a Master of Theological Studies from Boston University, and earned the Bachelor of Arts degree in education from West Virginia Wesleyan College.
"As a lifelong United Methodist, I have long admired the remarkable programs of mission and ministry led by Global Ministries," Boice said of her appointment. "I am delighted to engage this work in new ways and to have a small part in the continuing outreach of our church around the globe."
At Global Ministries, she succeeds the Rev. Russell Pierce who, in a relatively short period, developed and staffed Mission Engagement to promote the involvement of individuals, congregations, annual conferences and international partners in the work of Global Ministries and UMCOR. Pierce left the agency in late April to head a housing ministry in North Carolina.
"We are delighted to have a strong Mission Engagement team for Mary Lou to lead in this period of change and uncertainty in our church," Kemper said.


Scrap Happens Here with Darla: Share What You Love - Sketch Challenge!
Good Morning everyone! YAY! It's Friday...your weekend is almost here! Do you have any fun plans? Will you have any time to create? I have NO PLANS for the weekend! I do have to head down the mountain today, for Redding, to make a Costco run and do my taxes! My husband took the day off to go with me so we'll probably have a lunch date too!
Today's card is one that I created for a team sketch challenge. Sketches are FUN...they get me thinking differently. I especially like this one because of the angles!
Here's the sketch! Will you try it? There are so many options! Do you use embossing folders or designer paper....or do you use only cardstock? Do you change the circle to an oval or a square? That banner...do you want to make it from ribbon? Every single card in the challenge is different! One gal used a punched dog to replace the circle!
Let me show you what I did!!
My card base is a 5 1/2" X 8 1/2" piece of Whisper White cardstock with a 4 1/8" X 5 3/8" piece of Rich Razzleberry cardstock as the first layer. Next I added a 4" X 5 1/4" piece of Share What You Love Designer Paper. My banner is Old Olive cardstock embossed with the Dot to Dot embossing folder and cut into a banner with the Banner Triple Punch. The angled piece and band piece are also from the Share What You Love designer paper. I LOVE THIS PAPER!!!
The sentiment is from the Best Bird stamp set and is stamped onto a Stitched Shapes Circle. I stamped the background image in Mint Macaron. I punched the greenery with the Sprig Punch and cut it in half, added some Old Olive Linen Thread and Linen Thread tied together into a bow and attached with a glue dot. Last I added a flower punched with the Bitty Blooms punch pack (from the same designer paper) and added a pearl as it's center. Everything except the two layers and the banner are attached with dimensionals! I LOVE how it turned out! I have a friend whose anniversary is TODAY...YIKES...I'm gonna be late, but I'm gonna send it to her and her husband!
HEY...THANKS BUNCHES for stopping by today and allowing me to SHARE WHAT I LOVE to do with YOU! Have a wonderful day and terrific weekend! Hope you (and I) find time to create!