text:
\section{Introduction}
\label{se:intro}

Given a permutation $\pi$, a \emph{reversal} reverses a substring of $\pi$,
a \emph{transposition} cuts a substring of $\pi$ and pastes it in a different location,
and a \emph{transreversal} is a transposition of a substring with a reversal done before it is pasted.
In a \emph{prefix} reversal/transposition/transreversals the corresponding substring
is always a prefix of $\pi$.

The \emph{pancake flipping problem}~\cite{amm,BS03,HP95,HS93,HS97} deals with
finding the minimum number of prefix reversals (i.e., \emph{flips}) required to
sort a given permutation.
This problem was first introduced in 1975 by~\cite{amm} which describes
the motivation of a chef to rearrange a stack of pancakes from the smallest
pancake on the top to the largest one on the bottom by grabbing several pancakes
from the top with his spatula and flipping them over, repeating them as many times
as necessary.

Aside from being an interesting combinatorial problem, this problem and its variations
have applications in interconnection networks and computational biology.
The number of flips required to sort the stack of $n$ pancakes is the \emph{diameter}
of the $n$-dimensional \emph{pancake network}~\cite{HS93,HS97}.
The diameter of a network is the maximum distance between any pair of nodes in the network
and corresponds to the worst communication delay for broadcasting messages in the network~\cite{HS93,HS97}.
A well studied variation of pancake flipping problem is the \emph{burnt pancake flipping problem}~\cite{BS03,HS93,HS97}
where each element in the permutation has a sign, and the sign of an element changes with reversals.
Pancake and burnt pancake networks have better diameter and better vertex degree than the popular
hypercubes~\cite{HS93}.
There exists some other variations of pancake flipping, giving different efficient interconnection networks~\cite{BS03}.

A broader class consisting of similar sorting problems, called the \emph{genome rearrangement problems},
are extensively studied in computational molecular biology,
where the orders of genes in two species
are represented by permutations and the problem is to transform one into another
by using minimum number of pre-specified rearrangement operations.
In order to explain the existence of essentially the same set of genes but differences
in their order in different species, several rearrangement operations have been suggested,
including reversals~\cite{KS93,BP93,BHK02}, block interchange~\cite{BI96},
transpositions~\cite{BP95,EH05,H03}, transreversals~\cite{HS04}, fission and fusion~\cite{FF06},
prefix transposition~\cite{DM02}, etc.

The abovementioned sorting problems are mostly NP-complete or their complexity is unknown.
Caprara~\cite{C97} proved that sorting by reversals is NP-hrad,
whereas Heydari and Sudborough~\cite{HS} have claimed that
sorting by prefix reversals is NP-complete too.
The complexity of sorting by transposition and sorting by prefix transposition is still open.
As a result, many approximation algorithms are known for each of these problems and their variations.

A number of authors have also considered the problem of sorting permutations by using
more than one rearrangement operations (reversals, transpositions etc.)~\cite{W98,GPS99,LX99,HS04,E02,Atif08,LZ08},
mostly for signed permutations.
Rahman et.al.~\cite{Atif08} studied the problem of sorting permutations by transpositions and reversals,
where they give an approximation algorithm with approximation ratio $2.83$.

\subsection{Our results}
In this paper we study some variations of pancake flipping problem
from the view point of sorting permutations.
We consider the problem of sorting an (unsigned) permutation by prefix reversals and prefix transpositions.
We give a 3-approximation algorithm for sorting by prefix reversals
and prefix transpositions, and a 2-approximation algorithm for sorting by prefix reversals
and prefix transreversals.
Experimental result shows that our algorithms perform much better in practice.

Note that the problem of sorting by reversals and transpositions in~\cite{Atif08}
and the problem of sorting by prefix reversals and prefix transpositions considered
in this paper are not the same and they do not imply each other.

We also introduce the concept of \emph{forward march}. The idea of forward
march comes naturally from a greedy approach where someone may try to sort the permutation
from starting to end. While applying prefix
reversals and prefix transpositions, a prefix of the given
permutation may become sorted. Whenever this happens, we move
forward and apply the next operation in the remaining unsorted
suffix of the permutation. We give a 3-approximation algorithm for this problem
which also performs better on average.

The above problems that we consider in this paper are variations of the original
pancake flipping problem where the chef has two spatulas in his two free hands.
He can either lift some pancakes from the top of the stack and flip them (a prefix reversal)
or he can lift a top portion of the stack with one hand, lift another portion from the top with the other hand,
and place
the top portion under the second portion (a prefix transposition)
possibly with a flip (a prefix transreversal).
Also, time to time, when a top portion of the stack is sorted he can remove it from the stack (a forward march).

It is worth mentioning that the worst case ratios of our algorithms can only be realized
when an optimal algorithm applies no prefix reversals at all. But it is very likely that
an optimal algorithm will apply both operations.
Keeping this observation in mind, we derive mathematically the equations
for approximation ratio in terms of the number of prefix reversals applied by
an optimal algorithm.

We organize rest of the paper as follows. In Section~\ref{se:pre} we give
the definitions and other preliminaries. In Section~\ref{se:tr3},~\ref{se:tr2}, and~\ref{se:march}
we present the approximation algorithms.
In Section~\ref{se:alt} we derive equations for approximation
ratio in terms of number of prefix reversals applied by an optimal algorithm.
In Section~\ref{se:exp} we present our experimental results.
Finally, Section~\ref{se:con} concludes the paper.
\section{Preliminaries}
\label{se:pre}

Let $\pi=[\pi_0,\pi_1,\ldots,\pi_n,\pi_{n+1}]$ be a permutation of
$n+2$ distinct elements where $\pi_0=0$, $\pi_{n+1}=n+1$ and $1\leq
\pi_i\leq n$ for each $1\leq i\leq n$ (the middle $n$ elements of
$\pi$ are to be sorted). A \emph{prefix reversal} $\beta
=\beta(1,j)$ for some $3\leq j\leq n+1$ applied to $\pi$ reverses
the elements $\pi_1,\dots,\pi_{j-1}$ and thus transforms $\pi$ into
permutation
$\pi\cdot\beta=[\pi_0,\pi_{j-1},\ldots,\pi_1,\pi_j,\ldots,\pi_{n+1}]$.
A \emph{prefix transposition} $\tau=\tau(1,j,k)$ for some $2\leq
j\leq n$ and some $3\leq k\leq n+1$ such that $k\notin [1,j]$ cuts
the elements $\pi_1,\ldots,\pi_{j-1}$ and pastes between $\pi_{k-1}$
and $\pi_k$ and thus transforms $\pi$ into permutation
$\pi\cdot\tau=[\pi_0,\pi_j,\ldots,\pi_{k-1},\pi_1,\ldots,\pi_{j-1},\pi_k,\ldots,\pi_{n+1}]$.

An \emph{identity permutation $\iota_{n}$} is a permutation such
that $\pi_i=i$ for all $1\leq i\leq n$. Given two permutations, the
problem of sorting one permutation to another is equivalent to the
problem of sorting a given permutation to the identity permutation.
The \emph{prefix reversal and prefix transposition distance
$d(\pi)$} between $\pi$ and $\iota$ is the minimum number of
operations such that $\pi\cdot o_1\cdot o_2\cdot\ldots\cdot
o_{d(\pi)}=\iota$, where each operation $o_i$ is either a prefix
reversal $\beta$ or a prefix transposition $\tau$. The problem of
\emph{sorting by prefix reversals and prefix transpositions} is,
given a permutation $\pi$, to find a shortest sequence of prefix
reversals and prefix transpositions such that permutation $\pi$
transforms into the identity permutation $\iota$, i.e. finding the
distance $d(\pi)$.

A \emph{breakpoint} for this problem is a position $i$ of a permutation $\pi$
such that $|\pi_i-\pi_{i-1}|\neq 1$, and $2\leq i\leq n$. By definition,
position 1 (beginning of the permutation) is always considered a
breakpoint. Position $n + 1$ (end of the permutation) is considered a
breakpoint when $\pi_n\neq n$. We denote by $b(\pi)$ the number of
breakpoints of permutation $\pi$. Therefore, $b(\pi)\geq 1$ for any
permutation $\pi$ and the only permutations with exactly one
breakpoint are the identity permutations ($\pi=\iota_n$ , for all $n$).

The \emph{breakpoint graph} $G_\pi$ of $\pi$ is an undirected multi
graph whose vertices are $\pi_i$, for $0\leq i\leq n+1$, and edges
are of two types: \emph{grey} and \emph{black}. For each $1\leq
i\leq n+1$, the vertices $\pi_i$ and $\pi_{i-1}$ are joined by a
black edge iff there is a breakpoint between them, i.e., iff
$|\pi_i-\pi_{i-1}|\ne 1$. For $0\leq j<i\leq n+1$ and $j\neq i-1$,
there is a grey edge between $\pi_i$ and $\pi_j$ iff
$|\pi_i-\pi_{j}|=1$.

For convenience of illustration, in this paper the vertices of
$G_\pi$ are drawn horizontally from left to right in the order of
$\pi_0,\pi_1,\ldots,\pi_{n+1}$, the black edges
are drawn by horizontal lines, and the grey edges are drawn by
dotted arcs.
\section{3-approximation algorithm for prefix reversals and prefix transpositions}
\label{se:tr3}

\subsection{The lower bound}

For a permutation $\pi$ and an operation $o$, denote
$\triangle(\pi,o)=b(\pi)-b(\pi\cdot o)$ as the number of breakpoints
that are removed due to operation $o$.
Following are some important observations about breakpoints.

\begin{lemma}
\label{le:rev} $\triangle(\pi,\beta)\leq 1$.
\end{lemma}

\begin{lemma}
\label{le:tra} $\triangle(\pi,\tau)\leq 2$.
\end{lemma}

From Lemma~\ref{le:rev} and Lemma~\ref{le:tra} an optimal
algorithm for this problem can not remove more than two breakpoints
by a single operation.
So, a lower bound follows.

\begin{theorem}
\label{th:lb2.67} $d(\pi)\geq \lfloor\frac{b(\pi)}{2}\rfloor$.
\end{theorem}

\subsection{The algorithm}
Our algorithm works on considering different orientations of grey
and black edges. Note that if a permutation is not sorted there must be at least two grey
edges in the breakpoint graph and each grey edge will be incident to two black edges.
A grey edge with its two adjacent black edges must be of one of the four types as shown in Fig.~\ref{fig:srtd}.

\iffalse
\begin{figure}
  \centering
  \includegraphics[width=.75\columnwidth]{4types}
  \caption{4 types of grey edges}
  \label{fig:rtd0}
\end{figure}
\fi

\begin{lemma}
\label{le:type4}
Let $(\pi_1,\pi_j)$ be a Type 1 grey edge. Then
there exists at least one black edge $(\pi_{i-1},\pi_{i})$ for some $2\leq i\leq j$.
\end{lemma}

\begin{proof}
If no such black edge exists, then subsequence
$\pi_1\pi_2\ldots\pi_j$ is sorted. But in that case $(\pi_1,\pi_j)$
would not be a grey edge.
\qed
\end{proof}

We call such a black edge a \emph{trapped black edge}.

In our algorithm we scan the permutation from left to right to find the first black edge
incident to a grey edge. There are four possible scenarios for the four types of edges.
We consider the scenarios in the order as presented below in Fig.~\ref{fig:srtd} and apply
a prefix transposition or a prefix reversal accordingly.

\begin{figure}
  \centering
  \input{srtd.pstex_t}
  \caption{Edge types and Scenarios of SortByRT3.}
  \label{fig:srtd}
\end{figure}

\begin{lemma}
\label{le:gcases}
Given  a permutation $\pi$ and its associated breakpoint graph $G(\pi)$,
if any of the following two conditions is satisfied,
then a prefix reversal or a prefix transposition can be applied to $\pi$
such that it removes at least one breakpoint.

\begin{enumerate}
\item $G(\pi)$ contains a grey edge $(\pi_1,\pi_j)$ of Type 1 or Type 2 with $\pi_1\neq1$.
\item $G(\pi)$ contains a grey edge $(\pi_i,\pi_j)$ of Type 3 with $\pi_1=1$.
\end{enumerate}
\end{lemma}

\begin{proof}
If $\pi_1\neq1$ and there is a grey edge $(\pi_1,\pi_j)$ of Type 1, then Scenario 1 is
applicable: according to Lemma~\ref{le:type4}, there exists a trapped black edge
$(\pi_{i-1},\pi_{i})$ for some $2\leq i\leq j$ and we apply a prefix transposition
$\tau_1(1,i,{j+1})$ that creates adjacency between $\pi_{1}$ and $\pi_{j}$
without introducing any new breakpoint.
If on the other hand the grey edge $(\pi_1,\pi_j)$ is of Type 2, then Scenario 2 is applicable:
apply a prefix reversal $\beta_2(1,j)$ that removes a breakpoint.

If $\pi_1=1$ and the first grey edge is $(\pi_i,\pi_j)$, then $\pi_{0},\pi_1\ldots\pi_{i}$ is sorted.
If $(\pi_i,\pi_j)$ is of Type 3, then a prefix transposition $\tau_3(1,{i+1},j)$ removes one breakpoint
according to Scenario 3.
\qed
\end{proof}

\iffalse******************************************************

\begin{lemma}
\label{le:bcase} Let $\pi$ be a permutation of ${1,2...n}$ and
$G(\pi)$ be its associated breakpoint graph. Then, if any one of the
cases 1, 2 or 3 is not applicable, a prefix reversal operation can
be found, that does not remove any breakpoint but that must be
followed by three subsequent operations removing at least three
breakpoints.
\end{lemma}

\begin{proof}
If case 1 or case 2 is not satisfied, then $\pi_1=1$.
Let $\pi_1,\pi_2\ldots\pi_{i-1}$ be a strip for $1<i<n$. Then the
desired breakpoint is at ${\pi_{i-1},\pi_i}$. If the corresponding
grey arc does not form any type 1 edge, then it must be of type 2.
Let the endpoints are $\pi_{i-1}$, $\pi_{j-1}$. So, we can apply a
prefix reversal $\beta_4(1,j)$, which causes the desired breakpoint
to be at $(\pi_0,\pi_1)$ and the grey edge is now of type 3. So,
case 2 will be applicable. Now,
$\pi=\pi_0\pi_{j-1}\ldots\pi_i\pi_{i-1}\ldots\pi_1\pi_j\ldots\pi_n\pi_{n+1}$.
Here, $\beta_2(j-1,i-1)$ removes 1 breakpoint. Observe that, after
applying $\beta_2(j-1,i-1)$, $(\pi_0,\pi_i)$ is now the desired
breakpoint with i=1 and $\pi_i\neq1$. Hence, either case 1 or case 2
will be applicable.

If case 1 is applied then according to Lemma~\ref{le:type4} we will
get a breakpoint which is in between the two endpoints of that edge.
Let it be $\pi_l$. Then we will get $(\pi_0,\pi_l)$ as the desired
breakpoint during the next iteration. Similarly, we will get such a
$\pi_l$ if case 2 is applied. If $\beta_2(1,m)$ is applied, then
$l=m-1$.

So, in either case again either case 1 or case 2 will be applicable.
Hence, we get three consecutive operations removing at least 3
breakpoints.
\qed
\end{proof}

**************************************************\fi

\begin{lemma}
\label{le:bcase} Given a permutation $\pi$ and its associated breakpoint graph $G(\pi)$,
if none of the Scenario 1, 2 and 3 is applicable, then a prefix reversal can be applied
that does not remove any breakpoint but is followed by two subsequent operations removing
at least two breakpoints.
\end{lemma}

\begin{proof}
If scenario 1 or 2 is not applicable, then $\pi_1=1$.
Let $\pi_1,\pi_2\ldots\pi_{i-1}$, for some $1<i<n$, be the largest subsequence that is already sorted.
Then there is a breakpoint between $\pi_{i-1}$ and $\pi_i$.
If the grey edge adjacent to $\pi_{i-1}$ is not of Type 3, then it must be of Type 4.
Let the other endpoint of the grey edge be $\pi_{j-1}$.
So, we can apply, according to Scenario 4, a prefix reversal $\beta_4(1,j)$ that does not remove any breakpoint but
causes the grey edge to become of Type 2.
Then in the next step Scenario 2 will be applicable with a prefix reversal $\beta_2(j-1,i-1)$ that will remove one breakpoint.
After applying $\beta_2$, $(\pi_0,\pi_i)$ will become a breakpoint with $i=1$ and $\pi_i\neq 1$.
Hence, again, either Scenario 1 or Scenario 2 will be applicable, which will further remove a breakpoint.
So, as a whole, we get two consecutive operations removing at least two
breakpoints after applying a reversal that does not remove a breakpoint.
\qed
\end{proof}

Our algorithm (SortByRT3) is summarized in Algorithm~1. It
clearly runs in polynomial time.

\begin{algorithm}
\label{al:a2.67app} \caption{SortByRT3($\pi$)} \label{Algorithm1}
\begin{algorithmic}
\STATE Construct breakpoint graph $G_\pi$ of $\pi$
\WHILE{there is a breakpoint}
\IF{$\pi_1\neq 1$ }
       \IF{Scenario 1 is applicable}
       \STATE apply a prefix transposition $\tau_1$
       \ELSIF{Scenario 2 is applicable}
       \STATE apply a prefix reversal $\beta_2$
       \ENDIF
\ELSE
       \IF {Scenario 3 is applicable}
       \STATE apply a prefix transposition $\tau_3$
       \ELSE
       \STATE apply a prefix reversal $\beta_4$
       \ENDIF
\ENDIF
\ENDWHILE
\end{algorithmic}
\end{algorithm}

\begin{theorem}
\label{th:sortbyrt3}
SortByRT3 is a 3-approximation algorithm.
\end{theorem}

\begin{proof}
By Lemma~\ref{le:gcases}, if any of the Scenario 1, 2 or 3 is applicable,
then the algorithm can remove at least one breakpoint at each step.
Otherwise according to Lemma~\ref{le:bcase} it removes at least two breakpoints in three steps.
Hence, it sorts $\pi$ in
at most $\frac{3(b(\pi)-1)}{2}$ operations.
By Theorem~\ref{th:lb2.67}, $d(\pi)\ge \lfloor\frac{b(\pi)}{2}\rfloor$.
So, we get an approximation ratio of $\rho \leq3$. \qed
\end{proof}

\section{2-approximation algorithm}
\label{se:tr2}

Now we improve the ratio considering a third  rearrangement operation,
called \emph{prefix transreversal}.
A \emph{prefix transreversal} $\beta\tau=\beta\tau(1,j,k)$ for some
$2\leq j\leq n$ and some $3\leq k\leq n+1$ such that  $k\notin
[1,j]$ reverses the elements $\pi_1,\ldots,\pi_{j-1}$ and then
pastes it between $\pi_{k-1}$ and $\pi_k$ and thus transforms $\pi$ into permutation
$\pi\cdot\beta\tau=[\pi_0,\pi_j,\ldots,\pi_{k-1},\pi_{j-1},\ldots,\pi_{1},\pi_k,\ldots,\pi_{n+1}]$.

\subsection{The lower bound}

Another important observation about breakpoints regarding prefix
transreversals is the following.

\begin{lemma}
\label{le:trarev} $\triangle(\pi,\beta\tau)\leq 2$.
\end{lemma}

From Lemma~\ref{le:rev}, Lemma~\ref{le:tra} and
Lemma~\ref{le:trarev} a lower bound for sorting by prefix reversals and prefix transreversals
is the following.

\begin{theorem}
\label{th:lb2} $d(\pi)\ge \lfloor\frac{b(\pi)}{2}\rfloor$.
\end{theorem}

\subsection{The algorithm}
The next lemma is the key to our 2-approximation.

\begin{lemma}
\label{le:steps4}
Let $\pi$ be a permutation with $\pi_1=1$ and let its associated breakpoint graph be $G(\pi)$.
If $G(\pi)$ contains a grey edge of Type 4, then a prefix transreversal can be applied
that removes at least one breakpoint.
\end{lemma}

\begin{proof}
Let the Type 4 grey edge be $(\pi_{i-1},\pi_{j-1})$ with its two adjacent black edges
$(\pi_{i-1},\pi_i)$ and $(\pi_{j-1},\pi_j)$.
We can apply a prefix transreversal $\beta\tau(1,i,j)$ creating an adjacency between
$\pi_{i-1}$ and $\pi_{j-1}$ and thus removing a breakpoint.
\qed
\end{proof}

The above lemma along with Lemma~\ref{le:gcases} proves that in every situation
at least one breakpoint is removed by each operation.

\begin{lemma}
\label{le:ub2} For every permutation $\pi$, we have $d({\pi})\leq
b({\pi})-1$.
\end{lemma}

\begin{theorem}
\label{th:range}
$\lfloor\frac{b(\pi)}{2}\rfloor \leq d({\pi}) \leq b({\pi})-1$.
\end{theorem}

\begin{theorem}
\label{th:sortbyrt2}
An algorithm (let us call it SortByRT2) that produces prefix reversals, prefix transpositions,
and/or prefix transreversals according to Lemma~\ref{le:steps4} is an approximation algorithm with factor 2
for sorting by prefix reversals and prefix transreversals.
\end{theorem}

\section{3-approximation algorithm with forward march}
\label{se:march}

In this section we introduce a new concept that we call \emph{forward march}.
At the very beginning or after applying a prefix reversal or a
prefix transposition, a prefix $\pi_0,\ldots,\pi_i$, for $0\leq i\leq
n+1$ may be already sorted.  In this case we update $\pi$ as the unsorted suffix
of $\pi$, i.e., as $\pi=\pi_{i},\ldots,\pi_{n+1}$ and the size of $\pi$
is reduced by $i$, i.e., the value of $n$ is updated as $n=n-i$.
The next prefix reversal or prefix transposition is applied on
updated $\pi$. This concept of moving
forward along with the  sorting is called \emph{forward march}.

For our algorithm with forward march we redefine breakpoint and breakpoint
graph. In the redefined \emph{breakpoint graph} $G_\pi$ of $\pi$ there is a black
edge between $\pi_i$ and $\pi_{i+1}$ iff there is a breakpoint between them, i.e., iff
$|\pi_i-\pi_{i+1}|\ne 1$. Clearly, $\pi$ is sorted iff it has no
breakpoint. Note that at any time $\pi_0$ is the last element in the sorted part
of the permutation and there always exists a black edge between
$\pi_0$ and $\pi_1$. We call this black edge the \emph{starting
black edge}.

\subsection{The lower bound}

Due to breakpoint redefinition some of our previous observations are
modified.

\begin{lemma}
\label{le:rev3}
$\triangle(\pi,\beta)\leq 2$.
\end{lemma}

\begin{lemma}
\label{le:tra3}
$\triangle(\pi,\tau)\leq 3$.
\end{lemma}

 From Lemma~\ref{le:rev3} and Lemma~\ref{le:tra3} new lower bound is the following.

\begin{theorem}
\label{th:lb3} $d(\pi)\geq \frac{b(\pi)}{3}$.
\end{theorem}

\subsection{The algorithm}
Our algorithm works on considering different orientations of grey
and black edges. If $\pi$ is unsorted then it has at least two grey edges
and at least one black edge in addition to the starting black edge
$(\pi_0,\pi_1)$.

We consider different orientations of the four edge types of Fig.~\ref{fig:srtd}
described in Section~\ref{se:tr3}.
We try five scenarios in the order shown in Fig.~\ref{fig:rtd}, apply
a prefix transposition or a prefix reversal accordingly and perform a forward march
if possible. In fact, Lemma~\ref{le:ends} proves that Scenario 4 and 5 are sufficient to
sort $\pi$, and Scenario 1, 2 and 3 improve practical performance of our algorithm without
affecting approximation ratio. Our algorithm (SortByRTwFM3) is summarized in Algorithm~2.
It clearly runs in polynomial time.

\begin{figure}[th]
  \centering
  \input{rtd.pstex_t}
  \caption{Scenarios of SortByRTwFM3}
  \label{fig:rtd}
\end{figure}

\iffalse

\paragraph{Scenario 1}
Scenario 1 is a combination of two type 1 edges having one black
edge in common. It has two grey edges $(\pi_0,\pi_i)$ and
$(\pi_{i-1},\pi_{j})$, and three black edges $(\pi_0,\pi_1)$,
$(\pi_{i-1},\pi_{i})$ and $(\pi_{j-1},\pi_{j})$. A prefix
transposition $\tau_1(1,i,j)$ is applied that breaks the three black
edges and may/may not introduce a new black edge
$(\pi_{j-1},\pi_{1})$ depending on whether $(\pi_{1},\pi_{j-1})$ was
a grey edge or not. Since there was a grey edge between $\pi_0$ and
$\pi_i$ and after the transposition they become adjacent, as a
whole, $\tau_1$ removes at least two breakpoints and causes a
forward march.

For the following three scenarios, each of them combines a type 4
edge with at most one type 1 edge. But in any case it is required
that another black edge exists in between the two end of the grey
edge of type 4 edge. We call this black edge a \emph{trapped black
edge}. The following lemma ensures the existence of a trapped black
edge. (This lemma can be proved even for a type 4-like grey edge
that is not incident at $\pi_1$. But we do not need that for
applying a prefix reversal or a prefix transposition.)

\paragraph{Scenario 2}
This scenario is a combination of one type 1 edge and one type 4
edge. It has two grey edges $(\pi_1,\pi_{j-1})$ and
$(\pi_{i-1},\pi_{j})$, and three black edges $(\pi_0,\pi_1)$,
$(\pi_{i-1},\pi_{i})$ and $(\pi_{j-1},\pi_{j})$. A prefix
transposition $\tau_2(1,i,j)$ is applied which breaks the three
black edges and introduces a new black edge $(\pi_{0},\pi_{i})$. We
assume that a grey edge does not exist between $\pi_0$ and $\pi_1$,
otherwise it would fall in Scenario 1 and would allow a forward
march. Therefore, $\tau_2$ removes two breakpoints without any
forward march.

\paragraph{Scenario 3}
This scenario is the ``reflection'' of the grey edges of Scenario 2
and is again a combination of one type 1 edge and one type 4 edge.
Its two grey edges are $(\pi_0,\pi_{i})$ and $(\pi_{1},\pi_{j-1})$,
and three black edges are $(\pi_0,\pi_1)$, $(\pi_{i-1},\pi_{i})$ and
$(\pi_{j-1},\pi_{j})$. A prefix transposition $\tau_3(1,i,j)$ is
applied which breaks the three black edges and introduces a new
black edge $(\pi_{i-1},\pi_{j})$. Here $\pi_0$ and $\pi_i$ had a
grey edge and now become adjacent after the transposition. As a
whole, $\tau_3$ removes two breakpoints with a forward march.

\paragraph{Scenario 4}
This scenario consists of one type 4 edge with an ``isolated''
trapped black edge. That means, it has one grey edge
$(\pi_{1},\pi_{j-1})$, two black edges $(\pi_0,\pi_1)$ and
$(\pi_{j-1},\pi_{j})$, and a trapped black edge
$(\pi_{i-1},\pi_{i})$. A prefix transposition $\tau_4(1,i,j)$ is
applied which breaks the three black edges and introduces two new
black edges $(\pi_{0},\pi_{i})$ and $(\pi_{i-1},\pi_{j})$. The black
edge $(\pi_{0},\pi_{i})$ is introduced, because unlike Scenario 3
$(\pi_{0},\pi_{i})$ was not a grey edge before the transposition is
applied. Therefore, $\tau_4$ removes one breakpoint without any
forward march.

\paragraph{Scenario 5}
In Scenario 5, only one type 3 edge is considered. A prefix reversal
$\beta_1(1,j)$ is applied which breaks the black edges
$(\pi_{0},\pi_1)$ and $(\pi_{j-1},\pi_j)$ and add a new black edge
$(\pi_{0},\pi_{j-1})$ which is the starting black edge for next
operations until changed or removed. So, $\tau_5$ removes at least 1
breakpoint.

\fi

The following lemma is immediate from the scenarios presented in Fig.~\ref{fig:rtd}.

\begin{lemma}
\label{le:ub3} After each prefix reversal or prefix transposition
the number of breakpoints is reduced by at least one.
\end{lemma}

The following lemma proves that our algorithm always terminates by sorting the permutation.

\begin{lemma}
\label{le:ends} Scenario 4 and Scenario 5 are sufficient to sort the
permutation.
\end{lemma}

\begin{proof}
Since $\pi_1\neq 1$, we always have a grey edge of Type 1 or Type 2
whose left black edge is $(\pi_o,\pi_1)$.
If the grey edge is of Type 1, then by Lemma~\ref{le:type4} we can find a
trapped black edge and can apply Scenario 4. On the other hand, if the
grey edge is of Type 2, then Scenario 5 is applicable. By
Lemma~\ref{le:ub3} since every scenario reduces at least one
breakpoint, Scenario 4 and Scenario 5 can successfully sort the
permutation. \qed
\end{proof}

\begin{algorithm}
\label{al:a3app} \caption{SortByRTwFM3($\pi$)} \label{Algorithm2}
\begin{algorithmic}
\STATE Construct breakpoint graph $G_\pi$ of $\pi$ \WHILE{there is a
black edge}
  \IF{Scenario 1 is found}
    \STATE apply a prefix transposition $\tau_1$
  \ELSIF{Scenario 2 is found}
    \STATE apply a prefix transposition $\tau_2$
  \ELSIF {Scenario 3 is found}
    \STATE apply a prefix transposition $\tau_3$
  \ELSIF {Scenario 4 is found}
    \STATE apply a prefix transposition $\tau_4$
  \ELSE
    \STATE apply a prefix reversal $\beta_5$
  \ENDIF
  \STATE $G_\pi\leftarrow G_\pi$ after applying the operation
  \STATE update starting black edge to the first black edge of $G_\pi$ \hspace{25pt} // Forward march
\ENDWHILE
\end{algorithmic}
\end{algorithm}

\begin{theorem}
\label{th:sortbyrtwfm3}
SortByRTwFM3 is a 3-approximation algorithm.
\end{theorem}

\begin{proof}
By Lemma~\ref{le:ends} our algorithm successfully sorts a given
permutation $\pi$ and by Lemma~\ref{le:ub3} it sorts $\pi$ in at
most $b(\pi)$ operations. By Lemma~\ref{th:lb3},
$d(\pi)\ge\frac{b(\pi)}{3}$. So, we get an approximation ratio of
$\rho \leq3$. \qed
\end{proof}

\section{Adaptive approximation ratios}
\label{se:alt}

The algorithms presented in this paper realize their worst case approximation ratios
as a result of combination of the best
case behavior of an optimal algorithm, where no prefix reversal is
applied, and a worst case behavior of our algorithm, where no prefix
transposition (or prefix transreversal) is applied.
This is due to the inferiority of prefix reversals to prefix transpositions with respect
to their ability to remove breakpoints.
However, it is expected that an optimal algorithm would apply both operations.
Motivated by the above observation, we derive adaptive approximation ratios for our
algorithms in terms of the number of prefix reversals, $r$, applied by an optimal algorithm.
Although there is no change in the upper bound of the algorithm, the
approximation ratio will improve, because of the increased lower
bound.

\begin{theorem}
\label{le:ptr2.67}
When $r$ prefix reversals are applied by an optimal
algorithm, SortByRT3 sorts a permutation $\pi$ with
approximation ratio $\rho_r\le3-\frac{3r}{b(\pi)+r-1}$.
\end{theorem}

\begin{proof}
For $b(\pi)\geq r$, if an optimal algorithm uses $r$ prefix
reversals, it removes at most $r$ breakpoints (by Lemma
\ref{le:rev}). For the remaining $(b(\pi)-1)-r$ breakpoints it must
use at least $\lfloor\frac{b(\pi)-r}{2}\rfloor$ operations (by
Theorem~\ref{th:lb2.67}).

As a result, $d(\pi)\geq
r+\lfloor\frac{b(\pi)-r}{2}\rfloor\geq
r+\frac{b(\pi)-1-r}{2} = \frac{b(\pi)-1}{2}+\frac{r}{2}$

Therefore,
$\rho_r\leq\frac{\frac{3(b(\pi)-1)}{2}}{\frac{b(\pi)+r-1}{2}}
            =\frac{3(b(\pi)-1)}{b(\pi)+r-1}
             = 3-\frac{3r}{b(\pi)+r-1}$
\qed
\end{proof}

\begin{theorem}
\label{le:ptr2}
When $r$ prefix reversals are applied by an optimal
 algorithm, SortByRT2 sorts a permutation $\pi$ with
approximation ratio $\rho_r\le2-\frac{2r}{b(\pi)+r-1}$.
\end{theorem}

\begin{proof}
An optimal algorithm removes at most $r$ breakpoints by $r$ prefix
reversals (by Lemma \ref{le:rev}). For the remaining $(b(\pi)-1-r)$ breakpoints it must
use at least $\lfloor\frac{b(\pi)-r}{2}\rfloor$ operations (by
Theorem~\ref{th:lb2}).

As a result, $d(\pi)\geq
r+\lfloor\frac{b(\pi)-r}{2}\rfloor\geq
r+\frac{b(\pi)-1-r}{2} = \frac{b(\pi)-1}{2}+\frac{r}{2}$

Therefore,
$\rho_r\leq\frac{b(\pi)-1}{\frac{b(\pi)+r-1}{2}}
            =\frac{2b(\pi)-2+2r-2r}{b(\pi)+r-1}
             = 2-\frac{2r}{b(\pi)+r-1}$
\qed
\end{proof}

\begin{theorem}
\label{th:fm3}
When $r$ prefix reversals are performed by an optimal algorithm,
SortByRTwFM3 sorts a permutation $\pi$ with approximation ratio $\rho_r\le3-\frac{3r}{b(\pi)+r}$.
\end{theorem}

\begin{proof}
For $b(\pi)\geq2r$ an optimal algorithm applies $r$ prefix reversals
to remove at most $2r$ breakpoints (by Lemma~\ref{le:rev3}).
For the remaining $b(\pi)-2r$ breakpoints it must use
at least $\frac{b{\pi}-2r}{3}$ operations (by Theorem~\ref{th:lb3}).

Therefore, $d(\pi)\geq r+\frac{b(\pi)-2r}{3} =
\frac{b(\pi)}{3}+\frac{r}{3}$

So,
$\rho_r\leq\frac{b(\pi)}{\frac{b(\pi)+r}{3}}
            =\frac{3b(\pi)+3r-3r}{b(\pi)+r}
             = 3-\frac{3r}{b(\pi)+r}$
\qed
\end{proof}

\section{Experimental Results}
\label{se:exp}

We have implemented our algorithms and tested their average performance
on above 60,000 permutations taken randomly of size up to 3000.
In each case the cost of solution given by proposed algorithm is compared
to corresponding lower bound instead of comparing with the cost of optimal solution.
For both SortByRT3 (Theorem~\ref{th:sortbyrt3}) and SortByRTwFM3 (Theorem~\ref{th:sortbyrtwfm3})
worst cases occur very few times in practice and shows ratio near 2 in average
(Fig.~\ref{fig:experiment} (a) and (e) respectively).
For SortByRT2 (Theorem~\ref{th:sortbyrt2}) the practical ratio is no better than the
theoretical one due to its strategy of choosing scenarios most of the time which remove
only $1$ breakpoint in one operation (Fig.~\ref{fig:experiment}(c)).

The ultimate effect of inducing inferior operations
(Theorem~\ref{le:ptr2.67},~\ref{le:ptr2} and~\ref{th:fm3})
is the increase of lower bounds and thereby the decrease of approximation ratios.
This is reflected in Fig.~\ref{fig:experiment}(b), (d) and (f), respectively,
as the corresponding theoretical and practical curves decrease and become closer
to the optimal with the increase of $r$.

\iffalse************************
We have implemented our algorithms and tested their average performance
on above 60,000 permutations taken randomly of size up to 3000.
For each permutation $\pi$ we first compute $b(\pi)$ and then
compare the number of operations required by our algorithms to the corresponding lower bounds.
Both SortByRT3 (Theorem~\ref{th:sortbyrt3}) and SortByRTwFM3 (Theorem~\ref{th:sortbyrtwfm3})
perform with ratio $2$ as the input size increases
(Fig.~\ref{fig:experiment}(a) and (e) respectively).
Their theoretical and practical adaptive ratios (Theorem~\ref{le:ptr2.67},~\ref{le:ptr2}, and~\ref{th:fm3} respectively)
also decrease with the increase of $r$ and become closer to each other
(Fig.~\ref{fig:experiment}(b), (d), and (f) respectively).
Remember that, this happens because with increasing $r$ the theoretical adaptive ratios reach their best possible values.
For SortByRT2 (Theorem~\ref{th:sortbyrt2} and~\ref{le:ptr2}), the practical ratios are no better
than their corresponding theoretical ratios, because our implementations choose most of the time
the worst case scenario of the sorting where only one breakpoint is removed in each step
(Fig.~\ref{fig:experiment}(c) and (d) respectively).

******************************\fi

Observe that if we could compare our algorithms with corresponding optimal algorithms,
then the experimental ratios would be better.

\iffalse**********************************
\begin{figure}[ht]
\begin{center}
\subfigure[3-approximation
algorithm]{\includegraphics[width=.49\textwidth]{3r1_2}}
\subfigure[Forced prefix
reversals]{\includegraphics[width=.49\textwidth]{rr2500_2}}
\caption{Experimental results} \label{fig:exp}
\end{center}
\end{figure}
*******************************************\fi

\begin{figure}[htbp]
\begin{center}
\subfigure[SortByRT3]{\includegraphics[width=.45\textwidth]{app3}}
\subfigure[Adaptive SortByRT3]{\includegraphics[width=.45\textwidth]{app3_rev}}
\subfigure[SortByRT2]{\includegraphics[width=.45\textwidth]{app2}}
\subfigure[Adaptive SortByRT2]{\includegraphics[width=.45\textwidth]{app2_rev}}
\subfigure[SortByRTwFM3]{\includegraphics[width=.45\textwidth]{fmapp}}
\subfigure[Adaptive SortByRTwFM3]{\includegraphics[width=.45\textwidth]{fmapp_rev}}
\caption{Experimental results}
\label{fig:experiment}
\end{center}
\end{figure}

\section{Conclusion}
\label{se:con}
In this paper we have studied some variations of the pancake flipping problem from the view point of sorting
 unsigned permutations.
We have given a 3-approximation algorithm for sorting by prefix reversals and prefix transpositions.
Then we considered a third operation, called prefix transreversal, and provided a 3-approximation algorithm.
We also introduced a new concept called
forward march where we skip over the sorted prefix of the permutation and apply
operations on some prefix of the unsorted suffix of the permutation and contributed
a 3-approximation algorithm.
We have further analyzed the problems in more practical way and
presented better approximation ratios when a certain number of
inferior operations (i.e., prefix reversals) are applied by an optimal algorithm.
An experimental study shows that our algorithms performs much better in practice than
suggested by their approximation ratios.

It will be interesting to redefine the problems to ``force'' certain number of inferior operations
and analyze the approximation ratios of the algorithms. This idea can be applied for other
combination of more than one operation. The complexity of the problems are also unknown. In future it would
be interesting to see whether the problems are NP-hard.

redpajama_set_name: RedPajamaArXiv


Emergency vehicles will need to get permission from state governments to use beacons.
The blanket ban on red and blue beacon cars promised by Prime Minister Narendra Modi came into effect late last night. And the Centre has tried to make sure that nobody - not even the police - can misuse the flashing lights on vehicles that have, for decades, become a glaring symbol of power, and VIP culture in India.
Prime Minister Narendra Modi decided to ban red beacons around 10 days back, putting a firm end to the practice that let VIPs - mostly politicians and bureaucrats - claim the right to way as they navigated through India's congested streets.
Speaking on his decision in his monthly radio programme Mann ki Baaton Sunday, PM Modi said he wasn't just removing the red beacons from cars but also ensuring that "the VIP culture is removed from the minds" of the VIPs.
Last night's twin executive orders issued by Mr Gadkari's department is an improvement over the announcement made by Finance Minister Arun Jaitley, who said blue lights would be allowed for emergency vehicles. The orders learnt to have been vetted by the Prime Minister's Office ban both, red and blue beacons. The only one allowed a purple beacon is an ambulance.
All other emergency vehicles will be allowed to use multi-coloured red, blue and white lights. This short list includes vehicles deployed for fire control, vehicles of the police, defence forces or paramilitary forces on maintenance of law and order duties and disaster management vehicles.
But they too will not have a free run.
The lights can be used by designated security officials only when they are on law and order duties. This means an official cannot switch on the flashing lights on their way back home to beat the traffic blues.
More importantly, their vehicles will need a sticker - printed on "a water-mark paper" with a hologram - from the state government to use these lights. Also, the state government would have to make public the list of departments that are issued these stickers.
"Only one sticker shall be issued to the designated officer for one vehicle at one point of time," Abhay Damle, joint secretary of the Transport Ministry said in the notification that set the ironclad ground rules.
It is a message that may take some time to reach Congress-ruled Karnataka, given how initially Chief Minister Siddaramaiah, and later the Food and Civil Minister UT Khader have tried to cling on to the red beacon. Not for long. If they do, anyone can lodge a complaint to get them penalised for the violation.


text:
Haus Haan ist eine Wasserburg und ein ehemaliges Rittergut. Es ist im Kölner Stadtteil Höhenhaus an der Grenze zum Stadtteil Dünnwald gelegen.

Beschreibung
Es handelt sich um eine Anlage im Geviert, im Zentrum und nicht vollständig von Gebäuden umschlossen, steht das Haupthaus. Das Haupthaus liegt auf einer hoch aufgemauerten Insel und ist komplett von einem Wassergraben umschlossen. Auf die Insel führt vom Innenhof der Anlage eine stark ansteigende steinerne Bogenbrücke.

Das Herrenhaus selber ist ein schmuckloser Geviertbau von mit Fensterachsen auf jeder Seite, zweigeschossig und mit hohem Mansardendach. Das Herrenhaus ist zu drei Seiten ab dem Wassergraben von den ehemaligen Wirtschaftsgebäuden jüngeren Datums umgeben. Ein Tordurchgang (zur heutigen Straße "Zeisbuschweg") befindet sich gegenüber dem Zugang zum Herrenhaus.

Der Wassergraben der Burg wird durch einen kleinen Bachlauf gespeist, der am Dünnwalder Mauspfad vom Mutzbach linker Hand abzweigt und durch ein dort vorhandenes Wehr reguliert werden kann.

Geschichte
1203 wurde eine Burganlage an der dortigen Stelle erstmals urkundlich erwähnt. Bereits vor 1200 wurde an dieser Stelle durch den Ritter Seybold von Blech auf einer Rodung die erste Motte oder Burg errichtet. Im Jahre 1230 ging diese Anlage dann in den Besitz des Ritters Konstantin von Haane über. Die Namensgeber der heutigen Wasserburg ergeben sich aus Urkunden im Zusammenhang mit Rechtsstreitigkeiten mit dem adeligen Frauenkloster in Dünnwald über die Wasserrechte am Mutzbach.

Die Söhne des Konstantin von Haane, die Brüder Nikolaus und Jakob von Haane, gerieten nämlich 1264 mit dem Kloster Dünnwald in Streit über die Benutzung des Mutzbaches. Dem Dünnwalder Kloster stand das Recht zu, den Bach zum Betrieb seiner Mühle zu nutzen. Graf Adolf mit dem Barte hatte dem Kloster die Nutzung des Bachwassers gestattet. Die streitbaren Ritter von Haahn füllten jedoch den Burggraben mit dem Wasser des Mutzbaches. Die Gräfin Margarete von Berg und ihr Sohn Adolf setzen daher nach jahrzehntelangem Streit ein aus 12 Personen bestehendes Schiedsgericht ein um den Streit zu beenden. Der Streit endete zu Gunsten des Klosters, dem das alleinige Nutzungsrecht an dem Wasserlauf eingeräumt wurde. Das Kloster musste jedoch "um des Friedens Willen" den Rittern die Nutzung des Bachwassers an zwei Tagen und Nächten wöchentlich und zwar Samstag von 09:00 Uhr bis Sonntags 09:00 Uhr und Mittwochs von 09:00 Uhr bis Donnerstags 09:00 Uhr gestatten. Das Wasser durfte jedoch nur in den Burggraben, bzw. zur Burg aber nicht anderswohin geleitet werden. Zur Sicherung des Friedens sollte zudem eine Verwandte der Ritter in das Konvent der Schwestern in Dünnwald aufgenommen werden. Weiter musste das Kloster den Rittern 20 "mark cöllnischer" Währung zahlen, für im Rechtsstreit erlittene Schäden und Belästigungen.

Im Jahr 1355 ließ der Ritter Wilhelm von Haane eine Mühle bauen, nämlich dort, wo der Mutzbach von der untersten Heideterrasse in das Rheintal abfloss, etwa in Höhe des heutigen Dünnwalder Mauspfades. Die Mühle wurde wohl in Vereinbarung mit dem Dünnwalder Kloster betrieben, denn Wilhelm von Haane war dem Kloster sehr zugetan und machte reiche Stiftungen an das Kloster. Die Mühle wurde als Walkmühle betrieben. Bis zum Bau und Betrieb dieser Mühle musste man zum Walken der Tuche und des Leders weite Wege nach Mülheim am Strunder Bach machen. Diese lange im Besitz des Hauses Haan stehende Mühle wurde später "unters Walkmühl" (untere Walkmühle) genannt. Der Betrieb der Mühle wurde an Pächter vergeben.

Nach den Rittern von Haane ging die Burg im Rahmen der Erbfolge auf die Familie der Ritter von Lülsdorf über, die von 1373 bis 1710 hier wohnten und deren Stammsitz Haus Haan wurde. Durch Brandschatzung während des Dreißigjährigen Krieges wurde die Burg im Jahre 1628 in Mitleidenschaft gezogen und durch kaiserliche Truppen niedergebrannt. Das Herrenhaus in seiner heutiger Gestalt wurde im Jahre 1730 errichtet und 1786 renoviert.

In der Erbfolge kam die Burg an die Familie Droste zu Vischering, die dieses Anwesen 1812 an einen Herrn Brügelmann aus Ratingen veräußerte. Friedrich Wilhelm Brügelmann wurde als Verwalter auf Haus Haan eingesetzt und gründete 1822 die noch heute in Köln ansässige Firma Brügelmann. Das Haus Haan verkaufte er 1818 an den Freiherren von Fürstenberg zu Neheim, die späteren Grafen von Fürstenberg-Stammheim. Die Grafen von Stammheim veräußerten die Anlage im Jahr 1828 an die Stadt Köln. Mangels Nutzungskonzeptes verfiel die Anlage mit den Jahren und wurde in Teilen (Wirtschaftsgebäude) als Reiterhof genutzt. Die Stadt Köln veräußerte die Anlage 1986 und es erfolgte ein Umbau zu einer Eigentumswohnanlage.

Sagen, Gedichte

Sage vom Tunnel zum Dünnwalder Kloster
Die Sage berichtet, dass Haus Haan mit dem Dünnwalder Kloster durch einen unterirdischen Gang verbunden sei. Durch diesen haben sich der Sage nach die Nonnen in Sicherheit gebracht, wenn das Kloster feindlich überfallen wurde.

Gedicht "der Grafenstohl en dr Kirch" von Franz Peter Kürten
"Der Stammelder Graf, - der ale, dem em vürrige Jahrhondert gestorve es, - der kom vill nom Pastur un hett vill för de Kirch gedonn. Der hatt och ne Stohl en der Kirch, de ieschte vam Trett av, onger dem Prädigstohl. Do es jo och sien Wappe draan. De Bank wor zeglich för de Burglück vam Haan, sing Päächter."

Literatur
 August Brand: Dünnwald - Dorf und Kloster von 1943 bis 1803. Köln 1935, S. 95, 106.
 Johann Bendel: Heimatbuch des Landkreises Mülheim am Rhein. Köln-Mülheim 1925, S. 397.
 Manfred Grimm, Wolfgang Corzilius (Hrsg.): 900 Jahre Dünnwald, Geschichte im Wandel der Zeit. Köln 2017, S. 170, 171.
 Hermann Maria Wollschläger:  Kölner Burgenführer. Köln 1985.

Einzelnachweise

Wohngebäude in Köln
Höhenhaus
Haan
Haan
Haan
Baudenkmal in Köln
Haan

redpajama_set_name: RedPajamaWikipedia


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text:
Q: asterisk rejected because extension not found in context - trying to remove +1 from callerid I'm trying to remove the +1 from the callerid but I keep getting "asterisk rejected because extension not found in context. Here is my extensions_custom.conf:
[from-trunk-remove-plusone]
exten => s/+1NXXNXXXXXX,1,Set(CALLERID(num)=${CALLERID(num):2})
exten => _.!,n,Goto(from-trunk,$[EXTEN],1)

A: You should use '_' before any pattern, including pattern in callerid.
'!' sign mean "no more search" and ussless after dot(match anything).

redpajama_set_name: RedPajamaStackExchange


text:
Steffany Gretzinger
Forever Amen
Select ratingGive Forever Amen 1/5Give Forever Amen 2/5Give Forever Amen 3/5Give Forever Amen 4/5Give Forever Amen 5/5
Select ratingGive Blackout 1/5Give Blackout 2/5Give Blackout 3/5Give Blackout 4/5Give Blackout 5/5
Select ratingGive The Undoing 1/5Give The Undoing 2/5Give The Undoing 3/5Give The Undoing 4/5Give The Undoing 5/5
Steffany Gretzinger is listed in the credits for the following albums:
2011 Bethel Music Be Lifted High Vocals
Steffany Dawn Gretzinger (née Frizzell) is a Christian music singer-songwriter and ensemble vocalist formerly with Bethel Music. She released her first solo album, The Undoing, with Bethel Music in 2014. The album was a Billboard magazine breakthrough release, reaching number twenty in the magazine's Billboard 200, and also gained top five status among Christian and independent albums in September 2014.
Steffany Dawn Gretzinger is married to Stephen Gretzinger, and have one child (Wonder Grace). They used to live in Redding California, where she was a worship leader at Bethel Church, but having led her final worship service on April 21, 2019, they relocated to Nashville Tennessee. Gretzinger has been engaged in worship ministry since childhood and grew up in a musical household. Her mother, Kathy Frizell, was involved in the Christian music industry in Nashville, Tennessee, as a writer. Kathy is currently a worship leader at Wooster Church of the Nazarene in Wooster, Ohio. Steffany's dad, Ron Frizell, is one of the associate pastors on staff at Wooster Nazarene. Steffany Gretzinger attended the Bethel School of Supernatural Ministry in 2008.
Facebook: @SteffanyDawnGretzinger
Instagram: steffanydawn
Twitter: @SteffGretz
External links are provided for reference purposes. Christian Music Archive is not responsible for the content of external internet sites.
Created by: siremidor on 07-March-2020 - Last Edited by siremidor on 28-March-2020

redpajama_set_name: RedPajamaCommonCrawl


Neutral colors add texture and interest to your room décor while keeping it relaxed and calming. This crochet design is versatile enough to adapt to any color scheme you desire, or even scraps of many colors.
Gauge/Tension: Rounds 1-4 = 4" (10 cm) across with larger hook. CHECK YOUR GAUGE. Use any size hook to obtain the gauge.
Throw measures 42½ x 51½" (108 x 131 cm).


As founder, president, and regulatory affairs manager of BSI, Judith brings over 25 years of industry experience to BSI's clients. Judith's responsibilities include ensuring that quality systems are in place and functional, that personnel and other resources are available, and that staff understand the functions they are to perform. She monitors the quality, timeliness, and cost of project deliverables and is available to advise clients and staff. As Regulatory Affairs Manager, Judith is responsible for submitting and maintaining regulatory documents, managing regulatory submissions and correspondence, and interpreting regulations and policies of interest to BSI and its clients.
Judith's experience in the pharmaceutical industry has included medical writing, new product development and registration, and regulatory compliance. She began her career at American Cyanamid Company as a Research Scientist in Toxicology Research and later became Department Head, Toxicology Information Systems. At Cyanamid she was directly responsible for the preparation of numerous pharmacology, pharmacokinetics, and toxicology summary documents for submission to American, Canadian, and European regulatory agencies. She defined toxicology testing requirements and participated in the development of project plans and regulatory strategy for the registration of drug products and implantable medical devices.
Judith was an essential member of the project team responsible for implementing automated systems for collection, analysis, and reporting of toxicology laboratory data. When GLP regulations emerged, Judith developed and supported procedures for compliance, including facility and in-process inspections; data audits; protocol, report, and SOP preparation; archive administration; and toxicology software validation. She also provided GLP training for toxicology staff.
Other notable assignments included proposing exposure limits for medical products and preparing supporting monographs, conducting a study in workers to assess systemic exposure to an anticancer drug, and conducting studies in volunteers to assess efficacy of surgical scrub sponges.
Subsequent relocation and requests for contract services led Judith to organize BSI. After her experience at a large pharmaceutical company, Judith is well acquainted with industry standards and client expectations of a CRO.
Judith holds a B.A. in chemistry from Tufts University and a M.S. in biochemistry from MIT. She is a Registered Quality Assurance Professional in Good Laboratory Practice (RQAP-GLP).
Michele, Director of Finance and Administration, has been with BSI since 1987. Along with the administrative day-to-day operations at BSI, she oversees all accounting and financial procedures including payroll generation, quarterly payroll tax reporting and annual reconciliations. Michele works with other department directors to make sure project costs are tracked accurately and stay within contracted budgets. She performs client billing monthly or as milestones are reached and provides quarterly and annual statements. Michele writes business proposals in response to government requests for proposal and indirect cost agreements for government contracts. Michele also manages vendor services and contracts.
Susan has been the Director of Medical and Scientific Writing since 1997 and manages all of its personnel and activities and sets the departmental budget. Susan has 20 years of experience writing and editing scientific, environmental, and technical documents and has spent much of that time in supervisory positions. She has been the Principal Investigator for the National Toxicology Program's Technical Reports Preparation Support Services Contract since 1996 and has managed NTP Report production since 1993. She has also managed projects for BSI's pharmaceutical, environmental, and engineering clients. Before joining BSI in 1992, Susan was an environmental projects manager for a consulting firm and a Project Officer for the Environmental Protection Agency. Her responsibilities included managing personnel and writing environmental audit reports, standard operating procedures, quality assurance project plans, and sampling plans. Susan holds a M.A. in political economy with an emphasis in environmental policy.
Del has extensive experience with a wide variety of animal experimentation related to toxicology testing, and he is thoroughly familiar with the conduct of laboratory research studies and animal bioassays. Since joining BSI in 1994, Del has written, edited, and reviewed toxicology documents for submission to government agencies and incorporation into medical/scientific monographs for scientific content, accuracy, and internal consistency. He has written and edited preclinical pharmacotoxicologic summary documents for pharmaceuticals for United States and international regulatory submissions, and he has performed quality assurance audits for accuracy and consistency in regulatory documents for veterinary and human pharmaceuticals and agricultural chemicals. In his position as Senior Science Writer, he draws upon his expertise in the areas of chemistry, biochemistry, pharmacology, physiology, pathology, statistics, and toxicology. Prior to joining BSI, Del conducted biochemical and neurotoxicological research at the University of Arkansas for Medical Sciences and the National Center for Toxicological Research. Del holds a doctorate in interdisciplinary toxicology and an undergraduate degree in chemistry.
Lynn has been involved in all aspects of preparing National Toxicology Program Technical Reports including writing and editing, quality assurance, project scheduling and coordination, and staff development since joining BSI in 1991. She has reviewed portions of Food and Drug Administration (FDA) submissions for editorial consistency and readability. She has over 25 years of experience writing and editing scientific and engineering documents, standard operating procedures, Federal Register notices, technical art, procedure and style manuals, and proposals for contractors employed by the Departments of Defense, Energy, and Health and Human Services. Lynn holds a B.S. in solar engineering technology.
Perry has been employed with BSI since 2000 and has prepared over 40 NTP technical reports and toxicology studies. He has collaborated with other writers and science professionals in the writing, editing, and quality assurance of many more. Those reports and other documentation was created using Microsoft Word, Adobe Acrobat, and Quark Express software. Perry's other responsibilities at BSI include maintaining Microsoft Word and Quark Express templates and supporting other users of Word. He currently holds a B.A. in Professional and Technical Writing from the University of Arkansas at Little Rock (UALR) with an M.A. in Professional and Technical Writing from UALR expected in May 2019.
Karen joined BSI in 1998 as a statistician and programmer. She performed statistical analysis on clinical and nonclinical studies, developed data analysis plans, and validated statistical results according to standard operating procedures and Food and Drug Administration regulations. She has provided technical assistance in statistical analyses, computer graphics, and computer programming for the production of NTP reports; written macro programs designed to format electronic study data into final tables; and contributed her writing, editing, and auditing skills to the production of several NTP reports. Prior to joining BSI, Karen was a programmer analyst for the Arkansas Department of Health and an assistant professor of political science and public administration at the University of North Dakota. She has also been an associate director of the Survey Research Center and an assistant professor at the University of Arkansas at Little Rock, an assistant professor at the Clinton School of Public Service, and a research associate at the University of Arkansas for Medical Sciences.


A quick recap (and some fun facts!) of the first HT tournament, which took place on Saturday, March 17th, at 12:00 PM EST (5:00pm CET).
Players were told to submit their decklists prior to the start of the tournament bracket, and after compiling them, here are the numbers!
Out of 16 players, 11 brought a Mono Red deck.
happyjo is the only player to bring three Rush decks to the tournament (and win with all three).
Mono Red and Mono Green are found in all top three decks, with Mono Yellow being found in two (the last decklist being xged's GY Sacrifice).
The Twitch livestream had a peak viewership of 92, averaging out at 74!


text:
\section{Introduction}
\label{sec:intro}

Jets launched by supermassive black holes are presently being evaluated as important mechanisms for galaxy evolution, affecting multiple phases of the interstellar medium (ISM). By depositing energy in the hot and tenuous gas, jets are proposed to delay the inflow of intergalactic gas into ellipticals and moderate their growth \citep{bower06, croton06}. By depositing energy in the cold and dense gas, jets are proposed to influence the star-formation properties of disks \citep{wagner11, gaibler12}. Observational evidence that the impact of a jet upon dense clouds initiates molecular gas winds has been successfully gathered \citep[e.g.,][]{morganti05, rupke11, sakamoto14, garcia-burillo14, dasyra15, aalto16}.

In this letter, we provide observational evidence that the molecular gas accelerated or impacted by a jet is more highly excited and less optically thick than the rest of the ISM. We prove this for the galaxy IC5063, an elliptical with a molecular disk in its center. The jet launched from the black hole of IC5063 propagates through the disk, nearly parallel to its plane. Once the jet encounters clouds, it scatters gas, forming atomic and molecular winds \citep{oosterloo00,morganti07,morganti13,tadhunter14}. Using ultra-deep ESO VLT near infrared (NIR) data, we identified at least four discrete starting points of ionized and warm molecular gas winds near the jet trail \citep{dasyra15}. This constitutes the highest number of known jet-driven winds in a galaxy. The winds sweep the galaxy's inner kpc$^2$, allowing for a spatially-resolved study of the accelerated gas properties. Atacama Large Millimeter Array (ALMA) data have revealed the presence of cold molecular gas in most of these winds \citep{morganti15}.

\section{The ALMA data}
\label{sec:data}
New, band 8 data of IC5063 were taken with ALMA on May 18 2016 for the program 2015.1.00420.S (PI Combes). Forty two antennas observed the galaxy for 39 minutes on-source. Three 1.875\,GHz-bandwidth spectral windows were employed. Two of the spectral windows were partly overlapping to cover the $\pm$1000\,\hbox{\hbox{km}\,\hbox{s}$^{-1}$}\ range around \hbox{$\rm CO(4$-$3)$} . The third spectral window was used for duplication purposes in the $\pm$300\,\hbox{\hbox{km}\,\hbox{s}$^{-1}$}\ range: its role was to ensure that no significant continuum offset exists between the former windows due to flux and bandpass calibration uncertainties. The data were reduced within the Common Astronomy Software Applications (CASA) environment, version 4.6.0. The calibration script was executed as delivered by ESO. Pallas, J1924-2914, and J2056-4714 were respectively used as flux, bandpass, and phase calibrators. The flux calibration accuracy was better than 5\%, as cross-checked with J1924-2914, which is not variable as J2056-4714 is. To construct images from visibilities, we chose a 25\,\hbox{\hbox{km}\,\hbox{s}$^{-1}$}\ spectral bin and a 0.06\arcsec\ pixel scale. The synthesized beam size was 0.4\arcsec $\times$0.4\arcsec .

To study the gas excitation, we also used \hbox{$\rm CO(2$-$1)$}\ data from the program 2012.1.00435.S \citep{morganti15}. Thirty one antennas observed IC5063 in band 6 for 30 mins on-source. J2056-4714 was used as bandpass and phase calibrator, Neptune as flux calibrator. Four 1.875\,GHz-bandwidth spectral windows were employed, with one of them covering the $\pm$1000\,\hbox{\hbox{km}\,\hbox{s}$^{-1}$}\ range around \hbox{$\rm CO(2$-$1)$}. The flux calibration was performed in CASA 4.2.2. Imaging was carried out in CASA 4.6.0 (because of continuum subtraction improvements). The cube was created at a 25\,\hbox{\hbox{km}\,\hbox{s}$^{-1}$}\ spectral bin and at a 0.1\arcsec\ pixel scale. The synthesized beam was 0.56\arcsec $\times$0.53\arcsec .

All images were reconstructed using Briggs robust=0.5 weighting, and primary-beam corrected. No important flux losses were considered for them: the {\it uv} plane coverage was high and the area under examination  was small (3-5\arcsec\ in individual channels) compared to the primary beam in both bands (28\arcsec,\,14\arcsec ). To compare them, we re-gridded the \hbox{$\rm CO(2$-$1)$}\ cube to the pixel scale of the \hbox{$\rm CO(4$-$3)$}\ cube, and we smoothed by Gaussian convolution the \hbox{$\rm CO(4$-$3)$}\ cube to the resolution of the \hbox{$\rm CO(2$-$1)$}\ beam. In the common resolution, the noise is 0.26 mJy/beam for \hbox{$\rm CO(2$-$1)$} , and 3.4 mJy/beam for \hbox{$\rm CO(4$-$3)$} .

\section{Results: gas excitation differences in the wind and in the ambient medium}
\label{sec:results}

Images of the spatially-resolved line emission are shown in Fig.~\ref{fig:basics}, following the subtraction of the (also spatially-resolved) continuum. \hbox{$\rm CO(2$-$1)$}\ is bright along the jet propagation axis and in spirals arms, forming the S-shaped feature identified by \citet{morganti15}. Contrarily,  \hbox{$\rm CO(4$-$3)$}\ is mainly detected along the jet axis. In both lines, the maximum emission is detected near the north-west radio lobe, the south-east radio lobe, and the radio core. Gaussian modeling of the emission in both lines indicates that the projected rotational velocity reaches $\sim$200\,\hbox{\hbox{km}\,\hbox{s}$^{-1}$}\ within 600\,pc from the nucleus. High  \hbox{$\rm CO(4$-$3)$}\  velocity dispersion (either real or caused by the projection of several kinematic components) is seen north of the nucleus, near the north-west radio lobe, and along the biconical outflow detected by \citet{dasyra15} in NIR \,\hbox{$\rm{H_ 2}$}\ and \,\hbox{[\ion{Fe}{II}}]\ data. The latter outflow's starting point is mid-way between the nucleus and the north-west lobe, and its axis is oriented perpendicularly to the jet trail.

The total flux detected in \hbox{$\rm CO(4$-$3)$}\ is 118.0\,$\pm$\,5.0\, Jy\,\hbox{\hbox{km}\,\hbox{s}$^{-1}$} , whereas\, that detected\, in \hbox{$\rm CO(2$-$1)$}\ is 70.2 $\pm$ 4.7 Jy\,\hbox{\hbox{km}\,\hbox{s}$^{-1}$} .  The \hbox{$\rm CO(2$-$1)$}\ flux is 30\% lower than that measured from single-dish, APEX data. The difference is attributed to uncertainties in the continuum determination in the APEX data, in which the blue CO wing was covering most of the available band \citep{morganti13, morganti15}.

The overall  \hbox{$\rm CO(4$-$3)$} /\hbox{$\rm CO(2$-$1)$}\ flux ratio, \hbox{$\rm F_{43}/F_{21}$} , is indicative of a sub-thermally excited gas reservoir (see Section~\ref{sec:discussion}). However, when integrated within a beam's radius from the nucleus (at 20:52:02.37 -57:04:07.6) and the radio lobes (at 20:52:02.15 -57:04:06.7 and  20:52:02.54 -57:04:08.3), the flux in \hbox{$\rm CO(4$-$3)$}\  is $\sim$4 times higher than that in \hbox{$\rm CO(2$-$1)$}\ (Fig.~\ref{fig:spectra}).

To derive the fraction of the flux originating from the jet accelerated or impacted gas, we modeled the disk emission and subtracted it from the observed spectrum in each pixel. A Gaussian fitting algorithm was employed, prefered over a two-component Gaussian fitting algorithm for its lower errors. The disk velocity $V$ was tracing the peak of the line emission, never exceeding $\pm$250\,\hbox{\hbox{km}\,\hbox{s}$^{-1}$}\ in the inner 1\,kpc$^2$. The velocity dispersion $\sigma$ was constrained to values below 50\,\hbox{\hbox{km}\,\hbox{s}$^{-1}$} : this is the average $\sigma$ for both lines in regions that are located more than a beam away from the nucleus and the radio lobes. In the residual cubes, the integrated flux is 12.3($\pm$2.5) Jy\,\hbox{\hbox{km}\,\hbox{s}$^{-1}$}\ for \hbox{$\rm CO(2$-$1)$} , and 59.7($\pm$9.2) Jy\,\hbox{\hbox{km}\,\hbox{s}$^{-1}$}\ for \hbox{$\rm CO(4$-$3)$} . This result indicates that $\sim$half of the reservoir probed by \hbox{$\rm CO(4$-$3)$}\ is kinematically or excitationally affected by the jet. The \hbox{$\rm F_{43}/F_{21}$}\ ratio is 4.9($\pm$)1.7 for this gas,\,and 1.0($\pm$)0.4 for the rest of the gas in the disk. For the fastest gas in the wind, which is moving with -600$<$V$<$-400\,\hbox{\hbox{km}\,\hbox{s}$^{-1}$}\ and which is seen on the north-west radio lobe, \hbox{$\rm F_{43}/F_{21}$}\ is 8.0($\pm$2.4).

Regions with high CO excitation are shown in a \hbox{$\rm F_{43}/F_{21}$}\ map that we constructed after collapsing the disk-subtracted cubes in the \hbox{-600}$<$V$<$400\,\hbox{\hbox{km}\,\hbox{s}$^{-1}$}\ range (Fig. ~\ref{fig:residual_maps}). These regions often coincide with wind starting points known from NIR \,\hbox{$\rm{H_ 2}$}\ and \,\hbox{[\ion{Fe}{II}}]\ data \citep{tadhunter14,dasyra15}. Values $\ge$8 are seen north of the north-west radio lobe, where the \,\hbox{$\rm{H_ 2}$}\ is also highly excited \citep{dasyra15}, and where diffuse 17.8 GHz emission is detected \citep{morganti07}. Values approaching 16 are seen in blobs that nearly coincide with the biconical outflow axis perpendicular to the jet \citep[see the line defined by R1 and R2 in Fig. 8 of ][]{dasyra15}. Within 200\,pc from the nucleus, the wind associated with \hbox{$\rm F_{43}/F_{21}$}$\ge$6 regions was seen in \hbox{$\rm CO(2$-$1)$}\ by \citet{morganti15}. East of the south-east radio lobe, high-velocity Fe ions and highly excited CO molecules co-exist (Fig. ~\ref{fig:residual_maps}). Counter-rotating gas is detected near the \hbox{$\rm F_{43}/F_{21}$} $\sim$7 region north of the same radio lobe in both CO lines (Fig.~\ref{fig:ratio_maps}).
All the above-mentioned regions are also seen in \hbox{$\rm F_{43}/F_{21}$}\ maps that we created from the cubes prior to the disk subtraction (Fig.~\ref{fig:ratio_maps}).

\section{Discussion: gas mass in the wind}
\label{sec:discussion}

Our analysis indicates the presence of at least two distinct molecular gas components: a low-excitation component associated with clouds in the disk, and a high-excitation component associated with gas in the jet-driven winds or near jet-cloud impact points. To be bright in \hbox{$\rm CO(4$-$3)$}, which has a critical density of 1.7$\times$10$^5$ cm$^{-3}$, both components must contain clouds of high volume density. However, while the low excitation component is optically thick, the high excitation component is (partly) optically thin: \hbox{$\rm F_{43}/F_{21}$}\ values $>$4 can only be consistent with emission from optically thin gas at high temperatures.

From the antenna temperature definition, assuming that the molecular gas is in local thermodynamic equilibrium (LTE) and that its excitation temperature \,\hbox{$T_{\rm ex}$}\ greatly exceeds that of the cosmic microwave background (see below), we obtain analytic solutions for \hbox{$\rm F_{43}/F_{21}$}\ (with fluxes in units of Jy\,\hbox{\hbox{km}\,\hbox{s}$^{-1}$} ). For optically thick gas, \hbox{$\rm F_{43}/F_{21}$}\ = ${ \rm (\nu_{43}/\nu_{21})^3 [e^{(h \nu_{21} /kT_{ex})}-1]/[e^{(h \nu_{43} /kT_{ex})}-1]}$. An upper limit of 4 is reached at the Rayleigh-Jeans limit (as expected from the same line brightness temperature). For optically thin gas, \hbox{$\rm F_{43}/F_{21}$}\ = ${\rm (\nu_{43}/\nu_{21})^4 e^{-7h \nu_{10} /kT_{ex}}}$. An asymptotic value of 16 is obtained for  \,\hbox{$T_{\rm ex}$} $>$$>$7h$\nu_{10}$/k $\sim$ 39 K. From this relation, we find that \,\hbox{$T_{\rm ex}$} =32K, if all of the gas kinematically or excitationally affected by the jet (with \hbox{$\rm F_{43}/F_{21}$} =5) is optically thin. For the fastest gas in the wind (with \hbox{$\rm F_{43}/F_{21}$} =8),
\,\hbox{$T_{\rm ex}$}\ is 56K. Near the biconical outflow base, where \hbox{$\rm F_{43}/F_{21}$}\ is 11, \,\hbox{$T_{\rm ex}$}\ is 100K. The temperatures of the gas in the wind can thus be quite high for LTE, and they can be even higher for non-LTE.

It is unlikely that this result reflects infrared (IR) pumping of the populations of quantum states with high rotational number J. The molecules should see an IR source of $>$160K with a large filling factor \citep{carroll81} in all pertinent regions of Figs.~\ref{fig:residual_maps} and \ref{fig:ratio_maps}. Infrared pumping has been deemed unimportant for HCN in the wind of Mrk231 \citep{aalto12}. The high \,\hbox{$T_{\rm ex}$}\ is instead related to the creation of dense fragments once the jet impinges on molecular clouds. The contribution of the jet to the dissipation and heating of the clouds could thus have a negative impact on the overall star formation of IC5063. Still, it doesn't rule out a local enhancement of star formation in compressed clouds.

Given the above bimodality, we determined the gas mass in the wind and in the disk using the appropriate CO-luminosity-to-\,\hbox{$\rm{H_ 2}$} -mass conversion factor, $\alpha_{CO}$, for optically thin and thick emission, respectively. For the optically thick gas, we use Eq. 3 of \citet{solomon97} with $\alpha_{CO}$=4.6\,\hbox{$M_{\odot}$} /(K\,\hbox{\hbox{km}\,\hbox{s}$^{-1}$}\,pc$^2$), as the far infrared luminosity of IC5063 is 2$\times$10$^{10}$\,\hbox{$L_{\odot}$} .  For \hbox{$\rm F_{21}/F_{10}$}=4, a mass of 4.0($\pm$0.5)$\times$10$^8$\,\hbox{$M_{\odot}$}\ is obtained for the disk. For the optically thin gas, \hbox{$\rm F_{21}/F_{10}$} = $ {\rm (\nu_{21}/\nu_{10})^4 e^{-2h \nu_{10} /kT_{ex}}}$ and $\alpha_{CO}=0.26\,(\,\hbox{$T_{\rm ex}$} /30)\,e^{5.53/\,\hbox{$T_{\rm ex}$}-0.184}$ \,\hbox{$M_{\odot}$} / (K\,\hbox{\hbox{km}\,\hbox{s}$^{-1}$}\,pc$^2$), for a Galactic CO/\,\hbox{$\rm{H_ 2}$}\ abundance \citep{bolatto13}. \hbox{For $\rm F_{21}$=12.3($\pm$2.5) Jy\,\hbox{\hbox{km}\,\hbox{s}$^{-1}$}\ and \hbox{$\rm F_{43}/F_{21}$}=5, then $\alpha_{CO}$} \hbox{is 0.27\,\hbox{$M_{\odot}$}/\,(K\,\hbox{\hbox{km}\,\hbox{s}$^{-1}$}\,pc$^2$) and the wind mass  is 1.7($\pm$0.3)}  \hbox{$\times$10$^6$\,\hbox{$M_{\odot}$} . For \hbox{$\rm F_{43}/F_{21}$}=8, $\alpha_{CO}$ is 0.44\,\hbox{$M_{\odot}$} /\,(K\,\hbox{\hbox{km}\,\hbox{s}$^{-1}$}\,pc$^2$)} and the wind mass  is 2.4($\pm$0.5)$\times$10$^6$\,\hbox{$M_{\odot}$} . An order-of-magnitude difference in $\alpha_{CO}$ between the disk and the wind was already assumed by \citet{morganti15}, but the use of an optically-thick \hbox{$\rm F_{21}/F_{10}$} value led to a wind mass of 1.9$\times$10$^7$\,\hbox{$M_{\odot}$} . Our current knowledge that the wind is partly optically thin leads us to revise its molecular content down: 2$\times$10$^6$\,\hbox{$M_{\odot}$}\ is its lower mass limit, if all of its gas is optically thin. This is comparable to the atomic wind mass \citep[3.6$\times$10$^6$\,\hbox{$M_{\odot}$} ; ][]{morganti07}. The actual molecular wind mass will be derived when all data, including new CO (1-0) and (3-2) observations, are analyzed assuming non-LTE conditions: when both high-temperature gas and low-temperature gas (contributing to low J lines) are used to fit the CO spectral line energy distribution (SLED). Still, our simplified LTE analysis proves that molecular wind masses can be overestimated \citep[contrary to what is known from Mrk231;][]{cicone12}.

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

We obtained new ALMA \hbox{$\rm CO(4$-$3)$}\ data and combined them with previous \hbox{$\rm CO(2$-$1)$}\ data to study the molecular gas excitation in the jet-driven winds of IC5063. We found that \hbox{$\rm CO(4$-$3)$}\ is mainly detected along the jet. Half of its emission comes from gas that was impacted by the jet, while only one sixth of the \hbox{$\rm CO(2$-$1)$}\ emission comes from the same gas. In this gas, the average \hbox{$\rm F_{43}/F_{21}$}\ ratio is 5. In regions with a strong jet-cloud interaction, the ratio reaches 12 in the original cubes and approaches 16 in the disk-subtracted cubes. Contrarily, the same ratio for the rest of the gas in the disk is 1. We thus detect at least two gas components: one optically thick related to the disk, and another optically thin related to the winds. Because the outflowing molecular gas is partly optically thin, its mass is lower than that previously thought, as low as 2$\times$10$^6$\,\hbox{$M_{\odot}$} . This is comparable to the mass of the outflowing HI.  Excitation temperatures of 30-100K are common for the outflowing molecules. The skewing of the CO SLED toward higher J numbers can facilitate the detection of winds at high z.

\begin{acknowledgements}
K. D. acknowledges support by the European Commission through a Marie Curie Intra-European Fellowship (PIEF-GA-2013-627195;  'BHs shaping galaxies') awarded under the 7th Framework Programme. R. M. gratefully acknowledges support from the European Research Council under the European Union's 7th Framework Programme, ERC Advanced Grant RADIOLIFE-320745.
This paper makes use of the ALMA data 2015.1.00420.S and 2012.1.00435.S.  ALMA is a partnership of ESO (representing its member states), NSF (USA), NINS (Japan), together with NRC (Canada), NSC and
ASIAA (Taiwan) and KASI (Republic of Korea), in cooperation with the Republic of Chile.  The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ.
\end{acknowledgements}

\begin{figure*}[h!]
\begin{center}
\includegraphics[width=19cm]{basics.eps} \\
\caption{ {\it Left:} images of CO (4-3), (2-1), and their nearby continua, extracted from the optimal-resolution cubes (i.e., 0.4\arcsec$\times$0.4\arcsec\ beam in band 8 and 0.56\arcsec$\times$0.53\arcsec\ beam in band 6). The line fluxes in mJy/beam were averaged over the -100$<$V$<$100\,\hbox{\hbox{km}\,\hbox{s}$^{-1}$}\ range. Crosses indicate the locations of the nucleus and the two radio lobes, as seen in the \hbox{$\rm CO(2$-$1)$}\ continuum (see Sect.~\ref{sec:data} for the coordinates). {\it Right:} maps of the amplitude, velocity, and velocity dispersion of a Gaussian line-profile fit. All panels are centered at the nucleus, at 20:52:02.37 -57:04:07.6. They have a field of view (FOV) of 7\arcsec$\times$7\arcsec .}
\label{fig:basics}
\end{center}
\end{figure*}

\begin{figure*}[h!]
\begin{center}
\includegraphics[width=0.78\columnwidth]{spectra.eps}
\caption{ Integrated \hbox{$\rm CO(4$-$3)$}\ and \hbox{$\rm CO(2$-$1)$}\ spectra, extracted from the cubes at the common spatial resolution. The \hbox{$\rm CO(2$-$1)$}\ flux is multiplied by a factor of four to facilitate comparison with the \hbox{$\rm CO(2$-$1)$}\ flux.  {\it Upper left:} Emission integrated over the whole disk, that is within an ellipse with a 12\arcsec\ major axis, 4\arcsec\ minor axis, and \hbox{-65$^{\rm o}$} position angle.  {\it Upper right and bottom:} Emission integrated within a beam (i.e., within a radius of 0.28\arcsec ) from the nucleus, and from the north and south radio lobes. }
\label{fig:spectra}
\end{center}
\end{figure*}

\begin{figure*}[h!]
\begin{center}
\includegraphics[width=0.9\textwidth]{model_cube_ratio.eps} \\
\caption{ {\it Left, middle:} residual images from the subtraction of a disk model from the data (see Section~\ref{sec:results}). Their fluxes, integrated in the -600$<$V$<$400\,\hbox{\hbox{km}\,\hbox{s}$^{-1}$}\ range, are in units of Jy\,\hbox{\hbox{km}\,\hbox{s}$^{-1}$}\ per pixel. The common beam is 0.56\arcsec$\times$0.53\arcsec . Pixels with signal-to-noise (S/N)\,$<$5 have been masked. {\it Right:} \hbox{$\rm F_{43}/F_{21}$}\ of the residual images. Contours of the outflowing-to-ambient \,\hbox{[\ion{Fe}{II}}]\ emission from \citet{dasyra15} are overplotted, in steps of 0.2 starting from 0.1 for the fast winds near the lobes, and steps of 0.33 starting from 0.33 for the intermediate-velocity (component) of the other winds. The FOV and center are as in Fig.~\ref{fig:basics}.}
\label{fig:residual_maps}
\end{center}
\end{figure*}

\begin{figure*}[h!]
\begin{center}
\includegraphics[width=0.9\textwidth]{cube_ratios.eps} \\
\caption{ CO (4-3) and (2-1) images and \hbox{$\rm F_{43}/F_{21}$}\ ratio, integrated in 200\,\hbox{\hbox{km}\,\hbox{s}$^{-1}$}\ bins. All panels were constructed directly from the data, and, unlike Fig.~\ref{fig:residual_maps}, they contain the disk emission. The image units, beam, FOV, and center are as in Fig.~\ref{fig:residual_maps}. Pixels with S/N$<$3 have been masked. The contours in the last panel indicate where the \hbox{$\rm CO(4$-$3)$}\ emission reaches S/N of 5,\,10,\,and 20.}
\label{fig:ratio_maps}
\end{center}
\end{figure*}


Stay tuned... there should be a press release issued on the US version any day, since it goes on sale next month. 306 HP with the new engine.
Last gasp before it is totally replaced. Spy shots alreadyt circulating on the replacement.
We need some pics of this...

And note that it may be in common underneath with the MKR.
The 3.7 - naturally or unnaturally aspirated - is Lincoln only.
Shelby coupe = 3950 pds. 'vert = 4100.
Yes, lets get back to the Mondeo.
We all appreciate your work, Chris.. but you need to chill out. You know the best shots are taken on the sly.. not from acting outrageous yourself too.
There have been multiple Stigs... one was even "killed" off. The full story is on several different sites.
98' Toyota Supra has best cockpit, agree?
Absolutely, all business and the ergnomics are good.
But, the shifter is terrible... for track use it's very difficult to know exactly what gear you are in.
It's well off the beaten path.. .I doubt it will ever be built. Or could be, given the CVTs capacity.
But, that said, I respect the Murano and I've put a few thousand miles on them.


MONTREAL, QUÉBEC, Alderon Iron Ore Corp. (TSX: IRON) ("Alderon" or the "Company") is pleased to announce that it and The Kami Mine Limited Partnership ("Kami LP") have closed a previously announced loan facility (the "Loan Facility") with Sprott Resource Lending ("Sprott"), a global leader in resource asset investments. Alderon used the funds received from the settlement with Newfoundland and Labrador Hydro, together with a portion of the US$14 million Loan Facility to repay the Liberty Metals & Mining Holdings, LLC ("LMM") loan. The closing of the Sprott transaction comes as Alderon advances its updated Feasibility Study ("FS") scheduled for conclusion this fall. Upon completion, the updated FS is expected to demonstrate that the Kami Project is well-positioned to pursue project financing on account of improved project economics initially highlighted in the updated Preliminary Economic Assessment released on November 7, 2017.
Principal amount of US$14 million.
Interest at 10% per annum, payable monthly.
Original maturity date of December 31, 2019 (the "Maturity Date").
The proceeds of the Loan Facility were advanced as a single draw on the closing date (the "Closing Date.
The proceeds of the Loan Facility were used to repay the existing LMM loan and to reimburse Alderon for amounts that are pre-paid to LMM prior to closing.
Alderon is acting as guarantor for the Loan Facility.
Altius Minerals Corporation ("Altius"), through a wholly-owned subsidiary, participated in the Loan Facility by providing US$2 million of the US$14 million principal amount.
As consideration for the establishment of the Loan Facility, Alderon issued 4,123,740 common shares ("Common Shares") to Sprott and 687,290 common shares to Altius.
In the event that the Maturity Date is extended in accordance with the terms of the Loan Facility, an additional total of US$350,000 in Common Shares shall be issued to Sprott and Altius on the Maturity Date and at a price per share equal to a 10% discount to the volume weighted average trading price on the TSX for the five trading days prior to the Maturity Date. United States dollar amounts shall be converted into Canadian dollars using the daily average exchange rate for the conversion of United States to Canadian dollars set by the Bank of Canada as at the business day immediately prior to the date of issuance of the Common Shares. The Common Shares shall be issued based on a ratio of 12/14th to Sprott and 2/14th to Altius.
Prior to the Closing Date, Altius held 51,838,916 Common Shares (representing 39% of the Company's current issued and outstanding Common Shares). After the Closing Date, Altius now holds 52,526,206 Common Shares (representing 37.98% of the Company's current issued and outstanding Common Shares).
Sprott is an alternative asset manager and a global leader in precious metal and real asset investments. Through its subsidiaries in Canada, the US and Asia, the company is dedicated to providing investors with best-in-class investment strategies that include Exchange Listed Products, Alternative Asset Management and Private Resource Investments. The company also operates Merchant Banking and Brokerage businesses in both Canada and the US. Sprott is based in Toronto with offices in New York, Carlsbad and Vancouver and its common shares are listed on the Toronto Stock Exchange under the symbol (TSX:SII). For more information, please visit www.sprottinc.com.
Sprott Resource Lending is a globally recognized leader in natural resource financing and specializes in providing flexible debt solutions to mining companies. Since joining Sprott, the team has financed more than $1.0 billion in bespoke private debt investments. For more information, please visit www.sprottlending.com.


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text:
Sony's PlayStation VR Patents Reveal VR Sickness Reduction, And Full Body Tracking
two new patents for Sony's PlayStation VR have been revealed, giving players a look at some of the inside workings of the upcoming next-gen game console.
According to two new patents discovered by TheGamePost, Sony is working on new technologies to reduce the VR sickness caused by the PlayStation VR headset as well as the full-body tracking device. Even though the PS5 release date is around this year's holiday season, players have no idea how much PS5 will cost or what it will look like.
Recently Sony Officially unveiled the new PlayStation 5 DualSense controller, an evolution of DS4 that will feature haptic feedback. It will bring true immersion to the gamers holding the controller. As for the PlayStation VR, it looks like we might get an updated version of the PS VR for next-gen. The patent's abstract summary provides us with such details:
"A VR sickness reduction system, a head-mounted display, a VR sickness reduction method, and a program with which it is possible to further reduce VR sickness. An HMD (12) is provided with a display unit (38), which is disposed in front of the eyes of a user when the user wears the HMD (12). A shaking unit (42) can shake the head of the user wearing the HMD (12). An entertainment device (14) causes the display unit (38) to display a moving image representing a view as seen from a viewpoint. The entertainment device (14) controls the shaking of the shaking unit (42) in accordance with the acceleration condition of the viewpoint for the moving image displayed by the display unit (38). "
Read Also: Sony's PlayStation 5 Event Could Take Place 'Early To Mid June,' According To Jason Schreier
PlayStation VR 2 Incoming?
But that's not all, another patent for the Next-Gen VR was also revealed that provides us details about the Tracker Calibration Device:
"Provided are a tracker calibration device, tracker calibration method, and program that make it possible to precisely calibrate a plurality of types of trackers without measuring the relative positions of the trackers beforehand. A tracker data acquisition unit (50) acquires a plurality of items of first tracker data indicating the position of a first tracker expressed using a first coordinate system. The tracker data acquisition unit (50) acquires a plurality of items of second tracker data indicating the position and orientation of a second tracker expressed using a second coordinate system. On the basis of the plurality of items of first tracker data and the plurality of items of second tracker data, a parameter estimation unit (58) estimates parameter values for converting the positions expressed using the second coordinate system into expressions in the first coordinate system and estimates the relative position of the second tracker in relation to the position of the first tracker."
"It is necessary to perform calibration in advance so that the positions of the plurality of types of trackers can be expressed in one coordinate system. In addition, the calibration needs to be performed in a state where the relative positions and postures of the plurality of types of trackers are fixed."
These new PlayStation VR patents will allow gamers a much more stable and optimized VR Gaming Experience. Unlike the recently revealed "feeling deduction" robot companion, this one doesn't seem to be creepy or weird. From all the patents that are being revealed, Sony is really planning to blow minds once everything is officially revealed.
Moin Imran
Loves everything Destiny. Studies video game Lore and then write about it in chronological order as a hobby.


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Scores 36 while chasing 299
WicketkeeperEngland
Buttler scored 36 off 42 balls with the help of four fours for England during a 27-run defeat to Pakistan in the first ODI of the three-match series in Bloemfontein on Friday.
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Half-century while chasing 299
BatsmanEngland
Malan scored 59 off 55 balls with the help of eight fours for England during a 27-run defeat to Pakistan in the first ODI of the three-match series in Bloemfontein on Friday.
Scores century while chasing 299
Roy scored 113 off 91 balls with the help of 11 fours and four sixes for England during a 27-run defeat to Pakistan in the first ODI of the three-match series in Bloemfontein on Friday.
Jofra Archer
One wicket while bowling first
BowlerEngland
Archer registered figures of one for 81 for England during a 27-run defeat to Pakistan in the first ODI of the three-match series in Bloemfontein on Friday.
Three wickets while bowling first
Curran registered figures of three for 35 for England during a 27-run defeat to Pakistan in the first ODI of the three-match series in Bloemfontein on Friday.
Two wickets while defending 298
BowlerSouth Africa
Rabada registered figures of two for 46 for South Africa during a 27-run win against England in the first ODI of the three-match series in Bloemfontein on Friday.
Three wickets while defending 298
Magala registered figures of three for 46 for South Africa during a 27-run win against England in the first ODI of the three-match series in Bloemfontein on Friday.
Four wickets while defending 298
All RounderSouth Africa
Nortje registered figures of four for 62 for South Africa during a 27-run win against England in the first ODI of the three-match series in Bloemfontein on Friday.
Scores 37 while batting first
WicketkeeperSouth Africa
De Kock scored 37 off 41 balls with the help of five fours and one six for South Africa during a 27-run win against England in the first ODI of the three-match series in Bloemfontein on Friday.
BatsmanSouth Africa
Bavuma scored 36 off 28 balls with the help of four fours and one six for South Africa during a 27-run win against England in the first ODI of the three-match series in Bloemfontein on Friday.
Half-century while batting first
Miller scored 53 off 56 balls with the help of four fours and one six for South Africa during a 27-run win against England in the first ODI of the three-match series in Bloemfontein on Friday.
Scores century while batting first
Van der Dussen scored 111 off 117 balls with the help of six fours and one six for South Africa during a 27-run win against England in the first ODI of the three-match series in Bloemfontein on Friday.
BatsmanIndia
Yadav scored 47 off 34 balls with the help of six fours and two sixes for India during a 21-run defeat to New Zealand in the first T20I of the three-match series in Ranchi on Friday.
BowlerIndia
Singh registered figures of one for 51 for India during a 21-run defeat to New Zealand in the first T20I of the three-match series in Ranchi on Friday.
Yadav registered figures of one for 20 for India during a 21-run defeat to New Zealand in the first T20I of the three-match series in Ranchi on Friday.
Sundar scored 50 off 28 balls with the help of five fours and three sixes for India during a 21-run defeat to New Zealand in the first T20I of the three-match series in Ranchi on Friday.
BowlerNew Zealand
Ferguson registered figures of two for 33 for New Zealand during a 21-run win against India in the first T20I of the three-match series in Ranchi on Friday.
All RounderNew Zealand
Santner registered figures of two for 11 for New Zealand during a 21-run win against India in the first T20I of the three-match series in Ranchi on Friday.
Michael Bracewell
WicketkeeperNew Zealand
Bracewell registered figures of two for 31 for New Zealand during a 21-run win against India in the first T20I of the three-match series in Ranchi on Friday.
Finn Allen
Allen scored 35 off 23 balls with the help of four fours and two sixes for New Zealand during a 21-run win against India in the first T20I of the three-match series in Ranchi on Friday.
Daryl Mitchell
Unbeaten half-century while batting first
BatsmanNew Zealand
Mitchell scored 59 not out off 30 balls with the help of three fours and five sixes for New Zealand during a 21-run win against India in the first T20I of the three-match series in Ranchi on Friday.
Devon Conway
Conway scored 52 off 35 balls with the help of seven fours and one six for New Zealand during a 21-run win against India in the first T20I of the three-match series in Ranchi on Friday.
BowlerAfghanistan
Omarzai registered figures of three for 17 for Rangpur Riders during a six-wicket win against Sylhet Strikers in the Bangladesh Premier League (BPL) 2022-23 in Sylhet on Friday.
Hasan Mahmud
BowlerBangladesh
Mahmud registered figures of three for 12 for Rangpur Riders during a six-wicket win against Sylhet Strikers in the Bangladesh Premier League (BPL) 2022-23 in Sylhet on Friday.
Mahedi Hasan
Two wickets while bowling first
Hasan registered figures of two for 12 for Rangpur Riders during a six-wicket win against Sylhet Strikers in the Bangladesh Premier League (BPL) 2022-23 in Sylhet on Friday.


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Rhonda Hilario-Caguiat
Monkees Singer Davy Jones Dies at 66
Davy Jones, the former lead singer of the Monkees, died after a heart attack today in Florida, according to Reuters. He had been on a solo tour when he was admitted to a hospital after experiencing chest pains. Jones and his bandmates Mickey Dolenz, Michael...
By Rhonda Hilario-Caguiat


Will Smith is getting a lot of play on this site today. I almost went with Randy Moss instead.
Earth Day Is Coming Up..
.. I think. If not here is a pic of a girl molesting a tree anyway.
Posted on April 21, 2010 Categories NatureTags earth day, treeLeave a comment on Earth Day Is Coming Up..


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Johann Georg Schmidt (23 August 1694, Augsburg - 15 March 1767, Braunschweig) was a German engraver.

Life and work
Schmidt came from Augsburg and first worked in Dresden and then the studio of Johann Georg Beck, also from Augsburg.  After Beck died in 1722, Schmidt married his widow Anna Elisabeth (née Füllekrug), took over his studio and received the title of court-engraver.  Schmidt trained his master's son Anton August in this studio. Schmidt and Beck mostly made portraits of the Braunschweigischen clergy and court figures, though his works' were of lower quality than his predecessor and his son.

After his death in 1767, his stepson Anton August Beck took over his birth-father's business and successfully led it until he died in 1787.

Bibliography
 Horst-Rüdiger Jarck (Hrsg.): Braunschweigisches Biographisches Lexikon. 8. bis 18. Jahrhundert, Braunschweig 2006
 Gerd Spies (Hrsg.): Braunschweig – Das Bild der Stadt in 900 Jahren. Geschichte und Ansichten, Band 2, Braunschweig 1985

(External) Links

Notes

1694 births
1767 deaths
Engravers from Augsburg


The Hungers The World Neglects – Creo en Dios!
My friend Joe Costantino, S.J., pastor of the St. Ignatius of Loyola Church in Chestnut Hill MA, replied to my post of yesterday by sending me his bulletin reflection on Jesus' instruction to be salt of the earth.
Civil discourse certainly seems to be at a low ebb. Dialogue is now often reduced to a tweet or two. As for caring for the other? That too has descended to a new low. I am sure we all agree, Jesus did not give us a mandate to care only for those who are from our country or allow our care to extend just to those who have all their legal papers. As Christians we believe that, whether one acknowledges it or not, we are all daughters and sons of one God and sisters and brothers in Christ. Our care for the other – even when it "costs" us – should know no bounds. Exaggeration of civil discourse and care for the other are surely just two of the areas where we might be an additive, like salt, to what is already present in our world but always in need of being enhanced and nowadays even exaggerated.
You can read the entirety of Joe's bulletin here.
I read Father Joe's full message from the St. Ignatius bulletin! So wonderful! Jesus gives us all an affirmation of what we already are and an assignment to keep being just such!
Father Joe must have an enormous parish – as I read the list of the ordained at that parish I was amazed! We all need prayers, but let us today remember our leaders in prayer – like Susan and Father Joe – and never take them for granted!


Houston Rockets' shooting guard James Harden made history in a couple of good ways in the Rockets' 113-106 loss to the Golden State Warriors at the Toyota Center in Houston, Texas.
First off, Harden ended the game with 24 points, 11 rebounds, and 13 assists, which gave him his 20th triple double this season. This made the 2016-2017 season the first season in NBA history in which multiple players posted more than 20 triple doubles. Oklahoma City Thunder point guard Russell Westbrook is that other player this season, and he has done so 37 times already.
Next, Harden became the first player in NBA history to score over 2,000 points on his own in a single NBA season and assist on over 2,000 points in a single NBA season. He has scored 2,169 points (average of 29.3 points per game) and dished out an NBA-leading 840 assists (NBA-leading average of 11.4 assists per game) so far this season.
Harden and the Rockets (51-23) will look to rebound from their home loss to the Warriors (60-14) on Thursday, March 30th, 2017, at 10:30 PM EDT in a road game against the playoff-hungry Portland Trail Blazers (35-38) at the Moda Center in Portland, Oregon.
Next Next post: Triple Double Average: Could Russell Westbrook Really Do It?


Jake Hager won his MMA debut fight last night at Bellator 214, submitting his opponent J.W. Kiser in the first round.
Hager, formerly known as Jack Swagger, came out with R-Truth who rapped for his entrance theme and used the "We The People" catchphrase throughout. His video on the big screen also included shots from his time in WWE and he was sporting the "We The People" t-shirt as well.
The ending came at 2:09 after Hager controlled Kiser on the ground and then locked a head and arm chokehold to make him tap.
Hager is the latest WWE Superstar to make the transition to mixed martial arts. Several of his former colleagues tweeted their good lucks to Hager last night before the show. You can see his entrance and the ending below.


Scholastic Bowl is a competitive IHSA sanctioned activity. We compete in trivia or quiz competitions with other schools in preparation for the State Series. The Scholastic Bowl season starts in mid-October and runs into March.
This club tests your knowledge on many different topics and is a good preparation for college entrance tests. It also looks great on your college application.


Question #92143 posted on 04/03/2019 11:36 p.m.
Has this word indeed spread? How many of you have heard it? How do we get a word to spread (short of going totally frindle, I mean.
It's a good word, but ain't nobody using it. I would suggest creating a Provocity hashtag or meme format. Kids love things on the TwitterGram.


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Home / Business / Deus Ex: Human Revolution delayed
Deus Ex: Human Revolution delayed
MCV Staff 16th December 2010	Business
Fans will have to wait a bit longer for the latest Deus Ex title as Square Enix announces it has delayed the upcoming Human Revolution.
The eagerly-awaited prequel was originally due for release in Q1 2011 but has now been pushed back to the publisher's next financial year, meaning it won't be on shelves until after April 2011.
Square Enix has delayed that game in order to give it further polish" and focus on development, having seen disappointing sales and public reception to its most recent releases, according to Kotaku.
In a statement, the company said: With weak sales performances of console game titles that have been newly released during the current fiscal year as well as harsh market feedback regarding a key title, the Group recognises the reinforcement of development capability in our digital entertainment segment as our most critical managerial issue.
We therefore have decided to spend additional time to further polish our upcoming game, Deus Ex: Human Revolution, resulting in a shift in release timing from our prior plan of the current fiscal year to next fiscal year."
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