text:
\section{Introduction}
A 1.5 dimensional(1.5D)  terrain $T$ is an $x$-monotone polygonal chain in $\mathbb{R}^2$ specified by $n$ vertices $V(T) = \{v_1,..., v_i,..., v_n\}$, where $v_i = (x_i, y_i)$. The vertices induce $n-1$ edges $E(T) = \{ e_1,..., e_i,..., e_{n-1} \}$ with $e_i$ = $\overline{v_iv_{i+1}}$.

A point $p$ sees or guards $q$ if the line segment $\overline{pq}$ lies above or on $T$, or more precisely, does not intersect the open region bounded from above by $T$ and from the left and right by the downward vertical rays emanating from $v_1$ and $v_n$.

There are two types of terrain guarding problems: (1) continuous terrain guarding (CTG) problem, with objective of determining a subset of $T$ with minimum cardinality that guards $T$, and (2) discrete terrain guarding problem, with the objective of determining a subset of $U$ with minimum cardinality guarding $X$, given that the two point sets $U$ and $X$ are on $T$.

Many studies have referred to applications of 1.5D terrain guarding in real world~\cite{EA,finite_set,FA}. The examples include guarding or covering a road with security cameras or lights and using line-of-sight transmission networks for radio broadcasting.

\subsection{Related Work}
Ample research has focused on the 1.5D terrain guarding problem, which can be divided into the general terrain guarding problem and the orthogonal terrain guarding problem.

In a 1.5D terrain, King and Krohn \cite{NP} proved that the general terrain guarding problem is NP-hard through planar 3-SAT.

Initial studies on the 1.5D terrain guarding problem discussed the design of a constant-factor approximation algorithm. Ben-Moshe et al. \cite{F-app} gave the first constant-factor approximation algorithm for the terrain guarding problem and left the complexity of the problem open. King~\cite{5-app} gave a simple 4-approximation, which was later determined to actually be a 5-approximation. Recently, Elbassioni et al. \cite{4-app} gave a 4-approximation algorithm.

Finally, Gibson et al. \cite{D-PTAS} considered the discrete terrain guarding problem by finding the minimal cardinality from candidate points that can see a target point \cite{D-PTAS} and proved the presence of a planar graph that appropriately relating the local and global optima; thus, the discrete terrain guarding problem allows a polynomial time approximation scheme (PTAS) based on local search. Friedrichs et al. \cite{C-PTAS} revealed that for the continuous 1.5D terrain guarding problem, finite guard and witness sets ($G$ and $X$, respectively) can be constructed such that an optimal guard cover $G'' \subseteq G$ that covers terrain $T$ is present and when these guards monitor all points in $X$, the entire terrain is guarded. According to \cite{D-PTAS}, the continuous 1.5D terrain guarding problem can apply PTAS by constructing a finite guard and witness set with the former PTAS.

Some studies have considered orthogonal terrain $T$. $T$ is called an orthogonal terrain if each edge $e\in E(T)$ is either horizontal or vertical. An orthogonal terrain has four vertex types. If $v_i$ is a vertex of orthogonal terrain and the angle $\angle{v_{i-1}v_iv_{i+1}}=\pi/2$, then $v_i$ is a convex vertex, otherwise it is a reflex vertex. A convex vertex $v_i$ is left(right) convex if $\overline{v_{i-1}v_i}$($\overline{v_iv_{i+1}}$) is vertical. A reflex vertex $v_i$ is left(right) reflex if $\overline{v_{i-1}v_i}$($\overline{v_iv_{i+1}}$) is horizontal.

Katz and Roisman \cite{2-OTG} gave a 2-approximation algorithm for the problem of guarding the vertices of an orthogonal terrain. The authors constructed a chordal graph demonstrating the relationship of visibility between vertices. On the basis of \cite{F.Gavril}, \cite{2-OTG} gave a 2-approximation algorithm and used the minimum clique cover of a chordal graph to solve the right(left) convex vertex guarding problem.

Lyu and {\" U}ng{\"o}r~\cite{nlogm} gave a 2-approximation algorithm for the orthogonal terrain guarding problem that runs in $O(n\log m)$, where $m$ is the output size. The authors also gave an optimal algorithm for the subproblem of the orthogonal terrain guarding problem. On the basis of the vertex type of the orthogonal terrain, the objective of the subproblem is to determine a minimum cardinality subset of $V(T)$ guarding all right(left) convex vertices of $V(T)$; furthermore, the optimal algorithm uses stack operations to reduce time complexity.

The $O(n\log m)$ time 2-approximation algorithm has previously been considered the optimal algorithm for the orthogonal terrain guarding problem. However, some studies have used alternatives to the approximation algorithm.

Durocher et al. \cite{O-OTG} gave a linear-time algorithm for guarding the vertices of an orthogonal terrain under a directed visibility model, where a directed visibility mode considers the different visibility for types of vertex. If $u$ is a reflex vertex, then $u$ sees a vertex $v$ of $T$, if and only if every point in the interior of the line segment $uv$ lies strictly above $T$. If $u$ is a convex vertex, then $u$ sees a vertex $v$ of $T$, if and only if $\overline{uv}$ is a nonhorizontal line segment that lies on or above $T$. Khodakarami et al. \cite{range} considered the guard with guard range. They presented a fixed-parameter algorithm that found the minimum guarding set in time $O(4^k\cdot k^2 \cdot n)$, where $k$ is the terrain guard range.

\subsection{Result and Problem Definition}
In this paper, we define the CTG problem with two-sided guards and propose an optimal algorithm for the 1.5D CTG problem with two-sided guards. To the best of our knowledge, the 1.5D CTG problem with two-sided guards has never been examined.

\begin{figure}
\begin{center}
\includegraphics[scale=0.6]{fig1.jpg}
\caption{Point $p$ is two-sided guarded by $v_1$ and $v_n$}
\label{fig1}
\end{center}
\end{figure}

{\bf Definition 1} (Two-Sided Guarding). A point $p$ on a 1.5D terrain is two-sided guarded if there exist two distinct guards $u$, which is on or to
the left of $p$, and $v$, which is on or to the right of $p$, such that $p$ can be seen by both $u$ and $v$. Furthermore,
the guards $u$ and $v$ are called a left guard and a right guard of $p$.

Fig.~\ref{fig1} illustrates an example where vertex $v_1$ left guards $p$ and $v_n$ right guards $p$. In this paper, we define the following problem:

{\bf Definition 2}(CTGTG: Continuous Terrain Guarding with Two-Sided Guards) Given a 1.5D terrain $T$, find a vertex guard set $S$ of minimum cardinality such that every point of $T$ can be two-sided guarded.

\subsection{Paper Organization}
Section 2 presents preliminaries, Section 3 demonstrates how to create a finite point set for the CTGTG model, Section 4 gives an algorithm for the CTGTG, along with its proof, and Section 5 presents our conclusions.

\section{Preliminaries}
Let $p$ and $q$ be two points on a 1.5D terrain,
we write $p\prec q$ if $p$ is on the left of $q$. We denote the visible region of $p$ by
$vis(p) = \{v|v\in V(T)$ and $v$ sees $p\}$. For a $vis(p)$, let $L(p)$ be the leftmost vertex in $vis(p)$ and $R(p)$ be the rightmost vertex in $vis(p)$.

Given a CTGTG instance, let $OPT=\{o_1,o_2,...,o_m\}$ be an optimal guard set, where $o_k\prec o_{k+1}$ for $k=1,...,m-1$.
For a point $p$ on the terrain, let $O_R(p)$ and $O_L(p)$ be the subsets of $OPT$ such that $p$ is right guarded by every guard in $O_R(p)$ and left guarded by every guard in $O_L(p)$.
We also define $N_i^R$ as the rightmost point on the terrain that is not right guarded by
$\{ o_i,o_{i+1},...,o_m\}$ and $N_i^L$ as the leftmost point on the terrain that is not left guarded by $\{ o_1,o_2,...,o_i\}$.

An important visible property on 1.5D terrains is as follows:

\begin{lemma}[\cite{F-app}]
\label{order lemma}
Let $a$, $b$, $c$ and $d$ be four points on a terrain $T$ such that $a \prec b \prec c \prec d$. If $a$ sees $c$ and $b$ sees $d$, then $a$ sees $d$.
\end{lemma}

\begin{figure}
\begin{center}
\includegraphics[scale=0.7]{fig2.jpg}
\caption{Schematic of Lemma~\ref{order lemma}.}
\label{fig2}
\end{center}
\end{figure}

Fig.~\ref{fig2} is a schematic of Lemma 1. Because $T$ is an $x$-monotone chain, we use a straight line to demonstrate the relation between $x$-coordinate of points and an arc to show the visible relation among points on $T$. In this report, we use a straight line to simplify the explanations.

\begin{obs}
\label{obs_l}
Assume point $x$ is on $e_j$. If $x$ is left guarded by $v$ then $v_{j+1}$ is also left guarded by $v$.
\end{obs}

\begin{obs}
\label{obs_r}
Assume point $x$ is on $e_j$. If $x$ is right guarded by $v$ then $v_{j}$ is also right guarded by $v$.
\end{obs}

\section{Discretization}

\begin{figure}
\begin{center}
\includegraphics[scale=0.7]{VT_is_not_enough.jpg}
\caption{$V(T)$ is right guarded and left guarded by $\{v_1, v_2, v_4, v_5\}$, but not $T$.}
\label{V(T) is not enough}
\end{center}
\end{figure}

Although $V(T)$ are right guarded and left guarded, $T$ is not necessarily right guarded and left guarded. In Fig. \ref{V(T) is not enough}, $V(T)$ is right guarded and left guarded by $\{v_1, v_2, v_4, v_5\}$ with minimal cardinality. The vertices $v_1$ and $v_2$ are left guarded by $v_1$ and right guarded by $v_2$. Vertices $v_4$ and $v_5$ are left guarded by $v_4$ and right guarded by $v_5$. Vertex $v_3$ is left guarded and right guarded by $v_2$ and $v_4$, respectively. Only $v_3$ can right guard $p$ and left guard $q$ where $p$ is on $e_2$ and $q$ is on $e_3$, but $v_3 \notin \{v_1, v_2, v_4, v_5 \}$. In our example, we must create a point set $X$ such that if $X$ is right guarded and left guarded, then $T$ is also.

{\bf Definition 3} (Boundary Point). If line $\overline{v_iv_j}$ and $e_k$ have an intersection point $f\notin \{ v_k, v_{k+1} \}$, and $v_i$ and $v_j$ can see $f$ then $f$ is the boundary point.

In Fig.~\ref{fig:7}, we provide an example with four boundary points: $f_1, f_2, f_3$ and $f_4$. Boundary point $f_1$ is from $v_6$, $f_2$ is from $v_4$; and boundary points $f_3$ and $f_4$ are from $v_1$. We say $e_1$ has two boundary points, $f_1$ and $f_2$; each of $e_4$ and $e_6$ has a boundary point.

\begin{figure}
\begin{center}
\includegraphics[scale=0.5]{fig7.jpg}
\caption{Points $f_1$, $f_2$, $f_3$ and $f_4$ are boundary points on $T$.}
\label{fig:7}
\end{center}
\end{figure}

\begin{lemma}
\label{x lemma}
For an edge $e_i$ on terrain $T$, there exists at most two points $p$ and $q$ that exclude $v_i$ and $v_{i+1}$ such that $e_i$ is complete two sided guarded if $p$ and $q$ are two sided guarded.
\end{lemma}
\begin{proof}

According to the number of boundary points on $e_i$, we may consider the proof under the following heads: edge $e_i$ does not have boundary point or has one, two, or $k$ boundary points (where $k \geq$ 3).

In the first case, we assume $e_i$ does not have boundary point. Let point $p \notin \{ v_i,v_{i+1} \}$ be on edge $e_i$. If $p$ is right guarded and left guarded, then edge $e_j$ is also right guarded and left guarded.

In the second case, we assume $e_i$ has a boundary point $f$. We divided the edge into two line segments $\overline{v_i f}$ and $\overline{v_{i+1} f}$. Then, the first case can be applied to the line segments $\overline{v_i f}$ and $\overline{f v_{i+1}}$. Therefore, we create two points $p \notin \{ v_i,f,v_{i+1}\}$ on line segment $\overline{v_i f}$ and $q \notin \{ v_i,f,v_{i+1}\}$ on line segment $\overline{fv_{i+1}}$. If $p$ and $q$ are right guarded and left guarded, then $e_i$ is also right guarded and left guarded.

In the third case, we assume $e_i$ has two boundary points $f_1$ and $f_2$. We divided the edge into three line segments $\overline{v_if_1}$, $\overline{f_1f_2}$ and $\overline{f_2v_{i+1}}$. The line segments $\overline{v_if_1}$ and $\overline{f_2v_{i+1}}$ can be reduced to the first case. Therefore, we create two points $p \notin \{ v_i,f_1 \}$ on line segment $\overline{f_2v_{i+1}}$ and  $q \notin \{  f_2,v_{i+1} \}$ on line segment $\overline{f_2v_{i+1}}$.
If $p$ and $q$ are left guarded and right guarded, then line segment $\overline{f_1f_2}$ is also left guarded and right guarded.

In the final case, we assume $e_i$ has $k$ boundary points $f_1,...,f_k$. We divide the edge into $k+1$ line segments $L = \{ \overline{v_if_1},\overline{f_1f_2},...,\overline{f_k v_{i+1}} \} $. The line segments $\overline{v_if_1}$ and $\overline{f_kv_{i+1}}$ can be reduced to the first case.
Therefore, we create two points: $p \notin \{ v_i, f_1 \}$ on line segment $\overline{v_if_1}$ and $q \notin \{ f_k, v_{i+1} \}$ on line segment $\overline{f_kv_{i+1}}$.
If $p$ and $q$ are left guarded and right guarded, then each line segment $\overline{f_cf_{c+1}} \in L$ is also left and right guarded.
\end{proof}

From the construction of Lemma~\ref{x lemma}, in order to completely two-sided guard a terrain, it is sufficient to first select a finite subset $X$ of positions from the terrain to be two-sided guarded, such that $|X|\leq 2(n-1)$.

\section{4. Optimal Algorithm for the CTGTG}

In this section, we present an optimal algorithm for the CTGTG. The idea of the algorithm follows from Observation~\ref{include $v_1$ and $v_n$}. In each step of our algorithm, we add a vertex $v_i$ to our result $S$ such that if $v_i \notin OPT$ then $v_i$ can replace a vertex $v_j \in OPT$ and $|S| = |OPT|$.

\begin{obs}
\label{include $v_1$ and $v_n$}
The optimal solution of the CTGTG includes $v_1$ and $v_n$.
\end{obs}

This is because in the CTGTG for right and left guarded $T$, only $v_1$ can left guard $v_1$ and only $v_n$ can right guard $v_n$.

\begin{figure}
\begin{center}\includegraphics[scale=0.8]{fig3.jpg}
\caption{Position of $R(N^R_i)$ and $g \in O_R(N^R_i)$.}
\label{fig3}
\end{center}
\end{figure}

\begin{lemma}
\label{between}
$R(N^R_i)$ and $ g \in O_R(N^R_i)$ do not lie on the right side of $o_i$.
\end{lemma}

\begin{proof}
Assume $R(N^R_i)$($g \in O_R(N^R_i)$) is on the right side of $o_i$ and $x$ is on the edge $e_j =\overline{v_jR(N^R_i)}$($\overline{v_jg}$). We know that $x$ is right guarded by $o_k$ and $o_k$ is on the right side of $R(N^R_i)(g)$. According to Lemma \ref{order lemma}, if $o_k$ right guards $x$, then $N^R_i$ is right guarded by $o_k$. This contradicts the definition of $N^R_i$ and $o_k$ sees $N^R_i$. The schematic of Lemma~\ref{between} is given in Fig~\ref{fig3}.
\end{proof}

\begin{lemma}
\label{between_l}
$L(N^L_i)$ and $g \in O_L(N^L_i)$ do not lie the left side of $o_i$.
\end{lemma}

\begin{lemma}
\label{can't guard}
If $R(N^R_i) \notin O_R(N^R_i)$ and
$R(N^R_i) \prec x$,
then $g \in O_R(N^R_i)$ cannot left guard $x$.
\end{lemma}

\begin{proof}
We prove Lemma~\ref{can't guard} in two steps. The first step explains that if $g \in O_R(N^R_i)$ left guards $x_k \in \{x_j \mid R(N^R_i) \prec x_j \}$, then $x_k$ and $N^R_i$ can see each other. The second step explains that if $x_k$ and $N^R_i$ can see each other, and $g$ left guards $x_k$, then $N^R_i$ is right guarded by $g$.
First, let $N^R_i \prec g \prec R(N^R_i) \prec x_k$. Because $R(N^R_i)$ sees $N^R_i$, according to Lemma~\ref{order lemma} if $x$ and $g$ see each other, then $x_k$ and $N^R_i$ also see each other. This is illustrated in Fig.~\ref{fig:4}.

\begin{figure}
\begin{center}
\includegraphics[scale=0.8]{fig4.jpg}
\caption{If $O_R(N^R_i)$ left guard $x_k$, then $x_k$ and $N^R_i$ see each other.}
\label{fig:4}
\end{center}
\end{figure}

In the second step, we assume that $x_k$ is right guarded by $o_j$ and that $x_k$ is on the edge $e_k$ on the right side of $R(N^R_i)$. We know that if $O_R(N^R_i)$ left guards $x_k$, then $x_k$ and $N^R_i$ see each other. Because $o_j$ right guards $x_k$ and sees $v_l$, if $x$ sees $N^R_i$ then $o_j$ right guard $N^R_i$ too, as illustrated in Fig.~\ref{fig:5}.

\begin{figure}
\begin{center}
\includegraphics[scale=0.8]{fig5.jpg}
\caption{If $x_k$ and $N^R_i$ see each other, then $o_j$ right guards $N^R_i$.}
\label{fig:5}
\end{center}
\end{figure}

\end{proof}

\begin{lemma}
\label{can't guard l}
If $L(N^L_i) \notin O_L(N^L_i)$ and $x \prec L(N^L_i)$, then $g \in O_L(N^L_i))$ cannot right guard $x$.
\end{lemma}

\begin{lemma}
\label{can't guard_1}
If $R(N^R_i) \notin O_R(N^R_i)$, $x$ is right guarded by $o_j$ and $i \leq j \leq m$, then $x$ cannot lie between $g \in O_R(N^R_i)$ and $R(N^R_i)$.
\end{lemma}

\begin{proof}
We assume $x$ is on the $e_k = \overline{v_kR(N^R_i)}$ and $x$ is right guarded by $o_j$. We know that $o_j$ right guards $v_k$ by Observation 2. According to Lemma~\ref{order lemma}, if $x$ is right guarded by $o_j$ then $N_R(o_i)$ is right guarded by $o_j$. Therefore, we know that if $R(N^R_i) \notin O_R(N^R_i)$, then $x$ cannot lie between $g \in O_R(N^R_i)$ and $R(N_R(o_i))$.

\end{proof}

\begin{lemma}
\label{can't guard l_1}
If $L(N_L(o_i)) \notin O_L(N_L(o_i))$, $x$ is left guarded by $o_j$ and and $1 \leq j \leq i$, then $x$ cannot lie between $g \in O_R(N^R_i)$ and $R(N^R_i)$.
\end{lemma}

\begin{theorem}
If $R(N^R_i) \notin O_R(N^R_i)$, then $R(N^R_i)$ can replace $g \in O_R(N^R_i)$.
\end{theorem}
\begin{proof}
Based on Lemma~\ref{between}, Lemma~\ref{can't guard} and Lemma~\ref{can't guard_1},
if $g \in O_R(N^R_i)$ and $R(N^R_i) \notin O_R(N^R_i)$, then $g$ cannot left guard $x_k \in \{ x_j  \mid N^R_i \prec x_j \} $. Due to $g \prec R(N^R_i))$, we know $vis(R(N^R_i)) \supseteq vis(g)$ by Lemma~\ref{order lemma}.
\end{proof}

\begin{theorem}
If $O_L(N^L_i) \notin L(N^L_i)$, then $L(N^L_i)$ can replace $g \in O_L(N^L_i)$.
\end{theorem}

\section{Complexity}
Because our approach has two phases, we must first discuss the complexity of discretization. We obtain boundary points for a vertex $v$ on $E(T)$ in $O(n)$ by \cite{map}. Therefore, we compute all boundary points for each vertex of $V(T)$ on each edge $e \in E(T)$ in $O(n^2)$. We obtain at most 2$|V(T)|$ boundary points in $O(n^2)$.

\begin{figure}
\begin{center}
\includegraphics[scale=0.8]{fig8-1.jpg}
\caption{If $L(v)$ cannot see $x$ and $v$ sees $x$ then $v=L(x)$.}
\label{fig:8}
\end{center}
\end{figure}

Next, we demonstrate how to compute an optimal solution for the CTGTG. In step 1, we add $v_1$ and $v_n$ to our solution. In step 2, we compute the $vis(v_1)$ and $vis(v_n)$. In step 3, we add $R(x)$ to our solution, where $x$ is the nonright-guarded rightmost point. If a point $x$ exists that is not right guarded, then repeat step 3 until $X$ is right guarded. In step 4, we add $L(x)$ to our solution, where $x$ is the non-left guarded leftmost point. If a point $x$ exists that is not left guarded, then repeat step 4 until $X$ is right guarded. Finally, all points $x$ are right guarded and left guarded.

We show our algorithm for the CTG problem runs in $O(n)$ using two steps. Before the algorithm begins, we can compute $R(x)$ and $L(x)$ for each point of $X$ in $O(n)$. After this computation, we proceed to the algorithm in $O(n)$. Therefore, our proposed algorithm for the CTG problem runs in $O(n)$.

\begin{algorithm}[h]

  \SetAlgoNoEnd
  \caption{Compute all $L(x)$}
  \label{Compute all $L(x_i)$}
  \KwIn{$T$: terrain, $X$: point set}
  \KwOut{\{ $L(x_i)|x_i \in X$ \} }

  $Q \leftarrow X \cup V(T)$

  \For{$q_i \in Q$ processed from left to right } {
    $q_j = q_{i-1}$

    \While{$L(q_i) = \emptyset$}{
    \If{$q_i$ sees $L(q_j)$}{
    \If{$L(q_j)$ is not $v_1$}{
    $q_j=L(q_j)$
    }
    \Else{
    $L(q_i)=v_1$
    }
    }
    \Else{
    $L(q_i)=q_j$
    }
    }
  }
  \For{$x_i \in X$ processed from left to right } {
  Return $L(x_i)$
  }
\end{algorithm}

\begin{lemma}
\label{L(xi)}
If $L(v)$ cannot see $x$ and $v$ sees $x$ then $v=L(x)$.
\end{lemma}
\begin{proof}
Assume $p \prec L(v)\prec v \prec x$, $L(v)$ cannot see $x$ and $v$ can see $x$. If $p$ sees $x$ and cannot see $v$, then a vertex $q$ exists and lie above line $\overline{vL(v)}$ and $p \prec q \prec L(v)$, as illustrated in Fig.~\ref{fig:8}. However, the assumption that $L(v) \neq q$ is contradictory.
\end{proof}

We propose Algorithm~\ref{Compute all $L(x_i)$} to compute $L(x)$ for all points of $X$ in $O(n)$ according to Lemma~\ref{L(xi)} and Lemma~\ref{order lemma}. We unite $X$ and $V(T)$ in a set $Q$. Algorithm~\ref{Compute all $L(x_i)$} finds $L(q_i) \in Q$ from left to right.
We prove that the running time of Algorithm~\ref{Compute all $L(x_i)$} is $O(n)$.

\begin{theorem}
Algorithm~\ref{Compute all $L(x_i)$} runs in O$(n)$.
\end{theorem}
\begin{proof}
We count the number of times $q_i$ sees $L(q_j)$ in the algorithm.
If $q_i$ sees $L(q_j)$, then the algorithm does not visit the vetrices between $q_i$ and $L(q_j)$. Therefore, the number of times $q_i$ sees $L(q_j)$ is at most once for each point of $Q$. If $q_i$ does not see $L(q_j)$, then $q_i$ has found $L(q_i)$. Therefore, the number of times $q_i$ does not see $L(q_j)$ is at most once for each point $Q$.
\end{proof}

After computing $L(x_i)$ and $R(x_i)$ for $X$, we reach the algorithm for the CTGTG in $O(n)$. We divided our algorithm into left and right-guarding, and therefore we provide the algorithm for left-guarding that can be implemented in $O(n)$.

\begin{algorithm}[h]
  \SetAlgoNoEnd
  \caption{Left-guarding}
  \label{A2}
  \KwIn{$T$: terrain}
  \KwIn{$X$: point set}
  \KwOut{$P$ : left-guarding set}

  $P$ is null;

  $V(T')$=$V(T)$;

  \For{$x_i \in X$ processed from left to right } {
    \While {$g(x_i)$ is null}{
    $p_j$ is rightmost vertex in $P \cap V(T')$;

     \If{$x_i$ is guarded by $p_j$}
     {
      $g(x_i)$ is $p_j$;

      Remove the vertices between $x_i$ and $p_j$ from $V(T')$;
     }
     \ElseIf{$p_j$ on the left side of $L(x_i)$}
       {
         $g(x_i)$ be the vertex $L(x_i)$ ;

         Add $g(v_i)$ to $P$;

         Remove the vertics between $x_i$ and $L(x_i)$ from $V(T')$;
       }
       \Else
       {Remove $p_j$ from $V(T')$;}
    }
    	}
  \Return $P$
\end{algorithm}

\begin{theorem}
Algorithm~\ref{A2} runs in $O(n)$.
\end{theorem}
\begin{proof}
For each $x_i$, we examine whether $x_i$ is guarded by $p_a \in P$ from $x_i$ to $g(x_i)$. If $g(x_i)$ = $g_a$ = $v_b$, then Algorithm~\ref{A2} will not visit the point and vertex between $x_i$ and $v_b$.
We count the number of times $x_i$ is not seen by $P$.
We can check $p_j$ from $x_i$ to $L(x_i)$.
If $p_j$ does not see $x_i$, then we will not check $p_j$ for $\{ x_k \mid x_i \prec x_k \}$.
Assume $p_j$ does not see $x_i$, $p_k$ sees $x_i$, and $p_k \prec p_j \prec x_i$, if $\{x_l \mid x_i \prec x_l \}$ is seen by $p_j$, then $p_k$ sees $\{x_l \mid x_i \prec x_l\}$ according to Lemma~\ref{order lemma}.
The number of times $X$ is not seen by $P$ is $|V(T)|$, and the number of times $X$ is seen by $P$ is $|X|$.
Therefore, the algorithm visits the point and vertex at most $2|X|+|V(T)|$ times. After computing all $L(x_i)$, Algorithm~\ref{A2} runs in $O(n)$.
\end{proof}

\section{Conclusion}
In this paper, we considered the CTGTG problem and devised an algorithm that can determine the minimal cardinality vertex that guards $T$ under two-sided guarding. We showed that the CTGTG problem can be reduced to the discrete terrain guarding problem with at most $2|V(T)|$ points in $O(n^2)$ and solved the problem using our devised algorithm in $O(n)$ where $n$ is the number of vertices on $T$.

\bibliographystyle{elsarticle-num.bst}

redpajama_set_name: RedPajamaArXiv


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OngoingWorlds blog
News & articles about play-by-post games, for roleplayers & writers
-- Main Menu --
By Emily Wake
Child's Play – Back to School
Category: Inspiration for writing, Writing tips Tags: characters, parents, writing Leave a Comment
The back-to-school shopping season, second only to the holiday season in terms of consumer spending, has been thrown into uncertainty bordering on chaos as parents and retailers do their best to plan for what school will look like in the coming weeks. Most of the time office quality products are the best, for example this mohawk superfine paper.
Set against the backdrop of a highly contagious viral pandemic and the devastation it has woven across the U.S. economy, 2020's back-to-school season is unlike any other.
"It's the most challenging time in history for back to school," said Burt P. Flickinger III, managing director of Strategic Resource Group, a consumer consulting firm in New York City.
The back-to-school season is "a critical catalyst that the country needs for an economic comeback whether it's Wisconsin, the Great Lakes region or anywhere across America," Flickinger added.
Whether back to school ultimately serves as a jump-start to a pandemic-ravaged economy remains to be seen.
"What retailers have to do is understand the downdraft of back to school and catch the updraft of selling more goods related to living, learning and working from home," Flickinger added.
"Most parents don't know whether their children will be sitting in a classroom or in front of a computer in the dining room, or a combination of the two," Matthew Shay, president and chief executive of the National Retail Federation, said in a statement.
It's unlike anything anyone has ever seen.
"How do you forecast who needs new jeans or sneakers to wear to school and who doesn't because they are going to be staying at home?" said Dick Seesel, principal at the Mequon consulting firm Retailing in Focus and a former retail industry executive. "Do they still need school supplies if they are studying at home? Maybe. But do they need backpacks? Maybe not."Get the Coronavirus Watch newsletter in your inbox.
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If you're in a school system where the students wear uniforms and your school may or may not reconvene, parents and the retailers who sell school uniforms also have to deal with the uncertainties involved in that part of back-to-school shopping, Seesel said.
"The other thing you don't know, for the schools that are reopening, how long are they going to manage to stay open?" he added. "Nobody's had to deal with anything like this."
Toss in high unemployment and overall uncertainty as COVID-19 cases continue to spike and, "Consumers are very cautious right now," Seesel said. "They don't know what the next six months are going to look like.
"I've never seen anything that has put a dent in consumer demand quite like this," he added.
Parents left to make choices amid uncertainty
If you think retail forecasters have a tough job, try being a parent who is trying to plan for kids going back to school without knowing whether classes will be in person, online or both.
A recent survey of parents shows there will be plenty of penny-pinching, foot-dragging and angst.
About 64% of 18,000 parents surveyed said they were not excited about back-to-school shopping this year because of health risks going into stores or risks to their children going back into classrooms, according to Piplsay, a crowdsourcing research firm.
More than half (52%) of the respondents in its late July survey said they will spend less this school year than last year.
Brad Wright, a dad of three teens — twin daughters and a son — said his approach to back-to-school spending is the opposite of the panic buying and hoarding seen in the early days of the pandemic.
"You buy a little bit, wait to see what happens, then you buy a little bit more if necessary," said Wright, of Bellevue, Nebraska.
"You slow play this one," Wright added. "One pair of Lululemons might make it through the year."
Lululemon is a pricey active clothing line that teens crave. A pair of pants runs $88 to $118.
Appleton mom and early childhood teacher Amy Nogar is also on the wait-and-see side.
"We haven't done any back to school shopping yet," she said. "Before we do any shopping, we'll see what can be reused from last year."
One son, a high school junior, "will be doing online learning first semester for sure, so he won't need much," she said. His school-issued laptops to every student.
Her eighth grader "will be in-person, so we'll have to get him some things." He has a hand-me-down laptop if he needs to do remote classwork.
"We'd definitely spend less if both boys were remote learning because we already have the technology," Nogar said. "We're fortunate. I can see how it could be a challenge for some families."
Focus shifts to technology
If remote learning takes over, some parents might be forced to spend more for back to school this year because kids will need laptop computers, headphones and things such as flash drives, printers and new routers for home Wi-Fi connections.
Retailers have pivoted to meet that demand should it occur.
"Toward the end of the spring semester, we saw a huge uptick in electronic items, like headphones and chargers and headphone sets with microphones attached," said Phil Kelley, store director at the Meijer in Oak Creek.
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Health technology is advancing so rapidly that within a decade the small handheld medical reader used by Dr. Leonard McCoy in Star Trek — the tricorder — will look primitive.
We are moving into an era of data-driven, crowdsourced, participatory, genomics-based medicine. Just as our bathroom scales give us instant readings of our weight, wearable devices will monitor our health and warn us when we are about to get sick. Our doctors — or their artificial intelligence replacements — will prescribe medicines or lifestyle changes based on our full medical history, holistic self, and genetic composition.
Not long ago, our only recourse when we doubted our doctor's prescription was to seek a second opinion. Now when we need information about an ailment, we search on the Internet. We have access to more medical knowledge than our doctors used to have via their medical books and journals, and our information is more up-to-date than those medical books were. We can read about the latest medical advances anywhere in the world. We can visit online forums to learn from others with the same symptoms, provide each other with support, and discuss the side effects of our medicines. And we can download apps that help us manage our health.


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Cars > Iconic
Quite possibly the most special automobile ever built
Is there a car in history more remarkable than the McLaren F1?
First road car with carbon-composite monocoque chassis.
BMW-supplied 6.1-liter V12 engine is rated at 618hp.
Only 64 units were assembled in regular, road-going form.
V Vernon B. Sarne
The F1 was the first production car to be developed by Formula 1 engineers. No bullshit. PHOTO BY VERNON B. SARNE
Gather 10 automotive enthusiasts around a table and have each of them pick the greatest, most special car ever produced. I guarantee you'll get 10 different answers. But if there's one car that's almost a sure bet to always make it to such a distinguished list, it's the McLaren F1 road car that was officially presented to a stunned world on May 28, 1992.
Famously conceptualized by Formula 1 car designer Gordon Murray, the F1 is the one true production car that was born from the womb of the motorsport series. We always hear how certain technologies gradually trickle from race cars to street-legal cars, but the F1 didn't just get drips of technological advancement—it was immersed in it. Not only did it inherit carbon-composite construction (for its monocoque chassis) from the 1981 McLaren MP4/1, it was the first production car to be developed by Formula 1 aerodynamicists using a wind tunnel. And thanks to the ultra-lightweight materials used for the body, the engine and other mechanicals, the aptly named F1 had a curb weight of just 1,150kg. For context, the 935kg Smart Fortwo—a plastic-paneled hatchback so small you could probably park it in your living room—is lighter by a mere four sacks of rice.
Huge windshield wipers ensured that no raindrops would impede your spirited driving. PHOTOS BY VERNON B. SARNE
"We set out to produce the best road-going driver's car ever built—or ever likely to be built—and we are confident that this first McLaren production model represents the pinnacle of 20th-century high-performance sports car design," Murray was quoted by the press statement as saying.
The F1's driver was seated squarely in the middle of the cabin, ahead of two rear passengers. So the F1 was a 1+2 car like the three-seaters Formula 1 teams used for treating VIP sponsors and lucky fans to a rip-roaring experience around the track. One of the most abused adjectives in the lexicon of automotive PR writers is "driver-centric." For those who hate fake news, the F1 is the only road car that truly deserves that description.
To ensure that bystanders fully understood the grandeur of the F1, its designers gave it dihedral or butterfly doors, which moved up and then out to disgorge the driver and his companions in head-turning fashion. The otherworldly sports car was so visually striking and cutting-edge that it still freezes people motionless in their tracks today—25 years after it was launched.
The profile emphasized the car's low height. PHOTO BY VERNON B. SARNE
For the engine that would be tasked to provide propulsion for this once-in-a-generation project, McLaren commissioned BMW, which had previously collaborated with both Murray and McLaren International managing director Ron Dennis in Formula 1. For reliability's sake, normal aspiration was agreed upon. The German firm proceeded to deliver a 6,064cc 60° aluminum V12 that was tested for 618hp (at 7,400rpm) of output and 650Nm (from 4,000 to 7,000rpm) of torque. Topping out at 7,500rpm, this powerplant catapulted the F1 to a top speed exceeding 350km/h, decisively obliterating the record set by the Jaguar XJ220. The Bugatti-this or the Koenigsegg-that may have since overtaken the McLaren in this department, but the F1 held the title of "world's fastest production car" for years. No mean feat, especially considering that the BMW engine installed amidship benefited from neither turbocharging nor supercharging.
A purpose-built six-speed manual transmission boasted a full-synchromesh gearchange for quick and efficient shifts. It enabled the F1 to accelerate from rest to 100km/h in about 3.5 seconds, and then to 200km/h in about 8.5 seconds—both jaw-dropping figures in the '90s.
The 6.1-liter V12 engine was courtesy of BMW. PHOTOS BY VERNON B. SARNE
Like moths to the flame, affluent petrolheads lined up for the chance to own one. But with only 106 units made until May 1998, those chances were very low—even if said clients could afford McLaren's asking price of $815,000. To make matters even more desperate, only 64 units were assembled as regular road cars. The rest rolled off in these versions: F1 prototype (5 units), F1 LM (6 units), F1 GT (3 units), F1 GTR '95 (9 units), F1 GTR '96 (9 units), and F1 GTR '97 (10 units).
It is this scarcity that makes the motoring community groan whenever an owner wrecks his F1. I have no doubt Rowan Atkinson lost a few car-loving fans when he crashed his hypercoupe twice. But that's the trouble with high-performance automobiles with more power than you know what to do with. In the heat of the moment, not even 332mm (front) and 305mm (rear) brake discs can stop the dedicated Goodyear F1 (235/45 R17 front; 315/45 R17 rear) tires from rolling.
The V12 engine needed to let off a lot of hot air—hence these louvers for the tail deck. PHOTOS BY VERNON B. SARNE
I encountered one of these rare units at the BMW Classic facility in Munich, Germany, in 2011. Just getting near the F1 in the metal was an event in itself. With a height of just 1,140mm, the McLaren masterpiece looked like a toy that sent grown men back to their childhood. On second thought, this car is a toy.
Because the F1 on display was locked, I wasn't able to take photos of the interior. But just to give you an idea, below are two official pictures of the cabin from McLaren.
The driver-centric cabin accommodated three people. PHOTOS FROM MCLAREN
Among the noteworthy features of the F1 were two side compartments that could store a combined 227L of luggage; the world's smallest 10-disc CD player by Kenwood; and a set of titanium tools by Facom. Each of these items was meticulously specced just to complement a car for the ages. A car the likes of which we may never see again.
So, is the McLaren F1 the most special car ever made? Well, someone who just paid $15,620,000 for a unit in excellent condition seems to think so.
Vernon B. Sarne
Vernon is the founder and editor-in-chief of VISOR. He has been an automotive journalist for 26 years. He became one by serendipity, walking into the office of a small publishing company and applying for a position he had no idea was for a local car magazine. God has watched over him throughout his humble journey. He writes the 'Spoiler' column.
The car that gave Mazda its fortitude
Photos: 2015 Lamborghini Aventador LP750-4 Superveloce
Photos: 2014 McLaren P1
Photos: 2017 Honda NSX
Photos: 2011 Lexus LFA
President Duterte says gasoline can disinfect
Toyota is building a city to develop future tech
In Japan, Nissan unveils full-electric ambulance
The Nomos Autobahn has three new designs
We tried old-school touring with the Moto Guzzi V85TT
Vessel transporting Porsche cars goes ablaze off the Azores in Portugal


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The absolute worst thing you can do when you're feeling low is go on social media. It's a very, very bad idea. Why is that? Well, you give in to this false perception that everyone, every single person you know, or added on Facebook when you were 21 at a college party and forgot to unfriend years later, is living a better life that you.
Yesterday I went on Facebook to see approximately 2,347 people living the best version of their lives. One person posted a photo from inside the mosh pits of Coachella. Another a celebratory status about how their baby girl finally took a giant poop in the potty. And one person, I think I met on a spring break cruise, posted about how some Beachbody smoothie made her lose 15 pounds in a month. How can that be? Any smoothie I drink makes me gain 15 pounds in a month. Maybe that's because I add vanilla ice cream to them but whatever, okay? Whatever.
Everyone has their life plans figured out better than I do. All these people probably got back tax returns this year and contributed to their 401k and don't check their email 65 times an hour and don't know what anxiety feels like or depression feel like, right? Well of course that's all wrong. But in that moment I convinced myself otherwise. I guess this is just a reminder not to judge people's lives by their social media postings.
PS. I'm excited to hand you all my life secrets inside my new book for 40% off. ENJOY!


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Escorted Rail Tours to Berlin
The fascinating German capital
Berlin is a city with a fascinating and turbulent history that was once the symbol of the Cold War, marking the dividing point between East and West. Today, Berlin is a modern capital city and a popular and rewarding tour destination. There are traces of history and division all over the city, including remnants of the Berlin Wall, some sections of which are completely intact. The imposing Brandenburg Gate and famous Checkpoint Charlie are permanent reminders of Berlin's past.
The Reichstag is the seat of the German Parliament and is one of Berlin's most famous landmarks. Following a mysterious and controversial fire in 1930 - the Communists blamed the Nazis, who in turn blamed the Communists - it was rebuilt, only to be left unoccupied and abandoned after World War II. The German Democratic Republic (East Germany) used the Palace of the Republic in East Berlin, while the Federal Republic of Germany (West Germany) used the Bundeshaus in Bonn. Following the reunification of Germany in 1990, the Reichstag was fully refurbished by architect Norman Foster. His work included the addition of a huge glass dome on the roof, which provides incredible 360 degree views across the city. The dome is designed to direct sunlight into the building, while also allowing visitors to the dome to see into the Parliament chamber from above.
Alexanderplatz and the TV Tower
This grand parade ground, a familiar sight in most communist states, was once a symbol of East Germany. Today, Alexanderplatz is the largest city square in Germany. It is overlooked by the Television Tower. At 368 metres, the TV Tower is the tallest tower in Germany and provides unbeatable views across Berlin's city centre and surrounding region. At the tops, a revolving restaurant offers views while you eat, rotating twice every hour.
The Memorial for Europe's Murdered Jews
Located close to Brandenburg Gate is a permanent place of remembrance for Jews murdered during the holocaust. The poignant memorial consists of a simple grid pattern of concrete slabs set on a sloping field - the slabs begin to tower over you as you walk among them. The memorial is supplemented by an underground information centre containing the names of all known victims.
What has come to be known as the 'East Side Gallery' is in fact the longest surviving section of the Berlin Wall, at 1.3 kilometres in length. It runs along the banks of the River Spree, with 118 international artists from across the world immortalised on the Wall with graffiti art and paintings.
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Discover Poland
Reflect on a region's fascinating past as we explore unified Berlin, and discover Poland, including the medieval squares and castles of Wroclaw, Krakow and Warsaw. Take a poignant trip to Auschwitz and visit unique salt mines as we reveal the history, music and people of beautiful Poland.
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Magnificent architecture, iconic monuments and rejuvenated cities combine on a Berlin, Dresden and Prague tour, visiting three of the Continent's most important and most beautiful destinations on a journey into history.
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Step on board the Golden Eagle and be transported back to the romantic age of travel as we wend our way across Russia, Mongolia and Siberia in unprecedented luxury. This rail adventure takes you on a journey of over 8,000 miles; a true odyssey to the other side of the world.
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Grand Imperial Cities
Fascinating grand imperial cities and high-speed intercity train journeys showcase the turbulent history of Central Europe. Discover what turned these former Habsburg and Prussian cities into four of Europe's greatest destinations.
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Embark on an exciting thousand-mile journey along the mighty Danube, cruising through eight countries before arriving at the Black Sea. Admire the river's full spectrum of vistas - from Austria's wine regions to the imperial cities of Budapest.
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Witness the true splendour of Dr Zhivago landscapes from the warmth of your luxurious carriage, enjoying sleigh rides and choirs, saunas and yurts en-route to Vladivostok. Travel on the Golden Eagle Trans-Siberian Express train for an unforgettable 8,000-mile winter adventure. The maximum group number for this tour will be capped at 20, allowing for a more intimate, personal experience.
The Trans-Siberian: Moscow to Beijing
Let the Tsar's Gold Train take you on an incredible adventure across almost half of the surface of the world from the ornate splendor of Moscow to the bustling beauty of modern Beijing, through remote Siberia, beautiful Mongolia and the vast landscapes of the Gobi Desert.
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The idea of travelling aboard a night train holds an almost mysterious allure, conjuring images of moustachioed Hercule Poirot aboard the Orient Express or stepping into the high heels of Jack Lemon and Tony Curtis as they bunk down with Marilyn Monroe in Some Like It Hot.
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Experienced travellers from Great Rail Journeys Independent let us into the secrets of what makes for the perfect late escape for all those still hankering after an autumn getaway.
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Q: multiprocessing - FileNotFoundError: [Errno 2] No such file or directory I want to run a Rasa-Project whicgh was coded from another group. Rasa installation works fine (also rasa shell command). Now i want to use the Rasa UI by installing rasa-x. Following Errors appears in the Terminal:
Terminal Screen
I looked into the Folder .../multiprocessing/... and the spawn.py and synchronize.py folders are there. Anyone a idea ? Thank you so much

A: pip uninstall uvloop fixed my Problem.

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Subscribe "Ecology" Newsletter
Ancient temperature and sea level changes provide new insights into potential impact of climate change today
4 days ago | By Phys.org
Scientists studying ocean temperature and sea level changes from thousands of years ago have said their data could be crucial to understanding climate change and improving projections of how our world may change due to global warming.
New classification marks paradigm shift in how conservationists tackle climate change
A new study co-authored by researchers from the Wildlife Conservation Society's Global Conservation Program and the University of British Columbia Faculty of Forestry introduces a classification called Resistance-Resilience-Transformation that enables the assessment of whether and to what extent a management shift toward transformative action is occurring in conservation. The team applied this classification to 104 climate adaptation projects funded by the WCS Climate Adaptation Fund over the past decade and found differential responses toward transformation over time and across...
Earth Sciences Ecology


Some may argue that Valentines has become a consumerist holiday but its undeniably great for business! Last year over 22 million Brits brought into the day and this year won't be dissimilar as the spectrum of love widens to encompass: friends, children, parents, partners and even yourself. The love doesn't just end on the 14th either 'Belated Valentines' is rising in popularity with bargain hunters looking to save some money. So take the time to send your customers some love with our heart stickers and these brilliant ideas.
New customers are great and return customers are brilliant. When a customer receives your order you want to make sure they come back for more. One way to do that is to add a little something to their order. It could be a free sample, an extra product or a little trinket, but let's face it that can get expensive. So here's our simple method-- add a specially designed heart-shaped sticker. This'll mean you're within the Valentines theme and can design your sticker to match the rest of your branding; place it on your packaging or even the product itself. To each of the stickers, you can add an incentive for them to buy again, something like discount codes special use codes or a reward scheme. This will encourage return customers long after Valentine's Day.
Celebrating Valentines as a company can be a good way to show you appreciate your customers and foster good relations. Our heart labels can be great mediums to carry special messages. Over the run-up to Valentine's Day try adding our heart stickers to every order printed with a special message that's in keeping with your brand. This can also be applied to business to business too, a small heart on every box that's shipped out, each personalised with the companies name in a bright bold colour would put a smile on everyone's face throughout its journey. You can also use this to get appreciation back. As reviews are now pivotal to success it's always a good idea to ask for a review. This can be done by simply adding that you'd like to hear from them.
Annual celebrations are a good time to create a buzz around your brand especially on social media. It's time where a lot of traffic can be driven off the back of well-used hashtags. If you've got something to promote a heart label is a fun and effective way to get people involved. It can easily stand out and draw attention to itself, promoting your message to the consumer. Try adding hashtags, challenges or social media tags to increase engagement with your brand. Idea: Invest some time and design effort to create something special that stands out and get your customers to repost a picture of it and repost.
Including something small that represents your brand is a nice touch and improves the customer experience. Your most loyal customers would enjoy stickers to represent their love for your brand. Recently a clothing company called Collusion has talked about their use of free stickers with every purchase. Here's what they've had to say: "We use stickers rather than swing tags. They reduce waste and you get something out of it too". To their question of where their customers had put their stickers, they got a variety of replies ranging from laptops, phone cases to skateboards and sketchbooks. This is particularly interesting as these are things that other people will see daily, their customers are now acting as brand ambassadors, all of that from a simple sticker. We have a range of different sticker shapes and sizes, our most recent being the heart stickers. You could make your stickers seasonal allowing return customers to create a collection over the year.
Fallen head over heels for our heart stickers? Here's what you need to know. You can get them as stickers or as labels, this means they can be also be used as product labels. Our product labels available in 40mm and 50mm sizes and you can customise them from scratch or use our templates. They can stick to almost any material so they're perfect for all your needs. Our fast shipping will ensure you receive your sticker within 3-5 days or even quicker if you choose express production. If you're considering our heart labels don't forget we're currently running a discount on our heart stickers with code: LOVE10.


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Hertfordshire Constabulary
These are the best pictures from Operation Pram in Hertford
Chief Inspector Gerry McDonald and his officers pushed a pram and if they were unable to get it past a vehicle they handed out a fine
Matthew Mohan-Hickson
Updated 15:34, 10 NOV 2017
The Chief Inspector of East Hertfordshire pushed a pram around Hertford during a crackdown on vehicles blocking the pavement.
Officers launched the operation today (August 16) after receiving numerous complaints from residents about not being able to get wheelchairs and pushchairs down the pavements.
Pram pushed by police struggling to get through the pavement
During the operation Chief Inspector Gerry McDonald and his officers pushed the pram and if they were unable to get it past a vehicle they handed out a fine.
He said: "It is about being sensible.
"After numerous complaints from members of the public about not being able to get wheelchairs, pushchairs and other items through on pavements we started the operation to educate people before the school year starts.
Officer handing out first ticket during operation pram
"The reason we are using a pram as a measure clearly illustrates the issue and we are trying to find a balance between the need of everyone but what I can't have is parents and buggies and disabled people being forced into the road and that is why we are using this tool."
Operation pram will be expanding to other towns in East Herts including Bishop's Stortford soon.
While under the law it is not illegal to park on pavements, unless it is a lorry, it is against the law to block the pavement with a vehicle.
Dragon's Den paedeophile Richard Hazell has sentence increased after hearing at Court of Appeal
After testing the pram out and not being able to get it past a van, the police debated whether to hand out a fine or to just give advice to the driver before ultimately deciding to leave a ticket.
Sergeant Duncan Wallace said: "My evidence is that there is narrow gap on the pavement and this is a densely populated residential area where footfall is going to be high.
"The footfall will likely include people on mobility scooters, wheelchairs and they should not be asked to go out into the main carriageway.
Officers taking part in Operation Pram
"That is what the pavement is for."
During operation pram, which was carried out in the east of Hertford and on North Road near Hertford North station, the officers ran out of fine tickets to hand out.
Recap the updates on the operation in our live blog here


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Writing Biographical Fiction: Conrad de Montferrat
19th Century Depiction of Conrad de Montferrat
Of all the historical characters in my Jerusalem trilogy, Conrad de Montferrat is the one other writers unanimously paint as the villain par excellance. Even Andrew Latham, an otherwise meticulously accurate historian, found it convenient to cast Montferrat as a diabolic evil monster obsessed with this own power in The Holy Lance.
It's easy for novelists to fall into the cliché because one of the surviving primary sources, Itinerarium Peregrinorum et Gesta Regis Ricardi, delights in heaping abuse on the man who dared to defy Richard the Lionheart. The Montferrat of English legend, therefore, was a man who shot a cross-bow at his own father, killed his doctors, abducted a princess, bribed bishops, intentionally withheld food from crusaders, undermined all efforts by Richard of England to defeat Saladin, and finally met his just end at the hands of an assassin. It would have been easy to follow the tradition of making Montferrat into a sort of medieval Darth Vader.
But I don't like cartoon characters in my novels. I wanted a more nuanced and comprehensible man for my books. Turning to less biased, particularly German sources, I discovered what I was looking for: a man of "many parts" with a wealth of positive characteristics and achievements to balance the negative portrayal of the Itinerarium.
Conrad de Montferrat, born about 1145, was a first cousin of Emperor Friedrich Barbarossa and of the French King. His older brother, William, married Sibylla of Jerusalem. Conrad's younger brother, Rainier married Maria Comnena, the daughter of Emperor Manuel I. In short, Conrad de Monteferrat was closely related to the Holy Roman Emperor, the Emperor of the Eastern Roman (Byzantine) Empire, the King of France, and the ruling Queen of Jerusalem. Conrad de Montferrat was not — as some modern novelists would have you believe — an "adventurer" or a parvenu.
Furthermore, Conrad was a very well-educated, well-traveled and militarily experienced nobleman. He supported his father in his wars and in 1179 prominently defeated the forces of the Holy Roman Emperor taking the Imperial chancellor captive. He subsequently went to Constantinople, where he was greatly admired for his good looks, charm and military prowess. Although he wisely departed Constantinople after Emperor Manuel I's death -- and shortly before his younger brother and sister-in-law were murdered by the usurping Emperor Andronicus, at the invitation of Emperor Isaac Angelus Conrad returned in 1186 to marry the Emperor's sister Theodora. Conrad was raised to the rank of "Caesar," and put down a rebellion led by the popular general Alexios Branas in a battle where he demonstrated exceptional personal courage. His success led his brother-in-law to look on him with jealousy and suspicion, however, and Conrad soon feared for his life (his brother, after all, had been murdered in Constantinople only five years earlier). He fled Constantinople, and took ship for the Kingdom of Jerusalem, arriving there only days after the catastrophe of Hattin.
Conrad sailed into the harbor at Tyre when it was already invested by land by the Sultan's army. Negotiations for the surrender were allegedly already underway, whether as a ruse or in earnest. Conrad immediately and forcefully advocated defiance. With so many other cities ripe for surrender, Saladin chose not to fight for Tyre, but withdrew to capture Sidon, Beirut, Caesarea, Jaffa, etc. Meanwhile, the people of Tyre, which included not only the usual residents but the survivors of Hattin and refuges from across the north of the Kingdom of Jerusalem, swore allegiance to Montferrat.
When Saladin returned to finish off Tyre in November 1187, he brought with him Conrad's father, the aging Marquis de Montferrat, who had fought and been taken captive at Hattin. Saladin offered to release the Marquis in exchange for the surrender of Tyre. The chronicles tell a dramatic tale in which Conrad pointedly refused the deal, saying his father had "lived long enough already" and fired a crossbow in his direction (probably intended to miss or to kill one of his Saracen escort). Much has been made of this as proof of Conrad's perfidy or callousness. Yet, the chronicles agree that Conrad's father called out something to the effect of "well done" when Conrad refused to surrender. The old Marquis of Montferrat, who had fought long and hard for the Holy Land, did not want to see the last remaining bastion of the kingdom surrendered. I found myself liking Conrad for his iron nerves!
In addition to the old Marquis, Saladin had brought another means for reducing the city: the Egyptian fleet. Tyre was now truly besieged and crammed as it was with refugees and cut off from resupply the situation rapidly became critical. Montferrat devised a trick: he led the enemy to believe that people were rioting and some of the wealthier residents were going to attempt a breakout. The chain across the harbor entrance was lowered as if to let the ships escape. The Saracens took the bait. They shot into the harbor, thinking they were about to take the city by the back door. Instead, they found themselves attacked by the Pisan vessels in the harbor and fired on from the surrounding walls, towers and buildings. The very next day, January 1, 1188, Saladin ordered his army to disperse and withdrew.
All of the above reflects well on Conrad de Montferrat's capabilities as a determined, resourceful, and clever commander. But it was his political actions that generally draw approbation and they started a year and a half later when, out of the north, a small Frankish army led by none other than the architect of the disaster at Hattin, Guy de Lusignan, appeared before the gates of Tyre. King Guy ordered the gates of the last free city of his kingdom opened to him. Conrad de Montferrat refused. Again, I can't say that I blame him.
Guy continued south to lay siege to Acre, which was now held by a Saracen garrison. Thus, when the crusaders started to arrive in increasing numbers in 1190 and 1191 most of them joined the siege of Acre because it was the only active fighting available. While this should have increased Guy de Lusignan's stature, in fact, the arriving contingents of troops tended to recognize their own leaders rather than Guy. Then in November 1190 Guy's position was fatally undermined by the death of his wife and both his daughters. Guy, always unpopular, widely viewed by the barons of Jerusalem as a usurper, and discredited by Hattin, lost his last vestige of legitimacy with his wife's death. The High Court of Jerusalem recognized Sibylla's younger sister Isabella as the rightful ruler of Jerusalem after Sibylla's death.
Only there was a problem. The Constitution of Jerusalem recognized the rights of women to rule in their own right, but only if they had a male consort capable of leading the army of Jerusalem. Isabella's husband Humphrey de Toron had already betrayed the High Court when the High Court was trying to oppose Guy's usurpation of the throne in 1186. The High Court was not prepared to recognize Humphrey as king. That meant that Isabella had to be separated from him and married to a man more acceptable to the barons of Jerusalem. The details of this are described in The Abduction of Isabella. For now suffice it to say that Conrad was the man they chose.
The Itinerarium and most subsequent sources portray Conrad as the driving force behind his marriage to Isabella. He is described as scheming and bribing, as unscrupulous and duplicitous. These portrayals, however, completely ignore the essential fact that it was the High Court of Jerusalem that decided on the marriage of a female heir and the fact that the High Court consistently supported Conrad over Guy. The overblown outrage of the chronicles likewise obscures the plain fact that Isabella was below the age of consent at the time of her marriage to Humphrey (she was 11) and the marriage was without question invalid according to contemporary canon law. While it is also highly probable that Conrad was ambitious and coveted the crown, it is absurd to portray his marriage to Isabella as a travesty of justice or an act of moral depravity. In my novel, therefore, I emphasize the role of the High Court, while nevertheless depicting Conrad as very ambitious and eager to gain the favor of the High Court.
By the time the Kings of France and England arrived in the Holy Land, there were two rival claimants to the (largely fictional) throne of Jerusalem: 1) Conrad, supported by the High Court and deriving his claim through the legitimate heir, Isabella, and 2) Guy, clinging to the title he had from his now dead wife because he'd been crowned and anointed. Their rivalry immediately became a proxy war between Philip II of France, who backed his kinsman Conrad, and Richard I of England, who backed his vassal Guy. Unfortunately for Conrad, Philip II soon tired of crusading and sailed away, while Richard I remained and recaptured much of the fertile coastal plain although he was unable to regain Jerusalem. In my novels, it is this conflict that initially puts Balian and Richard on opposing sides and so in conflict with one another.
During the critical eleven months from October 1191 to September 1192, Richard I periodically sought a negotiated settlement with Saladin. Not surprisingly, Conrad feared that Richard would negotiate a deal that left him high and dry, and so he tried to cut a deal of his own. This has been portrayed as the height of infamy by the supporters of Richard, but it is hard to see why it was legitimate for Richard to negotiate with Saladin but not for Conrad. Saladin, meanwhile, had a strong interest in playing Conrad and Richard off against one another and sowing dissension in the Frankish camp. However, it appears that Conrad was so desperate (or determined) to get a little kingdom (or county) of his own that he was prepared to fight his fellow Christians, and this seemed to me very telling. Conrad was resourceful, brave, and clever, but he was also ruthlessly ambitious.
In fashioning the Conrad de Montferrat of my novel Envoy of Jerusalem I tried to do justice to him as a complex character full of charm, ambition, talent -- and opportunism. I believe he would have used his charm very judiciously and intelligently to win over the heiress of Jerusalem – even before the succession crisis. She was after all, a guest in "his" city of Tyre, which makes my version of events diverge from the usual portrayal of Isabella as abducted and abused by a man she hates. His ambition and talent are depicted in his defense of Tyre, his refusal to admit Guy, and bid his for the crown. However, on the assumption that a man with so many enemies was not always pleasant and congenial, I have also made him arrogant, self-willed, immune to advice and at times unscrupulous.
The Conrad de Montferrat is a major character in Envoy of Jerusalem.
Buy now in paperback or Kindle!
Posted by Helena P. Schrader at 30.4.17
Labels: Conrad de Montferrat, Guy de Lusignan, Isabella of Jerusalem
Mystic Scholar Monday, May 01, 2017
You and I might disagree on this point, Professor, but I believe a great many historians . . . lie.
How so? They lie when they refer to themselves as being "unbiased." Most of them are not.
Too many view these men with a twenty-first century point of view. They just can't help themselves and are thus . . . bigoted.
I like your take on Conrad and find myself in ready agreement. Considering the "law" of the Kingdom of Jerusalem, and the "lawful rights" of the High Court, it was Richard who was in the wrong and "greedy for power" by insisting that his VASSAL be named King of Jerusalem. Richard could easily see himself as "over-lord" of the "Latin east."
I like Richard, but this is how I see it.
Writing Biographical Fiction: Humphrey de Toron
Writing Biographical Fiction: Isabella I
Writing Biographical Fiction: Reynald de Châtillon
Writing Biographical Fiction – Richard the Lionheart


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U.S. Army Awards AM General $51.3 Million Contract For High Mobility Multipurpose Wheeled Vehicles
In Community + Industry, Platforms + Vehicles by Chad September 26, 2018
SOUTH BEND, Ind., September 26, 2018 – Global vehicle solutions provider, AM General, has been awarded a $51.3 million contract to recapitalize High Mobility Multipurpose Wheeled Vehicles (HMMWV) for the U.S. Army. The company will utilize its longstanding and proven Public Private Partnership (PPP) program with the Red River Army Depot (RRAD) to deliver mission-capable, like-new M1152 and M1165 HMMWV variants.
"We recognize the value of a modernized vehicle fleet for the U.S. Army and this contract award is a testament to our commitment for continued innovation and vehicle system improvements to ensure mission readiness for our service men and women," said Chris Vanslager, AM General Executive Vice President – U.S. Defense. "The HMMWV platform is incredibly nimble and adaptable; over the life of the program, it has received a multitude of improvements."
The current program will recapitalize existing U.S. National Guard assets. Selected vehicles will be disassembled at RRAD, go through a rigorous initial inspection, and modified in accordance with the recapitalization requirements. The recapitalized vehicle bodies will then ship to AM General's Mishawaka Manufacturing Campus, where they will be mated to a new production rolling chassis. The resulting product is a modernized HMMWV with automotive improvements including substantial increase in overall vehicle reliability, improved steering geometry for maneuverability, and increased-capacity 4L85E transmission, improved front mounted HVAC system, addition of Antilock Braking System and Electronic Stability Control, and an improved powertrain cooling system.
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I love golf as a multifaceted challenge. Not only as a social activity and competition, but it is also great to play with friends and family. I truly enjoy the challenges golf brings as a competition for each of us as competitors, challenging ourselves. The interaction of skills and the focus it takes to compete at different levels. I love the feeling in your stomach when pressure is on, that is not to say I am real good at handling it either. What is cool is your ability to pull off a shot under pressure when your stomach is flipping and your hands are shaking. This is what great players do, they can hit the shot. Not only do I love the skill sets it takes, I also love the humility and integrity that comes along with the game. Everyone can aspire to get better and enjoy the challenge along the way.
My journey through teaching golf started professionally in 1992. Since then I have taught thousands of students, with 25 years of teaching Junior Golf camps of all different skill sets. This includes camps for boys and girls of beginners,intermediate and advanced level skills. I've also hosted groups of Handicapped golfers, Ladies groups, First Tee groups and many more. I've had the fortune to work with many very good players with high skill sets and competitive drive. I am a passionate learner, willing to hear your story and help you accomplish your goals in the great game we all love.


text:
Camille-Mary Sharp
Supervisor: Prof. Irina D. Mihalache
HOME / Faculty & Staff / Faculty & Staff Directory / Camille-Mary Sharp
Email: camillemary.sharp@mail.utoronto.ca
Camille-Mary Sharp is a Ph.D. candidate at the Faculty of Information, University of Toronto. Bridging the fields of museum studies and political economy, her research explores the implications of sponsorship by the petroleum industry for museum practice in Canada. A graduate of the Museum Studies Master's at the Faculty of Information, Camille-Mary studies the work of museum professionals and the ways they navigate and negotiate funding dynamics. She has published her research in the Blackwood Gallery's (UTM) Society for the Diffusion of Useful Knowledge and presented at several conferences in Canada, including the Canadian Communication Association and the Alberta Museums Association. She was a participant of the Museum for Future Fossils, a collaborative summer school between New York University, Western University, and the University of Toronto. She is currently a participant of the Mellon-funded Museums and Public History working group, a joint project between the Jackman Humanities Institute and the University of Western Cape.
Museum studies; political economy of culture and critical philanthropy studies
B.A. (Hon.) History, Glendon College, York University
Master of Museum Studies, Faculty of Information, University of Toronto
Committees or Affliations
Participant, Museums and Public History Quadrant at the Jackman Humanities Institute (https://www.humanities.utoronto.ca/Museums_and_Public_History)
Member, Truth and Reconciliation Student Working Group at the Faculty of Information (TRSWG); Contributor, Coalition of Museums for Climate Justice (https://coalitionofmuseumsforclimatejustice.wordpress.com)


The third edition of the Trust's newsletter is now available for downloading. It includes articles on the Trust's Summer Party, the Bassetlaw Christian Network and a profile of the Trust's new president, David Atkins.
The second edition of the Trust's newsletter is now available for downloading. It includes a fascinating article on the restoration of the Evelyn Gibb's murals at St Martin of Tours, Bilborough, the bells and tower project at Averham and George Olifent – Master Locksmith.
The Nottinghamshire Historic Churches Trust Annual Report for 2014/2015 is now available to download. Click on the link below to download the PDF.
Documents for both churches and riders/striders/welcomers taking part in The Ride+Stride event on Saturday 12th September are now available for downloading from the Ride+Stride page. They include sponsorship forms, welcome and direction signs, a list of participating churches, a visitors' register, guidance etc.
The Nottinghamshire Historic Churches Trust Annual Report for 2013/2014 is now available to download. Click on the link below to download the PDF.
Click on the links below to download the Submission deadline dates for 2015 and general information regarding grant application.
The first edition of the Churches Trusts Forum Newsletter can now be downloaded from this website. It includes a short article by our Secretary, Anthea Moat, on the 'Funding and Faculties' training day held in April.