text:
\subsection{Problem Statement for Perimeter Guarding}
Let $\mathcal W \subset \mathbb R^2$ be a compact (i.e., closed and bounded)
two-dimensional workspace. There are  $m$ pairwise disjoint {\em
regions} $\mathcal R = \{R_1, \ldots, R_m\}$ where each region $R_i \subset \mathcal W$
is homeomorphic to the closed unit disc, i.e., there exists a continuous
bijection $f_i: R_i \to \{(x, y) \mid x^2 + y^2 \le 1\}$ for all $1 \le
i \le m$. For a given region $R_i$, let $\partial R_i$ be its (closed)
boundary (therefore, $f_i$ maps $\partial R_i$ to the unit circle
$\mathbb S^1$). With a slight abuse of notation, define $\partial \mathcal R
= \{\partial R_1, \ldots, \partial R_m\}$. For each $\mathcal R_i$, $P_i \subset
\partial R_i$ is called the {\em perimeter} of $R_i$ which is either a
single closed curve or formed by a finite number of possibly curved line
segments. In this paper, we assume a perimeter is given as a single p-chain (possibly
a polygon) or multiple disjoint p-chains. Let $\mathcal P = \{P_1, \ldots, P_m\}$,
which must be {\em guarded}. More formally, each $P_i$ is
homeomorphic to a compact subset of the unit circle. For
a given $P_i$, each of its maximal connected component (a p-chain) is
called a {\em perimeter segment} or {\em segment}, whereas each
maximal connected component of $\partial R_i \backslash P_i$ is called a
{\em perimeter gap} or {\em gap}. An example is illustrated in
Fig.~\ref{fig:example-boundaries} with two regions.

\begin{figure}[ht]
\iffull {} \else \vspace*{-1mm} \fi
\begin{center}
\begin{overpic}[width={\iffull 3.5in \else 3in \fi},tics=5]
{./figures/example-boundaries-eps-converted-to.pdf}
\put(26,20){{\small $R_1$}}
\put(20,39){{\small \textcolor{red}{$P_1$}}}
\put(66,28){{\small $R_2$}}
\put(54,40){{\small \textcolor{green}{$P_2$}}}
\put(82,44){{\small $\mathcal W$}}
\end{overpic}
\end{center}
\iffull {} \else \vspace*{-4mm} \fi
\caption{\label{fig:example-boundaries} An example of a workspace $\mathcal W$
with two regions $\{R_1, R_2\}$. Due to three {\em gaps} on $\partial R_1$,
marked as dotted lines within long rectangles, $P_1 \subset \partial R_1$
has three {\em segments} (or maximal connected components); $P_2 = \partial
R_2$ has a single segment with no gap.}
\iffull {} \else \vspace*{-3mm} \fi
\end{figure}

There are $n$ indistinguishable point robots residing in $\mathcal W$.
These robots are to be deployed to {\em cover} the perimeters $\mathcal P$ such
that each robot $1 \le j \le n$ is assigned a continuous closed subset
$C_j$ of some $\partial R_i, 1 \le i \le m$. All of $\mathcal P$ must be
{\em covered} by $\mathcal C = \{C_1, \ldots, C_n\}$, i.e.,
$\bigcup_{P_i \in \mathcal P} P_i  \subset \bigcup_{C_j \in \mathcal C} C_j$,
which implies that elements of $\mathcal C$ need not intersect on their
interiors. Hence, it is assumed that any two elements of $\mathcal C$ may share
at most their endpoints. Such a $\mathcal C$ is called a {\em cover} of $\mathcal P$.

Given a cover $\mathcal C$, for a $C_j \in \mathcal C$, $1 \le j \le n$, let $len(C_j)$
denote its length (more formally, measure). It is desirable to minimize
the maximum $len(C_j)$, i.e., the goal is to find a cover $\mathcal C$ such that
the value
$\max_{C_j \in \mathcal C} len(C_j)$
is minimized. This corresponds to minimizing the maximum workload for
each robot or agent. The formal definition of the Optimal Perimeter
Guarding ({\sc {OPG}}\xspace) problem is provided as follows.

\begin{problem}[Optimal Perimeter Guarding ({\sc {OPG}}\xspace)] Given the perimeter
$\mathcal P = \{P_1, \ldots, P_m\}$ of a set of 2D regions $\mathcal R =\{R_1, \ldots,
R_m\}$, find a set of $n$ polygonal chains $\mathcal C^* = \{C_1^*,
\ldots, C_n^*\}$ such that $\mathcal C^*$ covers $\mathcal P$, i.e.,
\begin{align}\label{eq:coverage}
\bigcup_{P_i \in \mathcal P} P_i  \subset \bigcup_{C_j^* \in \mathcal C^*} C_j^*,
\end{align}
with the maximum of $len(C_j^*), 1 \le j \le n$ minimized, i.e., among all
covers $\mathcal C$ satisfying~\eqref{eq:coverage},
\begin{align}\label{eq:objective}
\mathcal C^* = \underset{\mathcal C}{\mathrm{argmin}} \max_{C_j \in \mathcal C} len(C_j).
\end{align}
\end{problem}

Here, we introduce the technical assumption that the ratio between
the length of $\partial \mathcal R$ and the length of $\partial \mathcal P$ is polynomial
in the input parameters. That is, the length of $\partial \mathcal R$ is not much
larger than the length of $\partial \mathcal P$ .
The assumption makes intuitive sense as any
gap should not be much larger than the perimeter in practice. We note
that the assumption is not strictly necessary but helps simplify the
correctness proof of some algorithms.

Henceforth, in general, $\mathcal C^*$ is used when an optimal cover is meant
whereas $\mathcal C$ is used when a cover is meant. We further define the optimal
single robot coverage length as
\begin{align}\label{eq:l-star}
\iffull {} \else \vspace*{-1mm} \fi
\ell^* = \min_{\mathcal C} \max_{C_j \in \mathcal C} len(C_j).
\iffull {} \else \vspace*{-1mm} \fi
\end{align}

Fig.~\ref{fig:example} shows an example of an optimal cover by $8$ robots
of a perimeter with three components. Note that one of the three gaps
(the one on the top area as part of the hexagon) is fully covered
by a robot, which leads to a smaller $\ell^*$ as compared to other
feasible solutions. This interesting phenomenon, which is
actually a main source of the difficulty in solving {\sc {OPG}}\xspace, is explored
more formally in Section~\ref{section:analysis}
(Proposition~\ref{p:max-no-exclusion}).

Given the {\sc {OPG}}\xspace formulation, additional details on $\partial \mathcal R$ must
be specified to allow the precise characterization of the computational
complexity (of any algorithm developed for {\sc {OPG}}\xspace). For this purpose, it
is assumed that each $\partial R_i \in \partial \mathcal R$, $1 \le i \le m$,
is a simple (i.e., non-intersecting and without holes) polygon with an
input complexity $O(M_i)$, i.e., $\partial R_i$ has about $M_i$ vertices
or edges. If an {\sc {OPG}}\xspace has a single region $R$, then let $\partial R$ have
an input complexity of $M$. Note that the algorithms developed in this
work apply to curved boundaries equally well, provided that the curves
have similar input complexity and are given in a format that allow the
computation of their lengths with the same complexity.
Alternatively, curved boundaries may be approximated to arbitrary
precision with polygons.

For deploying a robot to guard a $C_j$, one natural choice is to send the
robot to a target location $t_j \in C_j$ such that $t_j$ is the centroid of $C_j$.
Since $C_j$ is one dimensional, $t_j$ is the center (or midpoint) of $C_j$.
After solving an {\sc {OPG}}\xspace, there is the remaining problem of assigning the $n$
robots to the centers of $\mathcal C^* = \{C_j^*\}$ and actually moving the robots
to these assigned locations. As a secondary objective, it may also be
desirable to provide guarantees on the execution time required for
deploying the robots to reach target guarding locations. We note that,
the task assignment (after determining target locations) and motion
planning component for handling robot deployment, essential for applications
but not a key part of this work's contribution, is briefly addressed in
Section~\ref{section:evaluation}.
\jy{Here we are doing sequential optimization and can provide some
guarantees. Can we do concurrent optimization here? It seems possible but
also hard. We might be able to show that the two objectives cannot be
simultaneously satisfied.}

With some $\mathcal C^*$ satisfying~\eqref{eq:coverage}
and~\eqref{eq:objective}, we may further require that $len(C_j^*)$ is
minimized for all $C_j^* \in \mathcal C^*$. This means that a gap $G \subset
((\bigcup \partial R_i)\backslash (\bigcup P_i))$ will never be partially
covered by some $C_j^* \in \mathcal C^*$.
In the example from
Fig.~\ref{fig:example-boundaries}, $G$ may be one of the gaps on
$\partial R_1$; clearly, it is not beneficial to have some
$C_j^*$ partially cover (i.e., intersect the interior of) one of these.
This rather useful condition (note that this is not an assumption but
a solution property) yields the following lemma.

\begin{lemma}\label{l:no-partial-coverage}
For a set of perimeters $\mathcal P = \{P_1,\ldots, P_m\}$ where $P_i \subset
\partial R_i$ for $1 \le i \le m$, there exists an optimal cover $\mathcal C^*
= \{C_1^*, \ldots, C_n^*\}$ such that, for any gap (or maximal connected
component) $G \subset ((\bigcup \partial R_i)\backslash (\bigcup P_i))$
and any $C_j^* \in \mathcal C^*$, $C_j^* \cap G = G$ or $C_j^* \cap G =
\varnothing$.
\end{lemma}

\begin{remark} Our definition of coverage is but one of the possible
models of coverage. The definition restricts a robot deployed to
$C_j, 1 \le j \le n$, to essentially {\em live} on $C_j$. The definition
models scenarios where a guarding robot must travel along $C_j$, which
is one-dimensional. Nevertheless, the algorithms developed for {\sc {OPG}}\xspace have
broader applications. For example, subroutines in our algorithms readily
solve the problem of finding the minimum number of guards needed if each
guard has a predetermined maximum coverage.
\end{remark}

\subsection{Guarding a Single Region}
\noindent\textbf{Perimeter with a single connected component}. For
guarding a single region $\mathcal R = \{R\}$, i.e., there is a single
boundary $\partial R$ to be guarded, all $n$ robots can be directly
allocated to $\partial R$. If the single perimeter $P \subset
\partial R$ further has a single connected component that is either
homeomorphic to $\mathbb S^1$ or $[0, 1]$, then each robot $j$ can
be assigned a piece $C_j \subset P$ such that $\bigcup_{C_j \in \mathcal C}
C_j = P$ and $len(C_j) = len(P)/n$. Clearly, such a cover $\mathcal C$ is
also an optimal cover.

\noindent\textbf{Perimeter with multiple maximal connected components}.
When there are multiple maximal connected components (or segments) in a
single perimeter $P$, things become more complex. To facilitate the
discussion, assume here $P$ has $q$ segments $S_1, \ldots, S_q$ arranged
in the clockwise direction (i.e., $P = S_1 \cup \ldots \cup S_q$),
which leaves $q$ gaps $G_1, \ldots, G_q$ with $G_k$ immediately following
$S_k$. Fig.~\ref{fig:single-perimeter} shows a perimeter with five segments
and five gaps.
\begin{figure}[ht]
\iffull {} \else \vspace*{-1mm} \fi
\begin{center}
\begin{overpic}[width={\iffull 3in \else 2.6in \fi},tics=5]
{./figures/single-perimeter-eps-converted-to.pdf}
\put(16,7){{\small $S_1$}}
\put(17,31){{\small $G_1$}}
\put(46,30){{\small $S_2$}}
\put(56.5,28){{\small $G_2$}}
\put(72,27.5){{\small $S_3$}}
\put(84.5,17.5){{\small $G_3$}}
\put(85,6){{\small $S_4$}}
\put(72,-4){{\small $G_4$}}
\put(59,0){{\small $S_5$}}
\put(45,4){{\small $G_5$}}
\end{overpic}
\end{center}
\iffull {} \else \vspace*{-1mm} \fi
\caption{\label{fig:single-perimeter} A perimeter with five segments
$S_1, \ldots, S_5$ and five {\em gaps} $G_1, \ldots, G_5$.}
\iffull {} \else \vspace*{-3mm} \fi
\end{figure}

Suppose an optimal set of assignments for the $n$ robots guarding $P$
and  satisfying~\eqref{eq:coverage} and~\eqref{eq:objective} is $\mathcal C^*
= \{C_j^*\}$. Let $G_{max}$ be a largest gap, i.e., $len(G_{max}) =
\max_{1 \le k \le q}len(G_k)$. Via small perturbations to the lengths
of $G_k$, we may also assume that $G_{max}$ is unique. On one hand,
it must hold that $len(C_j^*) \le (len(\partial R) - len(G_{max}))/n$,
as a solution where $n$ robots evenly cover all of $\partial R$ with
the gap $G_{max}$ excluded, satisfies the condition. On the other hand,
$len(C_j^*) \ge (\sum_{1\le k\le q}len(S_k))/n$ always holds because
the coverage condition requires $\sum_j C_j^* \ge \sum_{1\le k\le q}len(S_k)$.
These yield a pair of basic upper and lower bounds for the optimal single
robot coverage length $\ell^*$, summarized as follows.
\jy{We may address the issue of solution stability with respect to
perturbation (later).}

\begin{proposition}\label{p:single-bounds} Define
\[
\ell_{min} = \frac{\sum_{1\le k\le q}len(S_k)}{n}\,\,and\,\,
\ell_{max} = \frac{len(\partial R) -  len(G_{max})}{n},
\]
it holds that
\begin{align}\label{eq:lopt}
\ell_{min} \le \ell^* \le \ell_{max}.
\end{align}
\end{proposition}

Though some gap, if there at least one, must be skipped by the optimal
solution, it is not always the case that a largest gap $G_{max}$,
even if unique, will be skipped by $\bigcup_{C_j \in \mathcal C^*} C_j^*$.
That is, an optimal cover $C^*$ may enclose the largest gap.

\begin{proposition}\label{p:max-no-exclusion}
Given a region $R$ and perimeter $P \subset \partial R$, let
$G_{max}$ be the unique longest connected component of $\partial R
\backslash P$. Let $\mathcal C^*$ be an optimal cover of $P$. Then, there
exist {\sc {OPG}}\xspace instances in which $G_{max} \subset C_j^*$ for some $C_j^*
\in \mathcal C^*$.
\end{proposition}
\begin{proof} The claim may be proved via contradiction with the example
illustrated  in Fig.~\ref{fig:max-not-skipped} which readily generalizes.
In the figure, there are four gaps $G_1, \ldots, G_4$, in which three
gaps ($G_1$, $G_2$, and $G_4$) have the same length (i.e., $len(G_1)=
len(G_2)= len(G_4)$) and are evenly spaced (i.e., $len(S_1)= len(S_2)
= len(S_3\cup G_3\cup S_4)$). Here, $G_{max} = G_3$, which is
$1.5$ times the length of other gaps, i.e., $len(G_3) =
\frac{3}{2}len(G_1)$.
\begin{figure}[ht]
\iffull \vspace*{2mm} \else \vspace*{0mm} \fi
\begin{center}
\begin{overpic}[width={\iffull 3in \else 2.6in \fi},tics=5]
{./figures/max-not-skipped-eps-converted-to.pdf}
\put(27,34){{\small $S_1$}}
\put(48,44){{\small $G_1$}}
\put(69,34){{\small $S_2$}}
\put(69,9){{\small $G_2$}}
\put(62,1){{\small $S_3$}}
\put(48,-4){{\small $G_3$}}
\put(32,2){{\small $S_4$}}
\put(26,8){{\small $G_4$}}
\end{overpic}
\end{center}
\iffull {} \else \vspace*{-3mm} \fi
\caption{\label{fig:max-not-skipped} A case where the perimeter has
four segments or maximal connected components. Three of the gaps,
$G_1$, $G_2$, and $G_4$ are of the same length and are evenly spaced,
$G_3$ is $0.5$ times longer.}
\iffull {} \else \vspace*{-3mm} \fi
\end{figure}

For $n = 3$ robots, the optimal cover $\mathcal C^*$ must allocate each robot
to guard each of $S_1$, $S_2$, and $(S_3\cup G_3\cup S_4)$. Without
loss of generality, let $C_1^* = S_1$, $C_2^* = S_2$, and $C_3^* =
(S_3\cup G_3\cup S_4)$. This means that $G_3$ is covered by $C_3^*$
and not skipped by $\mathcal C^*$. In this case, $len(C_1^*) =len(C_2^*) =
len(C_3^*) = len (S_1)$.

To see that this must be the case, suppose on the contrary that $G_3$
is skipped and let $\mathcal C = \{C_1, C_2, C_3\}$ be an alternative cover.
By Lemma~\ref{l:no-partial-coverage}, an optimal cover must skip $G_3$
entirely. In this case, some $C_j$, say $C_1$, must have its left
endpoint\footnote{In this paper, for a non-circular segment or gap, its
left endpoint is defined as the {\em limit point} along the
counterclockwise direction along the perimeter and its right endpoint
is defined as the limit point in the clockwise direction along the
perimeter. So, in Fig.~\ref{fig:max-not-skipped}, for $S_1$, its left
endpoint touches $G_4$ and its right endpoint touches $G_1$.} coincide
with the right endpoint of of $G_3$ (the point where $G_3$ meets $S_4$).
Then $C_1$ must cover $S_4$ and $G_4$; otherwise, $C_2$ and $C_3$ must
cover $S_1 \cup S_2 \cup S_3$, which makes $len(C_2) + len(C_3) \ge
len(S_1 \cup S_2 \cup S_3) > 2len(S_1)$ and $\mathcal C$ a worse cover than
$\mathcal C^*$. By symmetry, similarly, some $C_j$, say $C_3$, must have its
right endpoint coincide with the left endpoint of $G_3$ and cover
$S_3$ and $G_2$. However, this means that both $G_2$ and $G_4$ are
covered by $\mathcal C$. Even if $G_1$ is skipped, this makes $len(C_1 \cup
C_2 \cup C_3) = len(S_4 \cup G_4 \cup S_1 \cup S_2 \cup G_2 \cup S_3)
> len (S_1 \cup S_2 \cup S_3\cup G_3\cup S_4) = 3len(S_1)$, again making
$\mathcal C$ sub-optimal. By the pigeonhole principle, at least one of the $C_1$,
$C_2$, or $C_3$ must be longer than $len(S_1)$. Therefore, skipping
$G_{max} = G_3$ in this case leads to a sub-optimal cover. The
optimal cover with $n = 3$ is to have $C^* = \{S_1, S_2,
(S_3\cup G_3\cup S_4)\}$.
\end{proof}

Proposition~\ref{p:max-no-exclusion} implies that in allocating robots
to guard a perimeter $P \subset \partial R$, an algorithm cannot simply
start by excluding the longest component from $\partial R
\backslash P$ and then the next largest, and so on. This makes solving
{\sc {OPG}}\xspace more challenging. Referring back to Fig.~\ref{fig:example}, if the
top gap is skipped by the cover, then the three robots on the right side
of the perimeter (two orange and one green) need to cover the part of the
perimeter between the two hexagons. This will cause $\ell^*$ to increase.

On the other hand, for an optimal cover $\mathcal C^* = \{C_1^*, \ldots, C_n^*\}$
of $P$, some $C_j^*\in \mathcal C^*$ must have at least one of its endpoint
aligned with an endpoint of a component $S_k$ of $P$ (assuming that $P
\subsetneq \partial R$).

\begin{proposition}\label{p:endpoint-alignment}
For an optimal cover $\mathcal C^* = \{C_1^*,\ldots, C_n^*\}$ of a perimeter
$P = S_1 \cup \ldots \cup S_q \subset \partial R = S_1 \cup G_1
\cup $ $\ldots \cup S_q \cup G_q$, for some $S_i \subset P$ and
$C_j^* \in C^*$, their right (or left) endpoints must coincide.
\end{proposition}
\begin{proof}
By Lemma~\ref{l:no-partial-coverage}, for any $G_k \subset \partial R
\backslash P$, and $C_j^* \in \mathcal C^*$, $G_k \cap C_j^* = G_k$ or
$G_k \cap C_j^* = \varnothing$. Since at least one $G_k$, $1 \le k \le q$,
must be skipped by $C_1^* \cup \ldots C_n^*$, some $C_j^*$, $1 \le j \le n$
must have its right endpoint aligned with the right endpoint of $S_k$,
which is on the left of $G_k$. Following the same argument, some
$C_{j'}^*$ and $S_{k'}$ must have the same left endpoints.
\end{proof}

Proposition~\ref{p:endpoint-alignment} suggests that we may attempt to cover
a perimeter $P$ starting from an endpoint of $S_1$, $S_2$, and so on.
Indeed, as we will show in Section~\ref{section:algorithm}, an efficient
algorithm can be designed exploiting this important fact.
\jy{There is something interesting here: it seems that the algorithm not only
finds a solution satisfying~\eqref{eq:objective}, but also ensures a local
optimal solution that minimizes the max coverage for all other robots that
do not cover $\ell^*$. This may be interesting to discuss further.}

\subsection{Guarding Multiple Regions}
In a multiple region setup, there is one additional level of complexity:
the number of robots that will be assigned to an individual region is
no longer fixed. This introduces another set of variables $n_1, \ldots,
n_m$ with $n_1 + \ldots + n_m = n$, and $n_i$, $1 \le i \le m$ being the
number of robots allocated to guard $\partial R_i$. For a fixed $n_i$,
the results derived for a single region, i.e.,
Propositions~\ref{p:single-bounds}--\ref{p:endpoint-alignment} continue
to hold.

\subsection{Perimeters Containing Single Components}
\input{04-01-single-comp.tex}

\subsection{Single Perimeter Containing Multiple Components}
\input{04-02-single-perimeter-multi-comp.tex}

\vspace*{-2mm}
\subsection{Multiple Perimeters Containing Multiple Components}
\vspace*{-1mm}
\input{04-03-multi-perimeter-multi-comp.tex}

\subsubsection{{\sc MultiRegionSingleComp}\xspace}
For the case of $m$ perimeters each containing a single segment, for
each $1 \le i \le m$, we set $len(\partial R_i) = 1$ and let $len(P_i)$
be uniformly distributed in $(0, 1]$. Fig.~\ref{fig:mpsc-example} shows
the result for an example with $m = 10$ and $n = 30$. For various values
of $m, n$, the running time of {\sc MultiRegionSingleComp}\xspace is summarized in
Table~\ref{eval:mpsc}, which scales very well with $m$ and $n$ (note that
the $n \le m$ case does not make much sense here).

\begin{figure}[ht!]
    \iffull {} \else \vspace*{-4mm} \fi
    \centering
		\iffull
		\includegraphics[keepaspectratio, scale=0.4]{./figures/mpsc-example-eps-converted-to.pdf}
		\else
    \includegraphics[keepaspectratio, scale=0.32]{./figures/mpsc-example-eps-converted-to.pdf}
		\fi
    \iffull {} \else \vspace*{-6mm} \fi
    \caption{\label{fig:mpsc-example}
    An example problem instance when $m = 10$ and $n = 30$. The black dots
		indicate deployed robot locations; the green and orange p-chains indicate
		the coverage.

		}
    \iffull {} \else \vspace*{-2mm} \fi
\end{figure}

\iffull
\begin{table}[ht!]
    \centering
    \begin{footnotesize}
    \begin{tabular}{|c|c|c|c|c|c|c|}
        \hline
        \diagbox{$m$}{$n$}       & $10^8  $ & $10^9   $ & $10^{10}$ & $10^{11}$ & $10^{12}  $ \\ \hline
        \rule{0pt}{2.5ex} $10^3$ & $0.001 $ & $0.001  $ & $0.001  $ & $0.001  $ & $0.001    $ \\ \hline
        \rule{0pt}{2.5ex} $10^4$ & $0.006 $ & $0.007  $ & $0.008  $ & $0.008  $ & $0.008    $ \\ \hline
        \rule{0pt}{2.5ex} $10^5$ & $0.075 $ & $0.088  $ & $0.102  $ & $0.107  $ & $0.106    $ \\ \hline
        \rule{0pt}{2.5ex} $10^6$ & $1.152 $ & $1.442  $ & $1.508  $ & $1.652  $ & $1.617    $ \\ \hline
        \rule{0pt}{2.5ex} $10^7$ & $13.963$ & $17.281 $ & $18.796 $ & $20.354 $ & $20.627   $ \\ \hline
        \rule{0pt}{2.5ex} $10^8$ & NA       & $176.115$ & $223.186$ & $227.250$ & $230.000  $ \\ \hline
    \end{tabular}
		\end{footnotesize}
    \caption{\label{eval:mpsc} {\sc MultiRegionSingleComp}\xspace~running time (seconds)}
\end{table}

To empirically verify the asymptotic running time upper bounds of
{\sc MultiRegionSingleComp}\xspace, we plot the running time over $m$ for a fixed value of
$n =10^{12}$. From the result (Fig.~\ref{fig:mpsc:mfixn}) it may be
observed that the asymptotic running time appears to be tight. We point
out that the $O(\sum_{1\le i \le m} M_i + n)$ part of the overall
running time $O(m(\log n + \log m) + \sum_{1\le i \le m} M_i + n)$ turns
out to be rather insignificant (at least up to $m = 10^8$ and $n = 10^{12}$)
and is subsequently ignored. The same applies to other algorithms as
well.
\begin{figure}[ht!]
    \vspace*{-2mm}
    \centering
    \includegraphics[keepaspectratio, scale=0.85]{./figures/mpscn12-eps-converted-to.pdf}
    \vspace*{-4mm}
    \caption{\label{fig:mpsc:mfixn}Running time: {\sc MultiRegionSingleComp}\xspace
		v.s. $O(m (\log m + \log 10^{12}))$.}
    \vspace*{-3mm}
\end{figure}

A similar study of checking the running time dependency over $n$ was
carried out as well but did not show a tight dependency of the running
time over $\log n$. This is because the $O(m\log n)$ part (from the
$\mathbf{while}$ loop in {\sc MultiRegionSingleComp}\xspace) is dominated by the
$O(m\log m)$ part (from the enhanced $\mathbf{while}$ loop with bisection).
\else
\begin{table}[ht!]
    \centering
		\vspace*{-4mm}
    \begin{footnotesize}
    \begin{tabular}{|c|c|c|c|c|c|c|}
        \hline
        \diagbox{$m$}{$n$}       & $10^8  $ & $10^9   $ & $10^{10}$ & $10^{11}$ & $10^{12}  $ \\ \hline

        \rule{0pt}{2.5ex} $10^6$ & $1.152 $ & $1.442  $ & $1.508  $ & $1.652  $ & $1.617    $ \\ \hline
        \rule{0pt}{2.5ex} $10^7$ & $13.963$ & $17.281 $ & $18.796 $ & $20.354 $ & $20.627   $ \\ \hline
        \rule{0pt}{2.5ex} $10^8$ & NA       & $176.115$ & $223.186$ & $227.250$ & $230.000  $ \\ \hline
    \end{tabular}
		\end{footnotesize}
		\vspace*{-3mm}
    \caption{\label{eval:mpsc} {\sc MultiRegionSingleComp}\xspace~running time (seconds)}
		\vspace*{-4mm}
\end{table}
\fi

For the case of a single perimeter with multiple components, a random
polygon is generated on which $2q$ points are randomly sampled that
yield $q$ segments (that form the perimeter) and $q$ gaps.
\iffull
Some example instances and the optimal solutions are illustrated in
Fig.~\ref{fig:more-spmc-ex}.
\else
An example instance and the optimal solution with $q=3$ and $n = 10$ is
illustrated in Fig.~\ref{fig:spmc-example}.
\fi
The computation time for various $q$ and
$n$ combinations is given in Table~\ref{eval:spmc}.
\iffull
\begin{figure}[ht!]

    \centering
		\includegraphics[keepaspectratio, scale=0.4]{./figures/spmc-example-eps-converted-to.pdf}
    \includegraphics[keepaspectratio, scale=0.4]{./figures/spmc-solution-eps-converted-to.pdf}
    \vspace*{2mm} \\
    \includegraphics[keepaspectratio, scale=0.4]{./figures/spmc-example-2-5-eps-converted-to.pdf}
    \includegraphics[keepaspectratio, scale=0.4]{./figures/spmc-solution-2-5-eps-converted-to.pdf}
    \vspace*{2mm} \\
    \includegraphics[keepaspectratio, scale=0.4]{./figures/spmc-example-4-10-eps-converted-to.pdf}
    \includegraphics[keepaspectratio, scale=0.4]{./figures/spmc-solution-4-10-eps-converted-to.pdf} \\

    \vspace*{2mm}
    \includegraphics[keepaspectratio, scale=0.4]{./figures/spmc-example-5-15-eps-converted-to.pdf}
    \hspace{5mm}
    \includegraphics[keepaspectratio, scale=0.4]{./figures/spmc-solution-5-15-eps-converted-to.pdf}
    \caption{\label{fig:more-spmc-ex} Four examples for the case of single
		region with multiple components. Problem parameters
		are as follows: first row, $q = 3$, $n = 10$; second row, $q = 2$,
		$n = 5$; third row, $q = 4$, $n = 10$; fourth row, $q = 5$, $n = 15$.}
\end{figure}
\else
\begin{figure}[ht!]

    \centering
    \includegraphics[keepaspectratio, scale=0.4]{./figures/spmc-example-eps-converted-to.pdf}
    \includegraphics[keepaspectratio, scale=0.4]{./figures/spmc-solution-eps-converted-to.pdf}
    \vspace*{-3mm}
    \caption{\label{fig:spmc-example}
    An example problem instance when $q = 3$ and $n = 10$. In this case, the
		optimal cover actually covers one gap.}
    \vspace*{-1mm}
\end{figure}
\fi

\begin{table}[ht!]
    \iffull {} \else \vspace*{-1mm} \fi
    \footnotesize
    \centering
    \begin{tabular}{|c|c|c|c|c|c|c|}
        \hline
        \diagbox{$q$}{$n$}       & $10^1   $ & $10^2   $ & $10^3  $  & $10^4   $ & $10^5$   \\ \hline
        \rule{0pt}{2.5ex} $10^2$ & $0.013  $ & $0.015  $ & $0.016 $  & $0.016  $ & $0.017$  \\ \hline
        \rule{0pt}{2.5ex} $10^3$ & $1.363  $ & $1.595  $ & $1.622 $  & $1.634  $ & $1.641$  \\ \hline
        \rule{0pt}{2.5ex} $10^4$ & $159.404$ & $188.497$ & $210.492$ & $212.473$ & $212.780$\\ \hline
    \end{tabular}
    \iffull {} \else \vspace*{-1mm} \fi
    \caption{\label{eval:spmc} {\sc SingleRegionMultiComp}\xspace~computation time (seconds)}

\end{table}

\iffull
For {\sc SingleRegionMultiComp}\xspace, the dependency of the running time over $q^2\log q$
appears to be tight (see Fig.~\ref{fig:spmc:qfixn}).
\begin{figure}[ht!]
    \centering
    \includegraphics[keepaspectratio, scale=0.85]{./figures/spmcn5-eps-converted-to.pdf}
    \vspace*{-4mm}
    \caption{\label{fig:spmc:qfixn}Running time of {\sc SingleRegionMultiComp}\xspace
		v.s. $O(q^2\log(q + 10^3))$.}
    \vspace*{-2mm}
\end{figure}
\else
\fi

For multiple perimeters containing multiple components, $m$ polygons
are created with $len(\partial R_i)$ randomly distributed in $[1, 10]$.
For setting $q_i$, we fix a $q$ and let $q_i = q(0.5 + random(0, 1))$.
Representative computation results of {\sc MultiRegionMultiComp}\xspace are listed in
Table~\ref{eval:mpmc}.
\iffull
\begin{table}[ht!]
    \footnotesize
    \centering
    \begin{tabular}{|c|c|c|c|c|c|c|}
        \hline
        \multirow{2}{*}{$q$} & \multirow{2}{*}{$n$} & \multicolumn{5}{|c|}{$m$} \\ \cline{3-7}
        \rule{0pt}{2.5ex} & & $10$ & $20$ & $30$ & $40$ & $50$ \\ \hline
        \rule{0pt}{2.5ex} $10^1$ & $10^2$ & $ 0.015$ & $ 0.027$ & $ 0.039$ & $ 0.045$ & $ 0.054$ \\ \hline
        \rule{0pt}{2.5ex} $10^1$ & $10^3$ & $ 0.047$ & $ 0.063$ & $ 0.076$ & $ 0.091$ & $ 0.108$ \\ \hline
        \rule{0pt}{2.5ex} $10^2$ & $10^2$ & $ 1.492$ & $ 2.784$ & $ 4.168$ & $ 5.404$ & $ 6.444$ \\ \hline
        \rule{0pt}{2.5ex} $10^2$ & $10^3$ & $ 2.191$ & $ 3.771$ & $ 5.523$ & $ 7.707$ & $ 9.369$ \\ \hline
        \rule{0pt}{2.5ex} $10^2$ & $10^4$ & $ 7.105$ & $ 9.619$ & $11.369$ & $12.760$ & $15.107$ \\ \hline
    \end{tabular}
    \caption{\label{eval:mpmc} {\sc MultiRegionMultiComp}\xspace~computation time (seconds)}
\end{table}
\else
\begin{table}[ht!]
    \vspace*{-2mm}
    \footnotesize
    \centering
    \begin{tabular}{|c|c|c|c|c|c|c|}
        \hline
        \multirow{2}{*}{$q$} & \multirow{2}{*}{$n$} & \multicolumn{5}{|c|}{$m$} \\ \cline{3-7}
        \rule{0pt}{2.5ex} & & $10$ & $20$ & $30$ & $40$ & $50$ \\ \hline

        \rule{0pt}{2.5ex} $10^1$ & $10^3$ & $ 0.047$ & $ 0.063$ & $ 0.076$ & $ 0.091$ & $ 0.108$ \\ \hline

        \rule{0pt}{2.5ex} $10^2$ & $10^3$ & $ 2.191$ & $ 3.771$ & $ 5.523$ & $ 7.707$ & $ 9.369$ \\ \hline
        \rule{0pt}{2.5ex} $10^2$ & $10^4$ & $ 7.105$ & $ 9.619$ & $11.369$ & $12.760$ & $15.107$ \\ \hline
    \end{tabular}
    \vspace*{-2mm}
    \caption{\label{eval:mpmc} {\sc MultiRegionMultiComp}\xspace~computation time (seconds)}
    \vspace*{-3mm}
\end{table}
\fi

\iffull
As for running time, Fig.~\ref{fig:mpmc:m} shows
the dependency on the number of regions $m$ appears to be linear with
$q$ fixed (recall we set $q_i = q(0.5 + random(0,1))$). This is tight
in viewing the main running time of {\sc MultiRegionMultiComp}\xspace which is
$O((\sum_{1\le i \le m} q_i^2) \log(n + \sum_{1\le i \le m} q_i))$; if
$q_i$ is fixed, then the time is linear with respect to $m$. An example
computation result for $m = 3$ is illustrated in Fig.~\ref{fig:mpmc-ex}.

\begin{figure}[ht!]
    \centering
    \includegraphics[keepaspectratio, scale=0.85]{./figures/mpmc_final-eps-converted-to.pdf}
    \caption{\label{fig:mpmc:m}Running time of {\sc MultiRegionMultiComp}\xspace
		v.s. the number of regions.}
\end{figure}

\begin{figure}[ht!]

    \centering
    \includegraphics[keepaspectratio, scale=0.25]{./figures/mpmc-example-eps-converted-to.pdf}
    \includegraphics[keepaspectratio, scale=0.25]{./figures/mpmc-solution-eps-converted-to.pdf}
    \caption{\label{fig:mpmc-ex} An example instance when $m = 3$, $n = 10$.}
\end{figure}
\else
Due to limited space, only selected essential performance data is
presented here. More complete performance data and associate analysis
can be found \cite{FenHanGaoYuRSS19EXT}.
\fi

\subsection{Algorithm Performance}
\vspace*{-1mm}
\input{05-01-performance.tex}
\subsection{Two Applications Scenarios}
\input{05-02-applications.tex}

\section{Introduction}\label{section:introduction}
\input{01-introduction.tex}

\section{The Optimal Perimeter Guarding Problem}\label{section:problem}
\input{02-problem-statement.tex}

\section{Structural Analysis}\label{section:analysis}
\input{03-structure-analysis.tex}

\section{Efficient Algorithms for Perimeter Guarding}\label{section:algorithm}
\input{04-algorithm.tex}

\section{Performance Evaluation and Applications}\label{section:evaluation}
\input{05-evaluation.tex}

\section{Conclusion and Discussion}\label{section:conclusion}
\input{06-conclusion.tex}

\textbf{Acknowledgments}.
This work is supported by NSF grants IIS-1617744, IIS-1734419, and IIS-1845888.
Opinions or findings expressed in this paper do not necessarily reflect
the views of the sponsors.
\iffull
\else
The authors would like to thank the anonymous RSS reviewers for their
constructive comments.
\fi

\bibliographystyle{IEEEtran}

redpajama_set_name: RedPajamaArXiv


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… Under the existing Grampians National Park Management Plan, rock climbing in Special Protection Areas is a prohibited activity however we recognise this plan is 10 years old and we need to review these areas in partnership with key stakeholders which may result in changes to boundaries. Further to the Special Protection Areas identified in the current management plan, 29 additional areas have also been set aside as Special Protection Areas, in which climbing is prohibited to protect their cultural and natural values. The materials being prepared will also have details of these places.
Grampians – Special Protection Areas – detailed in appendix 1 and figure 2.


text:
US to Pay Large Sums For Helping Jordan Make Peace With Israel
By Amy Kaslow Staff writer of The Christian Science Monitor
HAVING entered into a nonbelligerency pact with Israel last week, Jordan now expects to win financial favors from the United States.
A Jordanian official who accompanied King Hussein to Washington for the July 25 signing ceremony with Israel's Prime Minister Yitzhak Rabin, is unabashed in his contention that the US owes Jordan for coming to the peace table.
``Jordanians must feel that the US has given them something in return,'' says Jawad Al-Anani, Jordan's minister of state for prime ministerial affairs and minister of information. ``Historically, everybody has gotten something for peace,'' he says, referring to Washington's multibillion dollar aid to Egypt after it signed the Camp David accords with Israel 16 years ago.
Just after King Hussein delivered what many called a stunning address to a special joint session of Congress last week, US legislators voted to approve a package of assistance for Jordan, including debt relief and military aid.
While no dollar figure was attached to the military aid, Jordan will get free weapons and free spare parts. But, despite its standing request, Jordan will not be able to get F-16 fighter jets ``until such time as Jordan and Israel conclude a peace agreement,'' according to a document accompanying the bill.
Discounting Jordan's debt, Congress appropriated $100 million in order to relieve Jordan of $193 million it owed to the US government. This is the first of three stages in debt forgiveness planned over the next several years. But lawmakers in effect conditioned the next two stages on ``substantial further steps,'' including progress on a final peace with Israel, ending participation in the Arab boycott, and compliance with the United Nations-imposed embargo against Iraq.
Animosity toward Amman
``The restrictions on aid to Jordan were included at the specific request of members who still feel great animosity toward the kingdom because of what they perceive as Jordan's pro-Iraq stance during the Gulf war,'' says John Lawrence, who has represented Jordan as vice president of the Washington International Group.
But Mr. Al-Anani warns that if Jordan's economic situation does not improve ``sufficiently,'' there will be only marginal support for peace with Israel. Jordan, he contends, needs ``the US catalytic role to ensure that Jordan can ... take those steps for the peace process.''
Securing Jordan's cooperation in the sanctions against Iraq will take more than a congressional request, according to Pentagon and US Treasury officials. Closely involved in the oversight of compliance with the prohibition of defense-related sales and transfers to Iraq, these officials lament that the Clinton administration is extending assistance to Jordan while the Arab state continues to violate the embargo.
The US Customs Department is conducting at least 19 ongoing investigations of illegal exports to Iraq from US-based entities; many of the deals entail transfer through Jordan, a conduit for contraband to Iraq.
Al-Anani protests that these US probes on Jordan, which US officials have identified as the main center of military reexports to Iraq since the embargo was imposed. ``Turkey is violating, Syria is openly violating - [by] sending goods to Iraq,'' he says. ``People are saying that Iran is doing it. Why has Jordan been singled out as the country to watch, and make pay?'' Al-Anani asks.
Because suspicions run high that cargo ships are carrying embargoed goods bound for Iraq through Jordan's port of Aqaba, Al-Anani says his country incurs up to $315 million a year extra in freight and insurance charges. ``Everyone is monitoring Jor- dan; every violation we make is being raised.''
In recent weeks, says a Treasury official, policymakers from his department have been at loggerheads with their counterparts at the State Department over just how to fashion a new agreement concerning the inspection of cargo bound for Jordan's port of Aqaba. Since sanctions were imposed against Iraq in 1991, ships carrying goods into this port have been stopped and inspected by a team of US-led warships.
Clinton accedes
After vigorous opposition from Amman, the Clinton administration acceded to the Jordanians' request to end what they called a blockade. Washington agreed to give control of the cargo to a neutral party - Lloyd's Registry - in conjunction with Jordanian customs officials. Critics of the plan, including top officials in the Clinton administration, assert that the agreement will make it so easy for contraband to reach Iraq that it is the same as ending the embargo.
Despite strong pressure from State Department officials to further soften the US stand allowing Jordan to ``monitor'' the flow of goods into its port, US Treasury officials remained steadfast in their insistence that the goods must be ``inspected.''
``Jordanians have to be convinced that peace is its own reward, and that anything else [such as international assistance] is icing on the cake,'' says Patrick Clawson, a former International Monetary Fund economist who is now a strategic fellow at the Washington-based National Defense University.
Besides, he adds, the kingdom can afford to wait for the reward. ``Jordan's economic circumstances are much better than we thought they'd be after the Gulf war.'' He notes a 20 percent increase in the kingdom's gross domestic product from 1991 to 1993, despite the initial strain placed on Jordan's resources by refugees and so-called returnees who flocked to the country after being expelled from the Gulf.
Yet, Mr. Clawson says, ``the Jordanians have been able to persuade people that they're much more vulnerable than they really are.''
As public cries for vengeance, Jordan talks of wider intervention in Syria
In Trump peace conference, a perilous balancing act for Jordan
Syria crisis: Spooked by rebel gains, Jordan doubles down vs. Islamic State

redpajama_set_name: RedPajamaCommonCrawl


text:
About International Catholic Jurists Forum
In 2013 (19-20 September), the Pontifical Council for the Family and The Union of Catholic Jurists cohosted an International Conference, in Rome, entitled The Rights of the Family and the Challenges of the Contemporary World.
At this conference, Professor Jane Adolphe of Ave Maria School of Law, co-hosted the session on The Family from the International Political Perspective and later presented its outcome action points to the plenary session. One of which was the establishment of a website presence to compile, store, and share resources with other non-governmental organizations, and activists working within international and regional human rights systems on issues pertaining to family, life, and religious freedom.
A website was launched under the auspices of The International Center on Law, Life, Faith and Family (ICOLF) the following year, at the United Nations in New York, during the Twentieth Anniversary of the International Year of Family, in 2014.
From 2014 to 2021, ICOLF slowly developed into an international forum for Catholic jurists and scholars to study pertinent issues of the day touching on law, life, faith, and family:
persecution and genocide of Christians;
the nature and meaning of equality and non-discrimination;
the global compacts on migration and refugees;
the nature and meaning of international human rights; and
Clerical sexual misconduct.
Over the years, numerous international expert meetings and strategy sessions have been held at Ave Maria School Law in Naples, Florida or at the Cardinal Stefan Wyszynski University, in Warsaw. Outcome initiatives have included the publication of books and the creation of expert coalitions and related initiatives.
In 2021, the name of ICOLF was changed to The International Catholic Jurists Forum (ICJF) to better reflect its principal work of providing a meeting place for Catholic jurists and scholars from around the globe.
The International Catholic Jurists Forum (ICJF) was established to produce, compile, and share resources on fundamental human rights under attack in the regional and international human rights protection systems. It operates as a forum for Catholic jurists and scholars to study, research, and discuss important issues of the day related to attacks on the rights of the family, life, and religious freedom.
This mission is inspired by the Holy See's document The Charter of the Rights of the Family, which articulates fundamental principles, rights and duties knowable by right reasoned as illuminated by faith. Founded on a natural law perspective of human rights within the Catholic Intellectual Tradition, the Charter promotes and protects, in particular: a) the right to life, from the moment of conception to natural death; b) the rights and duties of the natural family, based on marriage between one man and one woman; and c) the rights and duties of parents to educate their child in accordance with their moral and religious beliefs.
Key Service Objectives
To flesh out the meaning and application of the Charter of the Rights of the Family
To defend human life from the moment of conception to natural death
To promote the natural family based on marriage between one man and one woman as the fundamental unity of society
To safeguard the rights and duties of parents to provide moral and religious education to their child
To advance the protection of children, and vulnerable adults from sexual exploitation and abuse and prevent the same abuse in trust relationships
To develop an understanding of the rights and duties of the child, the elderly, and persons with disabilities within the context of the family
To advance a natural law foundation of human rights
To promote freedom of religion and conscience and combat the persecution and genocide of Christians
To study international and regional human rights protection systems and the human rights language advanced within them
Jane Frances Adolphe
Dr. Adolphe is a civil lawyer called to practice law in the State of New York, USA and Province of Alberta, Canada; a canon lawyer ; a Professor of Law at Ave Maria School of Law (AMSL), in Naples, Florida (2001 – present) and an international human rights lawyer, who from 2003 to 2020, worked for the Holy See (Pope), Secretariat of State, Section for Relations for States, first as an outside consultant for Popes John Paul II and Benedict XVI, then as an inside expert in Vatican City State, during the final years of Pope Benedict VI's papacy, until his abdication. Adolphe resigned from her tenured position with the Holy See, in 2020.
While working for the Holy See, in her capacity as Professor of Law, Adolphe established the International Center on Law, Life, Faith and Family (ICOLF), in 2014, as a forum for Catholic jurists guided by the Holy See's Charter on the Rights of the Family. It was renamed the International Catholic Jurists Forum (ICJF), in 2021. Under the auspices of this forum, Adolphe has organized multiple international conferences on topics of relevance for the Holy See, some of which have resulted in the publication of books that she has co-edited: Clerical Sexual Misconduct: An Interdisciplinary Analysis (Cluny: 2020); Equality and Non-discrimination: Catholic Roots, Current Challenges (Pickwick: 2019); The Persecution of Christians in the Middle East: Prevention, Prohibition, Prosecution (Angelico Press: 2018).
Another notable book co-edited by Adolphe is St. Paul, the Natural Law and Contemporary Legal Theory (Lexington: 2012). A dialogue between theologians at Sacred Heart Major Seminary, in Detroit, Michigan, and law professors at AMSL, it was the outcome document of a speaking series organized by Adolphe and Dr. Robert Fastiggi during the "Year of St. Paul", declared by Pope Benedict XVI. The book responds to a specific request for a conference on the natural law made by Cardinal Joseph Ratzinger, Prefect of the Congregation for the Doctrine of Faith (as Pope Benedict XVI then was) to AMSL President and Dean, at the time, Bernard Dobranski.
Adolphe was awarded the top 20 persons (6th) of 2020 by Inside the Vatican Magazine for her courage and determination. She was described as a "tireless advocate for victims of abuse and persecution," and was also profiled as a guest on the Series: Where are they now?" regarding her athletic career with the University of Calgary Dinos basketball team, her career as a law professor, and work with the Pope. She recently appeared on EWTN live with Father Mitch Pacwa to speak about "Catholic thought and Human Rights." Most recently, Adolphe together with Elizabeth Westhoff of AMSL prepared a series of videos under the auspices of the ICJF to help launch the Global Call to Prayer for China Campaign organized by a coalition of lay Catholics and Christians from around the globe.
She began her legal career clerking with the Court of Appeal and Queens Bench in Calgary, Alberta, and the law firm Bennett Jones Verchere, then prosecuted criminal cases for the Alberta Crown Prosecutor's Office, and later worked as a legal consultant to a law firm in Rome, and to non-governmental organizations lobbying at United Nations' conferences, before participating as a member of various delegations of the Holy See at international meetings.
Her doctoral thesis in canon law is entitled: A Light to the Nations: The Holy See and the International Convention on the Rights of the Child. She has published numerous articles on international human rights and the Holy See, and holds a Bachelor of Arts and four law degrees: licentiate and doctorate in canon law (J.C.L/J.C.D) from the Pontifical University of the Holy Cross, in Rome, Italy; common law (LL.B), and civil law (B.C.L.) from McGill University in Montreal, Quebec. Adolphe also holds a Bachelor of Arts from the University of Calgary.
Michael Arthur Vacca
Michael Arthur Vacca, a devotee of the Sacred Heart of Jesus, is a licensed attorney in Michigan and holds a B.A. in Political Philosophy and English Literature from Hillsdale College in Hillsdale, MI. He holds a Juris Doctorate from Ave Maria School of Law in Naples, Florida. He has a certification in Catholic Healthcare Ethics from Catholic Distance University and the National Catholic Bioethics Center, and is a certified spiritual director. From 2010-2012, Michael served as a legal advisor for the Holy See's Pontifical Council for the Family in Rome, Italy, wherein he advocated for the defense of human life, religious freedom, and the natural family on the international, regional, and national level. Michael is a widely publicized legal scholar that has written on the natural moral law, human life, natural marriage, religious freedom, and bioethics issues. Michael serves as the Director of Ministry, Bioethics, and Membership Experience for Christ Medicus Foundation CURO. He is blessed to be married to his best friend Sarah.
Ryan T. Anderson
Ryan T. Anderson, Ph.D., is the President of the Ethics and Public Policy Center, and the Founding Editor of Public Discourse, the online journal of the Witherspoon Institute of Princeton, New Jersey. He is the author of When Harry Became Sally: Responding to the Transgender Moment and Truth Overruled: The Future of Marriage and Religious Freedom. He is the co-author of What Is Marriage? Man and Woman: A Defense and Debating Religious Liberty and Discrimination, and the co-editor of A Liberalism Safe for Catholicism? Perspectives from "The Review of Politics."
Anderson's research has been cited by two U.S. Supreme Court justices, Justice Samuel Alito and Justice Clarence Thomas, in two Supreme Court cases. He received his bachelor of arts degree from Princeton University, graduating Phi Beta Kappa and magna cum laude, and he received his doctoral degree in political philosophy from the University of Notre Dame. His dissertation was titled: "Neither Liberal Nor Libertarian: A Natural Law Approach to Social Justice and Economic Rights."
Anderson has made appearances on ABC, CNN, CNBC, MSNBC, and Fox News. His work has been published by the New York Times, the Washington Post, the Wall Street Journal, Oxford University Press, Cambridge University Press, the Harvard Journal of Law and Public Policy, the Harvard Health Policy Review, the Georgetown Journal of Law and Public Policy, First Things, the Claremont Review of Books, and National Review.
He is the John Paul II Teaching Fellow in Social Thought at the University of Dallas, a member of the James Madison Society at Princeton University, and a Fellow of the Institute for Human Ecology at the Catholic University of America.
For nine years he was the William E. Simon senior research fellow at The Heritage Foundation, and has served as an adjunct professor of philosophy and political science at Christendom College, and a Visiting Fellow at the Veritas Center at Franciscan University. He has also served as an assistant editor of First Things. Follow him on Twitter at @RyanTAnd and for his latest essays and videos you can follow his public Facebook page.
José-Luis Bazán
José-Luis Bazán is a legal advisor for Migration and Asylum and Religious Freedom and Secretary of the COMECE Working Group on Migration and Asylum.
Dana J. Becker
Dana J. Becker is a real estate attorney. She specializes in commercial real estate matters, including the acquisition and disposition of properties, mortgage and mezzanine financing, loan and real property portfolio transactions, condominium and co-op conversions, and retail and commercial leasing. Dana was the founding director of education for the World Youth Alliance Foundation and has served as a board member for the Catholic Education Institute since 2014. She has also served as a consultant to the Holy See Permanent Mission to the United Nations regarding the 45th Session of the Commission on Population and Development on Adolescence and Youth since 2012.
Mark Bonner
Professor Bonner began his legal career at the U.S. Department of Justice and served in a variety of capacities there for more than 25 years, including Assistant U.S. Attorney in Los Angeles and the U.S. Virgin Islands, and Resident Legal Advisor in Moscow. For 10 years, he directed the investigation and prosecution of high-profile federal cases involving international and domestic terrorism. He subsequently joined the U.S. Department of Treasury, where he held the position of Senior Advisor and Chief of Staff to the Undersecretary of the Treasury for Enforcement. Prior to coming to Ave Maria, Professor Bonner served as a Senior Advisor in the United States Department of Homeland Security's Office of International Affairs, where he oversaw the Department's activities within the Group of 8 (G8) countries. He also taught as an adjunct professor of law at Georgetown University Law Center for 13 years.
Dr. Robert Fastiggi, Bishop Kevin M. Britt Chair of Dogmatic Theology and Christology, has been at Sacred Heart Major Seminary since 1999. Prior to coming to Detroit, he taught at St. Edward's University in Austin, Texas from 1985-1999. Dr. Fastiggi received an A.B. in Religion (summa cum laude) from Dartmouth College in 1974; a M.A. in Theology from Fordham University in 1976; and a Ph.D. in Historical Theology from Fordham in 1987. He has done private research in Paris and Montréal, and he took part in a study-tour of Saudi Arabia and Bahrain sponsored by the National Council for U.S.-Arab relations. During his time at Sacred Heart, Dr. Fastiggi has taught courses in Ecclesiology, Christology, Mariology, church history, sacramental theology, and moral theology. He is a member of the Society for Catholic Liturgy, the Mariological Society of America, the International Marian Association, and a corresponding member of the Pontifical Marian Academy International (P.A.M.I).
He served as the executive editor of the 2009-2013 supplements to the New Catholic Encyclopedia and the co-editor of the English translation of the 43rd edition of the Denzinger-Hünermann compendium published by Ignatius Press in 2012. He also revised and updated the translation of Ludwig Ott's Fundamentals of Catholic Dogma for Baronius Press in 2018.
Maria Fedoryka
Dr. Maria Fedoryka is associate professor of philosophy at Ave Maria University in Florida, and an Associated Scholar with the Hildebrand Project. She lectures and publishes in both academic and popular fora in the field of the philosophy of love, examining issues spanning from the centrality of love in the being of God, to its role at the center of creation, to its meaning for marriage, family, sexuality, and gender. Her research also includes questions related to human affectivity, as well as issues in the philosophy of psychology related to the development of the human person. Among her popular publications are "Gender: What is it and Why Does It Matter?" in the Homiletic and Pastoral Review, and a booklet published by the CTS in the UK titled The Gift of Woman. Among her academic publications are "'God is Love'": Personal Plurality as the Completion of Aristotle's Notion of Substance and Love as the Absolute Ground of the Divine Being" (Proceedings of the ACPA), and "Human Sexuality: Battle for the Human Soul" in Clerical Sexual Misconduct: Challenges and Theological Considerations (ed. Jane Adolphe).
Dr. Mary Healy
Mary Healy is professor of Sacred Scripture at Sacred Heart Major Seminary in Detroit and an international speaker on topics related to Scripture, evangelization, healing, and the spiritual life. She is a general editor of the Catholic Commentary on Sacred Scripture and author of two of its volumes, The Gospel of Mark and Hebrews. Her other books include Men and Women Are from Eden: A Study Guide to John Paul II's Theology of the Body and Healing: Bringing the Gift of God's Mercy to the World. Dr. Healy is chair of the Theological Commission of CHARIS (Charismatic Renewal International Service) in Rome. She serves the Pontifical Council for Promoting Christian unity as a member of the Pentecostal-Catholic International Dialogue. In 2014 Pope Francis appointed her as one of the first three women ever to serve on the Pontifical Biblical Commission.
Roger Kiska
Roger Kiska is legal counsel at the Christian Legal Centre in London. He is both a Solicitor for England and Wales and a member of the Michigan State Bar. He has extensive experience before the European Court of Human Rights and has litigated at the Court of Justice of the European Union. Kiska frequently appears on television and radio including the BBC, Sky News, ITV, RT, LBC and Channel 5. In 2012 he was the recipient of the Scandinavian Human Dignity Award. He has served as an elected member of the European Union's Fundamental Rights Agency Advisory Panel. He has also published numerous scholarly articles and chapters in academic books.
Kiska earned his J.D. in 2003 at Ave Maria School of Law. He has a B.A. in Religion with a minor in History from the University of Manitoba in Canada in 1997. He also received an M.A. in History of Christian Thought at Vanderbilt University in 1999. Kiska is admitted to the State Bar of Michigan and also passed the Solicitor's Bar examinations for the United Kingdom. He resides in Bratislava, the capital city of the Slovak Republic.
Rev. Msgr. Piotr Mazurkiewicz
Rev. Mazurkiewicz is a priest from the Archdiocese of Warsaw (Poland), ordained in 1988, and a Professor of Political Science at Cardinal Stefan Wyszynski University in Warsaw (UKSW), where he directs the Institute of Political Science and holds the Chair of Social and Political Ethics in the Department of Historical and Social Studies.
He is a specialist in European studies, political philosophy, Catholic social teaching, social and political ethics, and a member of the Research Council of the Institute of Political Studies of the Polish Academy of Sciences and a member of the Board of the European Society for Research in Ethics "Societas Ethica". He serves the Polish Bishops' Conference, as a member of the Advisors' Group on the European Union and a member of the Council for Social Affairs.
In 2008, after collaborating with Commission of the European's Bishop Conferences of the European Community (COMECE), on many projects, including the report to the COMECE Bishops entitled: The Evolution of the European Union and the Responsibility of Catholics, he was elected General Secretary of COMECE, in 2008, by the member Bishops of COMECE, with agreement of the Holy See, for a three year mandate. In 2002, he presented his post-doctoral dissertation entitled: The Europeanisation of Europe: Europe's cultural identity in the context of integration processes at the Institute of Political Studies of the Polish Academy of Sciences. In 1996, he presented his doctoral thesis at the Department of Ecclesiastical, Historical and Social Studies of the Academy of Catholic Theology in Warsaw. It was entitled: The Church in an open society: Dispute about the Church's presence in Polish society during the transformation period.
Theresa Okafor
Theresa Okafor holds a PhD in Education from the University of Nottingham in the United Kingdom and a Post-Graduate Diploma in Mass Communication from the University of Lagos, Nigeria. She has served as a member of the Holy See delegation at the United Nations in New York (2013-2015).
Theresa is a promoter of pro-life and pro-family values at national and international levels. She also works closely with government officials, United Nations delegates, pro-life and pro-family organizations to protect the dignity of the human person, faith, marriage, children, quality education and the family from all who seek to undermine them. She has lectured and presented at the Catholic University of America, the University of Wisconsin, Lagos State Conference on Education, Catholic Bishops Conference on Education and Seminaries in Enugu, Onitsha and Nsukka.
Theresa has been featured in EWTN, NTA, Voice of Africa and in documentaries such as Humanum.it and the Power of Mothers. She is the recipient of four awards: The Natural Family Award by the World Congress for Families 2014; Rhodes Youth Forum Award (Greece 2010) for active participation; the Flynet Award (Nigeria, 2009) for educational promotion and a merit award from the National Association of Catholic University Students (Nigeria, 2008).
She is a member of the international advisory board of the Integral Economic Development Management (IEDM) program run by the Catholic University of America. She is a Director of the Foundation for African Cultural Heritage (FACH), a Director of the Quality Assurance and Research Development Agency, Nigeria (QAARDAN) and the CEO of Life League Nigeria. She is a member of the Governing Council of Wavecrest College of Hospitality Management, Lagos Nigeria. and the African representative of the World Congress for Families. She served as a board member of the International Network for Quality Assurance Agencies in Higher Education (INQAAHE) from 2009-2011 and is a founding member of the African Quality Assurance Network (AFRIQAN).
Jason Poblete
President of the Global Liberty Alliance, Jason I. Poblete practices international and national security law at Poblete Tamargo LLP in Alexandria, Virginia. He is one of the co-founders of the Global Liberty Alliance, where he serves as its President. A long-time defender of fundamental rights, Mr. Poblete was involved in the successful release of two Americans from Iran and is representing Americans unlawfully detained in other nations. On September 16, 2020, the James W. Foley Foundation gave Poblete the 2020 Hostage Freedom Award for his work to help free several Americans unlawfully detained in Iran and Venezuela. Prior to starting Poblete Tamargo LLP in 2010, Poblete practiced law at Reed Smith, and served as a senior staff member in the U.S. Congress. He has provided expert testimony on a range of legal and foreign policy matters, including on sovereignty and self-determination, export controls and economic sanctions, before the United Nations, the U.S. Congress, and foreign courts. In 2017 Jason co-founded a legal defense fund, the Global Liberty Alliance, to empower and train lawyers, reporters, and civil society leaders who work in nations struggling with rule of law issues. Born and raised in South Florida, he is a first-generation American whose family fled Communist Cuba during the Cold War.
Grégor Puppinck
Dr. Puppinck is the Director of the European Centre for Law and Justice, a non-governmental organization based in Strasbourg (France) with special Consultative Status with ECOSOC-UN.The ECLJ advocates for the protection of religious and conscientious freedoms, family, life and subsidiarity within various human rights institutions. The ECLJ is involved in most of the important cases in the field of bioethics, religious freedom, and state-church relationships before the European Court of Human Rights. Grégor Puppinck also serves as an expert at the Council of Europe for the Holy See and as an adviser to several Member States of the Council of Europe. He frequently provides expert briefings before various national, European and International bodies. He teaches human rights and advocacy at the Law School of Strasbourg. From 2003 to 2009, he taught human rights, international law and constitutional law. After earning his Master of Law from the Law School of Pantheon-Assas (University Paris II), he graduated from the "Institut des Hautes Etudes Internationales" (IHEI). He holds a Ph.D. in law with a dissertation on the elaboration of the norms in the field of bioethics and is the author of numerous academic articles. He is Knight Commander of the Order of Saint Gregory the Great and Cavaliere della Repubblica of Italy.
D. Brian Scarnecchia
Brian Scarnecchia, M.Div., J.D. is an Associate Professor of Law at Ave Maria School of Law in Naples, Florida where he has taught Property law, Origin of the United States Constitution, Criminal law and Bioethics. He is the author of Bioethics, Law and Human Life Issues: A Catholic Perspective on Marriage, Family, Contraception, Abortion, Reproductive Technology, and Death and Dying (Lanham, MD, Scarecrow Press, 2010) and co-author of The Millennium Development Goals in Light of Catholic Social Teaching (New York, C-Fam, 2009). Brian has also worked as the Director of the Legal Studies program and of the Human Life Studies program at Franciscan University of Steubenville in Steubenville and as an Assistant County Prosecutor for Jefferson County, Ohio. He currently serves on the Board of Directors for the Society of Catholic Social Scientists (SCSS) and is their main NGO representative to the United Nations. He is also the founding president of International Solidarity and Human Rights Institute (ISHRI), a non-governmental organization (NGO) in consultative status with the United Nations. Brian has also served as an expert on life and family issues for the Catholic Inspired NGO Forum (CINGO), which works in close association with the Pontifical Council for the Family and Secretariat of the Holy See.
Nina Shea
An international human-rights lawyer for over thirty years, Nina Shea joined Hudson Institute as a Senior Fellow in November 2006, where she directs the Center for Religious Freedom. Shea works extensively for the advancement of individual religious freedom and other human rights in U.S. foreign policy as it confronts an ascendant Islamic extremism, as well as nationalist and remnant communist regimes. She undertakes scholarship and advocacy in defense of those persecuted for their religious beliefs and identities and on behalf of diplomatic measures to end religious repression and violence abroad, whether from state actors or extremist groups.
Shea was appointed by the U.S. House of Representatives to serve seven terms as a Commissioner on the U.S. Commission on International Religious Freedom (June 1999 – March 2012). During the Soviet era, Shea's first client before the United Nations was Soviet Nobel Peace Laureate Andrei Sakharov. Since then, she has been appointed as a U.S. delegate to the United Nation's main human rights body by both Republican and Democratic administrations. She also served as a member of the Clinton administration's Advisory Committee on Religious Freedom Abroad. In 2009, she was appointed to serve as a member of the U.S. National Commission to UNESCO.
Shea played a leading role in building grassroot support for the adoption of the International Religious Freedom Act (1998). For seven years ending in 2005, she helped organize and lead a coalition of churches and religious groups that worked to end a religious war against non-Muslims and dissident Muslims in southern Sudan. In 2014, she initiated and helped lead a coalition of hundreds of prominent American religious leaders to issue The Pledge of Solidarity for Persecuted Iraqi, Syrian and Egyptian Christians and Other Minorities, which was released by a bi-partisan Congressional panel on May 7. In summer 2014, she met with Pope Francis to discuss the persecution of Christians in the Middle East.
At Hudson, she has organized conferences for Nigerian schoolgirls and others who survived Boko Haram attacks, Christian converts formerly imprisoned in Iran, Coptic bishops from Egypt, Catholic bishops from China and the Gulf, Muslim scholars, and many others. Shea advocates in the nation's capital on behalf of a broad range of persecuted religious minorities around the world; and, for such work, was honored by the Ahmadiyya Muslim Community USA with the Community's inaugural "Ahmadiyya Muslim Humanitarian Award."
She has authored and/or edited four widely-acclaimed reports on Saudi state educational materials that promote extremist views and in 2011 had an opportunity to travel to Saudi Arabia and speak directly about her findings with the Ministers of Education, Justice and Islamic Affairs. Her reports include: Ten Years On: Saudi Arabia's Textbooks Still Promote Religious Violence (2011), Update: Saudi Arabia's Curriculum of Intolerance (2008), Saudi Arabia's Curriculum of Intolerance (2006), and Saudi Publications on Hate Ideology Invade American Mosques (2005), all of which translated and analyzed Saudi governmental publications that teach hatred and violence against the religious "other."
She is the co-author of Silenced: How Apostasy & Blasphemy Codes are Choking Freedom Worldwide, with a Foreword by Kyai Haji Abdurrahman Wahid, the former President of Indonesia and head of Nahdlatul Ulama, the world's largest Muslim organization (Oxford University Press, 2011). Her most recent book, which she also co-authored, is Persecuted: The Global Assault on Christians (Thomas Nelson Publishers, 2013). She regularly presents testimony before Congress, delivers public lectures, organizes briefings and conferences, and writes frequently on religious freedom issues. Her writings have appeared in the Wall Street Journal, Washington Post, CQ Researcher, Weekly Standard, National Review Online, CNN, Fox, The Daily Beast, HuffingtonPost, and RealClearWorld, among others.
For the ten years prior to joining Hudson, Shea worked at Freedom House, where she directed the Center for Religious Freedom, an entity which she had helped found in 1986 as the Puebla Institute.
She is a member of the bar of the District of Columbia. She is a graduate of Smith College, and American University's Washington College of Law.
Pia de Solenni
Pia de Solenni is a theologian who formerly served as the chancellor of the Roman Catholic Diocese of Orange in California. Solenni is an alumna of Thomas Aquinas College where she earned a Bachelor of Arts degree in Liberal Arts-Great Books, and of the Pontifical University of Saint Thomas Aquinas, Angelicum, where she earned a Bachelor of Sacred Theology. Subsequently, she earned a doctorate in theology from the Pontifical University of the Holy Cross in Rome; for this work, she received the 2001 Award of the Pontifical Academies, presented by John Paul II. Dr. de Solenni has worked at the Family Research Council. Her work has appeared in The Wall Street Journal, The Washington Post, and National Catholic Reporter, and she has appeared on CNN, ABC News, MSNBC, Hardball with Chris Matthews, The O'Reilly Factor, and other television programs.
Geoffrey Bedford Strickland
Geoffrey Bedford Strickland, J.D., J.C.L., serves as International Associate and Rome Office Director for Priests for Life/Gospel of Life Ministries and as collaborator with the Pontifical Council for the Family. His research and publications pertain to the state of the family in the modern world and the dignity of human life in all periods of its existence. In his role as Rome Office Director and International Associate, he provides research and analysis of canonical and international legal themes pertaining to family and life issues. In his role as collaborator with the Pontifical Council for the Family, he has provided research and analysis regarding legal issues pertaining to the family and human dignity in the modern world, compiling an international legal database (organized by topic, region, and law), focusing upon areas pertaining to the family, human life in all periods of its existence, demographics, and gender ideologies. He assists in language related work (translation and interpretation) of Spanish, Portuguese, French, Italian, and Arabic, as well as in English language media efforts.
Dr. Marcela Szymanski
Dr. Marcela Szymanski lives in Brussels, Belgium, where she has been a public affairs consultant and an EU+NATO news correspondent (CNN en Español). She holds a BA in Communications, an MA in Economics and a PhD (abd) in International Politics from Georgia State University. She is an affiliate researcher with both the GSU and the University of the Americas in Puebla (UDLAP) writing on political change and democratization. Her public affairs clients have included not only industrial and financial concerns, but also Catholic Church foundations as they support the Church in countries at war, political prisoners, and non-Western countries suffering from substantial human rights violations by external actors. Since 2015 she is the Editor of the report "Religious Freedom in the World" for the pontifical foundation Aid to the Church in Need (her academic publications can be found online).
Elizabeth S. Westhoff
Known for her dedication to the Faith along with her humor and wit, Elizabeth is a strong believer that the Church should use every communications tool available to evangelize and share the beauty and truth of Catholicism. Elizabeth has a Master of Arts degree in English and American literature. A strategic marketing and communications executive who has served the Church for over 20 years, she is passionate about creating strong brands that communicate key messages, help inspire confidence, and take organizations to a new level. Known for her ability to craft effective messaging that resonates with both Catholic and secular audiences, Elizabeth has built brand recognition across Catholic and secular media, both nationally and internationally.
Elizabeth currently serves as Chief Marketing and Communications Officer at Ave Maria School of Law in Naples, FL, collaborating with various departments and faculty members to promote the law school's mission as a Catholic, conservative, competitive school of law that is founded in the Catholic intellectual tradition. Prior to her arrival at Ave Maria Law, Elizabeth served as Press Secretary to His Eminence Raymond Leo Cardinal Burke.
Elizabeth is the recipient of the Catholic Press Association Awards: First Place, Best coverage of the Year of Mercy, the Catholic Press Association Award: First Place, Best newspaper story and photo package, the Catholic Press Association Award: Honorable Mention, Best in-depth news/special reporting in a diocesan newspaper, the Catholic Academy of Communications Professionals: Gabriel Award for New Media Campaign of the Year, Hermes Creative Award for Video Production: Gold Winner and Honorable Mention, the Archdiocese of St. Louis Women's Visionary Award, the St. Louis Business Journal's Thirty Under 30 Award, former President and Vice-President of the National Communications and Development Section for Catholic Charities USA, host of several long-running Catholic radio shows on EWTN affiliate stations, a contributing author and speaker for Women In the New Evangelization, a regular guest and guest host on various Catholic radio networks, M.C. and speaker for various Catholic and secular organizations, and serves as a judge for the Catholic Media Awards in the areas of video production, social media campaigns, radio production, and blog production. Elizabeth is a Daughter of St. Francis de Sales in the Association of St. Francis de Sales (formerly a tertiary order) and a Dame of the Equestrian Order of the Holy Sepulchre of Jerusalem.


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The Soviet Surface to Air Missile System Simulator
by Dr Carlo Kopp, SMIEEE, SMAIAA, PEng
Updated February, 2011
Text © 2009-2011 Carlo Kopp
SNR-75 Fan Song Console emulation in simulator.
One of the valuable byproducts of the disintegration of the Soviet regime has been the release into the open source domain of a large volume of declassified technical material covering Soviet systems used through the Cold War period. These include a range of radar systems and SAM systems, especially those operated by Warsaw Pact nations. Numerous websites have appeared in Eastern Europe and Germany, which detail these weapon systems in a manner which a Cold War era Western technical intelligence analyst could only dream of.
An even more valuable contribution has recently appeared in Hungary, a high quality simulator program hosted on Windows, which provides faithful emulations of a range of Soviet SAM system engagement radar consoles. APA sought advice from several contributors with operational experience on these systems, and all confirmed that the simulator provides a high quality representation of the SNR-75 Fan Song E (SA-2 Guideline), SNR-125 Low Blow (SA-3 Goa), 1S32 Pat Hand (SA-4 Ganef) and most recently, the 5N62 Square Pair (SA-5 Gammon). This author has studied the original Russian language technical manuals for various components of the SA-5 Gammon, and the simulator indeed provides a faithful representation.
The author of this program intends to produce over time accurate simulators for a wide range of Soviet SAM and SPAAG systems operated by the Warsaw Pact. All simulator panel representations are based upon digital photographs of real panels in preserved examples of these systems, and functional modes represent reflect operational manuals for these systems.
While most of these SAM systems are no longer operational, and those which are, are typically no longer in the legacy configuration depicted, the simulator is valuable as it illustrates the high level of proficiency and high training standards required for these systems to be used effectively in combat. This clearly explains the enormous disparities in combat effect observed between operations by the Warpac advisor led PAVN pre-1973, by Soviet PVO troops along the Suez during the War of Attrition, and Serbian forces during OAF, in comparison with the woeful performance of the Syrians in 1982, and the Iraqis in 1991. The latter have become completely unrealistic yet widely accepted benchmarks of IADS combat effect and performance.
APA strongly recommends that visitors with a professional interest in Soviet SAMs invest the time to visit the site, play the recorded tutorials, and download the simulator for a test run.
Systems Currently Represented by the SAM Simulator
S-200VE Vega (SA-5B Gammon) / 2011
2K11 KRUG-M1 system (SA-4B Ganef) / 2010
S-125M1 Neva (SA-3B Goa) / 2009
S-75M Volkhov (SA-2E Guideline) / 2006 - 2009
SAM (Surface to Air Missile System) Simulator [Click to download ...]


Category: Ellenville - Thank you for visiting!
There are two sets of Ice Caves in Ellenville, NY; the commercial caves off route 52 and the open fault caves. To find the open fault caves, you can leave your car at the Berme Road Park (41°42'48.72"N 74°22'57.99"W) then take the carriage trail up the mountain. The trail to the large fault, or great crevice, ascending the mountian is unmarked and difficult to find if you don't know where it is (approximately: 41°42'59.01"N 74°22'27.40"W). If you go too far you will come to a wooden bridge which is the entrance to Shingle Gulley. That is just as interesting and exciting to climb. Once in either location, there are nooks, crannies and deep crevices which you could explore for weeks. The "Grand Canyon" is located approximately: (41°42'47.24"N 74°21'45.06"W).


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Column: Sour Grapes From Clintonistas Don't Reflect Change America Needs
This story was written by DI Board, The Daily Iowan
Presumptive Democratic nominee Barack Obama and runner-up Hillary Rodham Clinton have plans to campaign together in Unity, N.H., on Friday. The location is no circumstance; their aim is to promote Democratic Party unity.
This is what Obama needs from his party - a public display of affection between one-time bitter rivals. After all, despite the far-reaching hopes of downtrodden Rodham Clinton backers, Obama has won. He has won the delegate count, the number of states, and the number of votes counted. Never mind that Hillary has made veiled references to holding out a sliver of hope until the Democratic National Convention is held in August; judging from her campaign suspension speech, shouldn't it be fully expected of her to "endorse and throw [her] full support behind" the man who has essentially won her party's nomination?
The answer is no. Some disgruntled stragglers in the Rodham Clinton Camp continue to attack Obama for being a "talker" and not a "doer," but now it seems that they are occupying this role. By refusing to declare defeat, a small, sad gaggle of Hillary-supporters are refusing to support Obama. For fear of alienating the larger mass of impassioned Rodham Clinton supporters, Obama has avoided most all opportunities to declare the race over, instead praising the New York senator as a formidable opponent. It is hard for a party to affirm unity when "opponents" remain after the battle has been fought. If a party is to emerge in unified strength, there can be no internal hindrances.
The Democratic Party needs to become gathered and focused if it hopes to avoid a major collapse before the general election. According to *The Week* (Volume 8, Issue 363), in Kentucky, where Rodham Clinton enjoyed success among working-class whites, a startling number of up to 80 percent of registered Democrats told pollsters that if Obama wins the nomination, they will stay home or even vote for John McCain. Last week on "Your World with Neil Cavuto," another of Rodham Clinton's disenchanted supporters, Cynthia Lowney, displayed similar feelings, emphatically proclaiming that she will not vote for Obama because he has misled people and isn't qualified. Lowney admittedly would cast a McCain vote in November, although she believed that Rodham Clinton could still win the nomination.
Lowney does have a somewhat valid point: the nomination is ultimately up to the superdelegates. Even though it is impossible for Rodham Clinton to overcome Obama's lead among pledged delegates, it is still possible for the superdelegates to go with Hillary if they have questions or concerns about Obama's electability. Rodham Clinton's most ardent followers feel that she should stick it out if only for this reason. However, in an April interview with George Stephanopoulos, Rodham Clinton admitted that Obama most certainly is able to beat McCain. Thus, even with Hillary foreseeing no electability issues, the question remains: Why do some of her supporters remain in opposition? Are these the same folks that have screamed for change these last seven years? Change, but only on their terms? On their terms, or else?
Democrats should hope that Rodham Clinton and all of her former supporters now throw their full weight behind Obama, not in August. The two politicians could be negotiating about fundraising or potential Cabinet spots, but certain Rodham Clinton supporters have distracted them from the real issues by entertaining unpopular running-mate strategies and bickering about hypothetical superdelegate scenarios. Obama needs to shift focus to his race with McCain, not on how to overcome negative publicity from intra-party squabbles among bummed-out former Rodham Clinton backers. At a time when the entire red and blue electoral map is up for grabs, a time when a conservative Republican cndidate is capable of attracting moderate Democrats, a time when a history-making Democratic candidate has energized independents, minorities, and the youth - at this time it would seem Obama has bigger fish to fry. If his own party won't unite and rally around him, how can Democrats expect the country to?


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Home » Soccer » Transfer news LIVE: Chelsea plot Spurs hijack, Arsenal table £13m bid
Transfer news LIVE: Chelsea plot Spurs hijack, Arsenal table £13m bid
Ten Hag outlines importance of winning trophies for Man Utd
There are just six days of the January transfer window remaining and many clubs from across the Premier League and elsewhere are starting to wrap up their business in the mid-season market. The likes of Chelsea, Arsenal and Manchester United have already welcomed some new faces over the last few weeks but could still be poised to add further quality to their ranks before the all-important deadline at the end of this month.
Chelsea have spent over £150million on player recruitment in January alone but are said to be considering a late swoop for Sporting full-back Pedro Porro, who is also believed to be a priority target for Tottenham. The north Londoners have been in talks regarding a move for Porro in recent days but now seemingly face the possibility of seeing their plans wrecked by Chelsea if the Blues decide to firm up their interest between now and the end of the window.
Arsenal, meanwhile, are thought to be chasing a move for Real Valladolid youngster Ivan Fresneda and could be set to make him their third winter signing after the recent arrivals of Leandro Trossard and Jakub Kiwior. United have also been linked with a handful of big-name players since bringing in Wout Weghorst on loan from Burnley earlier this month, although it remains to be seen if the Red Devils will act to make further improvements to their squad before the window slams shut.
Follow Express Sport's live updates below.
Chelsea to hijack Tottenham deal?
Chelsea are weighing up a late move for the services of Sporting full-back and reported Tottenham target Pedro Porro before the end of the January window.
That's according to the Evening Standard, who claim that Chelsea are 'tracking' the 23-year-old as they seek injury cover for Reece James.
Tottenham have already seen a number of bids knocked back by Sporting but have agreed to meet with the Portuguese club this week in order to finally thrash out a deal.
Hello and welcome to Express Sport's live coverage of the latest transfer news and rumours from across the Premier League and elsewhere.
There are still plenty of deals left to be done with just six days until the January window slams shut, with the likes of Manchester United, Arsenal and Chelsea among the clubs to have been linked with a number of potential targets in recent days.
We'll be on hand to keep you updated with the biggest stories throughout the day, so stay tuned…
USA stars to watch in its first games since shock 'blackmail' scandal
Bournemouth agree £20.3m fee for Villarreal's Nicolas Jackson
January 25, 2023 Soccer Comments Off on Transfer news LIVE: Chelsea plot Spurs hijack, Arsenal table £13m bid


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Nogalitos de la Cruz es una localidad ubicada en el Municipio Armadillo de los Infante (municipio) del Estado de San Luis Potosí, (México) y se encuentra en las coordenadas:Longitud: 100º, 39`24.03" W , Latitud: 22º.19`38.04" N.  Está situado a 58 km de la capital del estado por carretera.

La población total viviendo en la localidad es de 106 personas, hasta el 2013 de los cuales 56 son hombres y 50 mujeres.

Toponimia
El nombre de Nogalitos de la Cruz procede de unos nogales que había en un terreno conocido como «La Larga» y que hoy han sido sustituidos por milpas, y de la Santa Cruz que tomaron como protectora del lugar.

Economía
Sus habitantes se dedican principalmente a la agricultura en baja escala, ya que la mayoría de las tierras de cultivo son de temporal (regadas con agua de lluvia), por lo que solamente se siembra una vez por año, en los meses de mayo, junio o julio en función de las lluvias. Generalmente lo que se siembra es frijol y maíz. Cuando llueve en el mes de agosto, normalmente se siembra cebada , avena, garbanzo o lenteja, plantas que resisten las bajas temperaturas, pues las primeras heladas comienzan a partir de mediados de octubre y en una sola noche pueden acabar con toda la siembra de especies como maíz y frijol, que no son resistentes al hielo.

Historia

La construcción más importante del pasado en Nogalitos es una presa que se ubica en el arroyo que pasa al sur del rancho. Éste antes era un río y tenía agua casi todo el año, aunque hoy por lo regular permanece seco por falta de lluvias. Los antiguos habitantes de este lugar manifestaban que este bordo de piedra china (la presa) había sido hecho por indios. Hoy se sabe que fue realizado por los huachichiles, tribus indígenas dispersas por la región y provenientes de las cercanías del Cerro de San Pedro, donde eran acosados por los mineros del lugar. Establecidos en terrenos al sur de lo que hoy es Nogalitos, construyeron la presa, aunque su factura no resistió una fuerte bajada del río en un año de intensas lluvias y se fracturó al poco tiempo de su hechura, quedando abandonada hasta nuestros días.

Nogalitos está levantado cerca de otro rancho muy antiguo que se ubicaba al sur, al otro lado del arroyo, y del que solo quedan señales de canales de riego muy rudimentarios y muy antiguos en algunas partes, ubicados a lo largo de lo que fue antes un río y que probablemente servirían para regar sus huertos, incluidas las higueras que le darían su nombre: San Antonio de las Higueras.

La casa más antigua de lo que hoy es el rancho fue un pequeño jacal con techo de zacate, a dos aguas, y con paredes de varas cubiertas con lodo, perteneciente a la familia Cervantes, primera en establecerse en el lugar.

Hitos cronológicos

 1874 Construcción de la Iglesia de la Santa Crúz.
 1934 Construcción de la primera Escuela Pública.
 1935 Construcción del panteón de Nogalitos.
 1952 Construcción de la Escuela Primaria.
 1980 Electrificación.
 1987 Agua potable.
 1992 Construcción de la telesecundaria.
 2014 Construcción de la carretera a San Luis Potosí (también conocida como carretera al mezquite).

Fiestas y costumbres

La Fiesta de Mayo se realiza; en la última semana de dicho mes y se ha venido festejando ininterrumpidamente desde el día 3 de mayo de 1874, en que se inauguró la Iglesia. El evento se hace en honor a la «Santa Cruz».

Crónica de la Fiesta de Mayo
 Primer día: los músicos llegan y se reportan con el mayordomo en el lugar indicado, y empiezan a tocar por la calle hasta llegar a la iglesia para presentarse, de ahí son llevados a la casa de la familia que arregló la Crúz Bendita y le tocan varias piezas intercaladas con los rezos de los presentes, el casero recibe a los invitados con fruta picada y agua de sabor, ya entrada la noche la Cruz Sagrada es cargada por cuatro fieles para dar inicio al Rosario de la Víspera, rezado por los habitantes de la comunidad acompañando la procesión con velas encendidas y entonando un cántico antiguo,  que llena de murmullos el lugar adelante de esta formación van los penitentes hombres y mujeres de rodillas que van pagando su manda,  con un vistoso escapulario  en el pecho hasta llegar a la iglesia donde es cantado el Santo Rosario, y la música sigue tocando afuera del recinto hasta pasada la media noche.

 Segundo día: después de anunciar el alba con cohetes y truenos, los músicos le tocan las mañanitas a la Santa Cruz dentro del recinto sagrado.  En el transcurso de la mañana los mayordomos generalmente identificados con un morral de ixtle al hombro como en tiempos pasados, recorren las casas con la música y una libreta en la que anotan las limosnas recibidas.  Ese día la Misa es cantada y ahí se llevan a cabo bautizos, primeras comuniones y bendición de imágenes,y cuando termina el evento, los mayordomos que salen le entregan al Padre un vaso con papelitos doblados a manera de rifa, para que sobre la base de ellos indique los nombres de los nuevos mayordomos que son: de pólvora y de música,  y serán los encargados de organizar la fiesta para el siguiente año; ambos tienen que hacer una junta en la localidad para definir la fecha y los detalles de la próxima fiesta y ponerse de acuerdo en la limosna a pedir, posteriormente se organizan con el encargado de la iglesia para programar las misas de la Novena y se mandan hacer los programas en los que se indican las actividades de la celebración del año entrante, los que serán repartidos en los ranchos cercanos y entre los amigos o familiares que están fuera de la localidad, esta conmemoración desde la antigüedad se hace de limosna, pedida por los mayordomos de la misma. Al término de la Misa principal por la tarde, la encargada de juntar la cera pasa por las casas que se apuntaron con alguna batea que es dada como ofrenda a la Crúz Bendita, las familias donantes antes de hacer la entrega de los arreglos ofrecen al acompañamiento fruta picada y agua de sabor, los músicos ahí les tocan algunas piezas musicales, generalmente la danza y la fila de las bateas esperan afuera del domicilio, éstos arreglos son cargados principalmente por niñas y son llevadas en agradecimiento por los favores recibidos a la Santa Cruz que espera en la iglesia engalanada con flores de cera blanca, "Que parece una novia vestida de azahares, dijo un párroco", para sacarla de paseo por el rancho donde son adornadas las calles con portadas de colores. Y nuevamente como en la Víspera, la procesión de congregantes continúa e inunda el ambiente con olor a copal, entre rezos, cánticos, penitencias, música, danza y cohetes. Desde lo alto del callejón solo se ven las luces de las velas encendidas, embriagando el aire tibio de la noche con un hálito de fe, de redención, de esperanza, de magia y misticismo en éste ranchito tan precario y olvidado, en el que su gente se eleva con esa fe que anima, y que va más allá de todas las dificultades de la vida. Esa es la esencia de esta Fiesta Patronal de Nogalitos de la Crúz. Por la noche los juegos, los puestos de comida, la quema de toritos adornados con cohetes de buscapiés, los danzantes con el "viejo de la danza", la música, la quema del castillo de pólvora con sus numerosas luces de colores, hacen de esta fiesta un lugar de luz.

 Tercer día: los músicos tocan nuevamente en la iglesia a la Cruz Bendita y esperan en el patio de la misma hasta la colocación en su nicho,  a esta tradición se le llama la "Alzada de la Santa Cruz" y se le tocan las golondrinas entre Cantos gregorianos muy antiguos. Por último los mayordomos dan a conocer los gastos y las limosnas recibidas, los visitantes se van y el rancho nuevamente queda solo, hasta el próximo año y la pregunta es, ¿volveré a oír los truenos de Mayo?...

Referencias
 Nogalitos de la Cruz en mipueblo.mx
 Nogalitos de la Cruz en el Catálogo de localidades de la Secretaría de Desarrollo Social (México)
  Festividades religiosas de San Luis Potosí

Localidades del estado de San Luis Potosí

redpajama_set_name: RedPajamaWikipedia


Here's an amazing two piece set with sequence top and satin frilled look skirt.
The skirt has can can present.
The top is made out of satin handworked on georgette only on the MRP version..
The top will have piping to prevent itching.
The top will have deep U back for better look.


text:
Kim Min-O  (born May 8, 1983) is a South Korean football player.

External links

1983 births
Living people
South Korean footballers
Ulsan Hyundai FC players
Gimcheon Sangmu FC players
K League 1 players
Korea National League players
Association football midfielders