text:
\section{Introduction}
\label{sec:introduction}
Interval graphs and their generalizations are often used to study problems in resource allocation, scheduling, and DNA mapping. In 2002, Vialette~\cite{DBLP:conf/cpm/Vialette02} proposed a geometric description of RNA
helices in an attempt to improve the  understanding of the computational complexity  for finding structured patterns in RNA sequences. In particular, Vialette modeled the RNA secondary structure using a set of 2-intervals, which inspired subsequent research (e.g., see~\cite{DBLP:reference/algo/Vialette08}) on examining the properties of the geometric graphs arising from such representations. The \emph{{2-interval pattern problem}\xspace}, introduced by Vialette~\cite{DBLP:journals/tcs/Vialette04}, is a widely studied pattern, and the main topic of this paper.

A \emph{2-interval} is the union of two disjoint intervals on the real line. Two 2-intervals $D_1$ and $D_2$ are \emph{disjoint} if their intersection is empty; that is, no interval of $D_1$ intersects any interval of $D_2$. We can define three different relations between two disjoint 2-intervals: one 2-interval lies entirely to the left of the other one (called \emph{preceding} and denoted by $<$), one 2-interval is nested within the other one (called \emph{nested} and denoted by $\sqsubset$), and the intervals of the two 2-intervals alternate on the real line (called \emph{crossing} and denoted by $\between$). See Figure~\ref{fig:exampleForRelations}(a) for an example; a formal definition is given in Section~\ref{sec:prelimins}. Two 2-intervals $D_1$ and $D_2$ are \emph{$R$-comparable} for some $R\in\{<,\sqsubset,\between\}$ if either $D_1RD_2$ or $D_2RD_1$. A set $\mathcal{D}$ of disjoint 2-intervals is $\mathcal{R}$-comparable, for some $\mathcal{R}\subseteq\{<,\sqsubset,\between\}$ and $\mathcal{R}\neq\emptyset$, if every pair of 2-intervals in $\mathcal{R}$ are $R$-comparable for some $R\in\mathcal{R}$. In the \emph{{2-interval pattern problem}\xspace}, we are given a set of 2-intervals and a set $\mathcal{R}\subseteq\{<,\sqsubset,\between\}$, and the objective is to compute a largest subset of 2-intervals that is $\mathcal{R}$-comparable.   Figure~\ref{fig:exampleForRelations}(b) illustrates such an example.

The {2-interval pattern problem}\xspace can model various scenarios in the context of RNA structure prediction. While looking for certain RNA structures, some common approaches to cope with intractability are either to restrict the class of pseudoknots~\cite{RivasRE99} or to  apply heuristics~\cite{10.1093/nar/28.4.991,RenRCH05,DBLP:journals/bioinformatics/RuanSZ04}. Vialette~\cite{DBLP:journals/tcs/Vialette04}   proposed that one can obtain a relevant set of 2-intervals from an RNA sequence by selecting stable stems, e.g., using a simplified thermodynamic model without accounting for loop energy~\cite{DBLP:journals/bioinformatics/RuanSZ04,DBLP:journals/tcs/Vialette04,DBLP:conf/wabi/ZhaoMC06}. Then, the prediction of the RNA structure is equivalent to finding a maximum subset of non-conflicting (i.e., disjoint) 2-intervals.

\begin{figure}[t]
	\includegraphics[width=.9\textwidth]{example2}
	\caption{(a) An example for showing the three possible relations between a pair of 2-intervals; here, the same-colour intervals form a 2-interval. Then, $(a,a')<(d,d')$, $(d,d')\sqsubset (b,b')$ and $(c,c')\between (d,d')$. (b) An instance of {2-interval pattern problem}\xspace with $\mathcal{R}=\{<,\between\}$ and the 2-intervals are $\{(u,w),(q,s),(r,u),(p,t)\}$. The 2-intervals $\{(p,t),(r,u)\}$ form a  largest subset that is $\mathcal{R}$-comparable.}
	\label{fig:exampleForRelations}
\end{figure}

\paragraph{Related work.} Vialette~\cite{DBLP:journals/tcs/Vialette04} observed that if $|\mathcal{R}|=1$, then the {2-interval pattern problem}\xspace is polynomial-time solvable by reductions to the maximum independent set  problem on interval graphs, or to the maximum clique problem on comparability graphs. The running time of these algorithms have been improved since then, and expressed in terms of the number of input 2-intervals and various  interval-related parameters such as their lengths or overlap~\cite{DBLP:journals/jco/ChenYY07}. For the case when $|\mathcal{R}|$ = 2, the problem is  solvable in polynomial time when $\mathcal{R}=\{<,\sqsubset\}$~\cite{DBLP:journals/tcs/Vialette04}. However, if $\mathcal{R}=\{<,\between\}$ or  $\mathcal{R}=\{\sqsubset,\between\}$, then the problem is known to be  $\mathsf{NP}$-hard, even if the intervals of every 2-interval have unit length~\cite{DBLP:journals/tcs/Vialette04,DBLP:conf/cpm/BlinFV04}. If $|\mathcal{R}|=3$, i.e., $\mathcal{R}=\{<,\sqsubset,\between\}$, then the $\mathsf{NP}$-hardness of the problem follows from the hardness of recognizing 2-interval graphs~\cite{DBLP:journals/dam/WestS84}.

The approximability of the $\mathsf{NP}$-hard models of the {2-interval pattern problem}\xspace was studied by Crochemore et al.~\cite{DBLP:journals/tcs/CrochemoreHLRV08}. They gave polynomial-time algorithms for the problem with approximation factors 4 when $\mathcal{R}=\{<,\sqsubset,\between\}$ or $\mathcal{R}=\{\sqsubset,\between\}$, and 6 when $\mathcal{R}=\{<,\sqsubset\}$. They also showed that the results hold for the weighted case, i.e., when each 2-interval is associated with a weight and the goal is to find a maximum weight subset. These factors are improved to 3 when the intervals of every input 2-interval have unit length~\cite{DBLP:journals/tcs/CrochemoreHLRV08}, where they also considered the case when the 2-intervals are weighted. For $\mathcal{R}=\{<,\between\}$ (and arbitrary input 2-intervals), Jiang~\cite{DBLP:journals/jco/Jiang07} improved the approximation factor to 2 and subsequently to $1+\epsilon$ for any $\epsilon>0$~\cite{DBLP:conf/cocoa/Jiang07}.

The problem is $\mathsf{W[1]}$-hard when $\mathcal{R}=\{<,\sqsubset,\between\}$, because in this case, the problem is equivalent to computing a maximum independent set on 2-interval graphs, and the latter is known to be $\mathsf{W[1]}$-hard~\cite{DBLP:journals/tcs/FellowsHRV09}; see Section~\ref{sec:hardness} for more details. For $|\mathcal{R}| = 2$, to the best of our knowledge, the only parameterized result is the work of Crochemore et al.~\cite{DBLP:conf/cpm/BlinFV04}  who proved that the problem is fixed-parameter tractable, but only when $\mathcal{R}=\{\sqsubset,\between\}$, the input intervals all have unit length and the tractability is with respect to the \emph{forward crossing number}: the maximum number of 2-intervals that cross a 2-interval ``from the right''.

\paragraph{Our results.} In this paper, we answer a question of Vialette~\cite{DBLP:reference/algo/Vialette08} by proving that the {2-interval pattern problem}\xspace is $\mathsf{W[1]}$-hard when $\mathcal{R}=\{\sqsubset,\between\}$ and $\mathcal{R}=\{<,\between\}$. Our $\mathsf{W[1]}$-hardness result is inspired by the reduction of the $k$-independent set problem used by Fellows et al.~\cite{DBLP:journals/tcs/FellowsHRV09}. Their reduction requires all three relations (i.e., they prove the $\mathsf{W[1]}$-hardness of the {2-interval pattern problem}\xspace when $\mathcal{R} = \{<, \between, \sqsubset\}$). Prior to our work, it was known that the complexity of the problem is polynomial when $\mathcal{R}=\{<, \sqsubset\}$~\cite{DBLP:journals/jco/ChenYY07}, but it was unknown whether the problem is fixed-parameter tractable (when parameterized by the size of an optimal solution) or it is $\mathsf{W[1]}$-hard for $\mathcal{R}=\{\sqsubset,\between\}$ and $\mathcal{R}=\{<,\between\}$. Hence, our $\mathsf{W[1]}$-hardness result fully settles the parameterized complexity of the {2-interval pattern problem}\xspace.

\section{Preliminaries}
\label{sec:prelimins}
In this section, we give some definitions and notation that will be used throughout the paper.

A 2-interval $D$ is the union of two disjoint intervals on the real line; that is, $D=(A,B)$ and the interval $A$ lies to the left of the interval $B$. For a pair of disjoint intervals $I,J$, we write $I<J$ when $I$ is to the left of $J$. Two 2-intervals $D_i$ and $D_j$ are \emph{disjoint} if $(I_i\cup J_i)\cap (I_j\cup J_j)=\emptyset$. Moreover, for two disjoint 2-intervals $D_i$ and $D_j$, we say that $D_i$ is \emph{preceding} (resp., \emph{nested} in, \emph{crossing}) $D_j$ if $I_i<J_i<I_j<J_j$ (resp., $I_j<I_i<J_i<J_j$, $I_i<I_j<J_i<J_j$. We write $D_i<D_j$ (resp., $D_i\sqsubset D_j$, $D_i\between D_j$) when $D_i$ is preceding (resp., nested in, crossing) $D_j$.

We say that two 2-intervals $D_i$ and $D_j$ are \emph{$R$-comparable}, for some $R\in\{<,\sqsubset,\between\}$, if (i) $D_i$ and $D_j$ are disjoint and (ii) either $D_i R D_j$ or $D_j R D_i$. Let $S$ be a set of $n$ 2-intervals on the real line, and let $\mathcal{R}\subseteq\{<,\sqsubset,\between\}$ such that $\mathcal{R}\neq\emptyset$. Then, a set $\mathcal{D}\subseteq S$ is called \emph{$\mathcal{R}$-comparable} if every pair of 2-intervals in $\mathcal{D}$ are $R$-comparable for some $R\in\mathcal{R}$. Given $S$ and some $\mathcal{R}\in\{<,\sqsubset,\between\}$, the objective of the {2-interval pattern problem}\xspace is to compute a largest subset $\mathcal{D}\subseteq S$ such that $\mathcal{D}$ is $\mathcal{R}$-comparable.

Given a graph $G$ and a parameter $k$, the $k$-independent set problem asks whether there is an independent set of size $k$ in $G$. Fellows et al.~\cite{DBLP:journals/tcs/FellowsHRV09} proved that the $k$-independent set problem is $\mathsf{W[1]}$-hard on 2-interval graphs when $\mathcal{R} = \{<, \between, \sqsubset\}$. Our $\mathsf{W[1]}$-hardness results are also based on showing reductions from the \emph{$k$-Multicoloured Clique Problem}, which is known to be $\mathsf{W[1]}$-hard~\cite{DBLP:journals/tcs/FellowsHRV09}. The problem is defined as follows.

\begin{framed}
\noindent {\bf Problem:} $k$-Multicoloured Clique.

\noindent {\bf Input:} A graph $G$, and a vertex-colouring $c:V(G)\rightarrow\{1,2,\dots,k\}$ for $G$.

\noindent {\bf Question:} Is there a clique of size $k$ in $G$ such that, for each $c\in\{1,2,\dots,k\}$, there is exactly one vertex in the clique that has colour $c$?
\end{framed}

\section{$\mathsf{W[1]}$-Hardness}
\label{sec:hardness}
In this section, we prove that the {2-interval pattern problem}\xspace is $\mathsf{W[1]}$-hard when $\mathcal{R}=\{\sqsubset,\between\}$ and $\mathcal{R}=\{<,\between\}$. Our reduction is inspired by that of Fellows et al.~\cite{DBLP:journals/tcs/FellowsHRV09}. Let $(G,c,k)$ be an instance of the $k$-multicoloured clique problem (we assume w.l.o.g. for our purposes that $c$ is a proper colouring\footnote{Otherwise, one can remove the edges whose end vertices are coloured with the same colour.}). We construct a set $\mathcal{F}$ of 2-intervals such that $G$ has a multicoloured clique of size $k$ if and only if $\mathcal{F}$ contains a set of $k'=2k+4{k\choose 2}$ disjoint 2-intervals that are pairwise comparable in one of the relations in $\mathcal{R}$; the value of $k'$ will be clear from our construction. We first describe an outline of the construction and the corresponding gadgets. Then, we give the details on how to organize the gadgets on the real line specific to each of the sets $\mathcal{R}=\{\sqsubset,\between\}$ and $\mathcal{R}=\{<,\between\}$. For a colour $i\in\{1,2,\dots,k\}$, let $V_i(G)$ denote the set of vertices of $G$ that have colour $i$. Moreover, for every distinct pair of colours $i,j$, let $E_{(i,j)}(G)$ denote the set of edges $(u,v)$ of $G$ such that $\{c(u),c(v)\}=\{i,j\}$. That is, $E_{(i,j)}(G)$ consists of all the edges whose end vertices are coloured with two distinct colours $i$ and $j$.

\paragraph{Outline.} The construction consists of two main types of gadgets: \emph{selection} and \emph{validation}. By selection gadgets, we ensure that 2-intervals representing $k$ vertices with distinct colours and ${k\choose 2}$ edges with distinct pairs of colours are selected. By validation gadgets, we ensure that the selected set of 2-intervals are valid in the sense that the $k$ selected vertices are actually adjacent in the graph and the selected edges are indeed over the selected set of vertices. We group the 2-intervals corresponding to vertices of the same colour together in a \emph{vertex-selection} gadget in such a way that any feasible solution for the {2-interval pattern problem}\xspace will have 2-intervals corresponding to one vertex per vertex-selection gadget. Similarly, we group the 2-intervals corresponding to edges with the same pairs of distinct colours $\{i,j\}$ together in a \emph{edge-selection} gadget such that any feasible solution for the {2-interval pattern problem}\xspace will have 2-intervals corresponding to one edge $(u,v)$ with $\{c(u),c(v)\}=\{i,j\}$. We will then organize the gadgets on the real line in such a way that any feasible solution will contain 2-intervals that are
$\mathcal{R}$-comparable.

Given $(G,c,k)$, we associate one 2-interval $I_v$ for each vertex $v\in V(G)$. Moreover, we associate four 2-intervals for each edge $(u,v)\in E(G)$: two 2-intervals $I_{(u,v)}$ and $I_{(v,u)}$ for each ``direction'' of the edge and two 2-intervals $I_{\{u,v\}}$ and $I'_{\{u,v\}}$ that are undirected. The 2-intervals for ``directed'' edges will be used for validation, and we will show below how they are constructed. Therefore, the number of 2-intervals of the constructed instance will be $|V(G)|+4|E(G)|$. We next give the details of each type of gadgets.

\paragraph{Vertex-selection gadget.} For each colour $c\in\{1,2,\dots,k\}$, we construct a vertex-selection gadget. The gadget has two components, which we denote  by $I_1(c)$ and $I_2(c)$; see Figure~\ref{fig:vertexGadget} for an illustration. The component $I_1(c)$ has $|V_c(G)|$ ``rows'' of intervals, each of which has $(k+1)$ ``columns''; each row corresponds to a vertex of $G$ with colour $c$. The intervals in the same column pairwise intersect. Moreover, for the intervals in a fixed column $j$, we assign an offset such that each interval in row $i>1$ intersects the interval that is in column $j+1$ and row $i-1$; see Figure~\ref{fig:vertexGadget}. The component $I_2(c)$ consists of two columns of intervals, and each columns has $|V_c(G)|$ rows. Here, we assign an offset such that the interval in the first column and row $i$ intersects the interval in the second column and row $i+1$ (see Figure~\ref{fig:vertexGadget}).

For each vertex $v\in V_c(G)$, we associate two 2-intervals $I_v$ and $I'_v$ as follows. The first (resp., second) 2-interval $I_v$ (resp., $I'_v$) is composed of the interval in the first (resp., last) column of $I_1(c)$ that corresponds to $v$ and the interval in the first (resp., second) column of $I_2(c)$ that corresponds to $v$. These 2-intervals are illustrated with dashed lines in Figure~\ref{fig:vertexGadget}. Each of the remaining $k$ columns in $I_1(c)$ corresponds to a colour in   $\{1,2,\dots,k\} \setminus\{c\}$.
 These $|V_c(G)|\times (k-1)$ intervals are later paired with intervals from edge-selection gadgets to form 2-intervals that correspond to ``directed'' edges. Notice that the intervals of the first column of $I_1(c)$ pairwise intersect, ensuring that at most one 2-interval corresponding to a vertex with colour $c$ can appear in any feasible solution. Similarly, for the $|V_c(G)|\times (k-1)$ intermediate intervals of $I_1(c)$ (i.e., the intervals of $I_1(c)$ excluding those in the first and last column), it means that all the edges of a $k$-multicoloured clique with at least one endpoint with colour $c$ are incident to the same vertex in $V_c(G)$.

\begin{figure}[t]
    \centering
	\includegraphics[width=\textwidth]{newVertexGadget-2}
	\caption{A vertex-selection gadget and the two 2-intervals $I_v$ and $I'_v$ corresponding to a vertex $v$.}
	\label{fig:vertexGadget}
\end{figure}

\begin{lemma}
\label{lem:vertexEnsuring}
Let $S$ be feasible a solution for the {2-interval pattern problem}\xspace, and consider the vertex-selection gadget $T$ corresponding to colour $c$. Moreover, let $M\subseteq S$ be the set of 2-intervals such that each 2-interval in $M$ has at least one interval in $T$. If $|M|\geq k+1$, then all the intervals in $M\cap T$ are selected from the same row of $T$.
\end{lemma}
\begin{proof}
Since there are $(k+1)$ columns in the component $I_1(c)$ of $T$,  $M$ cannot have more than $(k+1)$ 2-intervals, where each containing at least one interval from $T$. Hence, $|M|=k+1$,
 This means that $M$ must contain exactly one interval from every column of $I_1(c)$ and  hence, one from every column of $I_2(c)$. Consider the interval in the first column of $I_1(c)$ (that is in $M$) and assume that this interval is in row $i$, for some $1\leq i\leq |V_c(G)|$; it corresponds to a vertex $v\in V_c(G)$. We now show that every other interval in $M\cap T$ must also be in row $i$. Since $M\subseteq S$ and $S$ is a feasible solution, then the interval in the first column of $I_2(c)$ and row $i$ must also be in $M$ because these two intervals form one of the two 2-intervals corresponding to $v$. Now, suppose that the interval in $M$ that is from the second column of $I_2(c)$ is in row $i'$. Clearly, $i'\leq i$  (i.e., $i'$ lies below $i$) because otherwise the interval of $M$ that is in the first column of $I_2(c)$ would intersect this interval due to the offset. Since $M\subseteq S$ and $S$ is a feasible solution, $M$ must contain the interval in the last column of $I_1(c)$ that is in row $i'$ (as   only these two would form a valid 2-interval  while considering $I_2(c)$). If $i'<i$, then it is not possible to have exactly one interval from column $j$ of $I_1(c)$ in $M$ for all $j=2,3,\dots,k$ because the offset would imply that at least two intervals must intersect in $M$. Therefore, $i'=i$. In the same way, we can show that the subsequent intervals
 of $M\cap T$ must also be in row $i$.
\end{proof}

Observe that the assignment of two 2-intervals for each vertex $v\in V_c(G)$ and placement of their second intervals in $I_2(c)$ with an offset allowed us to argue that the remaining intervals are also selected from the same row of the vertex-selection gadget. We will use a similar construction to argue the same for edge-selection gadgets. Before we continue, one might wonder why we needed $I_2(c)$ and why could not we have only $I_1(c)$ with one 2-interval for each vertex. Although this would force the selection of remaining intervals from the same row, it is impossible to place such a gadget on the real line while maintaining $\mathcal{R}$-comparability. To ensure $\mathcal{R}$-comparability, we will need to place $I_1(c)$ and $I_2(c)$ on different parts of the real line, possibly far apart from each other.

\paragraph{Edge-selection gadget.} For each distinct pair of colours $(i,j)$, we construct an edge-selection gadget. The gadget has two main components, which we denote by $C_1(i,j)$ and $C_2(i,j)$. The component $C_1(i,j)$ has $|E_{(i,j)}|$ rows of intervals each of which corresponds to an edge $(u,v)$ of $G$ such that $\{c(u),c(v)\}=\{i,j\}$; see Figure~\ref{fig:edgeGadget}(a). Each row has four columns of intervals; the intervals in the same column pairwise intersect. Moreover, there is an offset such that an interval in column $t$ intersects the interval in column $t+1$ that is in the row immediately above it. The component $C_2(i,j)$ has $|E_{(i,j)}|$ rows and only two columns. There is also an offset between the intervals similar to the offset defined for the intervals in $C_1(i,j)$; see Figure~\ref{fig:edgeGadget}(b). The row $r$ in $C_1(i,j)$ corresponds to an edge $(u,v)\in E(G)$ if and only if the row $r$ in $C_2(i,j)$ corresponds to the edge $(u,v)\in E(G)$.

\begin{figure}[t]
    \centering
	\includegraphics[width=.85\textwidth]{newEdgeGadget}
	\caption{An illustration of the two components of an edge-selection gadget; namely, (a) $C_1(i,j)$ and (b) $C_2(i,j)$. The two 2-intervals $I_{\{u,v\}}$ and $I'_{\{u,v\}}$ corresponding to the edge $(u,v)\in E(G)$ are shown dashed-dotted red.}
	\label{fig:edgeGadget}
\end{figure}

Recall that for each edge in $E(G)$, we associate four 2-intervals; we next describe the construction of these 2-intervals. Let $(u,v)\in E(G)$ such that $c(u)=i$, $c(v)=j$ and $i<j$. Then, the 2-interval $I_{\{u,v\}}$ (resp., $I'_{\{u,v\}}$) is composed of the interval in the first column (resp., last column) of the row corresponding to $(u,v)$ in $C_1(i,j)$ and the first interval (resp., second interval) of the row corresponding to $(u,v)$ in $C_2(i,j)$. See Figure~\ref{fig:edgeGadget} for an illustration. The 2-interval $I_{(u,v)}$ (associated with the ``directed'' edge $(u,v)$) is composed of the interval in the second column of $C_1(i,j)$ and the interval in the vertex-selection gadget of $i$ that is in the row corresponding to vertex $u$ and the column for colour $j$. The 2-interval corresponding to the ``directed'' edge $(v,u)$ is constructed in a similar way: it consists of the interval in the third column of $C_1(i,j)$ and the interval in the vertex-selection gadget of $j$ that is in the row corresponding to vertex $v$ and the column for colour $i$. Figure~\ref{fig:vertexEdgeGadget} illustrates an example for constructing the two 2-intervals corresponding to such ``directed'' edges. Note that the latter two 2-intervals that correspond to ``directed'' edges are used for validation: they ensure that if the 2-intervals of a vertex $u$ with colour $i$ is selected, then all the selected edges with an endpoint of colour $i$ are incident to $u$.
\begin{lemma}
\label{lem:edgeEnsuring}
Let $S$ be a feasible solution for the {2-interval pattern problem}\xspace, and consider an edge-selection gadget $T$. If there are four 2-intervals in $S$ such that each of them has at least one interval in $T$, then all such four 2-intervals must have intervals from the same row of $T$.
\end{lemma}
\begin{proof}
The proof uses an argument similar to the one we used in the proof of Lemma~\ref{lem:vertexEnsuring}. Suppose that $T$ corresponds to edges with colours $i$ and $j$, where $i<j$. Now, consider the gadget $C_1(i,j)$. Clearly, $S$ can have at most one interval from each column of $C_1(i,j)$. Since $S$ has four 2-intervals that have at least one interval in $T$, the set $S$ contains exactly one interval from each column of $T$. Suppose that the interval of the first column of $C_1(i,j)$ (that is in $S$) is at row $t$ for some $1\leq t\leq |E_{(i,j)}|$. Notice that this interval forms a 2-interval with the first interval in row $t$ of $C_2(i,j)$ and so that interval must also be in $S$ (these two intervals form a valid 2-interval and $S$ is a feasible solution). We now show that the interval of the last column of $C_1(i,j)$ (that is in $S$) must also be at row $t$. Suppose for the sake of contradiction that it is at a row $t'\neq t$. First, by construction, this interval forms a 2-interval with the second interval in row $t'$ of $C_2(i,j)$ and so that interval must also be in $S$. If $t'>t$, then the second interval in row $t'$ of $C_2(i,j)$ intersects with the first interval in row $t$ of $C_2(i,j)$ by the construction and so they cannot both be in $S$---a contradiction. Moreover, if $t'<t$, then $S$ cannot contain an interval from both the second and third columns of $C_1(i,j)$ because at least one of them intersects the interval of $S$ that is in either the first or the last column of $C_1(i,j)$---a contradiction. Therefore, $t'=t$ and so the two intervals in $S$ that are in $C_2(i,j)$ are also from the same row $t$. Finally, the fact that $t'=t$ forces the intervals in the second and third columns of $C_1(i,j)$ (that are in $S$) to be also from the row $t$.
\end{proof}

\begin{figure}[t]
	\includegraphics[width=\textwidth]{newVertexEdge}
	\caption{An illustration of the two 2-intervals corresponding to the ``directed'' edges $(u,v)$ and $(v,u)$, assuming $c(u)=1$ and $c(v)=2$. The dashed (red) rectangles shown in gadgets $I_1(\cdot)$ indicate the first and last columns of intervals in the gadget.}
	\label{fig:vertexEdgeGadget}
\end{figure}

By the above constructions, we obtain the set $\mathcal{F}$ of 2-intervals as
\[
\mathcal{F}=\{I_v, I'_v|v\in V(G)\}\cup\{I_{\{u,v\}},I'_{\{u,v\}},I_{(u,v)},I_{(v,u)}|(u,v)\in E(G)\}.
\]
Since we associate each vertex with two 2-intervals and each edge with four 2-intervals, we have $|\mathcal{F}|=2|V(G)|+4|E(G)|$. The construction of our gadgets can all be done in $\mathsf{FPT}$-time. In the following, we show the arrangement of the gadgets on the real line specific to each of $\mathcal{R}=\{\sqsubset,\between\}$ and $\mathcal{R}=\{<,\between\}$. Then, we show that any $k$-multicoloured clique in $G$ corresponds to $2k+4{k\choose 2}$ pairwise disjoint 2-intervals of $\mathcal{F}$. For brevity, let $k'=2k+4{k\choose 2}$ for the rest of this section.

\subsection{Hardness for $\mathcal{R}=\{\sqsubset,\between\}$}
We now show how to arrange the gadgets on the real line when $\mathcal{R}=\{\sqsubset,\between\}$. To this end, consider the ordering $\{1,2,\dots,k\}$ of colours. We place the gadgets on disjoint regions of the real line from left to right as follows. First, for each pair of distinct colours $i$ and $j$, $1\leq i<j\leq k$, we place the gadget $C_2(i,j)$ on the line in this order; that is, we first place the gadgets $C_2(1,j)$ for all $j=2,\dots,k$, then the gadgets $C_2(2,j)$ for all $j=3,\dots,k$ and so on. Then, we place the gadgets $I_1(c)$ ($1\leq c\leq k$) from left to right in the increasing order of $c$. Next, we place the gadgets $C_1(i,j)$, $1\leq i<j\leq k$ in the same order as we placed their corresponding gadgets $C_2(i,j)$. Finally, we place the gadgets $I_2(c)$ ($1\leq c\leq k$) in the same order as we placed their corresponding gadgets $I_1(c)$. See Figure~\ref{fig:exampleCN} for an example. This forms our instance $(\mathcal{F},\mathcal{R}, k')$ of the {2-interval pattern problem}\xspace, where $\mathcal{R}=\{\sqsubset,\between\}$ and $k'=2k+4{k\choose 2}$. Clearly, this arrangement can be done in $\mathsf{FPT}$-time. Moreover, one can verify that any two 2-intervals in this instance are $\mathcal{R}$-comparable, where $\mathcal{R}=\{\sqsubset,\between\}$.
\begin{lemma}
\label{lem:nestCross}
Graph $G$ has a $k$-multicoloured clique if and only if the {2-interval pattern problem}\xspace on $\mathcal{F}$ has a feasible solution of size $k'$ with respect to $\mathcal{R}=\{\sqsubset,\between\}$.
\end{lemma}
\begin{proof}
$(\Rightarrow)$ Suppose that $G$ has a $k$-multicoloured clique. For each colour $c$, let $v_c$ be the vertex in the clique with colour $c$. Then, for every colour $c$, we select the two 2-intervals $I_{v_c}$ and $I'_{v_c}$ from the vertex-selection gadget corresponding to $c$. Moreover, for every pair of colours $i$ and $j$ with $i<j$, let $(u_i,u_j)$ be the edge in the clique such that $c(u_i)=i$ and $c(u_j)=j$. Then, we select the four 2-intervals $I_{\{u_i,u_j\}}, I'_{\{u_i,u_j\}}, I_{(u_i,u_j)}$ and $I_{(u_j,u_i)}$. In this way, we have selected $k'$ 2-intervals in total. Moreover, by the arrangement of gadgets on the real line, one can verify that this set of $k'$ 2-intervals is $\mathcal{R}$-comparable.

\begin{figure}[t]
	\includegraphics[width=\textwidth]{aCompleteExampleCN}
	\caption{The arrangement of gadgets for $\mathcal{R}=\{\sqsubset,\between\}$.}
	\label{fig:exampleCN}
\end{figure}

$(\Leftarrow)$ Consider a set $S$ of $k'$ 2-intervals that is a feasible solution for the {2-interval pattern problem}\xspace with respect to $\mathcal{R}=\{\sqsubset,\between\}$. First, observe that $S$ can have at most one interval from the first column of every vertex-selection gadget. We now show that it must contain at least one such interval from the first column of every vertex-selection gadget. Let $S_1\subseteq S$ (resp., $S_2\subseteq S$) be the set of 2-intervals such that each 2-interval in $S_1$ has at least one interval in a vertex-selection gadget (resp., an edge-selection gadget). Moreover, let $S_3\subseteq S$ (resp., $S_4\subseteq S$) be the set of 2-intervals such that each 2-interval in $S_3$ (resp., $S_4$) has exactly two intervals from the same vertex-selection gadget (resp., the same edge-selection gadget). Observe that $|S_2|\leq 4{k\choose 2}$ because the component $C_1(\cdot)$ of an edge-selection gadget has four columns and no two intervals in $S$ can come from the same column of any given $C_1(\cdot)$. This means that $|S_3|\geq 2k$. But, there are exactly $k$ vertex-selection gadgets and at most two 2-intervals of $S_3$ can be from the same vertex-selection gadget. Hence, $|S_3|=2k$ and so $|S_2|=4{k\choose 2}$. Since there are exactly ${k\choose 2}$ edge-selection gadgets, it follows that we have exactly four 2-intervals in $S$ that come from the same edge-selection gadget. By Lemma~\ref{lem:edgeEnsuring}, all the 2-intervals coming form the same edge-selection gadget lie in the same row of the gadget.

On the other hand, $|S_1\setminus S_3|\leq k(k-1)=2{k\choose 2}$ because we have $k$ vertex-selection gadgets, the component $I_1(\cdot)$ of any vertex-selection gadget has $k-1$ ``internal'' intervals, and at most one of such internal intervals (per column, per vertex-selection gadget) can be in $S$. Notice that a 2-interval has exactly one interval in a vertex-selection gadget if and only if it has exactly one interval in an edge-selection gadget. Therefore, $S_2\setminus S_4=S_1\setminus S_3$. Since $\{S_1,S_3,S_4\}$ (or, $S_2,S_3,S_4$) forms a partition of $S$, we must have $|S_2\setminus S_4|=|S_1\setminus S_3|=2{k\choose 2}$. That is, there are exactly $2{k\choose 2}$ 2-intervals that have exactly one interval in a vertex-selection gadget and the other interval in an edge-selection gadget. Notice that at most $k-1$ of such $2{k\choose 2}$ 2-intervals can come from the same vertex-selection gadget. Since there are $k$ vertex-selection gadgets, there are exactly $k-1$ of them from each vertex-selection gadget. This means that, for each vertex-selection gadget, there are $k+1$ 2-intervals in $S$ that come from this gadget. By Lemma~\ref{lem:vertexEnsuring}, these $k+1$ 2-intervals all come from the same row of the gadget. Hence, we select the $k$ vertices corresponding to these $k$ rows. We now claim that they are a feasible solution for the $k$-multicoloured clique. Clearly, each selected vertex has a unique colour. Moreover, take any colour $c$ and let $u$ be the vertex that we selected with colour $c$. Recall that all the intervals of $S$ that come from the vertex-selection gadget $c$ are in the same row as that of $u$. There are $k-1$ of them (excluding those corresponding to $u$ itself) and each is paired with an interval in an edge-selection gadget corresponding to the pair $(c,c')$ of colours, for all colours $c'\neq c$. Therefore, there exists an edge between $u$ and every other selected vertex and so the $k$ selected vertices are indeed a feasible solution for the $k$-multicoloured clique.
\end{proof}

By Lemma~\ref{lem:nestCross}, we have the following theorem.
\begin{theorem}
The {2-interval pattern problem}\xspace is $\mathsf{W[1]}$-hard when $\mathcal{R}=\{\sqsubset,\between\}$.
\end{theorem}

\subsection{Hardness for $\mathcal{R}=\{<,\between\}$}
We now show that the {2-interval pattern problem}\xspace is $\mathsf{W[1]}$-hard even when $\mathcal{R}=\{<,\between\}$. To this end, we show how to arrange the gadgets on the real line such that any pair of two 2-intervals are $\{<,\between\}$-comparable. Then, one can prove a result similar to Lemma~\ref{lem:nestCross} for $\mathcal{R}=\{<,\between\}$, concluding that the problem is $\mathsf{W[1]}$-hard even for $\mathcal{R}=\{<,\between\}$. Here, we only show the arrangement.

\begin{figure}[t]
	\includegraphics[width=\textwidth]{aCompleteExampleCP}
	\caption{The arrangement of gadgets for $\mathcal{R}=\{<,\between\}$.}
	\label{fig:exampleCP}
\end{figure}

Consider the ordering $\{1,2,\dots,k\}$ of colours. We place the gadgets on disjoint regions of the real line from left to right as follows. First, for each pair of distinct colours $i$ and $j$, $1\leq i<j\leq k$, we place the gadget $C_2(i,j)$ on the line in this order; that is, we first place the gadgets $C_2(1,j)$ for all $j=2,\dots,k$, then the gadgets $C_2(2,j)$ for all $j=3,\dots,k$ and so on. Then, we place the gadgets $C_1(i,j)$, $1\leq i<j\leq k$ in the same order as we placed their corresponding gadgets $C_2(i,j)$. Next, we place the gadgets $I_1(c)$ ($1\leq c\leq k$) from left to right in the increasing order of $c$. Finally, we place the gadgets $I_2(c)$ ($1\leq c\leq k$) in the same order as we placed their corresponding gadgets $I_1(c)$. See Figure~\ref{fig:exampleCP} for an example. This forms our instance $(\mathcal{F},\mathcal{R}, k')$ of the {2-interval pattern problem}\xspace, where $\mathcal{R}=\{<,\between\}$ and $k'=2k+4{k\choose 2}$. Clearly, this arrangement can be done in $\mathsf{FPT}$-time and one can verify that every of pair of 2-intervals are $\{<,\between\}$-comparable.
\begin{theorem}
The {2-interval pattern problem}\xspace is $\mathsf{W[1]}$-hard when $\mathcal{R}=\{<,\between\}$.
\end{theorem}

\section{Conclusion}
\label{sec:conclusion}
In this paper, we showed that the {2-interval pattern problem}\xspace is $\mathsf{W[1]}$-hard when $\mathcal{R}=\{\sqsubset,\between\}$ and $\mathcal{R}=\{<,\between\}$; hence, fully settling the parameterized complexity of the problem when parameterized by the size of an optimal solution. It would be interesting to examine $\mathsf{FPT}$-algorithms with respect to other parameters such as the maximum number of pairwise intersecting $2$-intervals.

\bibliographystyle{plain}

redpajama_set_name: RedPajamaArXiv


text:
The Ultimate Jaws Filming Location Map of Martha's Vineyard
By Jazmine Hogan Donaldson Oct 7, 2014, 3:00pm EDT
View as Map
Back in 1974, a few malfunctioning pneumatically powered prop sharks, water logged cameras, unwanted sailboats drifting into frame, seasick actors, a blown schedule, a really blown budget, and an up-and-coming director named Steven Spielberg made movie magic on Martha's Vineyard with Jaws. The film, based on Peter Benchley's bestselling novel, went on to win multiple Academy Awards and is considered the original summer blockbuster. Just why was one of the most successful motion pictures of all time filmed on the Vineyard?
Well, long before state's began offering film tax incentives, turning the Carolina's into the default stand-in for the Cape & Islands, the production went in search of "a vacation area that was lower middle class enough so that an appearance of a shark would destroy the tourist business." As we said, it was a long time ago. Anyway, cue Martha's Vineyard - and the John Williams score - for the fictional island of Amity. These days, the real island celebrates the fake island being terrorized by an enormous great white shark with the occasional JawsFest and plenty of readily-available "You're gonna need a bigger boat" type of swag. Since the movie was released almost 40 years ago, on June 1, 1975, here's hoping there's some sort of huge anniversary event being planned. In the meantime, we've mapped out many of the Amity filming locations, with help from Then & Now Movie Locations, The Worldwide Guide to Movie Locations, and this IGN round-up. Take the Jaws tour this way:
1. Opening Scene
"Jaws" begins here with a beach bonfire and the demise of poor Chrissie Watkins.
2. Brody House
265 East Chop Drive
Vineyard Haven, MA 02568
The house featured in the production has been completely renovated, but this is still Chief Martin Brody's address.
3. Amity Police Department
South Water Street & Davis Lane
Brody types up the first "shark attack" police report here just before the secretary tells him about a far more serious crime, some nine-year-olds karate-chopping fences. Ugh, kids. Oh, well, it's off to Amity Hardware for shark warning sign supplies.
4. Keisel's Bicycle Rental & Amity Gazette
2 South Water Street
The Amity Gazette and Keisel's Bicycle Rental are a stone's throw away from one another on S. Water Street. Here, shop owner Keisel complains to Brody about the karate-choppers damaging his bicycles and said fence.
5. Amity Hardware
South Water Street & Main Street
Brody grabs supplies for his "Beach Closed" mission at Amity Hardware and then walks through the center of town.
6. Chappy Ferry
53 Dock Street
The ferry worked as both a principal camera boat for the production and starred in the scene where Brody is browbeaten by the mayor into keeping the beaches open for the Fourth. You know, for the tourists. "Martin, it's all psychological. You yell barracuda, everybody says, "Huh? What?" You yell shark, we've got a panic on our hands on the Fourth of July."
7. Amity Town Hall
Sure, things have changed some at Edgartown's actual Town Hall, but there's no doubt still a blackboard around awaiting a Quint-style scrape.
8. Billboard/Lighthouse
35 Aquinnah Circle
Aquinnah, MA 02535
This is where the Mayor, Brody and Hooper argue about keeping the beaches open, referencing the defaced "Amity Island Welcomes You" billboard.You should probably check out Gay Head Light while you can, the place is battling erosion and there's a fundraising effort underway to move the lighthouse back from the crumbling clay cliffs.
9. Swimming Beach/Alex Kintner Attack
Joseph Sylvia State Beach
Oak Bluffs, MA 02539
"Alex...?""Alex...?"
10. The Bridge!
If there's one can't-miss "Jaws" location, it's the bridge between Edgartown and Oak Bluffs. What makes it special? Well, there's the "Jaws" connection and the fact that you're not actually supposed to jump off. Thus, the Jaws Bridge (officially it's the American Legion Memorial Bridge) is pretty much the most popular 12-20 foot jump you'll find.
11. Quint's Shop
Menemsha Inn Road
Chilmark, MA 02535
Mayor Vaughn finally asks Brody to hire an expert to hunt down and kill the shark. Cue Captain "here's ta swimmin' with bow-legged women" Quint. While his workshop was built for the production and no longer standing, the adorable fishing village/tourist haven of Menemsha remains, unlike the "Orca."
© 2022 Vox Media, Inc. All rights reserved.
Link copied to the clipboard.
South Beach, Edgartown, MA 02539
265 East Chop Drive, Vineyard Haven, MA 02568
South Water Street & Davis Lane, Edgartown, MA 02539
2 South Water Street, Edgartown, MA 02539
South Water Street & Main Street, Edgartown, MA 02539
53 Dock Street, Edgartown, MA 02539
70 Main Street, Edgartown, MA 02539
35 Aquinnah Circle, Aquinnah, MA 02535
Joseph Sylvia State Beach, Oak Bluffs, MA 02539
Sengekontacket Pond, Massachusetts 02539
Menemsha Inn Road, Chilmark, MA 02535

redpajama_set_name: RedPajamaCommonCrawl


text:
Posted on October 6, 2016 October 6, 2016 by The Bloc
Artist to Watch: Whitney
This may be a little late to the game, but having knowledge of this band could be important.
Whitney is a Chicago-based duo comprised of two former members of Smith Westerns: Max Kakacek and Julian Ehrlich. Ehrlich was also the drummer for Unknown Mortal Orchestra.
Their one and only album, Light Upon the Lake, was released in early June with a few singles coming out before then.
Describing their sound poses a bit of a challenge, which is possibly their appeal. Considerably unique for an indie band, Ehrlich's vocals are really high and soft, almost sounding feminine but it manages to blend well with their style.
The band uses a fair amount of horns to accompany their both electric and acoustic guitars, and the occasional piano chords. Their sound is relatively light and does not take the heavy rock element many bands tend to have. The record is easy listening.
Ehrlich's high voice really accompanies this soft vibe that gives the record a very acoustic feel. A good portion of the record's songs revolve around a soft or twangy guitar riff, that is then combined with easy drums.
The few songs that have horns give the record a touch of jazz as well, only giving them more of a unique sound. Their feel bounces back from jazz to soft country, all while maintaining the status of a true indie rock band. It's hard to not nod your head to every song as the easy beat plays along.
Personal Picks:
"No Woman": This track was released before the album but still holds as one of the more significant songs on the record. With piano, horns, then an acoustic chord that plays throughout, this is the first song on the album, and the first introduction to Ehrlich's unique voice. It's a soft song with a simple chorus that is more focused on a smooth guitar riff and strings than words. After every chorus, the song fades to silence then picks up again, and it just works. The simple rhythm of the chords that's then accompanied by the strings then that electric guitar give this song a real smooth feeling.
"Golden Days": My personal favorite song on the record, it's easily the loudest and most hardcore song on the album. Still keeping with the same vibe and high-pitched voice, it is hardcore compared to the rest of the record. With more electric guitar, the drumbeat is louder and more of a component of this track. Probably the most indie rock sounding song on the record, this track has a really positive vibe with riffs of guitar and horns that play along with it. Again this combination really works well together and every time I hear it I find myself either tapping along or nodding my head. There's even a horn solo followed by some "Na Na Na's" to end the track.
"On My Own": Starting off with that twangy electric guitar riff, the high vocals and a smooth bass line are the backbone of this song. Representative of the band's style, this track holds true to what to the album has to offer. The use of horns and a simple, catchy beat make up the rest of the song. This track is easy, catchy and not too serious.
"Light Upon the Lake": The vocals play the major role in this song. Harmonized over his own vocals, Ehrlich's voice powers this record through. A really soft song with no beat, the vocals are joined together with electric and acoustic guitar riffs that make this song one of the more simpler ones on the album. There are also harmonies with strings laid under them to give this song a bit of a different feel at times. It is smooth, calm, relaxing and another easy listen.
Featured Photo Credit: Featured photo courtesy of Whitney's Facebook page.
Vidal Serfaty is a junior broadcast journalism major and can be reached at vidals37@gmail.com.
This entry was posted in:Bloc Blogs, Music Lounge, Reviews
Tagged with:album, light upon the lake, music, review, the band, whitney
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Courtesy of the Nicaragua Dispatch we have Daniel Ortega, whose foreign assistance is in jeopardy, using a tight pinch to his advantage: he turns around the threat and puts NGOs in the gunsight. Now it may be illegal for Nicaraguan pro-democracy NGOs, we can assume - to receive funding from the United States.
The Yanqui Imperialista American government is out of your (thinning) hair.
Everyone has just remembered who the frikking boss is around here.
Many other Nicaraguans suffer, since this doesn't affect just the pro-democracy crowd. Oh well, Ortega's presidency was never really about them anyway.


text:
Apertura and Clausura Seasons – A change in Format for Scottish Football?
The Scottish Premiership is not a league without its detractors. Whether this be due to the one sided (two sided before Rangers' implosion) nature leading to an overly predictable end result; or the number of meaningless games for clubs safe from relegation at an early stage but without the staying power and/or stamina to challenge for the title; or indeed the complication of having the top/bottom six split for the final weeks of the season.
League reconstruction has often been discussed and different league formats outlined, dismissed and voted on. This has included discussions on increasing or decreasing the number of teams, splitting into the top or bottom six or introducing relegation playoffs to add further interest and offer an opportunity for additional turnover in terms of variety of teams participating.
But could the Scottish Professional Football league (SPFL) learn something from Latin America and introduce a league system widely used in that part of the world? This would be the "Apertura and Clausura" format, translated as "Opening and Closing", widely used in the Americas.
The basic premise is that throughout the nominal August-May (orthodox) season, two mini-seasons take place. An Apertura in the first half and a Clausura after a winter break (or summer break in South America). Both the Apertura and Clausura would have a champion, with a playoff between both champions (if not the same team) to determine the overall winner, or indeed a wider NFL style playoff system to determine a champion. Such a format, or variations thereof are in place in countries such as Mexico, Colombia, Argentina, Costa Rica and Chile. Slight variations to formats exist like the number of teams in the championship playoff picture, the presence of a playoff for an overall winner and then the method by which relegation is determined – this can be complicated and relies on averages over a number of seasons.
The advantages of this format include a shorter season, breeding incessant competition and ensuring that a far greater proportion of matches are meaningful and competitive. There are fine margins, dropped points can derail a championship push or push teams towards the bottom. The pressing need for points accumulation and limited room for error mean that teams push harder for wins and are less likely to settle for draws. The shorter seasons also mean that there are climaxes every four or five months, with championship deciders taking place on a frequent basis. What is also evidenced is that the shorter format gives smaller clubs a fighting chance to compete for championships – a good run of form can catapult a team up the league. There are also more one off games against the bigger teams which can turn into "six-pointers" and in turn lead to a variety of winners or limit teams dominating to the same extent. Smaller squads are also perhaps not exposed to the same extent as happens through longer seasons where bigger squads can provide greater consistency, dealing with injuries and fatigue to a greater extent.
There are however disadvantages and drawbacks to this format, some of which overlap with the advantages listed above. The incessant competition and need for success, coupled with shorter seasons breeds short-termism at boardroom level with a run of bad results leading to exponentially increased pressure on managers and players. In turn this also reduces the willingness to take risks, meaning that youngsters are often overlooked in favour of the steady hand of a more experienced player within a side. This is evidenced in the leagues which utilise the format. There is also the disparity with the wider European season, including European competition which in turn feeds into International Tournaments. A knock on effect could be that exerting so much effort into an Apertura season could mean that for midweek Continental games players could become fatigued or burnt out more frequently.
In Scotland, the orthodox long season is used. Over the past few years Celtic have had the title sewn up by March or April with competition from the likes of Aberdeen burning out early in the new year as squad size and the lack of ability to refresh in the January transfer window hits, alongside the longer term accumulation of dropped points when compared to Celtic who drop points less frequently. As a result much of the excitement and focus towards the end of the season (aside than for Celtic fans) relates to the scrap for relegation and potentially positional placing allowing for qualification for European competition.
Looking at the main advantages of the split season as outlined above therefore, an argument could be made that this would be a viable and refreshing revamp to the Scottish season. The shorter Apertura and Clausura seasons would certainly increase the competition, allowing the likes of Aberdeen, Rangers, Hibs or Hearts to mount a serious challenge – looking back over the mid season point from previous years, there are relatively few points between teams and it is generally well into the new year before Celtic have pulled away. So it is a viable argument to suggest that there could be alternative winners relatively quickly with this new format given the shorter season.
The introduction of more one off, or bigger, meaningful games would also lead to further interest as can be seen over recent years in Cup competitions. A number of so called smaller clubs, including Hibs, Hearts, St Johnstone, Aberdeen and Inverness have all won cup competitions which shows that focus on a single short term competition and only needing to beat the biggest teams on one off occasions increases the variety of winners and spread of success amongst clubs. Overall therefore, looking at the advantages, there is a strong case for this format within Scottish Football in the interests of increasing competition.
From a scheduling perspective, the season is already relatively naturally split in half either side of Christmas – even with a Winter break scheduled in January in recent years. The transfer windows in summer and winter also fit in with this idea, meaning that teams could refresh between mini-seasons. Winners and indeed sides finishing bottom of both Apertura and Clausura seasons would play off for the championship itself and also relegation places. In the event that there were the same winners or bottom sides then this would just involve a minor adjustment to other playoff competitions between the runners up and third placed teams from both mini seasons for European spots and similarly the bottom sides for relegation. Effectively, at most there would be a couple more showpiece games at the end of the long season to decide a championship, European places or relegation.
As above however, there are disadvantages to this format which would also likely be seen within Scottish Football. There is already a problem with short-termism in terms of manager turnover and lack of opportunity for young players. A further reduction in patience or room for mistakes may exacerbate these existing issues. The number of players on short term or loan contracts would also likely increase – signing for a mini-season "push" at a title or to avoid relegation, leading to a disconnect between fans and team as players are not given a chance or signed to become embedded in the culture of the club.
Furthermore, the widening of competition and associated reduction in success levels for some of the bigger teams – who have an associated bigger influence over proceedings – is unlikely to go down well and be accepted, self preservation will always rule in these situations as has been seen in previous restructuring discussions.
Weighing the above up, while there are risks to added short term thinking and lack of flexibility for youngsters in this format, it is not considered that this would be significantly worse than the current situation, particularly once things bedded down. There is a situation at the moment where a run of six, seven or eight defeats can lead to a manager sacking – this wouldn't change to any great extent. Even if a team were certain of finishing bottom in the Apertura then a change of manager and some signings within the winter break (as would happen now) would give the team a fighting chance of staying up, albeit via a playoff after a more positive showing in the Clausura.
Furthermore youngsters are only really given a chance when they are exceptional talents or indeed good enough for the first team. Budgetary constraints limit the ability for Scottish sides to pay large transfer fees and so the impact on youth players would not be overly significant, most clubs are forced to promote from within in any case.
Overall therefore, there would be an increase in competition, wider variety of successful teams and more high profile, meaningful games. In turn this would lead to greater fan interest, greater attendance at games from fans wishing to see their club win a championship and also greater exposure to the land of milk and honey that is TV broadcasting and subsequent revenues.
As such, there is a compelling case for the SPFL to take their lead from our Latin American primos and switch up to an Apertura and Clausura season – it may just be the innovative solution the league system needs.
Published by sgmuri87
Football fan and keen traveller, based in Scotland. Fully paid up and battle weary member of the Tartan Army. Also enjoy watching football from across Europe and the world.	View all posts by sgmuri87
Scottish football, World Football
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Tradition versus Finance, Hampden versus Moving
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text:
Steve McQueen: A Biography
Written By: Marc Eliot
Narrated By: Marc Eliot
Publisher: Tantor Media
One of the top box-office draws of the 1960s and '70s with now-classics such as The Magnificent Seven, The Great Escape, The Thomas Crown Affair, and Bullit, Steve McQueen is renowned as one of the most exciting actors ever to come out of Hollywood. Now, in Steve McQueen: A Biography, bestselling author Marc Eliot gives unique insight into McQueen's life, from his films to his three marriages, many affairs, and struggles with addictions. This definitive biography, filled with original research and new interviews, will dazzle fans with its eye-opening portrayal of one of America's most memorable stars.
Brian McColgan
The book focused alot on his hollywood life, and the countless women SteveM slept with (particularly while he was married to his wife Neal sp?). I was more interested in his character - and in particular his fixation with racing-cars and motorcycles etc. While Eliot covered this in the book, I cringed everytime he incorrectly pronounced lemans (lay-mohn) as lay-maans. Further, I think the film did a bit better than Eliot characterized it as (IIRC - Speed when they showed it indicated it had pulled in about $40 million US all-in to that date). Further, there was not much detail about his family life, I guess that only came up when he was married to Ali McGraw. In the end, I found I did not much like the character Eliot portrayed. It seemed very ego-centric. Perhaps SteveM was not a likable guy all in - I just felt their was always more depth to him (his acting may have fooled me)!
by Marc Eliot


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I heard this on the way home. So I thought that I would share it with you all.
I wonder how I missed this one.
Just been listening to LP on YouTube.
This is rather emotional, imo.
Les Paul, the jazz guitarist and inventor who created one of the world's most famous electric guitars, has died. He was 94.
The Gibson Les Paul is the instrument of choice for Paul McCartney, Slash and U2's the Edge. It's still a firm favourite with younger bands such as Gallows. Les Paul helped create the famous model in the 1952, along with designer Ted McCarty.
Born in Wisconsin in 1915, Paul turned an early obssession with music into a successful career as a jazz guitarist, playing with the likes of Nat King Cole and Bing Crosby.
In 1939, Paul built one of the first solid-body electric guitars, known as "The Log", which prompted Gibson to approach him. Paul's legacy stretches much further than his signature guitar, however. As an inventor, Paul pioneered many studio techniques including multitrack recording, which allowed musicians to record parts separately before mixing them together into a finished track.
Paul reportedly died of complications from pneumonia at White Plains Hospital.
I'm rather surprised to be honest with you. my taste in Music recently has been loud and aggressive, rock, heavy rock, metal, heavy metal and nu metal.
So I was taken to a little quiet bar by some friends and image my surprise when I found I actually like the live music being played there.


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JUST IN: Appeal Court grants Lagos approval to join VAT collection suit
US force frees abducted citizen, kill seven bandits in…
WAEC blames Ekiti delayed results on website traffic,…
Video: How Lagos trader preserves fruits in drainage
An Appeal Court sitting in Federal Capital Territory (FCT) Abuja has granted Lagos State Government approval to join the ongoing suit between the Federal Government and River State Government to determine the collection of Value Added Tax (VAT) across the country.
After granting Lagos state government request, the appellate court ordered all processes earlier filed to be served on the Attorney-General and Commissioner for Justice for the state, Moyosore Onigbanjo.
The Apex government through the Federal Inland Revenue Service (FIRS) had filed an appeal at the appellate court to challenge a ruling made by a High Court sitting in Rivers State that awarded VAT collection to state governments.
At the resumed hearing of the matter on Thursday, the judges led by Justice Haruna Tsammani approved the state request and adjourned the case to October 7th, 2021.
Aside from that, the case would be now be heard at the Appellate Court in Port Harcourt as against the court sitting in Abuja.
Earlier, Onigbanjo had told the court that the constitution recognised states to collect VAT and the FIRS were aware of the provision of the law that guaranteed that.
He added that the principles for joinder of a party, seeking to be joined, must be a necessary party that has shown that its interest, legally and financially, would be affected.
While Onigbanjo explained that the case of joinder sought was to prevent multiplicity of action, counsel to the Rivers State government, Ifedayo Adedipe, supported the application by the Lagos State government.
The counsel to the FIRS, Mahmoud Magaji, meanwhile, opposed the application for joinder while relying on Section 243 of the Constitution.
He stated that the Constitution does not support applications for joinder and Lagos State was not a party to the suit at the trial court.
DSS distances personnel from Akunyili's murder
Nigerian actor under Indian Police detention for drugs peddling


text:
Q: how to check file availability by using sql Is there any possibility to check file availability in a particular location using mysql.
SELECT
tsc_uploaded_file_list.increment_id,
tsc_uploaded_file_list.document_id,
tsc_uploaded_file_list.document_category,
tsc_uploaded_file_list.uploaded_date,
tsc_uploaded_file_list.uploaded_time,
tsc_uploaded_file_list.phone_qunatity,
as file_availability  ('available',or 'not available ') in location concat 'tsc_uploaded_file_list.file_name,'.'tsc_uploaded_file_list.file_location'
FROM
tsc_uploaded_file_list

enter image description here

A: I think you need something like this -
SELECT
fl.increment_id,
fl.document_id,
fl.document_category,
fl.uploaded_date,
fl.uploaded_time,
fl.phone_qunatity,
concat(fl.file_name, 'Available in', fl.file_name)
FROM tsc_uploaded_file_list fl
WHERE fl.file_name = 'Your_name'
AND fl.file_location = 'File_location'

redpajama_set_name: RedPajamaStackExchange


Beautiful work and great photos.
Wow, that looks amazing! The detail work is top notch!
Glad to see you are still making progress Stew. Beautiful work.
Its runs a little lumpy because I only roughly centred the valves by eye and I had left some of the brackets lose so things should get better . I've still got to make the radius link to complete all the motion works but I'm very pleased that I've reached this important milestone.
A RUNNAH! That's a marvellous milestone, Stew!
It looks very, busy, with all the linkages moving in different directions.
That's great Stewart, quite an achievement to get to this point. Well done!
Stew, that is so cool! You should feel good about that! Just love watching all that linkage go this-way-and-that!
Thanks for your support and encouragement chaps.
With a long term projects these important milestones help give your enthusiasm a boost. Once I have the last motion link made and after a little more tinkering, its going to be set aside whilst I get busy with a little short term project I have planned then I'm going to start on the tender, I have a part finished tender that I bought so I have a bit of a head start, once I have that finished it will be dusted off and a start made on finishing it off, but there is still a lot of work to be done on it.
Bad Behavior has blocked 16297 access attempts in the last 7 days.


The "Tour 'de Lancelin" is on, (Sat 5th Oct) so get yourselves ready for the new "detour" route as you'll cycle through some wonderful rolling countryside. Marvel at the Gravity Centre as you speed along Military Road towards Gingin Brooke Road. As we turn left at this intersection it will mark the halfway point, where we will be guests of Bill & Lill at the Willowbrook Farm caravan park who will be providing complimentary coffee, tea and scones.
After farewelling Bill & Lill you'll start heading north to Cowalla Road where some spectacular countryside will find you on the run home to Lancelin. Alongside frolicking heifers, flowering wattle (non allergic) and through the orange groves, you'll be in cyclists paradise. As you get your first whiff of the Lancelin sea breeze, you'll be reenergised by the spectacular wind turbines daring and challenging you for wattage output. Turn into KW Road and Lancelin is a mostly down-hill run all the way. Lancelin Lodge is looking forward to welcoming us back once again – booking details will be following shortly. But for now cancel all your plans for the weekend of October 5th & 6th because it's "tour time".
All Club members welcome for the weekend. Full ride distance is 135k (one way), but you can ride just a section (1st half, 2nd half or whatever), or don't even ride – just come up and join us for occasion and then stay for the Club BBQ on the Saturday night. And then… for the diehards it is a ride home the same route on Sunday morning.


It is my pleasure to write to you as the 11th Representative Professor of the storied Department of Ophthalmology, Kyoto Prefectural University of Medicine on this occasion. This department, with a history spanning over 130 years, has seen its alumni go into the medical field and make important contributions to medicine. Bearing the weight and wonder of their achievements, I hope to take a new step towards the future.
The mission of the clinical department in medicine lies in treatment, research, and education.
Our department revolves around five specializations of the cornea, glaucoma, the vitreous, ocular function, and reconstructive surgery, and has built a specialty outpatient clinic for various services in dry eye, allergies, keratoconus and contact lenses, uveitis, neuro-ophthalmology, low vision, and SJS (Stevens-Johnson Syndrome). Providing the best care for patients means you need a medical team with a good relationship of trust. Founded on a stable relationship based on mutual trust and respect, we will further enhance our outpatient services, hoping to provide optimal care with the whole department, including related medical institutions.
Aiming for optimal care means working with various new treatments. We offer new treatments as part of clinical research or clinical trials, and we want to be involved in delivering that care safely to patients. Additionally, we aim to be a trusted medical group in cooperation with pharmacists and other allied health professionals.
Many incurable or difficult-to-treat diseases exist. Basic research based on an understanding of ocular diseases will lead to breakthroughs in medical conditions and treatments for the next generation. Avidly and humbly, we work in clinical research, and hope to develop as a group with friendly competition.
My hope is that with optimal care and by putting cutting-edge research into practice, we will educate the next generation and create a specialist ophthalmologist group that will be trusted by patients and medical staff.
I thank everyone for their support and guidance.


text:
Panyassis of Halicarnassus, sometimes known as Panyasis (), was a 5th-century BC Greek epic poet from Halicarnassus in the Persian Empire (modern-day Bodrum, Turkey).

Life
Panyassis was the son of Polyarchus () from Halicarnassus, but the historian Duris of Samos claimed that Panyasis was the son of Diocles () and from Samos. In addition, the historian Herodotus was either his nephew or his cousin. There was also another person of the same name, possibly the grandson of the poet, who wrote a work in two books on dreams.

In 454 BC, Panyassis was executed for political activities by the tyrant of Halicarnassus and grandson of Artemisia, Lygdamis ΙΙ (), after an unsuccessful uprising against him.

Panyasis was ranked by the Alexandrian School with the great epic poets.

The Suda encyclopedia mentions Panyassis.

Works
Panyassis enjoyed relatively little critical appreciation during his lifetime, but was posthumously recognised as one of the greatest poets of archaic Greece. His most famous works are: the Heracleia about the hero Heracles, written in epic hexameter, and the Ionica about the histories of the Ionian cities of Asia Minor, reportedly written in pentameter. These works are preserved today only in fragments. It is believed that he also wrote other works which have since been lost.

References

Ancient Halicarnassians
Ancient Greeks from the Achaemenid Empire
Early Greek epic poets
5th-century BC Greek people
5th-century BC poets
Executed ancient Greek people
5th-century BC executions
Year of birth unknown
Year of death unknown

redpajama_set_name: RedPajamaWikipedia


The Gas Target Force DOP is a microsolver used in building larger fluid simulations. The Fluid Solver and Smoke Solver DOPs that allow microsolvers to be added before or after the main solver step to extend or tweak the simulation. Alternatively, enterprising people may attempt to build an entire new solver out of microsolvers.
The Gas Target Force DOP builds a force field that directs smoke towards a target shape. It does this by building a Signed Distance field out of the target smoke, using 0.5 as the cut off surface. A force is then applied to the smoke, proportional to the density, in the direction of this target.
When the shape is reached the inward pointing force will be canceled out by hydrostatic pressure.
How strongly the force is applied.
Instead of building a goal field from the target relationship of this object, an existing scalar field will be used. The name used defaults to goal and is set in the Fields tab.
If not set, the vector force field of the goal is only built on the first frame. This saves a lot of work if the goal field isn't animated.
When set the Density Field and Goal Field are both treated as signed distance fields. The force is no longer scaled by the density field and no expansion term is applied to the positive error. These changes are appropriate for liquid simulations.
If set no signed distance field is computed. Instead, an error field is built. This error field is used as a goal divergence in computing the desired force vectors. This allows the matching of grey scale fields rather than just the 0.5 cutoff of a fog surface.
When the Density Field closely matches the Goal Field the error, and hence magnitude of the forces, decreases. Normalizing the error tries to preserve the total force to help the convergence feel constant.
When in hard-target mode, this is the radius to blur the gradient field with. A blurred gradient avoids harsh discontinuities where smoke is pulled in opposite directions, resulting in a smoother separation when topology changes.
Controls the range that the goal distance ramp operates on. The minimum goal distance refers to the left side of the ramp, the maximum the right side. Negative values imply inside the goal object.
Scales the force according to how far from the goal object it is. This can be used to disable the suction effect at a far distance, or to cut off the inward force once the smoke reaches the goal.
Each of the fields that cotnrol the smoke attraction can be visualized in a number of ways. The help for the Scalar Field Visualization or Vector Field Visualization provides more details about how these work.
These parameters control what name will be used for the input fields and the internal fields.
The smoke field to drive to the goal shape. The force is scaled by this field.
The target shape. The 0.5 contour is used as the goal perimeter.
An SDF version of the target shape built from the 0.5 contour of the goal.
A vector field pointing towards the goal field. This is what is used for the force.
The vector field to add the force to.
The scalar field to use as a collision hint when soft target is enabled. The generated force field will know to avoid the collision objects so specified.


· A reminder that tomorrow is Devil Day! Bring in your money to buy some tasty treats while supporting OT Clubs.
· Thank you to everyone who participated in the We Create Change Campaign. Together we raised over $700.00 taking us one step closer to building a well. In third place Ms Wright's class with $93.00, in second place was Ms Farquharson's class with $128 and in first place was Mrs Hanley's class with over $200.
· Attention Peer tutors: there will be a meeting today- period 3- we will meet in room 110 at the beginning of period 3.
· Wellspring Fundraiser today are teachers dressing up in costumes, Ms Hume's open yoga session will be outside at the end of third and start of fourth, Mr Perera and Mr Wood staying three legged during lunch, more healthy snacks in student success and background music in the Library.


Information about the Moon is published in Section D of The Astronomical Almanac. Such information includes the phases of the Moon for the year; notes and formulae for the mean elements of orbit and rotation, selenographic coordinates, and librations; and a daily physical ephemeris. Additionally, presented only in the AsA Online, are lunar polynomial coefficients for use in calculating apparent right ascension and declination and horizontal parallax. These are available in ASCII and PDF formats.


text:
Grupo Salinas Founder and Chairman Ricardo B. Salinas Addresses FIU Highilighting Opportunities at t
With a presentation entitled "Selling to the Poor: a 100-Year Success Story," Mr. Salinas shared some of the entrepreneurial and social development opportunities of businesses that focus on low-income consumers, a market referred to by University of Michigan Business School Professor C.K. Prahalad as the "Bottom of the Pyramid."
"The best solution to the problem of poverty is to create wealth," argued Mr. Salinas. "We need to look for new entrepreneurial solutions to old problems," he added.
MIAMI, March 5 /PRNewswire/ — Grupo Salinas, a group of dynamic, fast- growing and technologically advanced companies deeply committed to the modernization of the countries where they operate, is pleased to announce a successful visit by its chairman and founder, Ricardo B. Salinas, to the city of Miami.
Following a meeting with Miami Mayor Manny Diaz, who presented Mr. Salinas with a "Distinguished Visitor" proclamation, Mr. Salinas addressed the Greater Miami Chamber of Commerce at its Board of Governors Luncheon, with several hundred of Miami's most prominent business leaders.
Later in the day, Mr. Salinas visited the campus of Florida International University (FIU), where he spoke to faculty and students of the College of Business Administration, as part of the Wertheim Lecture Series.
However, the development of new businesses requires finding excellence in the employees and the right people with the right values.
Source: IT Business Net (link opens in a new window)


Give your kitty or pooch the classy treatment with the regal and sophisticated HOOPET Dog Cat Knit Sweater.
This knit sweater comes available to you in three different colors to allow you to choose the right one to fit your pet's personality.
The neck of this HOOPET Dog Cat Knit Sweater is a turtle neck style that fits their form perfectly in order to keep the warmth trapped in.
It has a space for each leg in order to keep them cozy from the top down. This sweater is made out of woolen material that is sure to keep them snug.
really goods. size m 3,5 kg the chihuahua. quality is good, looks expensive.
Kachestvo idealjnoe. razmer XL nemnogo boljshoj dlja sobaki 6 kg. Uzhe zakazala for razmer menjshe. Budu eshjo zakazivatj u etogo prodavca.
this quality really super store!!! fur coat sweater 2 took on the "chinese 4 kg, size l. fit all. delivery fast, track trackable.-seller good luck! all recommend!!!
baby super. soft. no smell. thread not stick. the new york city 2 kg. back 22 cm. just right. recommend store. отслеживался goods. 2 items.
cool super quality nice!! Is a FABRIC Elastic and comfortable. free shipping abriga But FABRIC Is More thin q Others jerseys, Is More To AUTUMN To clothing. But Is super quality nice and note you are CHEST perritas las free. recommend 100% arrive Some-10 days. les Done a Hole ponerles To BACK fashion backpack free shipping More hitch the strap harness By inside and power comodamente.
I ordered for a cat (04.09 order came 14.09). the quality is good, soft, odorless, track to track. I recommend!
Ever super happy!! the quality excellent!!! zel Shipping ever super Canary fast. thank you very much.
Stylish, soft, weightless. I think our sneeze will fall.


Mr. Anand Awasthi famously known as Jadugar Anand was born in Jabalpur, Madhya Pradesh in Central India. He started learning magic tricks at a very tender age of seven. Jadugar Anand prefers to call himself a self taught magician but he acknowledges that he is product of a long cherished Indian tradition. He has not only beaten Houdini's record of "escape from the box in the sea", but also has three world records under his belt.
Mr. Anand is the Fastest Magician on the Planet. Anyone can make an elephant disappear quickly, but how many can make it appear in a matter of seconds. He makes the Statue of Liberty disappear in slow motion, a trick performed for the first time in India. His world of illusion has been hailed by audiences and critics alike as one of the greatest magic shows of Asia, which is not merely performing tricks but creating miracles beyond your wildest imaginations.
STATUE OF LIBERTY DISAPPEARANCE (FIRST TO INTRODUCE IN INDIA)..
Beside Golchha Apartment, Civil lines, Jabalpur,M.P.


text:
Congestion Charge a Health Benefit?
By KizzieFK Last edited 137 months ago
KizzieFK Congestion Charge a Health Benefit?
In the realm of fuzzy math and statistical manipulation, nothing sounds so wonderful as things that'll add years to your life and nothing so scary as things that'll take those years away. And though we're not scientists or number-crunching pros, we don't want to feel like suckers when it comes to fear mongering figures.
So let's take a look at London's newest set of mortality figures, which supposedly triumph the roughly quarter decrease in traffic due to the congestion charges on the city center. See if you can wrap your head around this fact BBC News reports from a study in Occupational and Environmental Medicine:
Scientists from two London colleges calculated that since 2003, 1,888 extra years of life had been saved among the city's seven million residents.
OK, scientists, we're with you! We want to add years to our lives! We love our lungs! We know pollution is bad for us, and cars cause lots of pollution. Congestion charges are saving our lives!
But wait, what do the numbers really mean? Lets take a look at the figures, further analyzed by more scientists, to understand where these numbers are coming from.
Within the central charging area itself — where relatively few people actually live — the benefits seemed more significant, with an extra 183 years of life saved for every 100,000 residents.
So let's do the math on the best-affected area: 183 years divided by 100,000 people is an awfully small number. Further divided by the four-year time range? Miniscule. Multiplied by 365 days? Still just a fraction. Multiplied by 24 hours? Now we're getting somewhere: The scientists are talking about 4 hours of life per person.
Looking at the figures per person, however, isn't even accurate. Those saved years go disproportionately to sustain those with existing heart and lung problems by helping them breathe in more oxygen and fewer nasty tarry particles. Sure, we're happy that Grandma will have a better time breathing, but touting this small change as a real health benefit for the whole population? That might be going too far.
And what about the bulk of Londoners, who don't live in the congestion zones and are subjected to vehicles free to run rampant with their particulate emissions? The unnamed scientists found that outside of the city center, the reduction in pollution resulted in 18 years of life per 100,000 residents, or about 24 minutes per person.
And that original, impressive-sounding number — 1,888 extra years of life for Londoners — if really divided among the population, amounts to about 35 minutes of life per person.
We're not saying we want more pollution or think 35 minutes of life aren't valuable. We just don't know if it's a significant enough increase to warrant patting the congestion charge on the back.
Congestion charge photo courtesy of otzberg's Flickrstream
Last Updated 28 February 2008


If you're looking for a diverse and successful fishing experience in Texas, Galveston Bay is the perfect place to cast your rod. Whether you prefer inshore fishing or deep-sea fishing, Captains Ralph Frazier and Zach Lewis can steer you to where the fish are biting.
Featuring the largest jetties in the U.S. and miles of beachfront fishing, the Galveston Bay complex teems with a wide range of species, including the three most sought-after by anglers: redfish, speckled trout, and flounder.
If you prefer larger quarry and more of a battle with the elements, offshore fishing might be a better choice for you. To pursue tuna, red snapper, amberjack, or even sharks, schedule your next charter with Frazier's Guide Service.


text:
Emerging Growth Companies: You Have Been Warned
By Kevin LaCroix on May 21, 2012
In order to try to boost the number of companies going public, the recently enacted JOBS act provides for certain procedural and reporting advantages for "Emerging Growth Companies," which are defined in the Act as companies within five years of their IPO and with revenues less than $1 billion. A number of companies planning IPOs are already taking advantage of the new provisions. But at the same time, those same companies are warning investors that their status as Emerging Growth Companies may itself be a risk of which investors should be aware.
As discussed at greater length here, the JOBS Act contains a number of IPO "on ramp" procedures designed to ease the process and burdens of the "going public process" for Emerging Growth Companies (EGCs). The "on ramp" advantages are intended to ease the going public process. For example, EGCs can elect to submit their IPO registration statement for SEC review on a confidential, nonpublic basis, although the registration statement must be publicly filed at least 21 days before the IPO roadshow.
The Act also provides for reduced disclosure and reporting burdens for EGCs for as long as five years after an IPO – as long as the company continues to meet the definitional requirements. For example, an EGC will not be subject to Section 404(b) of the Sarbanes Oxley Act requiring an outside auditor's attestation report on the company's internal controls. Similarly, an EGC would be exempt from the requirements under the Dodd-Frank Act to hold shareholder advisory votes on executive compensation and on golden parachutes.
Since the enactment of these provisions, a number of commentators have noted that while these JOBS Act provisions may serve the laudable goal of easing the IPO process, these provision also introduce risks for investors. Nor are these remarks just coming from sideline commentators. Indeed many of the most specific warnings are coming from the companies themselves.
In her May 15, 2012 CFO.com article entitled "A New Risk Factor: The JOBS Act" (here), Sarah Johnson reports that for many of the companies taking advantage of the JOBS Act IPO on-ramp provisions, the fact that the companies are relying in the JOBS Act "is itself a risk factor." Her article notes that in recent days, at least 13 companies "have warned investors in their prospectuses filed with the Securities and Exchange Commission that the JOBS Act's breaks on SEC rules could actually be a turnoff." By way of example, she quotes Cimarron Software's recently filed S-1, in which the company states that "we cannot be certain if the reduced disclosure requirements applicable to emerging growth companies will make our common stock less attractive to investors."
In a May 14, 2012 post on his CorporateCounsel.net blog entitled "JOBS Act: EGC Status as a Risk Factor" (here), Broc Romanek takes a detailed look at one of the recent IPO filings, the S-1 that LegalZoom filed in connection with its proposed initial public offering. He notes that right on the cover page of the filing, the company warns that "we are an 'emerging growth company' under the federal securities laws, and will be subject to reduced public company reporting requirements." Among other things, the company notes in its filing that it will be taking advantage of the JOBS Act reporting exemptions as long as the company qualifies to do so, adding that "we cannot predict if investors will find our common stock less attractive because we rely on these exemptions." The company further notes that "if some investors find our common stock less attractive as a result, there may be less active trading for our common stock and our stock price may be more volatile."
These disclosures not only have the virtue of warning investors that the companies' status as emerging growth companies may make their stock less attractive. The warnings may, according to one commentator quoted in the CFO.com article, provide "cheap insurance" that could help the company if it later runs into trouble. As the commentator noted, if the emerging growth company is later sued, the company can say "We warned you that there weren't auditors looking independently at this."
These emerging growth companies advisory statements may indeed represent good precautionary disclosure. But it is fair to ask whether the cautionary statements go quite far enough. It is one thing to say that the company's reduced reporting requirements may make the company's stock less attractive. What the companies don't seem to be saying, at least not directly, is that the reduced reporting requirements could make their reported financial results less reliable. As a plaintiff's lawyer quoted in the CFO.com article notes, the emerging growth companies' precautionary disclosure may forewarn that their stock may not trade as high or as frequently as it might otherwise, but they are not saying that as a result of the reduced reporting requirements you "may get a nasty surprise" when the company no longer qualifies for the exemptions.
All of which says that while companies are now just trying to adjust to the newly enacted IPO process and reporting provisions, we will have to wait to see how all of this plays out in the securities litigation arena. For now, the companies taking advantage of the new rules do seem to be recognizing that while the new processes do present certain advantages, they do involve possibly increased risks as well.
The one thing that is certain is that because of the JOBS Act's broad definition of "emerging growth companies," a very larger percentage of companies going public will be eligible to take advantage of the new rules. Indeed, according to one report, of the 113 companies that went public in 2011, only 15 (or 13%) would not have qualified for the JOBS Act's IPO on-ramp procedures.
In other words, the disclosure issues discussed above, and the related liability concerns, could be an issue for a significant number of companies. Indeed, if the JOBS Act achieves its fundamental goals, these considerations could be a concern for an increasingly larger number of companies.
Delaware Seminar on Corporate and LLC Law: On Tuesday May 22, 2012, I will be participating in a panel the Delaware State Bar Association Corporate Law Section's annual "Recent Developments in Delaware Corporate and Alternative Entity Law" seminar. The seminar will be co-chaired by Francis Pileggi of the Eckert Seamans firm and also the author of the Delaware Corporate and Commercial Litigation Blog, and his law partner Kevin F. Brady and R. Montgomery Donaldson of the Montgomery McCracken Walker & Rhoads firm. Pileggi's recent post on his blog about the event can be found here.
The panel I will be participating in is entitled "Corporate Law Updates Via Blogs," and my fellow panelists will include Doug Batey of the Stoel Rives law firm and the author of theLLC Law Monitor blog; University of Illinois Law Professor Christine Hurt, of The Conglomerate blog; and Boston College Law Professor Brian Quinn, of The M&A Law Prof blog. Batey's recent blog post about our upcoming panel can be found here.
Our panel should afford the panelists an opportunity to reflect and comment upon the blogging process and experience. Along those lines, in an interesting May 18, 2012 post entitled "What Then is Blogging" (here), Dick Cassin of the indispensable The FCPA Blog sets out some of his views and thoughts about blogs and blogging. (Thanks to Cassin for quoting one of my prior blog posts).
Looking for Life in All the Wrong Places?: A May 18, 2012 Wall Street Journal article entitled "Searching a Billion Planets for Life" (here) describes scientists' efforts to write a recipe for "perfect planet"—that is, a place that is "not too cold, not too hot, not too toxic and chemically suitable for life as we know it" as a way to aid in the search for "potentially habitable alien worlds."
The challenge for the scientists is that the process of trying to come up with the recipe leaves them "grappling with the nature of life itself." Perhaps the most fundamental problem is that the analysis depends on presumptions "based on life as we know it" – that is, life on Earth.
The potential limitations of this Earth-biased analysis are revealed most dramatically just by looking at what has happened in recent years to our knowledge about life on Earth. Through a series of interesting discoveries, our awareness of the range of conditions in which life on Earth can thrive has expanded far beyond what was previously thought possible.
An interesting article in the May/June 2012 issue of The Economist's Intelligent Life magazine entitled "Some Like it Very Hot" (here) takes a look at the scientific advances that have revealed the teeming existence of "hyper-resilient microbes," organisms that can survive "levels of heat, cold, pressure, radiation and salt or acid concentrations that previously would have been thought fatal to all living things." These previously unknown organisms, now known as extremophiles, have been found deep beneath the sea floor; in the depths of Mexican caverns; in the core of nuclear reactors; in hydrothermal vents on the sea bed; and are constantly being discovered in ever more unlikely and seemingly inhospitable environments.
Among many other things, these discoveries show that "life can sustain itself in many more environments than was previously thought possible." This realization not only has enormous implications for the study of life on Earth; it has also given new life to the "idea that life is dispersed throughout the universe and is disseminated on meteorites or asteroids." Or to put it another way, "the bandwidth of survivable environments – and therefore, forms of life, has broadened enormously."
The implication for scientists hoping to increase their chances of finding life beyond Earth by narrowing their search only to the "perfect planets," may be that by narrowing their search, they may actually diminish their chances of finding outside our planet. But on the positive side, the likelihood that life outside of earth might exist and someday might actually be discovered both seem to have increased significantly.
Personally, I find all of this quite fascinating and even exciting. The possibility that life in the universe is not rare but could actually be quite common and even widely dispersed represents an entirely new way of looking at things. Instead of the Earth as a lone life-bearing vessel whirling through an empty, heartless void, it could instead be one of countless places where life is thriving. Of course, the possibility that life elsewhere might be merely microbial might not satisfy the most febrile science fiction fantasies. It would of course be much more exciting if there seemed to be a greater likelihood of discovery of intelligent life beyond earth. But it may be too much to hope for, to expect to find intelligent life beyond earth. After all, think of how hard it is to find intelligent life on our own planet.
In Case You Missed It: For the second weekend in a row, a major European soccer title has been determined in a last-minute come from behind victory. Last Sunday, it was Manchester City scoring two goals in stoppage time in their final game of the season to capture the English Premier League crown. This Saturday, Chelsea, playing against Bayern Munich on the German team's home field, won the UEFA Champions League club team title in almost equally dramatic fashion, winning in a penalty kick shootout.
Bayern Munich had many chances to put the game away, and seemingly had the game won when they finally scored on a Thomas Müeller header in the 82nd minute. But then with just two minutes left in regulation, on Chelsea's first corner kick of the game, Didier Drogba scored on a header to tie the game. As regulation time expired the game went into extra time (a thirty minute overtime period).
Drogba's fine goal to tie the game looked like it might have been naught when early in extra time he committed a foul by tripping Franck Ribèry in the penalty area. It seemed like another golden opportunity for Bayern Munich to put the game away, but Chelsea's goalie, Petr ČechArjen Robben's penalty kick. The 30-minute period ended with the teams still tied, setting up a penalty kick shootout. , stopped
Bayern Munich once again appeared to have the advantage as its goalie, Manuel Neuer, stopped the first Chelsea penalty kick from Juan Mata. After each team had attempted three penalty kicks, Bayern had made all three of its attempts, while Chelsea had only made two. Bayern substitute, Ivica Olic then missed his team's fourth shot while Ashley Cole made the next shot for Chelsea, bringing the two teams even. On Bayern Munich's fifth and final shot, Bastian Schweinsteiger , who looked as if taking the penalty kick was about the last thing in the world he wanted to do, hit the post. Drogba, looking calm and confident, smashed his kick into the corner of the net, securing Chelsea's improbable victory. The game-winner might be the 34-yearold Drogba's last act for Chelsea, as his contract with the team expires this summer.
It was a great game, although the Bayern Munich fans are not the only ones unhappy about the outcome. Tottenham Hotspurs, who finished fourth in the English Premier League and therefore otherwise qualified for the UEFA Champtions League competition, were dispossessed of the spot by Chelsea's win. Chelsea, which didn't otherwise qualify for the Champions league (since they finished sixth in the Premier League), secured an automatic spot in next year's Champions League competition with their win on Saturday. Since only four teams from each participating country can compete, that meant that Chelsea's win forced Tottenham out of its spot.
With all of this great end of season soccer just completed, it is even more exciting to look forward to the Euro 2012 national team championship competition, which kicks off on June 8, 2012 in Poland and Ukraine.
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A former Jigawa state Governor, Sule Lamido, on Thursday mocked President Muhammadu Buhari and a Chieftain of the All Progressives Congress (APC), Bola Tinubu, over the current fuel situation in Nigeria.
Speaking in Abuja, Lamido, who is currently facing corruption charges, said Buhari should lead a protest against the fuel situation.
Lamido also questioned the integrity of the All Progressives Congress, APC-led Federal.