text:
Alfons (Alfonso, Anfusus) (n. cca. 1120 – d. 10 octombrie 1144), a fost un normand din dinastia Hauteville, devenit principe de Capua de la 1135 până la moarte.

Alfons era cel de al treilea fiu al regelui Roger al II-lea al Siciliei cu prima sa soție, Elvira de Castilia. El a primit numele după bunicul său pe linie maternă, regele Alfonso al VI-lea al Castiliei.

Cu toate că data nașterii sale este necunoscută, el avea vârsta necesară pentru a duce războaie pentru a se menține la conducerea unui principat, atunci când, în 1135, tatăl său i-a acordat Principatul de Capua, detronându-l astfel pe principele de atunci, răsculat împotriva sa, Robert al II-lea, din dinastia Drengot. Roger al II-lea l-a numit pe cancelarul său Guarin să acționeze ca administrator al lui Alfons. Aceste măsuri au adus Capua în sfera de influență a puterii familiei Hauteville. În 25 iulie 1139, în virtutea tratatului de la Mignano, Alfons a obținut recunoașterea papală din partea lui Inocențiu al II-lea.

La moartea ducelui Sergiu al VII-lea de Neapole, care deschisese porțile orașului în fața lui Roger, Alfons a fost ales duce de Neapole. În aprilie 1140, împreună cu fratele său mai mare, Roger al III-lea, pe care tatăl lor îl numise duce de Apulia și Calabria, Alfons a invadat Abruzzo, cucerind un larg teritoriu al acestei regiuni, inclusiv importantul oraș costier Pescara. El și-a extins stăpânirea ajungând până la râul Tronto. Alfons a murit în 10 octombrie 1144, în timpul unei a doua invazii alături de fratele său, de această dată în Latium, împotriva papei Lucius al II-lea, în cadrul căreia cei doi normanzi au ajuns până la Rieti și Cagnano Amiterno.

Surse
Norwich, John Julius, The Kingdom in the Sun 1130-1194, Londra, Longman, 1970.

Decese în 1144
Normanzi
Italia normandă

redpajama_set_name: RedPajamaWikipedia


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

Genomic rearrangements are known to play a central role in the
evolutionary history of the species. Several operations act on the
genome, shaping the sequence of genes. A number of models to sort
a genome into another have been studied: reversals,
transpositions and more recently Double-Cut-and-Join (DCJ).
Another operation, called
\emph{block interchange}, consists in exchanging two intervals of a
genome.

Block interchanges scenarios have been studied for the first time by
Christie \cite{Christie96}. He proposed a polynomial-time algorithm
for computing the distance between two linear chromosomes with unique
gene content. Lin \etal \cite{Lin05} proposed later a better algorithm.
Yancopoulos \etal \cite{Yancopoulos05} introduced the DCJ operation
which consist in
cutting the genomes in two points and joining the four resulting
extremities in a different way. Interestingly, they noticed that a
block interchange can be simulated by two consecutive DCJs: an
excision followed by a reintegration.

Another very important feature in genome evolution is that genomes
often undergo duplication events: both segmental and whole-genome
duplications. Genome duplication events are followed by other
rearrangements events which result in a scrambled genome. Genome
halving consists in finding the sequence of events that allow to go
back from the scrambled genome to the original duplicated one.

Genome halving has been studied under several models: reversals
\cite{Mabrouk98}, translocation/reversals \cite{Mabrouk03}, DCJ
\cite{Warren08}, breakpoints \cite{Tannier08}. Most of the results led
to polynomial time algorithms. Particularly, under the DCJ model,
Mixtacki \cite{Mixtacki08} gave some useful results and data structures.
In this paper, we derive our results from those
results. Very recently, Kov{\'a}{\v c} \etal \cite{Kovac10} addressed
the problem of
reincorporating the temporary circular chromosomes induced by DCJs
immediately after their creation considering genome halving.
Although this problem is obviously related to the
problem we address, the aim and results are not the same. We are interested
in linear genomes, not in multilinear ones,
and we focus on pure block interchange scenarios whereas Kov{\'a}{\v c}
\etal focused on scenarios made of reversals, translocation, fusion,
fissions along with block interchanges.

Section \ref{sec:pre} gives definitions. In Section \ref{sec:lb}, we
first give a lower bound on the distance with helpful properties for
the rest of the paper. In Section \ref{sec:dist}, we prove the
analytical formula for the distance. We conclude in Section
\ref{sec:scenario} with a quadratic time and space algorithm to
obtain a parsimonious scenario.

\section{Preliminaries: duplicated genomes, rearrangement, genome halving problems}
\label{sec:pre}

In this section we give the main definitions and notations used in the paper.

\subsection*{Duplicated Genomes}

A genome is composed of genomic markers organized in linear or circular
chromosomes. A linear chromosome is represented by an ordered sequence of
unsigned integers, each standing for a marker, surrounded by two abstract
markers $\circ$  at each end indicating the telomeres. A circular chromosome
is represented by a circularly ordered sequence of unsigned integers
representing markers. For example,
$(\fst{1}~~\fst{2}~~\fst{3}) ~
(\circ~~\fst{4}~~\fst{5}~~\fst{6}~~\fst{7}~~\circ)$ is a genome
constituted of one circular and one linear chromosome.

\begin{definition}
A \emph{rearranged duplicated genome} is a genome in which each marker appears
twice.
\end{definition}

In a rearranged duplicated genome, two copies of a same marker are called paralogs. We distinguish paralogs by denoting one marker by $\fst{x}$ and its paralog by $\snd{x}$. By convention $\snd{\snd{x}}=x$.
For example, the following genome is a rearranged duplicated genome:
$(\circ~~\fst{1}~~\snd{1}~~\fst{3}~~\fst{2}~~\fst{4}~~\fst{5}~~\fst{6}~~\snd{6}~~\fst{7}~~\snd{3}~~\fst{8}~~\snd{2}~~\snd{4}~~\snd{5}~~\fst{9}~~\snd{8}~~\snd{7}~~\snd{9}~~\circ )$.

An \emph{adjacency} in a genome is a pair of consecutive markers.
For example, the genome $(\circ~~\fst{1}~~\fst{2}~~\circ)~ (\fst{3}~~\fst{4}~~\fst{5})$ has six adjacencies, $(\circ ~~\fst{1}),~(\fst{1}~~\fst{2}) ,~ (\fst{2}~~\circ)$, and $(\fst{3}~~\fst{4}) ,~ (\fst{4}~~\fst{5}) ,~ (\fst{5}~~\fst{3})$.
The linear
or circular order of the markers in a chromosome naturally induces an order
on the adjacencies that we denote by $<$. For example in the previous genome
the order induced on the adjacencies is:
 $(\circ ~~\fst{1}) < (\fst{1}~~\fst{2}) < (\fst{2}~~\circ)$, and $(\fst{3}~~\fst{4}) < (\fst{4}~~\fst{5}) < (\fst{5}~~\fst{3}) < (\fst{3}~~\fst{4})$.

A \emph{double-adjacency} in a genome $G$ is an adjacency $\aff{a}{b}$
such that  $\ass{a}{b}$ is an adjacency of $G$ as well. Note that a genome always has an even number of double-adjacencies.
For example, the four double-adjacencies in the following genome are indicated by dots :
$$G = (\circ~~\fst{1}~~\snd{1}~~\fst{3}~~\fst{2}~\cdot~\fst{4}~\cdot~\fst{5}~~\fst{6}~~\snd{6}~~\fst{7}~~\snd{3}~~\fst{8}~~\snd{2}~\cdot~\snd{4}~\cdot~\snd{5}~~\fst{9}~~\snd{8}~~\snd{7}~~\snd{9}~~\circ )$$

A consecutive sequence of double-adjacencies can be rewritten as a single marker; this process is called \emph{reduction}. For example, genome $G$ can be reduced by rewritting $\fst{2}~.~\fst{4}~.~\fst{5}$ and $\snd{2}~.~\snd{4}~.~\snd{5}$ as $\fst{10}$ and $\snd{10}$, yielding the following genome:
$$G^r = (\circ ~~\fst{1}~~\snd{1}~~\fst{3}~~\fst{10}~~\fst{6}~~\snd{6}~~\fst{7}~~\snd{3}~~\fst{8}~~\snd{10}~~\fst{9}~~\snd{8}~~\snd{7}~~\snd{9}~~\circ )$$

\begin{definition}
A \emph{tandem-duplicated genome} is a rearranged duplicated genome which can be reduced to a genome of the form $(\circ~~\fst{x}~~\snd{x}~~\circ )$.
\end{definition}

In other words, a tandem-duplicated genome is composed of a single linear chromosome where all adjacencies, except the two containing the marker $\circ$ and the central adjacency, are double-adjacencies.
For example, the genome $(\circ~~\fst{1}~\cdot~\fst{2}~\cdot~\fst{3}~\cdot~\fst{4}~~\snd{1}~\cdot~\snd{2}~\cdot~\snd{3}~\cdot~\snd{4}~~\circ )$ is a tandem-duplicated genome that can be reduced to
$(\circ~~\fst{5}~~\snd{5}~~\circ )$
by rewritting $\fst{1}~\cdot~\fst{2}~\cdot~\fst{3}~\cdot~\fst{4}$ and $\snd{1}~\cdot~\snd{2}~\cdot~\snd{3}~\cdot~\snd{4}$ as  $\fst{5}$ and $\snd{5}$.

\begin{definition}
A \emph{perfectly duplicated genome} is a rearranged duplicated genome such that each adjacency is a double-adjacency.
\end{definition}

For example, the genome $(1~~{2}~~{3}~~4~~\snd{1}~~\snd{2}~~\snd{3}~~\snd{4})$ is a perfectly duplicated genome.

\subsection*{Rearrangements}
\label{sec:rearrangement}

A rearrangement operation on a given genome cuts a set of adjacencies of the
genome called \emph{breakpoints} and forms new adjacencies with the exposed
extremities, while altering no other adjacency. In the sequel, the adjacencies
cut by a rearrangement operation are indicated in the genome by the symbol $\breakpoint$.

An \emph{interval} in a genome is a set of markers that appear consecutively
in the genome. Given two different adjacencies $(a~~b)$ and $(c~~d)$ in a genome
$A$ such that $(a~~b) < (c~~d)$, $[b~;~c]$ denotes the interval of $A$ beginning
with marker $b$ and ending with marker $c$.

In this paper, we consider two types of rearrangement operations called \emph{block interchange (BI)} and  \emph{double-cut-and-join (DCJ)}.

A \emph{block interchange} (\bi) on a genome $G$ is a rearrangement
operation that acts on four adjacencies in $G$,
$(a~~b) <  (c~~d) \leq (u~~v) < (x~~y)$ such that the intervals $[b~;~c]$ and
$[v~;~x]$ do not overlap,
swapping the intervals $[b~;~c]$ and $[v~;~x]$.
For example, the following block interchange acting on adjacencies
$(\snd{1}~~\fst{2})< (\fst{6}~~\snd{6})< (\snd{3}~~\fst{8})< (\snd{8}~~\snd{7})$
consists in swapping the intervals $[\fst{2},\fst{6}]$ and $[\fst{8},\snd{8}]$.
\begin{center}
$(\circ~~\fst{1}~~\snd{1}~\breakpoint~\mathbf{\fst{2}~~\fst{3}~~\snd{2}~~\fst{4}~~\fst{5}~~\fst{6}} ~\breakpoint~\snd{6}~~\fst{7}~~\snd{3} ~\breakpoint~~\mathbf{\fst{8}~~\snd{4}~~\fst{9}~~\snd{5}~~\snd{8}}~ \breakpoint~\snd{7}~~\snd{9}~~\circ)$

$\downarrow$

$(\circ~~\fst{1}~~\snd{1}~~\mathbf{\fst{8}~~\snd{4}~~\fst{9}~~\snd{5}~~\snd{8}}~~\snd{6}~~\fst{7}~~\snd{3}~~\mathbf{\fst{2}~~\fst{3}~~\snd{2}~~\fst{4}~~\fst{5}~~\fst{6}}~~\snd{7}~~\snd{9}~~\circ)$
\end{center}

A \emph{double-cut-and-join} (DCJ) operation on a genome $G$ cuts two different
adjacencies in $G$ and glues pairs of the four exposed extremities to form two
new adjacencies.
Here, we focus on two types of DCJ operations called \emph{excision} and \emph{integration}.

An \emph{excision} is a DCJ operation acting on a single chromosome by extracting an interval from it, making this interval a circular chromosome, and making the remainder a single chromosome (1 join). For example, the following excision extracts the circular chromosome $(\fst{2}~~\fst{3}~~\fst{4})$:
$$(\circ~\fst{1}~\breakpoint~\mathbf{\fst{2}~~\fst{3}~~\fst{4}}~\breakpoint~\fst{5}~~\fst{6}~\circ) \rightarrow (\mathbf{\fst{2}~~\fst{3}~~\fst{4}}) (\circ \fst{1}~~\fst{5}~~\fst{6}~\circ)$$

An \emph{integration} is the inverse of an excision; it is a DCJ operation that acts on two chromosomes, one being a circular chromosome, to produce a single chromosome.  For example, the following operation is an integration of the circular chromosome $(\fst{2}~~\fst{3}~~\fst{4})$:
$$\mathbf{(\fst{2}~\breakpoint~\fst{3}~~\fst{4}}) (\circ \fst{1}~~\fst{5}~~\fst{6}~\breakpoint~\circ) \rightarrow (\circ~\fst{1}~~\fst{5}~~\fst{6}~~\mathbf{\fst{3}~~\fst{4}~~\fst{2}}~\circ)$$

We now give an obvious, but very useful, property linking BI operations to DCJ operations.

\begin{property}
\label{1BIto2DCJ}
A single BI operation on a linear chromosome is equivalent to two DCJ operations: an excision followed by an integration.
\end{property}

\begin{proof}
Let $(\circ~~1~~U~~2~~V~~3~~\circ)$ be a genome, $U$ and $V$ the two intervals
that are to be swapped by a block interchange operation, $1$ $2$ and $3$ the
intervals constituting the rest of the genome (note that each of them may be
empty).

The first DCJ operation is the excision that produces the adjacency
$(1~~V)$ by extracting and circularizing the interval $[U~;~2]$:
$$(\circ~~1~\breakpoint~U~~2~\breakpoint~V~~3~~\circ) \rightarrow
(\circ~~1~~V~~3~~\circ)(U~~2~)$$

The second DCJ operation is the integration that produces the adjacency
$(U~~3)$ by reintegrating the circular chromosome $(U~~2)$ in the
appropriate way:
$$(\circ~~1~~V~\breakpoint~3~~\circ)(U~~2~\breakpoint) \rightarrow (\circ~~1~~V~~2~~U~~3~~\circ)$$\qed
\end{proof}

A \emph{rearrangement scenario} between two genomes $A$ and $B$ is a sequence of rearrangement operations allowing to transform $A$ into $B$.

\begin{definition}
A \emph{BI (resp. DCJ) scenario} is a rearrangement scenario composed of BI (resp. DCJ) operations.
\end{definition}

The length of a rearrangement scenario is the number of rearrangement operations composing the scenario.
\begin{definition}
The \emph{BI (resp. DCJ) distance} between two genomes $A$ and $B$, denoted by $d_{BI}(A,B)$ (resp. $d_{DCJ}(A,B)$), is the minimal length of a  BI (resp. DCJ) scenario between $A$ and $B$.
\end{definition}

\subsection*{Genome Halving}
\label{sec:halving}

We now state the genome halving problem considered in this paper.

\begin{definition}
Given a rearranged duplicated genome $G$ composed of a single linear chromosome, the \emph{BI halving problem} consists in finding a tandem-duplicated genome $H$ such that the BI distance between $G$ and $H$ is minimal.
\end{definition}

In order to solve the BI halving problem, we use some results on the \emph{DCJ halving problem} that were stated in \cite{Mixtacki08} as a starting point. Unlike the BI halving problem, the aim of the DCJ halving problem is to find a perfectly duplicated genome instead of a tandem-duplicated genome.

\begin{definition}[\cite{Mixtacki08}]
Given a rearranged duplicated genome $G$, the \emph{DCJ genome halving problem}
consists in finding a perfectly duplicated genome $H$ such that the DCJ distance
between $G$ and $H$ is minimal.
\end{definition}

The BI and DCJ genome halving problems lead to two definitions of \emph{halving distances}: the \emph{BI halving distance} (resp. \emph{DCJ halving distance}) of a rearranged duplicated genome $G$ is the minimum BI (resp. DCJ) distance between $G$ and any tandem-duplicated genome (resp. any perfectly duplicated genome) ; we denote it by $d^t_{BI}(G)$ (resp. $d^p_{DCJ}(G)$).\\

\section{Lowerbound for the BI halving distance}
\label{sec:lb}

In this section we give a lowerbound on the BI halving distance of a rearranged duplicated genome. We use a data structure representing the genome called the \emph{natural graph} introduced in \cite{Mixtacki08}.

\begin{definition}
The natural graph of a rearranged duplicated genome $G$, denoted by $\NG(G)$, is the graph whose vertices are the \emph{adjacencies} of $G$, and for any marker $u$ there is one edge between  $\aff{u}{v}$ and  $\asf{u}{w}$, and  one edge between  $\aff{x}{u}$ and  $\afs{y}{u}$.
\end{definition}

Note that the number of edges in the natural graph of a genome $G$ containing $n$ distinct markers, each one present in two copies, is always $2n$. Moreover, since every vertex has degree one or two, then the natural graph consists only of cycles and paths. For example, the natural graph of genome $G = (\circ~~ \fst{1}~~\snd{2}~~\snd{1}~~\snd{4}~~\fst{3}~~\fst{4}~~\snd{3}~~\fst{2}~~\circ)$ is depicted in Fig. \ref{fig:NGdef}.

\begin{figure}[htbp]
    \centering
\begin{tikzpicture}
    \matrix[row sep=1mm,column sep=2mm,ampersand replacement=\&] {
      \node[draw,circle] (LA1)  {\paff{\circ}{1}}; \&
      \node[draw,circle] (B2A2) {\pass{2}{1}}; \&
      \node[draw,circle] (B1R)  {\paff{2}{\circ}}; \&
      \node[draw,circle] (A1B2) {\pafs{1}{2}}; \&
      \node[draw,circle] (A2D2) {\pass{1}{4}}; \&
      \node[draw,circle] (C1D1) {\paff{3}{4}}; \&
      \node[draw,circle] (C2B1) {\pasf{3}{2}}; \&
      \node[draw,circle] (D2C1) {\pasf{4}{3}}; \&
      \node[draw,circle] (D1C2) {\pafs{4}{3}}; \\
    };

    \draw (A1B2) to [out=60,in=120] (A2D2);
    \draw (A1B2) to [out=-60,in=-120] (C2B1);

    \draw (B2A2) to [out=0,in=180] (B1R);
    \draw (B2A2) to [out=180,in=0] (LA1);

    \draw (A2D2) to [out=60,in=120] (C1D1);

    \draw (D2C1) to [out=60,in=120] (D1C2);
    \draw (D2C1) to [out=-60,in=-120] (D1C2);

    \draw (C1D1) to [out=60,in=120] (C2B1);

\end{tikzpicture}

\caption{The natural graph of genome $G = (\circ~~ \fst{1}~~\snd{2}~~\snd{1}~~\underline{\snd{4}~~\fst{3}}~~\underline{\fst{4}~~\snd{3}}~~\fst{2}~~\circ)$ ; it is composed of one path and two cycles.}
\label{fig:NGdef}
\end{figure}

\begin{definition}
    Given an integer $k$, a \emph{$k-$cycle} (resp. \emph{$k-$path}) in the
    natural graph of a rearranged duplicated genome is a cycle (resp. path)
    that contains $k$ edges. If $k$ is even, the cycle (resp. path) is called
   \emph{even}, and \emph{odd} otherwise.
\end{definition}

\def\EC{\ensuremath{\mbox{EC}}}
\def\OP{\ensuremath{\mbox{OP}}}

Based on the natural graph, a formula for the DCJ halving distance was given in \cite{Mixtacki08}. Given a rearranged duplicated genome $G$ such that the number of even cycles and the number of odd paths in $\NG(G)$
are respectively denoted by $\EC$  and $\OP$, the  DCJ halving distance of $G$ is:
    $$d^p_{DCJ}(G) = n - \EC - \left\lfloor \frac{\OP}{2} \right\rfloor $$

In the case of the BI halving distance, some peculiar properties of the natural graph need to be stated, allowing to simplify the formula of the DCJ halving distance, and leading to a lowerbound on the BI halving distance.

In the following properties, we assume that $G$ is a genome composed of a
single linear chromosome containing $n$ distinct markers, each one present
in two copies in $G$.

\begin{property}
The natural graph $\NG(G)$ contains only even cycles and paths:
\label{prop:EC}
\label{prop:1EP}
\begin{enumerate}
\item All cycles in the natural graph $\NG(G)$ are even.
\item The natural graph $\NG(G)$ contains only one path, and this path is even.
\end{enumerate}
\end{property}

\begin{proof}
    First, if \aff{a}{x} is a vertex of the
    graph that belongs to a cycle $C$, then there exists an edge between
    \aff{a}{x} and a vertex \asf{a}{y}. These two
    adjacencies are the only two containing a copy of the marker $a$ at the
    first position. So, if we consider the set of all the first markers in
    all adjacencies contained in the cycle $C$, then each marker in this set is
    present exactly twice. Therefore, the cycle $C$ is an even cycle.

    Secondly, the graph contains exactly two vertices (adjacencies) containing the
    marker $\circ$ which are both necessarily ends of a path in $\NG(G)$. Thus
   there can be only one path in the graph. Since the number of edges in the
   graph is even and all cycles are even, then the single path is also even. \qed
\end{proof}

We now give a lowerbound on the minimum length of DCJ scenario transforming
$G$ into a tandem-duplicated genome.

\begin{lemma}
    Let $d^t_{DCJ}(G)$  be the minimum DCJ distance between $G$ and any
   tandem-duplicated genome. If $\NG(G)$ contains $C$ cycles then a
   lowerbound on $d^t_{DCJ}(G)$ is given by:
    $$d^t_{DCJ}(G) \geq n - C - 1$$
\label{DCJdistLB}
\end{lemma}

\begin{proof}
    First, since all cycles  of $\NG(G)$ are even and $\NG(G)$ contains no odd
    path,
   then, from the DCJ halving distance formula, the DCJ halving distance of
   $G$   is $d^p_{DCJ}(G) = n - C$.

    Now, since any  tandem-duplicated genome can be transformed into
    a perfectly duplicated genome with one DCJ, then $d^t_{DCJ} + 1
    \geq d^p_{DCJ}$. Therefore, we have $ d^t_{DCJ} \geq d^p_{DCJ} - 1 \geq
    n - C - 1$.  \qed
\end{proof}

We are now ready to state a lowerbound on the BI halving distance of a rearranged duplicated genome $G$.

\begin{theorem}
    If $\NG(G)$ contains $C$ cycles, then a lowerbound on the BI halving distance
    is given by:
$$d^t_{BI}(G) \geq \left \lfloor \frac{n - C}{2} \right \rfloor$$
\end{theorem}

\begin{proof}

We denote by $\ell(S)$ the length of a rearrangement scenario $S$.
   Let $S_{BI}$ be a BI scenario transforming $G$ into a
   tandem-duplicated genome.
    From property \ref{1BIto2DCJ}, we have that $S_{BI}$ is equivalent to
    a DCJ scenario $S_{DCJ}$ such that  $\ell(S_{DCJ})=2*\ell(S_{BI})$.
    Now, suppose that $\ell(S_{BI}) < \lfloor \frac{n - C}{2}
    \rfloor$, then $\ell(S_{BI}) \leq \lfloor \frac{n - C}{2}
    \rfloor - 1 \leq \lceil \frac{n - C - 1}{2} \rceil - 1$.

    This implies $\ell(S_{DCJ}) \leq 2\lceil \frac{n - C - 1}{2}
    \rceil - 2 \leq n - C - 2 < n - C - 1$. Thus, from Lemma
   \ref{DCJdistLB} we have $\ell(S_{DCJ}) < d^t_{DCJ}$
    which contradicts the fact that $d^t_{DCJ}$ is the minimal number
    of DCJ
    operations required to transform $G$ into a tandem-duplicated genome.

    In conclusion, we always have $d^t_{BI}(G) \geq \lfloor \frac{n - C}{2} \rfloor$.  \qed
\end{proof}

\section{Formula for the BI halving distance}
\label{sec:dist}

In this section, we show that the BI halving distance of a rearranged duplicated genome $G$ with $n$ distinct markers such that  $\NG(G)$ contains $C$ cycles is exactly:

$$d^t_{BI}(G) = \left \lfloor \frac{n - C}{2} \right \rfloor$$

In other words, we show that enforcing the constraint that 2 consecutive DCJ have to be equivalent to a BI doesn't change the distance (even though it obviously restricts the DCJ that can be performed at each step of the scenario).

In
the following, $G$ denotes a rearranged duplicated genome $G$
constisting in a single linear chromosome with $n$ distinct markers
after the reduction process, and such that $\NG(G)$ contains $C$ cycles.
We begin by recalling some useful definitions and properties of the DCJ
operations that allow to decrease the DCJ halving distance by $1$ in the resulting genome.

\begin{definition}
A DCJ operation on $G$ producing genome $G'$ is \emph{sorting} if it decreases the DCJ halving distance by $1$: $d^p_{DCJ}(G') = d^p_{DCJ}(G)-1 = n-C-1$.
\end{definition}

Since the number of distinct markers $G'$ is $n$ and $d^p_{DCJ}(G') = n-C-1$, then $\NG(G')$ contains $C+1$ cycles. In other words, a DCJ operation is sorting if it increases the number of cycles in  $\NG(G)$ by $1$.

Given $(\fst{u}~~\fst{v})$ an adjacency of $G$ that is not a double-adjacency,
we denote by $\DCJ(\fst{u}~~\fst{v})$ the DCJ operation that cuts adjacencies $(\snd{u}~~\fst{x})$ and  $(\fst{y}~~\snd{v})$ to form adjacencies $(\snd{u}~~\snd{v})$ and  $(\fst{y}~~\fst{x})$, making $(\fst{u}~~\fst{v})$ a double-adjacency.

\begin{property}
Let  $(\fst{u}~~\fst{v})$ be an adjacency of $G$ that is not a double-adjacency,
 $\DCJ(\fst{u}~~\fst{v})$ is a sorting DCJ operation.
\end{property}
\begin{proof}
$\DCJ(\fst{u}~~\fst{v})$ increases the number of cycles in  $\NG(G)$ by $1$, by creating a new cycle composed of adjacencies  $(\fst{u}~~\fst{v})$ and  $(\snd{u}~~\snd{v})$. \qed
\end{proof}

\begin{figure}[!h]
\centering
\begin{tikzpicture}
    \matrix[row sep=1mm,column sep=8mm,ampersand replacement=\&] {

\node (L) {$(~\circ$}; \&
\node (f2) {$\fst{2}$}; \&
\node (f1) {$\fst{1}$}; \&
\node (s2) {$\snd{2}$}; \&
\node (f3) {$\fst{3}$}; \&
\node (s1) {$\snd{1}$}; \&
\node (s3) {$\snd{3}$}; \&
\node (R) {$\circ~)$}; \\
};
\draw[very thin] (0.1,-0.3) -- ++(1,0) -- ++(0,0.6) -- ++(-1,0) --
++(0,-0.6) -- ++(0,0.6) -- ++(1,0) -- ++(0.5,1) node[above]
{$I\aff{2}{1} = \oiss{2}{1}$};
\draw[very thick] (-3.4,-0.4) -- ++(5.8,0) -- ++(0,0.8) -- ++(-5.8,0)
-- ++(0,-0.8) -- ++(-0.3,-0.7) node[below] {$I\afs{1}{2} = \cifs{2}{1}$};
\draw[very thin] (-2.6,-0.6) -- ++(5.2,0) -- ++(0,1.2) -- ++(-5.2,0) --
++(0,-1.2) -- ++(0,1.2) -- ++(-0.5,1) node[above] {$I\asf{2}{3} = \oifs{2}{3}$};
\draw[very thick] (-2.3,-0.5) -- ++(5.5,0) -- ++(0,1) -- ++(-5.5,0) --
++(0,-1) -- ++(5.5,0) -- ++(0.3,-0.7) node[below] {$I\afs{3}{1} = \cifs{1}{3}$};
\draw[very thin] (-1.1,-0.3) -- ++(1,0) -- ++(0,0.6) -- ++(-1,0) --
++(0,-0.6) -- ++(0,0.6) -- ++(-0.3,0.7) node[above] {$I\ass{1}{3} = \oiff{1}{3}$};

\end{tikzpicture}
\\

\caption{ $\mathcal{I}(G) ~ = ~ \left\{ ~~ \oiss{2}{1} ~,~~
      \mathbf{\cifs{2}{1}} ~,~~ \oifs{2}{3} ~,~~ \mathbf{\cifs{1}{3}}
      ~,~~ \oiff{1}{3} ~~ \right\}$, the set of intervals of $G =
  (\circ~~\fst{2}~~\fst{1}~~\snd{2}~~\fst{3}~~\snd{1}~~\snd{3}~~\circ
  )$ depicted as boxes. The two boxes with thick lines represent two
  overlapping intervals of $\mathcal{I}(G)$ inducing a \BI\xspace which
  exchanges $\fst{2}$ and $\snd{3}$.}
    \label{fig:intervaldef}
\end{figure}

\begin{definition}
Let $(\fst{u}~~\fst{v})$,  $(\snd{u}~~\fst{x})$, and  $(\fst{y}~~\snd{v})$ be adjacencies of $G$. The \emph{interval} of the adjacency  $(\fst{u}~~\fst{v})$, denoted by $I(\fst{u}~~\fst{v})$ is either:
\begin{itemize}
\item the interval $[\snd{x}~;~\snd{y}]$ if $(\snd{u}~~\fst{x}) < (\fst{y}~~\snd{v})$.  In this case, we denote it by $]\snd{u}~;~\snd{v}[$, or
\item the interval $[\snd{v}~;~\snd{u}]$ if $(\fst{y}~~\snd{v}) < (\snd{u}~~\fst{x})$.
\end{itemize}
\end{definition}

For example, the intervals of the adjacencies in genome $(\circ~~\fst{2}~~\fst{1}~~\snd{2}~~\fst{3}~~\snd{1}~~\snd{3}~~\circ )$ are depicted in Fig \ref{fig:intervaldef}.
Note that, given an adjacency  $(\fst{u}~~\fst{v})$ of $G$,  if  $(\fst{u}~~\fst{v})$ is a double-adjacency then the interval $I(\fst{u}~~\fst{v})$ is empty, otherwise  $\DCJ(\fst{u}~~\fst{v})$ is the excision operation that extracts the interval $I(\fst{u}~~\fst{v})$ to make it circular, thus producing the adjacency $(\snd{u}~~\snd{v})$.

Two intervals  $I\aff{a}{b}$ and $I\aff{x}{y}$ are said \emph{overlapping} if
their intersection is non-empty, and none of the intervals is included in the
other.
It is easy to see, following Property \ref{1BIto2DCJ}, that given two
adjacencies $\aff{a}{b}$ and $\aff{x}{y}$ of $G$ such that
$I\aff{a}{b}$ and $I\aff{x}{y}$ are non-empty intervals, the
successive application of $\DCJ\aff{a}{b}$ and $\DCJ\aff{x}{y}$ is
equivalent  to a BI operation if and only if $I\aff{a}{b}$ and
$I\aff{x}{y}$ are overlapping. Note that in this case neither
$\aff{a}{b}$, nor  $\aff{x}{y}$ can be double-adjacencies in $G$ since
their  intervals are non-empty. Figure \ref{fig:intervaldef} shows an
example of two overlapping intervals.

The following property states precisely in which case the successive application of $\DCJ\aff{a}{b}$ and $\DCJ\aff{x}{y}$ decreases the DCJ halving distance by $2$, meaning that both DCJ operations are sorting.

\begin{property}
Given two adjacencies $\aff{a}{b}$ and $\aff{x}{y}$ of $G$, such that
$I\aff{a}{b}$ and $I\aff{x}{y}$ are overlapping, the successive application of $\DCJ\aff{a}{b}$ and $\DCJ\aff{x}{y}$ decreases the DCJ halving distance by $2$ if and only if  $x \neq \snd{a}$ and $y \neq \snd{b}$.
\end{property}
\begin{proof}
If $x \neq \snd{a}$ and $y \neq \snd{b}$, then the successive application of $\DCJ\aff{a}{b}$ and $\DCJ\aff{x}{y}$ increases the number of cycles in $\NG(G)$ by $2$, by creating two new 2-cycles. Otherwise, $\DCJ\aff{a}{b}$ first creates a new cycle that is then destroyed by  $\DCJ\aff{x}{y}$.
\qed
\end{proof}

We denote by $\mathcal{I}(G)$, the set of intervals of all the adjacencies of $G$ that do not contain marker $\circ$.

\begin{remark}
Note that, if $G$ contains $n$ distinct markers, then there are $2n-1$ adjacencies in $G$ that do not contain marker $\circ$,  defining $2n-1$ intervals in  $\mathcal{I}(G)$.
\label{maxEdges}
\end{remark}

\begin{definition}
Two  intervals $I\aff{a}{b}$ and $I\aff{x}{y}$ of $\mathcal{I}(G)$ are said \emph{compatible} if they are overlapping and  $x \neq \snd{a}$ and $y \neq \snd{b}$.
\end{definition}

In the following, we prove the BI halving distance formula by showing that if genome $G$ contains more than three distinct markers, $n~>~3$,  then there exist two compatible intervals in $\mathcal{I}(G)$, and if $n=2$ or $n=3$ then $d^t_{BI}(G)=1$ and $2 \leq d^p_{DCJ}(G) \leq 3$.
This means that there exists a \BI ~halving scenario $S$ such that all \BI ~operations in $S$, possibly excluding the last one, are equivalent to two successive sorting DCJ operations.

From now on, until the end of the section,
$\aff{a}{b}$ is an adjacency of $G$ that is not a double-adjacency, $A$ is a genome consisting in a linear chromosome $\mathfrak{L}$ and a circular chromosome $\mathfrak{C}$, obtained by applying the \emph{sorting DCJ}, $\DCJ\aff{a}{b}$, on $G$.

If there exists an interval $I\aff{x}{y}$ in $\mathcal{I}(G)$ compatible with  $I\aff{a}{b}$, then applying $\DCJ\aff{x}{y}$ on $A$ consists in the integration of the circular chromosome $\mathfrak{C}$ into the linear chromosome $\mathfrak{L}$ such that the adjacency $\ass{x}{y}$ is formed.
Such an \emph{integration} can only be performed by cutting an adjacency $\asf{x}{u}$ in $\mathfrak{C}$ and an adjacency $\afs{v}{y}$ in $\mathfrak{L}$ (or inversely) to produce adjacencies $\ass{x}{y}$ and $\aff{v}{u}$.  This means that there must be an adjacency \aff{x}{y} in either $\mathfrak{C}$ or $\mathfrak{L}$ such that $\snd{x}$ is in $\mathfrak{C}$ and $\snd{y}$ in $\mathfrak{L}$ or inversely.
Hence, we have the following property :

\begin{property}
$\mathfrak{C}$ \emph{cannot} be reintegrated into $\mathfrak{L}$ by
applying a sorting DCJ,  $\DCJ\aff{x}{y}$, on $A$ if and only if either:

\begin{itemize}
\item[(1)] for any adjacency $\aff{x}{y}$ in $\mathfrak{C}$
  (resp. $\mathfrak{L}$), markers $\snd{x}$ and $\snd{y}$ are in
  $\mathfrak{L}$ (resp. $\mathfrak{C}$),
  or

\item[(2)] for any adjacency $\aff{x}{y}$ in $\mathfrak{C}$ (resp. $\mathfrak{L}$), markers $\snd{x}$ and $\snd{y}$ are also in $\mathfrak{C}$ (resp. $\mathfrak{L}$).
\end{itemize}

\label{formuleENR}
\end{property}
\begin{proof}
If there exists no  adjacency $\aff{x}{y}$ in $A$ such that $\snd{x}$ is in $\mathfrak{C}$ and $\snd{y}$ in $\mathfrak{L}$ or inversely, then $A$ necessarily satisfies either $(1)$, or $(2)$. \qed
\end{proof}

\begin{definition}
An interval $I\aff{a}{b}$ in  $\mathcal{I}(G)$ is called
\emph{interval of type 1} (resp. \emph{interval of type 2}) if $\DCJ\aff{a}{b}$ produces a genome $A$ satisfying configuration $(1)$  (resp.  configuration $(2)$) described in Property \ref{formuleENR}.
\end{definition}

For example, in genome  $(\circ~~\fst{2}~~\fst{1}~~\snd{1}~~\fst{3}~~\snd{2}~~\snd{3}~~\circ)$,  $I\asf{1}{3}$ is of type 1 as  $\DCJ\asf{1}{3}$ produces genome
$(\circ~~\fst{2}~~\fst{1}~~\snd{3}~~\circ) ~ (\snd{1}~~\fst{3}~~\snd{2})$ ;  $I\ass{2}{3}$ is of type 2 as  $\DCJ\ass{2}{3}$ produces genome  $(\circ~~\fst{2}~~\fst{3}~~\snd{2}~~\snd{3}~~\circ) ~ (\fst{1}~~\snd{1})$.

Now we give the maximum numbers of intervals of type 1 and type 2 that can be contained in genome $G$.

\begin{lemma}
The maximum number of intervals of type 1 in $\mathcal{I}(G)$ is 2.
\label{maxType1}
\end{lemma}

\begin{proof}
First, note that there cannot be two intervals $I$ and $J$ of $\mathcal{I}(G)$
such that $I \neq J$, and both  $I$ and $J$ are of type 1.
Now, if $I$ is an interval of type 1, there can be at most two different
adjacencies $\aff{x}{y}$ and $\aff{u}{v}$ such that
$I\aff{x}{y} = I\aff{u}{v} = I$. In this case $G$ necessarily has a chromosome of the form $(\ldots ~~\snd{x}~~\snd{v}~~\ldots ~~\snd{u}~~\snd{y}~~\ldots)$ or $(\ldots ~~\snd{u}~~\snd{y}~~\ldots ~~\snd{x}~~\snd{v}~~\ldots)$.
Therefore, there are at most two intervals of type 1 in $\mathcal{I}(G)$.   \qed

\end{proof}

\begin{lemma}
The maximum number of intervals of type 2 in  $\mathcal{I}(G)$ is $n$.
\label{maxType2}
\end{lemma}

\begin{proof}
First, note that for two adjacencies $\aff{x}{y}$ and $\asf{x}{z}$ in $G$ that
do not contain marker $\circ$, if $\aff{x}{y}$ is of type 2 then $\asf{x}{z}$
cannot be of type 2.
Now, there is only one marker $u$ such that  $\asf{u}{\circ}$ is an adjacency
of $G$. Let $\aff{u}{v}$ be the adjacency of $G$ having $u$ as first marker,
then at most half of the intervals in $\mathcal{I}(G) - \{I\aff{u}{v}\}$ can
be of type 2.
Therefore, there are at most $n$ intervals of type 2 in $\mathcal{I}(G)$.   \qed

\end{proof}

\begin{theorem}
If $\NG(G)$ contains $C$ cycles, then the BI halving distance of $G$
    is given by:
$$d^t_{BI}(G) =  \left \lfloor \frac{n - C}{2} \right \rfloor$$
\label{th:distance}
\end{theorem}

\begin{proof}

    Since there are $2n - 1$ intervals in $\mathcal{I}(G)$, and at
    most $n+2$ are of type $1$ or $2$, then if $G$ is a genome
    containing more than three distinct markers $n~>~3$, then
    $2n-1~>~n+2$ and there exist two compatible intervals in
    $\mathcal{I}(G)$ inducing a BI operation that decreases the DCJ
    distance by $2$.

Next, we show that if $n = 2$ or $n = 3$, then $d^t_{BI}(G)=1$ and $2
\leq d^p_{DCJ}(G) \leq 3$.

If $n = 2$, then the genome can be written, either as
$(\circ~\fst{a}~\fst{b}~\snd{b}~\snd{a}~ \circ)$, in which case a BI
can swap $\fst{a}$ and $\fst{b}$ to produce a tandem-duplicated
genome, or as $(\circ~\fst{a}~\snd{a}~\fst{b}~\snd{b}~\circ)$, in
which case a BI can swap $a$ and $\snd{a}~\fst{b}$ to produce a
tandem-duplicated genome.

If $n = 3$, then the genome has two double-adjacencies to be
constructed, of the form $\ass{a}{b}$, $\ass{x}{y}$, with $\aff{a}{b}$
and $\aff{x}{y}$ being two adjacencies already present in the genome
such that $\fst{b} = \fst{x}$ or $\fst{b} = \snd{x}$ and $a$ and $y$
are distinct markers. One can rewrite $\aff{a}{b}$ and $\aff{x}{y}$ as
single markers since they will not be splitted, which makes a genome
with 4 markers such that at most 2 are misplaced. Then, a single BI
can produce a tandem-duplicated genome.

Now, it is easy to see to see that if  $n = 2$ or $n = 3$, then $d^p_{DCJ}(G) = n- C \leq 3$. Finally, if  $n = 2$ or $n = 3$, then $d^p_{DCJ}(G) \geq 2$, otherwise we would have  $d^p_{DCJ}(G) = 1$ which would imply, as $G$ consists in a single linear chromosome, $d^t_{BI}(G) = 0$.
In conclusion, if $n~>~3$ then there exist two compatible intervals in  $\mathcal{I}(G)$, otherwise if  $n = 2$ or $n = 3$, then $d^t_{BI}(G)=1$ and  $2 \leq d^p_{DCJ}(G) \leq 3$. Therefore $d^t_{BI} = \lfloor \frac{d^p_{DCJ}}{2}\rfloor = \lfloor \frac{n-C}{2}\rfloor$. \qed

\end{proof}

\section{Sorting algorithm}
\label{sec:scenario}

In Section \ref{sec:dist}, we showed that if a genome $G$ contains more than
three distinct markers after reduction then there exist two compatible
intervals in $\mathcal{I}(G)$ inducing a BI to perform.
If $G$ contains two or three distinct markers then the BI to perform can be
trivially computed.
Thus the main concern of this section is to describe an efficient algorithm
for finding compatible intervals when $n~>~3$.

As in Section \ref{sec:dist}, in the following, $G$ denotes a genome consisting
of $n$ distinct markers after reduction.
It is easy to show that the set of intervals
$\mathcal{I}(G)$ can be built in $O(n)$ time and space complexity.

We now show that finding 2 compatible intervals in  $\mathcal{I}(G)$ can be done in $O(n)$ time and space complexity.

\begin{property}
If $n~>~3$
, then all the smallest intervals in $\mathcal{I}(G)$ that are not of type 2 admit compatible intervals.
\label{smallestOK}
\end{property}

\begin{proof}

    Let $J$ be a smallest interval that is not of type 2 in
    $\mathcal{I}(G)$. As $J$ is not of type 2, then $J$ has compatible
    intervals if $J$ is not of type 1.

Let us suppose that $J$ is of type 1, then for any adjacency $(a ~ b)$ such
that markers $a$ and $b$ are not in $J$,  $\snd{a}$ and $\snd{b}$ are in $J$,
and then $I(a ~ b)$ is strictly included in $J$ and $I(a ~ b)$ can't be of
type 2. Such adjacency does exist as there are $n~>~3$ markers not included in $J$.
Therefore $J$ cannot be a smallest interval that is not of type 2.
\qed
\end{proof}

We are now ready to give the algorithm for sorting a duplicated genome $G$ into a tandem-duplicated genome with $\lfloor \frac{n - C}{2} \rfloor$ BI operations.

\begin{algorithm}
\caption{Reconstruction of a tandem-duplicated genome}
\label{alg1}
\begin{algorithmic}[1]

\WHILE{$G$ contains more than $3$ markers}
\STATE Construct $\mathcal{I}(G)$
\STATE Pick a smallest interval $I(a ~~ b)$ that is not of type 2 in $\mathcal{I}(G)$
\STATE Find an interval $I(x ~~ y)$ in $\mathcal{I}(G)$ compatible with $I(a ~~ b)$
\STATE Perform the \BI ~ equivalent to $\DCJ(a ~~ b)$ followed by $\DCJ(x ~~ y)$
\STATE Reduce $G$
\ENDWHILE
\IF{$G$ contains $2$ or $3$ markers}
\STATE Find the last BI operation and perform it
\ENDIF
\end{algorithmic}
\end{algorithm}

\begin{theorem}

Algorithm \ref{alg1} reconstruct a tandem-duplicated genome with a BI scenario of length $\lfloor \frac{n - C}{2} \rfloor$ in $O(n^2)$ time and space complexity.
\end{theorem}

\begin{proof}
Building $\mathcal{I}(G)$ and finding two compatible intervals can be done in $O(n)$ time and space complexity. It follows that the while loop in the algorithm can be computed in $O(n^2)$ time and space complexity.

Finding and performing the last \BI~operation when  $2\leq n\leq 3$ can be done in constant time and space complexity.

Moreover, all \BI~ operations, possibly excluding the last one, are computed as
pairs of sorting DCJ operations, which ensures that the length of the scenario
is $\lfloor \frac{n - C}{2} \rfloor$. \qed
\end{proof}

\section{Conclusion}

In this paper, we introduced the BI halving problem. We use the DCJ model
to simulate BI operations and we showed that it is always possible to choose two consecutive
sorting DCJ operations such that they are equivalent to a BI operation.
We thus provide a quadratic time and space algorithm to obtain a
most parsimonious scenario as any computed BI scenario is in fact an optimal DCJ scenario.
Finally, one direction for further studies of variants of the BI halving problem is to consider multichromosomal
genomes and BI operations acting on more than one chromosome.
\bibliographystyle{plain}

redpajama_set_name: RedPajamaArXiv


text:
Home > JOURNALS > DLJ > Vol. 31 > Iss. 2 (2008)
Cravath by the Sea: Recruitment in the Large Halifax Law Firm, 1900-1955
Jeffrey Haylock, Dalhousie UniversityFollow
Canada, law firms, legal profession, law school, United States, Cravath, New York, Halifax, nepotism, legal education, legal history
The traditional view is that regularized, meritocratic hiring in Canadian law firms had to wait until the 1960s, with the rise in importance of Ontario university law schools. There was, however, more regional variation than this view allows. After an overview of the rise of large firms in the U.S. and Canada, and of the modern hiring strategies (the "Cravath system") that developed in New York in the early twentieth century, the author considers whether Halifax firms were employing these strategies between 1900 and 1955. Nepotistic hiring continued unabated; however, the three large firms of the period recruited young students with good academic records with increasing regularity,in the New York manner. The article concludes by proposing that the difference between firms' hiring in Toronto and Halifax might be explained by the enthusiasm with which the bar in each of these cities adopted modern professional views on legal education.
Jeffrey Haylock, "Cravath by the Sea: Recruitment in the Large Halifax Law Firm, 1900-1955" (2008) 31:2 Dal LJ 401.
Legal History Commons, Legal Profession Commons

redpajama_set_name: RedPajamaCommonCrawl


text:
Bread dance! In the first half, it was hit, and the courage is crazy.
NBA ushered in a hot battle today, by the Warriors Familia City, https://www.maillotbasket6.com this is the depending between Curi Brothers. Due to the lack of Enabide, the Philadelphia team is in a very good situation, and the Warriors all the way to the first round of the colleague, and the Enged continues to lack, this thought is a no suspected game, but the first half Warriors It has been pressed against, until the third section of the Warriors have been over 2 points, and the final Warriors have once again sent a wave of victory in the fourth quarter. In the competition, I was excited to jump and danced to the kick dance to celebrate.
The Philadelphia team started lineups in Maxi, Kabuli, Nian, Zhuang God, Sebur. The Warriors started lineups for Curi, Weights, Poole, Green, Luni.
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The third section of the Warriors sacrificed the climax of the 12-2 death of 14-2, and the three sections ended the Warriors lead 2 points. The fourth warrior has developed a new weapon of 10,000 crazy. The score of the single section of 30 to 12, and the division quickly came to more than 20 points, and the final Warriors were 116 more than 96 victory.
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The audience is divided into double, Cebul 7 points 5 rebounds 2 assists, Niome 9 points 4 rebounds 2 assists, Dramund 1 points 12 rebounds 2 assists, Maxi 19 points 3 rebounds 5 assists, Sasis Turi 24 points 1 rebound, Milton 9 points 4 rebounds 4 assists, Cocmaz 9 points 5 rebounds 1 assists, Danny Glin 10 points 2 rebounds 1 assists, Joe 8 points 2 rebounds.
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Philadelphia team's technical statistics were 41 rebounds, assists 17 times, and 42.5% of the shooting 80 shots were shot, including 28.6% of the three-pointers 28 vitamins 8.90.9% of the hit rate of 20 10 times to steal 10 times, lost 19 times, cover 7 times, foul 22 times.
The Warriors team's technical statistics were 41 rebounds, assists 32 times, 52.5% of the shooting 80 voted 42, including 39.5% of the three-pointers of 38 shots, 24 penalties 17, 70.8% of the basket Rate, seduce 7 times, lost 16 times, cover 5 times, foul 21 times.
Curry is picking back
From the perspective of the team's technical statistics, the Warriors' three-pointers have higher than the 15% of the Philadelphia, and they have entered 7 three-pointers. In addition, one will be more than 15 times, indicating that the warriors play more overall and more Skilling, this is the reason why the Warriors won on the spot.
The Warriors in this field is the best in the library. He came out of 35 minutes 16 in 9, including 25 points 4 plates 10 assist in the three-pointers 11. In addition, Weilinson came in 34 minutes in 34 minutes, among which 2 brought the ball 6 brought 19 points 6 plates 1 help 1 broken 1 cap.
Pooler air relay
Philadelphia This is the best in the small bed, and his scene was 33 minutes 16 shots 8, of which three points 5 gave 24 points 1 sheet 2 broken. Maxi came 33 minutes to get 19 points 3 plates 5 bokeh.
After winning this game, the Warriors got 5 winners with 16 wins and 2 negative continued rankings, the Philadelphia team ranked 10 wins and 9th. The brothers in this library have many opposition opportunities, and finally, the brother's skills are high, and the victory has won the data. Of course, the performance of the small library is very good.
Green hollow bugy
The fans of the Warriors of this season are very happy, because the Warriors in the first half will not be anxious, and the brave three crazy is still crazy. When Klei wounds, the Warriors can take a championship.
When the NFL master coach is a experience to see how the coaches "arrange" players
Executive Talking Hot Two Wars: Referee & Security will be highly alert Yeki brother is a key object


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In 2016 John Maatta became the CEO of Wizard world and seems to have orchestrated a real turnaround. Maatta was the CEO of the CW Television Network at Warner Bros. so it was just a matter of time before he got back into his element of programming. His resume is impressive because he served as General Counsel of WB Television Network and was the COO of CW under Viacom before it got spun off to CBS. Mr. Maatta has over 25 years of experience and was responsible for many of the initial distribution deal. He has a sound education background and holds a Bachelor of Arts in Government from the University of San Francisco and a Juris Doctorate from the University of California Hastings College of Law.
A couple of weeks ago WIZD teamed up with Sony Pictures Entertainment to incubate new talent and this news has flown under the radar until recently. Mr. Maatta's background was likely a key factor in the formation of this venture with Sony. Sony plans to use these events to incubate talent. A perfect example of this is the "Black Panther" movie which is expected to surpass $1.0 billion in box office sales in the coming weeks according to Forbes. It's this type of talent that Sony is searching for in this forum as they look for Black Panther 2.0. Think of the licensing potential when they do land the right actor or genre of movie. Incubators are long term in nature, but the potential here can't be quantified, but this partnership is very valuable indeed and talent will flock to their shows in the hope that they get discovered. This partnership strongly positions them in the show market because it assures the long-term viability of being able to attract stars and up and coming artists. Sony can also capitalize on merchandising and using the shows as a platform to present and showcase their own projects. It is very synergistic.
The recently announced WizPop/CNLive deal enhances WIZD's global brand in China. According to WIZD an "estimated 390 million Chinese nationals are English speakers and English learners." The new show is expect to reach 90% of the viewers who get CN Live service. That means 90 million of the 100 million viewers across China. In addition there is a free non-subscription channel that reaches an estimated 680 million internet users. There are a lot of mind boggling numbers swirling around, but what it distills down to, is a lot of advertising dollars. Since there is no current comparison for existing programming, it's helpful to look at comparables in the E-sports marketplace where its $25 CPM. Assuming just 5% of the subscribers and a $25 CPM it works out to $125,000 per episode daily. It's 4 hours of streaming, so likely quadruple (multiply by 4) this number. The point is, this is a mammoth marketplace and the JV agreement should translate into earnings in short order.
A recent article on Black Panther: Lessons In Hollywood Diversity and Pride wrote, "Black Panther" has unequivocally become one of many recent inflection points for the African American community, especially following the success of extraordinary black voter turnout in tough southern elections. It could be argued that since the end of the historic and groundbreaking Obama presidency, black people have been searching for a superhero, or a "yes we can" leader like T'Challa. For two hours, he becomes more than a comic-book superhero. He transforms into a symbol of hope for African Americans, much like President Obama was during the previous eight years. This "superhero" movie taps into a whole new market of African American fans which Wizard World's Comic-Con events may see a slight bump in attendance.
This feel good moment has Asian Americans asking, "when is our Black Panther moment?". Asian Americans may never get the defining moment that Black Panther embodies for African Americans, but that might also be okay. As a community, we must support the efforts of African American filmmakers if we hope to see more diverse representation that will allow each of our stories to be told.
Until black folks and Indigenous peoples regain their humanity in the context of Hollywood cinema, equitable portrayals of Asian Americans cannot exist either. To paraphrase the words of the late Japanese American activist Yuri Kochiyama, it is only through black liberation that we will find our own equality.
Wizard World has 15 shows scheduled this year and at least 500,000 visitors. WIZD also does 20 concert type shows a year. Many celebrities at show do photo ops, signings and present awards. Celebrities are a key draw at these show, but equally benefit them as they get to meet with fans and have a chance to network with producers and directors looking for fresh new actors and content. This weekend's show will be in Cleveland March 2,3,4 with celebrities from hit shows such as Gotham, Dr. Who, Buffy The Vampire Slayer, Sailor Moon, Star Trek, Power Rangers, Napoleon Dynamite, Attack On Titan, Smallville, Torchwood and more! Check out last year's 2017 event in Cleveland by watching the YouTube video above.
There are 68 million shares outstanding with 48 million shares owned by insiders leaving a 20 million shares left in the float. There are no convertible notes that could lead to dilution. The company has $13.0 million in revenue over a 9 month period from the last quarterly filing in September 2017. The companies recent announcements with SONY and Associated Television International have fueled a bounce which caused the stock price to nearly triple off its early January lows. The company's RSI is just under 70.
WIZD is one of the largest producers of fan convention shows. The shows attract over 500K visitors annually and growing. The new CEO really delivered this year and his experience in network television allowed them to sign with China CN Live with an audience of 800 million. They are in a great position to monetize their content production. It is also synergistic with their trade shows. Monetization seems to be an underlying theme this year with over 15 shows. The company could see an additional bump due to the large success from "The Black Panther" movie. With the turnaround of the business imminent and the expansion in the media realm, this niche sector play should see expansion, and growth of its brand name. The teaming with Sony is a first step in what could be the beginning of a buyout? It seems like other partners like Marvel, based on the success of "The Black Panther," could be developed in future. Media content producers are normally valued in the billions so there is quite a bit of upside in this stock.
Disclosure: PSInvestor does not hold a position in the above-mentioned company, nor have they been compensated by the company or 3rd party. To read our full disclaimer, please click here. Like our articles? Comment below! CEO's… want us to write about your company? Contact us today.
Excellent article, very in depth and insightful!! This is the type information in a clean, concise package that traders love. Thank you.


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Tony Sirico's Net Worth, Bio, Early Life, and Other Updates(2022)
Tony Sirico is a well known American actor, who got fame from the character of Pauie "Walnuts" Gualtieri, in The Sopranos. Tony also appeared in many films of Woody Allen. But he died on July 8,2022.
In this post, we are going to describe Tony's early life, career, net worth, bio, and other details.
Tony Sirico: Early Life
Tony Sirico was born on 29 July, 1942, in New York. His real name is Gennaro Anthony Sirico Jr. His brother Robert Sirico, is co-founder of free-market Action Institute. From his childhood he was arrested many times for acts like robbery, assault, and misbehaving.
In 190 he was caught from a hotel with a .32 calibre gun and for another criminal action he was imprisoned for four years. Once he was arrested with so many drugs. After 1989 he appeared in the documentary film "The Big Bang" Tony spoke everything about himself.
Know More:Is the 4th Stimulus Check Could Come Back as the Nation Slides Towards a Recession?
Tony Sirico: Career
He started his acting debut in 1974 with Crazy Joe, and his first acting coach was Michael Gazzo. Goodfellas, Mob Queen, Mighty Aphrodite, Love and Money, Fingers, The One Man Jury, Defiance, The Last Fight, Innocent Blood, Bullets over Broadway, The Pick-up Artist, Gotti, The Search for One-eye Jimmy, Cop Land, Turn of Faith, Hello Again, Mickey Blue Eyes, and Wonder Wheel are Tony's best known films.
In Dead President and Deconstructing Harry, he plays the policeman character. His most appreciated movie is The Sopranos, for which he won Emmy awards. Actually Tony auditioned for Uncle Junior but Dominic was already selected for that role. Then Director Davis Chase offered his Paulie Gualtieri role and he played.
In 2013, Family Guy's Vinny character, also voiced by Tony, is a dog. "Stewie, Chris, & Brian's Excellent Adventure", show Sirico appeared for one episode. Again Tony played Vinny in season 15 premiere, "The Boys in The Band". In 2018, Tony casted again with the team of The Sopranos for Sarah .
Tony Sirico: Personal Life
When it comes to personal life Tony remains quiet. So most of his personal life was never disclosed on social media. But we come to know that Tony has two children Joanne and Richard. As we know anything else we will update you soon.
Tony Sirico: Achievements
Gennaro Anthony Sirico Jr. R.I.P.
Tony was nominated many times and won Screen Actor Guild awards for his The Sperons and once he won Emmy Awards. Tony's television appearance was also appreciable. He worked in many series and shows.
Tony Sirico: Net worth
Tony appeared in 89 episodes of The Sopranos and he earned a good salary. Aside from this he also cast movies and shows. Tony's net worth is estimated at $ 8 million.
Tony Sirico: Reason Behind Death
Sirico, a charming actor, died on 8 July 2022. This is unbelievable but he died in his House at Florida at an age of 79, just before 12 dates of his 80th birthday. From a long time Toy was suffering from Dementia, no other reason was suggested for his death.
R.I.P. Tony Sirico, a fucking legend. A real-life gangster who cleaned up his life, took several small parts in New York gangster movies (including Tony Stacks in Goodfellas), and then got the role of a lifetime as Paulie Walnuts. This week sucks. pic.twitter.com/kc8OLJDKT5
— William Friedkin Truths (@LazlosGhost) July 8, 2022
Tony Sirico: Biography
Name Tony Sirico
Real Name Gennaro Anthony Sirico Jr.
Height 5 ft 10 in
Siblings One
Wife Not Known
Children Two
Date of Death 8 July 2022
Profession American actor
Net Worth $ 8 Million
Eye Colour Brown
Hope you like it. Stay tuned with us for more updated like this.
Read Also: Cole Sprouse Net Worth Income, Salary – How Rich is Cole Actually in 2022?
Howie Mandel Net Worth, Income, Career, Cars & Latest Updates
1 Tony Sirico: Early Life
2 Tony Sirico: Career
3 Tony Sirico: Personal Life
4 Tony Sirico: Achievements
5 Tony Sirico: Net worth
6 Tony Sirico: Reason Behind Death
7 Tony Sirico: Biography
Categories: Celebrity News, Entertainment


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Last Updated: Thursday, 14 May 2020 22:26
Written by John Holland
Koshigaya-Negi
Allium fistulosum is a type of onion that has a long white stalk that connects an elongate bulb, not much thicker than the stalk, to long, hollow, tube-like leaves. Allium fistulosum are called Negi in Japanese, and are known by a number of names in English. These include Welsh Onion and Japanese Bunching Onion. Allium fistulosum grown in Koshigaya are called Koshigaya-Negi, and are known for having a strong stalk that does not break into pieces during cooking. Although it is unknown exactly when such high-quality Negi were first cultivated in the Koshigaya area, there is documentation suggesting that it was during the Edo Period (1603 - 1867). Koshigaya City's administration has encouraged the cultivation of Koshigaya-Negi in Mashimori, Nakajima and other areas of the city, where there is farmland surrounded by natural embankments, and much farmland in these areas has been converted into Negi fields. Koshigaya City is now well known for its Negi, and ranks with Fukaya City as a famous Negi-producing area.
Arrowhead Tubers
The Arrowhead is a perennial aquatic herb belonging to the Alismataceae family, and is called Kuwai in Japanese. The Arrowhead has creeping roots that spread underground, with the tip of the roots swelling to form edible tubers. In Japan the Arrowhead is considered to be lucky because of the way in which a large sprout grows from its tubers, and Arrowhead tubers are often used in dishes eaten at New Years and on other special occasions. The Arrowhead is said to have been imported from China in the Nara Period (710 - 794), and has been cultivated in the Koshigaya area since the middle of the Edo Period (1603 - 1867). Arrowhead tubers are now cultivated in the Dewa and Ogishima areas of Koshigaya City. Arrowhead tubers are harvested for shipping in November and December, and because harvesting is carried out by hand in cold conditions, the scale of cultivation is limited, and has decreased slightly in recent years. However, Koshigaya City still leads the other main Arrowhead tuber-producing areas in Hiroshima Prefecture and Aichi Prefecture as the largest producer of arrowhead tubers in Japan. After harvesting, large tubers are shipped to the Keihin Area (Tokyo and Yokohama), and small tubers are shipped to the Kansai Area (Osaka and Kyoto). Again, to promote the consumption of Arrowhead tubers, Kuwai confectionary and a low-malt, Kuwai beer are now being produced in Koshigaya.
Cut tulips are one of Koshigaya City's major horticultural products, and to meet customer demand, tulip bulbs are ordered from Toyama and Niigata Prefectures, and from as far away as Holland. After being stored at low temperature in the city's storehouse, tulip bulbs are raised in greenhouses throughout the city. The growing season is from the start of December until early April, and various measures are continually being taken to improve the quality of the tulips produced and to reduce the costs involved in their production. The tulips produced are shipped to Tokyo and other towns and cities in the Kanto Area (the Tokyo Metropolitan Area and Kanagawa, Chiba, Saitama, Gunma and Tochigi Prefectures), with the largest shipments being made at Christmas and New Years, and during the graduation season. A variety of other flowers are also produced in Koshigaya City. These include freesias and lilies, which are raised from bulbs to be sold as cut flowers, as well as orchids and roses. To increase public awareness about horticulture in Koshigaya City, flower growers from throughout the city hold the Hana Fiesuta, a festival of flowers, in the concourse of Shin-Koshigaya Station every January. Again, flower exhibitions are held in the 1st floor lobby of the Koshigaya City Office in March and June. The exhibition in March features tuips, and the exhibition in June features orchids, lilies and other flowers.
Tarobee-Mochi
It is thought that the cultivation of Tarobee-Mochi began early in the Edo Period (1603 - 1867) with Tarobee Aida's selective cultivation of glutinous rice. Aida, who held the hereditary position of headsman of the Shichono Village (Shichono-Mura), selectively cultivated varieties of glutinous rice that matured early and were tall in height in an attempt to avoid crop damage caused by typhoons. Aida succeeded in creating a variety of glutinous rice suited to cultivation in low-lying, damp areas in 1596, and this variety came to be known as Tarobee-Mochi. Tarobee-Mochi, which is known for its unique taste, chewiness and stickiness, was extremely popular from start of the Meiji Period (1868 - 1912) until early in the Showa Period (1926 - 1989), and received the honors of being offered to the imperial family and receiving the patronage of the Imperial Household Agency. Again, it is said that in the early part of the Showa Period, there was much competition amongst confectioners from Tokyo who sought to buy Tarobee-Mochi from Dewa Village (Dewa-Mura). However, during the Second World War, the promulgation of laws relating to the control of food quality saw the price of Tarobee-Mochi reduced to that of other types of rice. This combined with Tarobee-Mochi's small yield and tendency to topple in high winds, saw a decrease in the number of farmers cultivating it. At present there are very few farmers cultivating Tarobee-Mochi, so to preserve this variety of glutinous rice, since 1993,Koshigaya City's administration has offered contracts to farmers for its cultivation and is running programs to promote its cultivation.


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Q: How to validate a valid month / year between a range How can I validate the date input from users following the format mm/yyyy and also the yyyy range is from 2002 until 2030. So the month should be between 1 to 12 and all of the years below 2002 and 2030 in invalid. Here is my current regular expression:
^(0[1-9]|1[012])[- /.](20)\d\d$

A: Since you're forced to use regex, here you are:
^(0[1-9]|1[012])[- /.](20(?:0[2-9]|[12]\d|30))$

It works similar to the month validation pattern you wrote - 0[2-9] matches 2002 to 2009, [12]\d matches 2010 to 2029, and 30 matches 2030.

A: You can Validate a Gregorian date using the checkdate() function; however this requires you to be in a DateTime/Date format, it's useful for making sure people don't do stuff like: 35/02/2014
However, something like this could work?
([0-2][0-9]|31)\/(0[1-9]|1[0-2])\/(200[2-9]|20[1-2][0-9]|2030)

And then cast the string to a DateTime object and run the checkdate() function upon it to check it's gregorian?

A: ^(0[1-9]|(1[0-2]+)+)\/(20(0[2-9]|([1-2][0-9])|30))$

You can use this pattern. You can test it here also. http://regexr.com/3a60s
Breakdown:
^(

*

*0[1-9]|(1[0-2]+)+)

*\/

*(20(0[2-9]|([1-2][0-9])|30)
)$
Explanation:

*

*Matches between 01 to 09, or 10 to 12.

*Matches your "/"

*Matches 3 year sets starting with 20.

*

*2002 to 2009 with 0[2-9]

*or 2010 to 2029 with [1-2][0-9]

*or 2030, which is matched with the literal 30

A: You may check by pattern.. this way

<input type="text" pattern="^(0[1-9]|1[012])[- /.](20(?:0[2-9]|[12]\d|30))$" />

redpajama_set_name: RedPajamaStackExchange


A carte-de-visite portrait of two London hatters with an array of their stock. The reverse of the mount carries an advertisement for their business at 27 Coventry Street.
The other man, the 'Gibus' of the partnership, also appears on the 1861 census, a lodger at 77 York Road in Lambeth. A 40-year-old hatter at the time of the 1861 census, he was born in Paris. Although he gave his name as 'Meriade Gibus', his real name was in fact Meriade Anquez. The Gibus brothers Antoine and Gabriel were famous Parisian hatters who had invented the collapsible opera hat – known as the Gibus or 'chapeau claque' in French to this day - and patented many variations of their original design between 1834 and 1870. Although both brothers had sons that followed them into the family business, the man in this portrait appears to have had no legitimate connection to the family and was presumably trading under their famous name without their consent.
On 3 July 1853 he married Sarah Annie Smith, daughter of a builder, at St John the Evangelist in Waterloo. According to their marriage certificate, Anquez was a hatter living in Waterloo Road; his father, Martial Anquez, was a hairdresser. The couple separated in 1858 and in 1866 Mrs Anquez petitioned for divorced citing her husband's cruelty and adultery [though given the limited grounds on which divorce could then be granted, this may have been merely a formality to comply with the terms of the law]. Meriade Anquez died on 10 May 1893 at 19 Mornington Crescent, Camden. At the time of his death, he was still trading as a hatter under the name of Gibus with a shop at 10 Chandos Street, on the corner of St Martin's Lane. His effects were valued at £260. An advertisement was placed in the French press [Le Temps, 14 November 1893] but no heirs coming forward his estate passed to one John Macqueen, a hat manufacturer to whom Anquez owed money at the time of his death.
Photographed by Henry [Henri] Daubray of 70 Regent Street, London. Born in Paris in 1817, Daubray had formerly operated from a studio at 27 Coventry Street, so must have been personally acquainted with the two hatters.


Most recent portraits and head shots By Pip. Colour promotional photos by Garry Lake and black & white by Adrian McCourt.
Michael has established himself as one of the UK's most versatile actors, both onstage and screen. With a career that spans from film and television, to Classical, Modern and Musical Theatre.
On film he is known for his roles in THE BANK JOB, THE RIOT CLUB and as the Factory Foreman in the Oscar winning film of LES MISÉRABLES. On TV, his portrayal of Myles Standish in the U.S. TV movie SAINTS AND STRANGERS gained him rave reviews. He also played Phamer McCoy, in the Emmy and Golden Globe winning series HATFIELDS AND MCCOYS starring Kevin Costner and Bill Paxton.
On stage he has earned great acclaim working with many of the best theatre companies in the UK, playing London's West End and touring the world. Highlights include working at the Donmar Warehouse, playing Puck in A MIDSUMMER NIGHT'S DREAM at Shakespeare's Globe, a season with The Royal Shakespeare Company in THE CANTERBURY TALES, and in 2003 he was nominated for Laurence Olivier Award for his leading role as Joe Casey in Tim Firth's and Madness' OUR HOUSE, when he was twenty two years old.
Michael trained with the National Youth Music Theatre and earned his degree at the Guildford School of Acting. He grew up in Hull, East Yorkshire. He's married to the stage actress Caroline Sheen and they have a daughter together called Flora.
Copyright © 2013 Michael Jibson. All rights reserved.


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Q: compressing font files in amazon s3 I am using Amazon S3 to serve static files for my website. My server side code is built on Django 2.0. I am using boto3 and django-storages packages to server static files. AWS_IS_GZIPPED is set to True in settings.py file.
All the static files (CSS, JS, images) are compressed. Response header has content-encoding as gzip for these requests. But, font files are not getting compressed. Is there a different way to compress font files when served from S3?
You can clearly see this behaviour when you inspect my website. Click here to go to the website.

A: "https://blockchainsemantics.s3.amazonaws.com/static/fonts/NexaBold.c9f309b3d479.otf" This is one of your font files from your website, you check response headers for the font request, you will see it is as application/octet-stream MIME type, which will not get compressed while getting served from S3 or CloudFront, you can check the supported compression MIME types of CloudFront here "https://docs.aws.amazon.com/AmazonCloudFront/latest/DeveloperGuide/ServingCompressedFiles.html", If you are worried about performance, serve static files Through a CDN like CloudFront, it will cache the object in edge location.


Comedian and former TV show host Bill Nye "The Science Guy" collaborated on a new global warming-themed hip-hop song lecturing listeners about the evils of climate change skepticism.
Nye is featured in a new song by Canadian rapper Baba Brinkman that drones on for more than 5 minutes about why millennials, among others, should paint scarlet letters on so-called man made global warming skeptics.
WARNING – Do not listen without alcohol. Drink responsibly.
The song, titled "The Beef," hashes out a laundry list of grievances environmentalists and politicians level against people who strike skeptical positions against scientists who claim global warming is real and man-made.
It's lyrics are a hodge-podge of words and spliced together sentences bemoaning how the skeptics' views on global warming still get media attention despite politicians and celebrities best efforts to drown them out.
Brinkman prattles on about how skeptics bring up "the phony hiatus" on global temperature increases as if it's real.
Skeptics have for years pointed to what they call a mismatch between climate model predictions and actual temperature observations.
A group of climate scientists conducted a study in February confirming the "hiatus" in global warming that Brinkman referenced. The scientists essentially admitted that their climate models were wrong, and, in fact, temperature increases had been arrested.
Get Climate Hustle on DVD or Blu-ray today!
He must think he is right, pity ignorance is given prominence on such an important propaganda matter!
Bill Nye is an idiot. Not a very deep thinker for sure.
He has no idea how stupid he is.


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Home / Featured Articles / What it means that the Sacramento Kings are staying
What it means that the Sacramento Kings are staying
By Kels Dayton
Long live the Sacramento Kings.
At around 7 p.m. eastern tonight, I found out that my favorite NBA team is, this time for sure, going to exist next season.
I found out that the squad I've been rooting for since I was 12 years old is staying right where it belongs, and that I can look forward to the NBA Draft, and next season, and getting NBA League Pass again.
I couldn't be more estatic.
The author will have the chance to be completely flabbergasted by DeMarcus Cousins for years to come. (Rocky Widner/Getty Images)
What does it feel like to realize that your favorite team is going to be around for a while, that you won't have to be an NBA nomad with no real rooting interest anywhere?
Put it this way:
The Kings were horrible this year, but it feels like they just won a playoff series. I'm pouring champagne all over myself as we speak. In fact, I just plastic-wrapped my keyboard.
To put it another way: this is the exact opposite of the 2002 Western Conference Finals.
Maybe it's karma (although that's a tough sell to Seattle fans), or maybe it's just luck. But this time around, the Kings came out on top with everything on the line. Eleven years ago, I collapsed to the floor in devastation. Today, I couldn't have been happier if Amanda Pflugrad suddenly showed up at my house.
This was a fight Sacramento deserved to win. The Kings have some of the most passionate fans in the league, and thanks to the Herculean efforts of mayor and former Phoenix Suns guard Kevin Johnson, they have a group of investors willing to spend an ungodly amount of money on the team, and a plan for a new arena that passed 7-2.
The fact that this whole thing became a bidding war was unfortunate and wrong, because Sacramento never wavered on whether or not it wanted to keep the Kings. Fans still showed up in droves. Politicians fought tooth and nail for the right to use public money on a new arena.
Kings fans sold out the final game of the season in Sacramento, and gave Sleep Train Arena an NBA Finals atmosphere once again. A guy named Carmichael Dave even put together a bus tour and traveled the country to spread the word about the passion his city had for its team.
In truth, only reason the Kings were even in the position to be relocated was because of the vindictive Maloof family, which backed out on an arena deal they had agreed to last year and sold the franchise to Seattle businessman Chris Hansen in stealth. They were hellbent on screwing Sacramento over, hoping to pull the moving fans away in the middle of the night like the Baltimore Colts.
Thankfully, it didn't work.
It feels pretty great to know that the collective efforts of a fan base and a city can be enough to stop an inept ownership group.
It feels even better that I'm going to have a team to root for next season, and in the seasons to come.
Long live my team.
← Older The Decision: Andrew Wiggins Edition
Newer → Pacers upset Heat, referees, win series 2-2
Zaila Avant-garde, at 14, is spelling champion, math whiz, and hoop phenom
Simone Fontecchio, Maodo Lo among non-NBA players outshining NBA stars at Olympics
Finals Preview: Which matchups will determine Suns-Bucks winner?


The Invisible Man got good news for you! He mentioned that heroes are in need of equipment and changed Grand Arena Rewards: instead of Dragon Souls he put Perfect and Ghost Items. But he reduced number of Epic Items, for now the Guilds can chose the day when they get rewards.
The chests with Perfect and Ghost equipment can be sold in market for gold right from the Guild's Storage.
However,those, who like to sell Dragon Souls, shouldn't be sad: now on these Souls can be sold not only by contracts, and now you can trade them for crystals.
Unfortanutely,The Fort Commander has learnt about it and blinded by greed, he decided to set a price for mask creation.
But Titans in oder to sweeten the pill, have deducted this price from the cost of further upgrades.
Titans are not only kind, but fair as well. Since the Heroes' might has increased lately, they've raised characteristics' requirements in fights with Deities.
And finally, you will get the Defeneder's Souls from the attacking monsters, till the Mask is upgraded completely.
ucted this price from the cost of further upgrades.


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Q: How can I write a function that doesn't print out uppercase words from the list? I've a list ["ABC", "JAVA", "Python", "user", "CODE"] and I want the functions print out ["Python", "user"].
Here is my progress so far:
def no_upper(my_list : list):
    new_list = my_list
    for word in my_list:
        if word.isupper():
            my_list.remove(word)
        return new_list
if __name__ == "__main__":
    my_list = ["ABC", "JAVA", "Python", "user", "CODE"]
    new_list = no_upper(my_list)
    print(new_list)

A: *

*Enclose your strings in quotes.

*Your function tries to modify my_list rather than actually building your new_list.  Just build the new list and return it without trying to remove the items from the input -- modifying a list you're iterating over will usually have unexpected/buggy results, and even if it worked to do that, there's no good reason to mess around with the caller's data that way.

>>> def no_upper(my_list: list) -> list:
...     return [word for word in my_list if not word.isupper()]
...
>>> no_upper(["ABC", "JAVA", "Python", "user", "CODE"])
['Python', 'user']

A: If you objective is to "remove" words written entirely in capital letters:
lst = ["ABC", "JAVA", "Python", "user", "CODE"]
[x for x in lst if x != x.upper()]

OUTPUT
['Python', 'user']

A: Try with a list like this:
my_list = ["ABC", "Java", "Python"]

Unless Python will raise an UnboundLocalError, since ABC without quotes ('') or double quotes ("") is parsed as a variable, but there's no ABC variable in your program.
You can also use inline syntax to solve your problem, like this:
def noUpper(l: list):
    return [x for x in list if not x.isupper()]


Old Growth – Memory, Like a Movie!
My start point was at the top left hand corner of the map seen below.
Thanks to Ourcortes.com and all the folks who maintain the trails.
Phew! I am so glad to look at the map of the trails I walked late last afternoon. It would have been kinda handy to have had it in my hand at the time! From my understanding, and befuddled mind, I must have walked all around the edge of the map! It was over two, and nearer to three, hours I was on my feet deep in the magical mossy old growth forest. It was getting dark by the time I completed the walk and I was definitely getting anxious considering I didn't know where I was, or how much trail lay between me and where I'd parked the car! Somehow all turned out well and I had one of the most memorable walks. Ever.
I think I took the Swim Rocks trail. It was a choice between that and this way…!
Yes a walk which is linked to an adventure back in 1967. I came to Cortes with two friends by water taxi, stayed a night with their acquaintances, swam in Gunflint Lake and then flew back to Campbell River on Vancouver Island the next day by sea plane (or float plane as they are called). The whole experience left a deep impression and almost by chance I find myself here again AND yesterday I walked in the forested-edge of Gunflint Lake! Forty + years later.
I have had the time and the mental space to reflect on the intervening years. Nothing and everything has changed. How so? Time, and space, have a way of twisting and curling and evaporating and reemerging which defies the ordinary mind and its capacity to understand. I'll say no more!
With much gratitude to those who have facilitated this trip including those who have donated CAD (Canadian Dollars). Rain and sun, mist and blue sky – all magical. And memorable – in the way a movie is memorable when it touches ones heart. Thank you to those near and far for making this trip possible.
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Does not your mobile phone take pictures? Photographing the map might have helped.
Yes it could have taken a picture of a map on my phone…if the walk had been pre planned! It wasn't.
What a wonderful trip and beautiful walk/adventure! Thank you for sharing. I always enjoy your posts and reading about your travels and reflections.
Ashley! I am touched that you read here.


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Q: Fourier transformation of an Image in R I am using the package imager to transform a set of images to fourier space:
library(imager)
face2 <- load.image(path)
FFT(face2)

Unfortunately, I obtain this error
Error in FFT_realim(im.real, inverse = inverse) :
cimg::stderr(): Reference to 'stderr' stream not allowed in R mode ('cimg_use_r' is defined).

Even if I try with one of the images that comes with the package, it still doesn't work
FFT(boats)

Although the error here is slightly different:
Error in FFT_realim(im.real, inverse = inverse) :
      CImgList<double>::FFT(): Specified real and imaginary parts (256,384,1,3) have non 2^N dimension along the Y-axis.

I have no idea of what is going on, so any help would be much appreciated


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Chaverri is a surname. Notable people with the surname include:

 José Joaquín Chaverri Sievert (born 1949), Costa Rican diplomat
 Carlos Meléndez Chaverri (1926–2000), Costa Rican historian


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Tsunami wrecks Niuatoputapu
The island of Niuatoputapu in northern Tonga was severely damaged by tsunami waves early yesterday morning, September 30, 2009, following an 8.1 earthquake between northern Tonga and Samoa. Photos by Pesi Fonua.
Replacement ferry service for Tonga soon
A new interim inter-island passenger vessel for Tonga is expected to be in service soon, to replace the sunken ferry MV Princess Ashika.
Donations for Ashika victims exceed $1 million
Donations to assist families who lost relatives in the Ashika ferry disaster, are flowing into Tongan trust funds, with over $1 million pa'anga collected so far from local and overseas people.
Ashika Memorial at sea (Part three)
Ha'apai, Tonga
On August 25, 2009 a flotilla of vessels carrying about 500 mourners gathered in Ha'apai waters, around a point where four orange buoys floated in the water marking the last position of the MV Princess Ashika. They held a memorial and mass funeral ceremony at sea for the 74 people who were lost when the inter-island ferry sank on August 5. Part Three: Photos by Linny Folau on the MV Pulupaki and Pesi Fonua on the VOEA Pangai.
More photos of Ashika Memorial at sea
A mass fuenral ceremony at sea for the 74 people who were lost when the Princess Ashika sank on August 5, was held at midday yesterday, August 25 at the spot where the ferry sank, 11 nautical miles, south-west of Nomuka Island, in Tonga's Ha'apai Group, where about 500 people gathered on a flotilla of boats. Part Two: Photos by Linny Folau on the MV Pulupaki and Pesi Fonua on the VOEA Pangai.
Mass burial at sea for Ashika victims
Ha'apai,Tonga
A mass funeral ceremony at sea for the 74 people lost on the Princess Ashika on August 5, was held at midday yesterday, August 25, at the spot where the ferry sank, 11 nautical miles, south-west of Nomuka Island, in Tonga's Ha'apai Group, where about 500 people gathered on a flotilla of boats. Photos by Linny Folau on the MV Pulupaki and Pesi Fonua on the VOEA Pangai.
Families of Ashika victims to visit wreck site
A special memorial service will be held today, August 25 at the site where the MV Princess Ashika sank, an open sea area 11kms SSW of Nomuka Island in remembrance of the many lives lost on August 5.
Bereaved families end 17-nights vigil
After 17 nights of camping in tents outside the Shipping Corporation of Polynesia Ltd. office at Queen Salote Wharf, anticipating news of relatives in the August 5 sinking of the MV Princess Ashika, bereaved families put closure to the hope of recovery and returned home on Friday July 21.
Aerial and surface search ends
The aerial and surface search for survivors from the MV Princess Ashika disaster has ended, Tonga's Police Commander Chris Kelley announced on 21 August.
Operation Ashika names 70 missing passengers and crew
There were 128 persons on board the Princess Ashika when it left Nuku'alofa on its August 5 voyage, Operation Ashika confirmed on August 19. These have been established as: 54 rescued, 2 bodies recovered, 72 missing persons (68 passengers and 4 crew).
ROV video shows Ashika on seabed
Sitting in an upright position, the sunken MV Princess Ashika can be clearly seen in a video captured by a Remote Underwater Operating Vehicle working at over 100 metres on the Ha'apai seabed, including evidence of human remains observed by a navy survey team yesterday.
Fasi-moe-afi church members lost on wedding trip
Fasi-moe-Afi bridegroom, Sione Valele 'Elone (43), was on his way to Ha'apai to be married to his sweetheart, Vahengalu He of Pangai. Travelling with him on the fatal voyage of the Princess Ashika on August 5 were his cousin, choir-master, Veuveuso 'Elone (34) and a friend, a North Otago rugby player, Matoni 'Aho (29).
"No comment" as sorry SCP Board awaits inquiry
Almost two weeks after the sinking of their vessel, MV Princess Ashika the Chairperson and members of the board of the Shipping Corporation of Polynesia Ltd. made a first public statement on August 17, expressing their condolences and sympathy to families who have lost members.
'Unaloto (5) loses parents and two sisters
The loss at sea of a young family of four - Manukeu and Losaline Kauhala and two their three daughters - is a tragedy that has struck a heavy blow to the heart of two Tongatapu families.
Newly-wed Heilala loses husband
Newly-wed Heilala Fetu'u (23) longs to see the husband she married on July 30 and who was lost at sea only one week later. By Linny Folau
HMNZ Manawanui arrives to assist Operation Ashika
A New Zealand navy vessel the HMNZ Manawanui arrived in Tonga at the weekend with a support team to assist in the reconnaissance of the sunken ferry MV Princess Ashika in the Ha'apai Group. Photos by Patricia Car
Blue Ribbon campaign remembers lives lost at sea
A Blue Ribbon campaign in solidarity of the lives lost at sea was launched on August 14 in an emotional ceremony held outside the Shipping Corporation Office at Queen Salote Wharf, where many families have been camping outside in tents for days waiting on news of loved ones who were passengers on board the sunken ferry MV Princess Ashika.
Ashika Relief Fund collects over $600,000
Donations to the Ashika Relief Fund have reached over $600,000 pa'anga the Chief Secretary and Secretary to Cabinet, Busby Kautok, said on August 14 on receiving a $2,000 donation from the Staff Association Committee of the Westpac Bank of Tonga.
Operation Ashika releases first list of missing passengers and crew
Operation Ashika this afternoon released 37 names, on the first confirmed list of passengers and crew missing following the sinking of the MV Princess Ashika on August 5, 2009.
Grandfather grieves for three family members
A grieving father, Rev. Sione Taufa (63), was thankful today after he was allowed to see his daughter Vaefetu'u Mahe (22), whose body was the second and last to be recovered after the tragic sinking of the MV Princess Ashika on August 5.


It has been our vision for some time now, but finally, we are excited to introduce you all to our next evolution of Koh… Koh Lounge.
It all started as our incredibly popular pop-up concept found both on the beach for the Air Show and on the Quay for Christchurch Food Festival, but we wanted to take it to the next level. Now, it has finally found its home in the vibrant heart of The Bournemouth Triangle.
Stood beside our Flagship Restaurant on Poole Hill, Koh Lounge is our welcoming sanctuary where we invite you to "escape the everyday". All warm lighting, beige colours and golden murals behind day beds, gold lanterns and a striking dark wood bar, we have ventured away from our usual burnt orange tones.
Kick back in the ambient surroundings, engross yourself in the exquisite architecture of the wooden pergola or simply nestle in a quiet corner watching the world go by.
One month on from opening, the venue is already a hive of activity at every point in the day; with bottomless coffee to meet the needs of those hot desking or on business, worldly beers for those on a creative jaunt and as the sun sets, the perfect scene for an evening soirée.
Think Friday Club cocktail gathering; a meeting with colleagues over a creamy latte in the afternoon; a bite to eat with their beautiful sharing platters or a couple of late bourbons at the end of a long week.
And the murals aren't the only change with our Lounge.
On the menu, the drinks and tapas are equally as distinctive, with carefully crafted cocktails by connoisseur and all round great guy, Wandering Bartender, Max. The beautiful wooden sharing boards are also new with little tapas bites re-invented from your favourite classics in a new dining concept.
Pop in and say hello to Super General Manager and familiar face Mark Hooper as he returns to Koh Bournemouth to take on the Lounge with Max and Bar Manager Mike Bryant.


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Photo: The Kop van Zuid area in Rotterdam
Kop van Zuid
5 out of 8 visitors find this information valuable.
If you cross the city from North to South over the Erasmus Bridge, you will arrive in a modern city district. It is a wonderful place for people who love architecture. Amid a selection of shiny high rise, a number of buildings hark back to days gone by.
Admire the architecture at the Kop van Zuid.
Enjoy lunch with a view of the water at Hotel New York.
Stroll along Wilhelminakade and admire the skyline of Rotterdam.
Cruise Terminal and Hotel New York
To the right of the bridge is Wilhelminakade with its fully renovated Cruise Terminal, the former arrival and departure hall of the Holland America Line. Today, you can see big cruise ships dock here. It also boasts renovated warehouses that now serve as home to students, as well as the Marine Safety Center and Hotel New York. Hotel New York was the Holland America Line's head office built by C.B. van der Tak, Drooglever Fortuyn, and J. Müller in 1901. It was converted into a hotel/grand café in 1993.
Offices and coastline
Facing the bridge is the Wilhelminahof with its new Tax Office and Justice offices, the new courthouse, an office tower, and access to the Wilhelminaplein metro station. The work of art to the right of the bridge was created by the architect P. Wilson and in addition to the time and temperature, also indicates the (estimated) world population. The other digits are random and have no meaning.
De Rotterdam by Rem Koolhaas is one of the most notable buildings on the Kop van Zuid. The three interconnected towers, that rise nearly 150 meters up into the sky, form a 'vertical city' with luxury apartments, a four-star hotel, offices, shops, restaurants and cafés, sports and parking facilities
Spending the night in Rotterdam
Are you searching for a hip design hotel, a romantic bed & breakfast, or a pleasant holiday home for your family? Rotterdam has suitable accommodations for every taste and budget. Check out the comprehensive selection and book your perfect holiday here!
Rotterdam is a young and dynamic city with a world-class port. The city of Rotterdam is internationally known for its modern architecture and design.


Shreveport-born man with philosophical bent traveled a secular path from–and back to–the South, in a culture of imbued religiosity.
Meet Charles Thomas Beaird, one of the last openly self-described "liberal Republicans". An early "champion" of civil rights legislation, Beaird served in the military and was a nontheist, according to his obituary.
A fortunate man, Beaird returned from war to an existing family enterprise with promise of fortune. Alongside Beaird's ongoing industrial business interests, he became immersed and involved in politics where he lent support to various interests in service as advocate, director (Federal Reserve Bank of Dallas) or co-chair (of Shreveport's Biracial Commission, for example). He served in office for four years.
After working to turn a democratic community into a Republican one, and eventually realizing that he was liberal, he continued to serve the GOP party in a fiscally-conservative mindset, but would eventually pivot to publishing and real estate. He would direct the formerly conservative Shreveport Journal under a new, liberal mindset and champion organized labor ( a "rare phenomenon" in the South) alongside conservative-interest campaigns like the flouridation of the community's water supply.
Beaird would ultimately run philanthropic real estate projects and fight to improve housing and living conditions for one of Shreveport's poorest districts, and he'd win several awards, which include the Liberty Bell Award from the Shreveport Bar Association, the Philanthropist of the Year Award from the Association of Fund Raising Professionals, the Jacques Napier Steinau Award of the National Conference of Christians and Jews, and the Ralph Waldo Emerson Award given by All Souls Unitarian Universalist Church.
Mr. Beaird wore a real rose, pinned to his lapel each day that he went to work, and a symbolic rose logo adorns the downtown Shreveport Beaird Tower.
His wife identified as Presbyterian.
Wikipedia authors. Charles T. Beaird. Retreived 10/16/2018.
Obituary, via Full Wiki. Charles T. Beaird. Retreived 10/16/2018.


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Q: forEach not returning parts of string separately I currently just tried this:
var languages = ['HTML', 'CSS', 'JavaScript'];
languages.forEach(function(language) {
    alert('I love ' + languages + '!');
});

although it is returning the alert 3 times, it is returning it saying "I love HTML,CSS,Javascript!" three times, instead of each language, one at a time. I can't figure out why that would be?

A: your callback function:
function(language) {
    alert('I love ' + languages + '!');
}

doesn't do anything with language. It should be:
function(language) {
    alert('I love ' + language + '!');
}


Its an established fact that the skin is the first to be affected and show visible signs of ageing. To help fight this there are a number of products available, the problem with some of these is that they work from the outside in, they will for sure control ageing signs, but do not really fight the cause.
HGH supplements are regularly used by sport persons to improve their performance and increase muscle mass. There are though, many other benefits to be gained by taking HGH supplements which most of us are not aware of. Taking HGH supplements will help to improve the texture and tone of the skin. How this happens is easy to explain.
The daily functioning of our body depends on hormones and other independent functions. These hormones produce proteins and the like that are the very core of our bodies functions. Human Growth Hormone (HGH) is hormone that is stored and synthesised in our anterior pituitary gland. Situated at the base of our brain, it is responsible for the release of certain hormones that stimulate proteins required for the formation of Collagen, Elastin and other functions related to regeneration.
Elastin as a protein is responsible for the elasticity in our skin, helping skin return to its original shape after being pinched or pulled. Another protein is Collagen that constitutes muscle tissue and helps keep the skin firm and supple. As these proteins naturally decline with age our skin begins to become loose and saggy. Collagen helps to repair the work of the cells and is also present in most other tissues.
As we get older, the natural level of HGH in our body will reduce. This weakens the ability to produce the proteins such as elastin and collagen. To maintain these levels of HGH, there are effective supplements available to buy.
These work differently to regular anti-ageing creams, lotions, cosmetic treatments, these HGH supplements work on the body from within and will help fight the signs and effects of ageing naturally.
HGH works by increasing the number of times a skin cell in the dermal layer divides, this helps to generate collagen and elastin which helps to fill facial tissues, restoring reduced elasticity and glow. HGH will also promote new muscle growth in the face. These supplements will invigorate the levels of HGH within our body, these raised levels will help rebuild the layers beneath the skins surface to make it smoother, rejuvenated and much younger l ooking.


Easter is coming. Every year, everyone celebrates this special holiday by eating loads of chocolate.
In partnership with Glasgow Women's Aid, Sanctuary Students have set up a donation point at Reception for collection of Easter Eggs to be distributed to children within the local area.
It would be highly appreciated if you could find the time to donate some Easter Eggs and put a smile on a child's face this Easter!
The donation drive will be running until Wednesday 17th April.
If you don't have the time to get one you can donate £1 and we will get an Egg on your behalf.
Easter Egg Hunts at the Residences Cleaning, Bins and Recycling Thank you for the music but... Fire Safety & How to Avoid False Fire Activations Green Living and Saving Energy UofGLiving Wee Green Guides Register your bike with the police Become a Living Support Assistant for 2019-2020!


An 8-channel IO control scheme with "watch dog timer.
The 1-wire IDE (DS2408) must be controlled every couple minutes. Otherwise the 4060 count will come to its maximum, all outputs will be blocked. This prevents the heater is left on while the software is stopped for example.
The 4060 timer is reset by the strobe output of the ds2408.


Busking at Insadong by Nakwon Music Mall – Peter's Site!
I have always enjoyed watching buskers perform, and I have been fortunate enough over the years to have seen some amazing musicians, magicians, and performers – plus a few real weirdos of course – just by walking down the right (or wrong) street at the right (or wrong) time.
Even when their performances weren't exactly in line with my musical tastes, I respected the fact that they had the courage to share with complete and sometimes totally disinterested strangers the things they love doing. Regardless of the presence or absence of skills and talents, I was always envious of them and often imagined myself standing in their place, drawing a generous and huge crowd.
Despite that dream, I had never busked until the supportive and professional staff behind the Nakwon Supporters Program invited myself and my fellow 2Much band mates to do exactly that on Seoul's historic and famous Insadong Street right by Nakwon Music Mall.
Saturday, May 28 was the big day. Fellow Nakwon Supporter Mimi Roh started the afternoon's entertainment with her big red guitar and three songs: "Blank Space" by Taylor Swift and two of her own compositions: "Sparklin' Bright" and "Ponder The Sky". I really admire her for writing and performing her own songs.
Even if I could write my own songs, performing them would be much, much scarier than performing well-known and much-loved hits. There's nothing hard about that at all once you learn the song, but performing your own song is, especially while busking, akin to sharing a part of your soul with a bunch of strangers. That takes more courage than I possess.
Ian Burgos, Liyuan "Maggie" Huang, Jake Botello, and I (Malcolm McLaughlin was busy that day – see below) then took center stage for our own three-song set.
"Every Breath You Take" by The Police was our first song. It's a personal favorite of mine because of its distinctive and very cool-sounding arpeggios. Plus, it's simply a great song. I've seen Sting twice in concert and both times "Every Breath You Take" was the highlight. Performing it is made all the more enjoyable by the combination of Ian and Maggie's sweet voices.
Our second song was "Happy" by Pharrell Williams, and what a perfectly named song it is. It's not only a whole lot of fun to play, it never fails to get a huge response from our audience, and that more than doubles the fun.
Malcolm and Yun-seon's wedding next month offers another musical first: the happy couple wisely invited 2Much to perform a few songs on their most special of days. Performing at their wedding is sure to be another highlight on this unique and fun musical journey we're all lucky enough to be on. No jeans and T-shirts for that gig, and that'll be another first.
Tagged2016GuitarNakwon SupportersPeter's BandPeter's Music Videos!
Next Article June 2016 Fitness Diary!


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module Saper
  module Arguments
    class Variable < Argument

      #
      # TODO: docs
      #
      def valid?(value)
        value.is_a?(String) || value.is_a?(Symbol)
      end

    end
  end
end

redpajama_set_name: RedPajamaGithub