text:
\section{Introduction}

Recent research addresses  the issue of reducing the  amount of energy
consumed by  computer systems while maintaining  satisfactory level of
performance.   This can  be done  at  different levels  of a  computer
system.  One possibility is to  specify a good scheduling mechanism in
the operating system level. Here  we have two mechanisms at hand.  One
common method  for saving  energy is the  \emph{power-down mechanism},
which is to  simply suspend the system during  long enough idle times.
Another common method is \emph{speed  scaling}, which is to adjust the
processor  speed low  enough to  meet the  jobs requirements.  In this
paper  we study  the problem  of designing  scheduling  algorithms for
minimizing the consumed energy using both mechanisms.

The question whether this problem can be solved in polynomial time was
posed by Irani and Pruhs~\cite{IraniPruhs:Algorithmic-problems}, who
called it \emph{speed  scaling with  power  down scheduling}
problem.   We provide  an  $O(n^3)$  algorithm in  this  paper for  the
special case  of agreeable deadlines.  Jobs may be   released at different
time moments, and may have  distinct deadlines. The agreeable deadline
property  just  means  that   later  released  jobs  also  have  later
deadlines.  This  holds, for example, when  the deadline of  each job is
exactly $F$ units after  its release time,  which arises when one
wants to maintain a guarantee of service for the flow time of the jobs.

\section{Problem definition}

An  instance   of  our  scheduling  problem  consists   of  $n$  jobs,
$1,2,\ldots, n$, where each job $j,~ 1 \leq j \leq n$, is specified by
a release time/deadline interval\footnote{Notation: $[t_0,t_1)$ stands
  for the half  open interval $\{t:t_0\leq t <  t_1 \}$.} $[r_j, d_j)$
in which it  must be scheduled and a workload  $w_j$.  An instance has
the \emph{agreeable deadlines property}  if the jobs can be renumbered
such that both their release times and deadlines are in non-decreasing
order, i.e.  $i <  j$ implies $r_i  \leqslant r_j$ and  $d_i \leqslant
d_j$.

A schedule is defined by three functions
\begin{eqnarray*}
  \text{mode}  & : & \mathbbm{R} \rightarrow \{\text{on},
  \text{off}\}\\
  \text{speed} & : & \mathbbm{R} \rightarrow \mathbbm{R^+}\\
  \text{job} & : & \mathbbm{R} \rightarrow \{\text{none}, 1, \ldots, n\},
\end{eqnarray*}

with the following properties

\begin{enumerate}
  \item $\forall t : \text{speed} (t) > 0 \Rightarrow \text{mode} (t) =
  \text{on}$

  \item $\forall t : \text{speed} (t) = 0 \Leftrightarrow \text{job} (t) =
  \text{none}$

  \item $\forall t : \text{job} (t) = j, j \neq \text{none} \Rightarrow t \in
  [r_j, d_j)$

  \item $\forall j\neq \text{none} : \int \text{speed} (t) \text{d} t = w_j$ where the integral
  is over all times $t$ such that $\text{job} (t) = j$

  \item for every time $t$, there is a positive length interval $I \ni t$ on
  which the schedule is constant. Moreover $I$ is of the form $(- \infty, u),
  [t', u)$ or $[t', + \infty)$ for some time points $t', u$.
  \label{piecewiseconstant}
\end{enumerate}

The last property is in fact a simplifying assumption to avoid degenerate schedules.
The    interpretation    is    that    at    a    time    $t$    where
$\text{job}(t)=\text{none}$, the machine is idle but switched on when
$\text{mode}(t)=\text{on}$      and     is     shut      down     when
$\text{mode}(t)=\text{off}$.   There   is   a  non-negligible   energy
consumption during the idle time periods, but one avoids the cost of
shutting down and rebooting the machine.

The cost (i.e., the consumed energy) of a schedule is specified by three parameters:
an exponent $\alpha \in [2, 3]$, a wake-up cost $L > 0$ and a ground
dissipation energy $g > 0$, and it has two components:

\begin{enumerate}
\item The \emph{speed cost}, that is the energy consumed in all times $t$ such that $\text{job} (t) = j \neq \text{none}$.
This cost is defined as $c_{\text{speed}} = \int_{} \text{speed} (t)^{\alpha} \text{d} t$.

\item The \emph{mode cost}, that is the cost of the ground dissipation
  energy plus the wake-up energy.
\end{enumerate}
A schedule with property (\ref{piecewiseconstant}) partitions the time into a sequence $S$
of disjoint, inclusion-wise maximal intervals, such that $\text{mode} (t) =
\text{on}$ if and only if $t \in \cup S=\cup_{I_k \in S} I$.
The sequence $S$ is called the \emph{support} of the schedule, and the
energy consumption generated by this support constitutes its  mode cost which is defined
as $c_{\text{mode}}= L \cdot (|S| + 1) + g \cdot | \cup S|$. Note that  we count a wake-up cost
$L$  for the two  half-infinite intervals  surrounding $S$.

Hence, the total cost is just the sum $c_\text{speed} + c_\text{mode}$
and the  problem studied in this  paper consists in  finding a minimum
cost schedule for an agreeable deadline instance.

The outline  of the  paper is  as follows. After  a brief  survey over
related work,  we start  showing  structural  properties of  optimal
schedules, in particular we introduce  the notion of prefix and suffix
of  a  block.   Finally  we  define the  dynamic  program,  prove  its
optimality and analyse its complexity, while mentioning implementation
issues. The  algorithm has been  implemented in Python and  can handle
instance of 300 jobs within a second.

\section{Previous work}

Our  scheduling  problem  for  general instances  (with  non-agreeable
deadlines)  was raised  in~\cite{IraniPruhs:Algorithmic-problems}.  No
polynomial time algorithm is known for this problem, nor has it
been  shown to  be NP-hard.   The current  best positive  result  is a
$137/117$-approximation provided  in \cite{Abers.Antoniadis:Race}. The
same paper  also gives an  NP-hardness proof, however for  a different
energy   mode,   when   $c_{\text{speed}}$   is   defined   as   $\int
f(\text{speed} (t))  \text{d} t$ for some  piecewise linear monotone
function $f$.

The general problem contains  two subproblems, which have been studied
and  solved  individually.  The  first  one  does  not consider  speed
scaling, and restricts to speeds 0  or 1, depending on the mode.  Here
essentially  the  goal  is  to  minimize  $c_\text{mode}$  only.  This
subproblem  has been solved  in $O(n^5)$  time by  dynamic programming
\cite{baptiste2007polynomial}. For  agreeable instances the complexity
has been  improved to $O(n^2)$ \cite{chau2011}.  The second subproblem
does  not consider  the power  down  mechanism, and  restricts to  the
single mode  'on' and  to ground dissipation  energy $g=0$.   Here the
problem is  to minimize $c_\text{speed}$ only.  This  problem has been
solved by a widely celebrated  greedy algorithm due to Yao, Demers and
Shenker \cite{yao1995scheduling} in  $O(n^3)$ time.  The complexity of
this algorithm, known  as YDS, has been improved  to $O(n^2\log n)$ in
\cite{li2006discrete}  and even  to $O(n^2)$  for  agreeable instances
\cite{wu2010min}.

Different  variants of  this problem  have  been studied  in the  past
years, which include the online setting, as well as different objective
values,  like   minimizing  throughput  or  flowtime.    We  refer  to
\cite{Albers:energy-efficient-algorithms} for an overview.

An important ingredient  for the algorithm presented in  this work, is
the aforementioned YDS algorithm.   For completeness we roughly sketch
it now.   At each step of  the algorithm, the  interval $I^{\star}$ of
maximum density is  selected among all $O(n^2)$ intervals  of the form
$[r_i,d_j]$. The \emph{density of an interval} is defined as the ratio
$s=W/(d_j-r_i)$, where $W$ denotes the  total workload of all jobs $k$
with  $[r_k,d_k]\subseteq  [r_i,d_j]$.   The  key  idea  is  that  any
feasible schedule must have for  $[r_i,d_j]$ an average speed at least
$s$.  Then all those  jobs are  scheduled in  $I^\star$ at  speed $s$
using the EDF (Earliest-Deadline-First)  policy.  No job will miss its
deadline  by maximal  density of  $I^\star$.   For the  sequel of  the
algorithm the  time interval $I^{\star}$ is  \emph{blacked out}.  This
means  that  when  computing  densities  of  candidate  intervals  for
subsequent iterations, the blacked out intervals are excluded, and the
schedule  for the  remaining  jobs  must exclude  them  as well.   The
algorithm ends when all jobs are scheduled.

\section{Structure of an optimal schedule}

When a job $j$ is running at speed $s$ its execution takes $w_j / s$ time units and
the consumed energy is $(s^{\alpha} + g) w_j / s$. This amount of energy is
minimum for speed $s^{\star} := (g / (\alpha - 1))^{1 / \alpha}$, which
we  call  the  \emph{critical  speed}.  Note  that  $s^\star$  is  job
independent. The \emph{density} of an interval $I$
is defined as $\sum w_j / |I|$ over all jobs $j$ with $[r_j, d_j) \subseteq I$. An interval is
called \emph{dense}, if its density is at least $s^{\star}$, and \emph{sparse}, otherwise.

\begin{lemma} \label{lem:structOpt}
  {\cite{IraniShuklaGupta}}  Given an instance of  the  speed scaling
  with  power down scheduling  problem, there  is an  optimal schedule
  $(\text{mode},\text{speed},\text{job})$ with the following properties.

  \begin{description}
    \item[job span] for every time $t$, if $\text{job} (t) = j \neq
    \text{none}$ then for all times $u \in [r_j, d_j)$ with $\text{mode} (u) =
    \text{on}$, we have $\text{speed} (u) \geqslant \text{speed} (t)$

    \item[earliest deadline first] for every time pair $t < u$ if $\text{job}
    (t) \neq \text{none} \neq \text{job} (u)$, then $\text{job} (t) \leqslant
    \text{job} (u)$.

    \item[dense intervals] dense intervals $I$ are scheduled according to the
    YDS rule.

  \item[domination] for any other optimal schedule
    $(\text{mode'},\text{speed'},\text{job'})$,  and  a smallest  time
    $t$  such   that  $\text{mode}(t)\neq  \text{mode'}(t)$   we  have
    $\text{mode}(t)=\text{on}$ and $\text{mode'}(t)=\text{off}$.
  \end{description}
\end{lemma}

In  particular  the  first   property implies  that  whenever  $j$  is
scheduled, the speed is the same. The next two properties imply
that dense intervals divide the problem into independent subproblems, as we
describe now.

\begin{definition}
  \label{def:subsinstance} A  subinstance of our  problem is specified
  by a pair $(i,j)$ with $i \in \{1, \ldots, n\}$, $j \in \{i-1,
  \ldots, n\}$. For convenience we denote  $d_0 = r_1 - L / g$ and $r_{n
    + 1} = d_n  + L / g$. It consists of the  interval $I= [d_{i - 1},
  r_{j + 1})$ and a job set $J$. If $i = j + 1$, then $J = \emptyset$,
  else $J  =\{i, \ldots, j\}$. The release  time/deadline intervals of
  these jobs are restricted by intersection to $I$.
\end{definition}

\begin{figure}[ht]
\def<desired width>{14cm}

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  \fi
  \global\let<desired width>\undefined
  \makeatother
  \begin{picture}(1,0.42777051)%
    \put(0,0){\includegraphics[width=\unitlength]{example.pdf}}%
    \put(0.00300667,0.32185653){\makebox(0,0)[lb]{\smash{w1=1}}}%
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\endgroup
\caption{Structure of an optimal schedule  for an instance of 11 jobs.
  The boxes represent job executions where the height equals speed and
  the area  equals the workload of  the job.  The  different colors of
  the boxes  distinguish critical speed, less than  critical speed and
  more than critical speed.  The thick line below represents the mode.
  Finally  the   intervals  at   the  bottom  represent   the  release
  time/deadline  intervals of each  job $j$,  labeled by  its workload
  $w_j$.   Here the  schedule  consists  of 2  blocks  separated by  a
  shutdown interval.  Jobs 1,5,6,7,11  are scheduled at critical speed
  $s^\star$,  while   job  9  is  scheduled  with   higher  speed,  as
  $[r_9,d_9)$ is a dense interval.  Note that the schedule is idle but
  not shutdown between jobs 1 and 2.} \label{fig:structOpt}
\end{figure}

Note that  in case $d_{i -  1} < r_{j +  1}$ or $d_{i -  1} < d_i$
or $r_j < r_{j + 1}$, the subinstance $(i,j)$ is infeasible as the
release time/deadline interval of $i$ or $j$ is restricted
to the empty interval.

We extend also  the definition of the cost  function for subinstances.
The schedule of a subinstance $(i,  j)$, consisting of job set $J$ and
interval  $I$,   is  defined  by  the  functions   $\text{speed}  :  I
\rightarrow  \mathbbm{R^+}, \text{mode}  : I  \rightarrow \{\text{on},
\text{off}\}$ and $\text{job} : I \rightarrow \{\text{none}\} \cup J$.
For  the  mode  cost,  let  $S  :=  \{t \in  I  :  \text{mode}  (t)  =
\text{on}\}$ be the support of the  schedule, and $k$ be the number of
intervals in $I \backslash \cup S$. Then, $c_{\text{mode}} := k L + g|
\cup S|$.  The interpretation is  that if immediately before and after
$I$ the machine  is on, then shutdown intervals at  the borders of $I$
also do generate a wake-up cost.

We choose $d_0$ far enough from $r_1$ such that w.l.o.g. an optimal schedule
for the subinstance $(1,k)$ will  start  with  a shutdown  interval.  A  symmetric
property is true  for subinstances of the form  $(k,n)$. Therefore the
cost of the subinstance $(1,n)$ is consistent with the cost definition
for the complete instance.
Note that the optimum for a subinstance of the form $(i, i - 1)$ equals $\min
\{L, g (r_i - d_{i - 1})\}$.

Now consider all inclusion-wise maximal dense intervals. They partition the
time line into a sequence of alternating dense and sparse intervals.

The following  lemma follows directly from the  definitions. We stress
here that independence of the subschedules is implied by the agreeable
deadline assumption.   Lemma~\ref{lem:structOpt} states that there
is an  optimal schedule,  satisfying the \emph{earliest  deadline first
  property}, which means that whenever  job $j$ is scheduled, all jobs
$i<j$ already completed.  So the agreeable deadline assumption happens
to  be quite  strong, which  permits a  dynamic  programming approach.
However the problem does not become trivial, since one still needs to
decide when the machine is to be shutdown and when to be idle.
\begin{lemma}
  \label{lem:densePartition} Sparse intervals $I$ are associated to pairs $(i,
  j)$, such that the portion of an optimal schedule for the
  original instance restricted to $I$, is also an optimal schedule for the subinstance $(i, j)$.
  Moreover none of these subinstances contain dense intervals.
\end{lemma}

\section{Suffixes and  prefixes}

In  this section,  we consider  an  optimal schedule  of an  arbitrary
subinstance consisting of a job set  $J$ and an interval $I$ such that
all  subintervals of  $I$ are  sparse. Whenever,  in this  section, we
refer to release times/deadlines  $r_k, d_{\ell}$, they are restricted
to $I$.

\begin{lemma}
  \label{lem:belowCriticalSpeed}For all times $t \in I$, $\text{speed} (t)
  \leqslant s^{\star}$.
\end{lemma}

\begin{proof}
  Let  $t$ be  a time  that maximizes  $\text{speed} (t)$,  and assume
  $\text{speed}  (t) >  s^{\star}$ for the sake of contradiction. We
  consider an inclusion-wise  maximal interval $A \ni t$  on which the
  speed is constantly $\text{speed} (t)$. Let $i, \ldots,  k$,
  $i  \leqslant  \text{job} (t)  \leqslant   k$, be the jobs scheduled in this
  interval.  If $A =  [r_i, d_k)$, then  $A$ is a dense  interval, a
  contradiction to  Lemma  \ref{lem:densePartition}. Thus, the  inclusion  $A
  \subseteq [r_i,  d_k)$ is strict.  Assume $d_k >  u$ for $u  = \max
  A$ (the  other case  is symmetric). By  Lemma~\ref{lem:structOpt}, we
  have $\text{mode} (u)  = \text{off}$, and there is  a time $t'$ such
  that job $k$  is scheduled  in $[t',  u)$. For a  small enough
  $\delta \geqslant 1$, the execution of job $k$ can be extended to $[t',  u')$ for $u' =
  t' +  \delta (u -  t')$ and lower  its speed to $\text{speed}  (t) /
  \delta$. This   strictly decreases the  overall cost, a contradiction to the optimality
  of the schedule.
\end{proof}

The support of  the schedule consists of blocks  separated by shutdown
intervals. We shall show now that the boundaries  of  these  blocks  have a  particular
structure (see Figure~\ref{fig:prefix}).

\begin{definition}
  A suffix is  a job pair $(a,  b)$ such that all jobs  $a, \ldots, b$
  are scheduled at critical speed between  $r_a$ and $u$ with $u = r_a
  +  (w_a   +  \ldots  +  w_b)/s^{\star}$,  and  $\text{mode}  (u)  =
  \text{off}$. The definition of a prefix is just symmetric.
\end{definition}

\begin{figure}[ht]
\centerline{\input{prefix.pdf_t}}
  \caption{Illustration of a suffix  $(a,b)$ and a prefix $(b+1,c)$ in
    a schedule.  Note that job $a$  starts at its release time and job
    $c$ ends at its deadline.}
\label{fig:prefix}
\end{figure}

\begin{lemma}
  \label{lem:suffixPrefix}Let  $[t, u)$  be an  inclusion-wise maximal
  shutdown interval in $I$, that  is $\text{mode} (t')  = \text{off}$
  for all $t' \in [t, u)$. If  $t$ is not the start of $I$, then there
  is a  suffix $(a, b)$ ending  at $t = r_a  + (w_a + \ldots  + w_b) /
  s^{\star}$. If $u$ is not the end of $I$, then there is a prefix ($b
  +  1, c)$  starting at  $u  = d_c  - (w_{b  +  1}+ \ldots  + w_c)  /
  s^{\star}$.  Moreover, if both cases hold ($\inf I < t < u <\sup I$)
  then without loss of generality $r_{b + 1} > t$.
\end{lemma}

\begin{proof}
  Suppose that  there is an  execution interval $[t_0, t)$  where some
  job $b  = \text{job}  (t_0)$ is scheduled  at $\text{speed}  (t_0) <
  s^{\star}$. For a small enough $\delta>1$ let $t' := t_0 + (t - t_0)
  / \delta$. Consider  a new schedule where the  execution interval is
  \emph{compressed} to  $[t_0, t')$, the speed in  there is multiplied
  $\delta$, and the  shutdown interval is extended to  $[t', u)$. This
  new   schedule  has   a  strictly   decreased   cost,  contradicting
  optimality.

  This shows that if $t$ is not the start of $I$, then some job $b$ is
  scheduled right before $t$, say in some interval $[t_0, t)$, at critical
  speed. We will now show that there is a job $a$ such that between $r_a$ and
  $t$, jobs $a, \ldots, b$ are all scheduled at critical speed. If $t_0 = r_b$, we
  simply set $a = b$. Otherwise assume that $r_b < t_0$. If right before $t_0$ the
  schedule mode is off, then we can slightly shift the execution interval
  of $b$ to $[t_0 - \varepsilon, t - \varepsilon)$, to obtain a schedule
  of the same cost but with dominating work towards the beginning. W.l.o.g.
  we can assume that right before $t_0$ a job $b - 1$ is
  scheduled in some interval $[t_1, t_0)$. By the job span property of Lemma~\ref{lem:structOpt}
  and Lemma \ref{lem:belowCriticalSpeed} it is scheduled at speed $s^{\star}$. We
  iterate the arguments on $t_1$ and $b - 1$, eventually reaching a job $a$
  with the required property.

  The  same argument applied  symmetrically shows  the existence  of a
  prefix $(b + 1, c)$ if $u$ is not the end of $I$. Now if both suffix
  and prefix exist,  and $r_{b + 1} \leqslant t$,  then we could shift
  the execution of $b  + 1$ from $[u, w_{b + 1}  / s^{\star})$ to $[t,
  w_{b  +  1}  /  s^{\star})$,  yielding a  schedule  with  more  work
  dominating  towards the  beginning.  The  cost of  the  new schedule
  remains either the same or it is reduced by $L$, if $b+1$ were alone
  in its  block. Therefore  we can assume  w.l.o.g. that $t < r_{b + 1}$.
\end{proof}

To proceed to our dynamic programming algorithm we need one more property of
suffixes and prefixes implied by the following definition.

\begin{definition}
For a given subinstance $(i, j)$ we define two functions $f, h : \{i, \ldots,
j\} \rightarrow \{i, \ldots, j\}$ as follows: $f (a)$ is the highest index job
$b\leq j $ such that for all $a\leq k<b$, $r_a + (w_a + \ldots +
w_k) / s^{\star} \geqslant r_{k + 1}$, while $h (k)$ is the highest index job
$c\leq j$ such that for all $k<\ell \leq c\}$, $d_c - (w_{\ell} +
\ldots + w_c) / s^{\star} \leqslant d_{\ell - 1}$.
\end{definition}

\begin{lemma}
  \label{lem:fh}Any suffix $(a, b)$ satisfies $b = f (a)$ and any prefix $(k,
  c)$ satisfies $c = h (k)$.
\end{lemma}

The function $f$ requires a little more attention. Since by Lemma
\ref{lem:belowCriticalSpeed}, the job $a - 1$ cannot be scheduled with higher than
critical speed, we can assume that a suffix $(a, b)$ is such that $a$ is the
smallest index job with $f (a) = b$. So from now on we restrict the domain of
$f$ to those jobs. This allows $f$ to be invertible, i.e. $a = f^{- 1}
(b)$.  Note that by definition of $f$, the job $j$ is in the co-domain
of $f$, meaning that $f^{-1}(j)$ is defined.

\section{The dynamic program}

For every  subinstance $(i,  j)$, we denote  by $Y_{i, j}$  the minimum
$c_\text{speed}$ cost
plus  $g (r_{j  +  1}  - d_{i  -  1})$, and  by  $O_{i,j}$ the  minimum
$c_\text{speed}+c_\text{mode}$ cost.
If subinstance $(i,j)$ is infeasible we set $Y_{i,j},O_{i,j}$ to $+\infty$.
For convenience we denote $g^{\star} := (g + (s^{\star})^{\alpha}) / s^{\star}$.

\begin{figure}[ht]
\centerline{\input{fourCases.pdf_t}}
  \caption{The four cases in (\ref{eq:defO}) of the dynamic program.}
\label{fig:fourCases}
\end{figure}

\begin{theorem}
  The value $O_{i,j}$ satisfies the following recursion.
  If $j=i-1$, then $O_{i,j}=min\{L, g(r_{j+1}-d_{i-1})\}$, otherwise, let $k=f^{-1}(j)$.

\begin{equation}
\label{eq:defO}
  O_{i,j} = \min \left\{ \begin{array}{l}
       Y_{i,j}\\
         L + g^{\star} (w_i + \ldots + w_{h (i)}) + O_{h (i) + 1, j}\\
       Y_{i, k - 1} + g^{\star} (w_k + \ldots + w_j) + L\\
       \min Y_{i,a - 1} + g^{\star} (w_a + \ldots + w_b) + L + g^{\star} (w_{b +
       1} + \ldots + w_c) + O_{c + 1, j},
     \end{array} \right.
\end{equation}
  where the inner minimization is over all jobs $a\in\{i+1, \ldots j\}\cup\{b,c\}$ with $b = f(a), b < j$ and $c = h (b + 1)$.
  As usual if there are no such jobs, the value of this inner minimization is $+ \infty$.
\end{theorem}

\begin{proof}
The case $j=i-1$ is simple, since the optimal empty schedule is either
idle or shutdown depending on the span of $[r_{j+1},d_{i-1})$.

Now  for  some  $i\leq  j$,  consider the  subinstance  $(i,  j)$.  By
induction on  $j-i$, we can  show that for  each of the four  cases in
(\ref{eq:defO}) there is a feasible schedule with the corresponding cost.  For the
remainder of the proof, we consider a schedule $S$ minimizing
$c_\text{speed}+c_\text{mode}$ for this subinstance, and we show that one
of the four cases yields its cost.

If $S$ is never power down, then the contribution of $c_{\text{mode}}$ is
exactly  $g  (r_{j  + 1}  -  d_{i  -  1})$,  and the  contribution  of
$c_{\text{speed}}$ is minimal. So the first case applies.

Now suppose that there is some interval $[t, u)$ where the schedule is
power down,  $[t, u)$  is inclusion-wise  maximal and it is the first interval.
There are several cases now, depending on the conditions $t =  \min I$, $u = \max I$, where  $I$ is the interval
associated to the sub-instance $(i,j)$.

It cannot be that both conditions  are true, since this means that the
schedule is empty, which contradicts the case assumption $i\leq j$.

If  $t = \min  I$ and  $u< \max I$,  then by  Lemma \ref{lem:suffixPrefix}
there is a prefix $(i, c)$ of the form $c = h (i)$. The portion up to
$d_c$ of this  schedule has a contribution to cost equal to $L + g^{\star}  (w_i + \ldots +
w_{c})$,   and  by  the  composition  of  schedules,   its   remainder
has a contribution of  $O_{c +1,j}$.   Hence, the second case  of
(\ref{eq:defO}) applies.

If $t > \min I$ and $u = \max I$, similarly there is a suffix $(k, j)$
and the cost of the schedule up  to $r_k$ is $Y_{i,k-1}$, since there are
no power down states, while the remainder contributes a cost of  $g^{\star} (w_k +
\ldots  +  w_j)   +  L$.   This  time  it  is   the  third  case  of
(\ref{eq:defO}) which applies.

If   $t   >   \min  I$   and   $u   <   \max   I$,  again   by   Lemma
\ref{lem:suffixPrefix}, there is a suffix $(a, b)$ and a prefix $(b_{}
+ 1, c)$ around a power down interval  $[t, u)$, and by Lemma \ref{lem:fh} we
have $b = f  (a), c = h (b + 1)$. Then, the   cost of the schedule decomposes
into the cost $Y_{i,  a-1}$ for the part  before $r_a$, since it  does not contain
power down states,  the cost $g^{\star} (w_a +  \ldots + w_c) +  L$ for the
part in $[r_a, d_c)$, and the cost  $O_{c+1, j}$ for the remainder, by the composition
of schedules. In  this final case, the last  case of (\ref{eq:defO})
applies.
\end{proof}

\section{Complexity analysis}

The dynamic program uses $O(n^2)$ variables, and for each one of them a minimization over
$O(n)$ values is required. Therefore, it can be run in $O (n^3)$ time.

For a fixed subinstance $(i, j)$ the functions $f, h$ can be computed by
simple scanning procedures in linear time as following (we omit their proof of correctness).

\begin{itemize}
  \item Initially $\ell := i$ and $t := r_i$. For all $k = i, i + 1,
  \ldots, j$, if $t < r_k$, then $\ell := k$, $t := r_k .$ In any
  case $f (\ell) := k$, $t := t + w_k / s^{\star}$.

  \item Initially $\ell := j$ and $t := d_j$. For all $k = j, j - 1,
  \ldots, i$, if $t > d_k$, then $\ell := k$, $t := d_k$. In any
  case $h (k) = \ell$, $t := t - w_k / s^{\star}$.
\end{itemize}

The computation of the values $Y_{i, j}$ however is crucial, there are $O
(n^2)$ of them and the best known algorithm to compute the optimal schedule
for each of  them runs in time $O  (n^2)$ \cite{li2006discrete}, which
would lead  to a total  running time of  $O (n^4)$. We now  describe a
procedure which  permits to compute $Y_{i,j}$ iteratively  from $Y_{i -
  1, j}$ in total time $O(n^2)$. Therefore we can compute all
optimal $c_\text{speed}$ subschedules in total time $O (n^3)$.

\subsection{Computing $Y_{i, j}$}

The general outline is as follows. We first compute
$Y_{1,   n}$    in   time   $O(n^2)$   using    the   algorithm   from
\cite{li2006discrete}. Then in  a first right to left  scan we compute
all values  $Y_{1, j}$ for $j =  n-1,\ldots, 1$.  After  that for every
$j$, we  apply a left to right  scan to compute all  values $Y_{i, j}$
for $i = 2, \ldots, j$. This left to right scan works as follows.

It receives as input the $c_\text{speed}$-optimal schedule $S$ for the
subinstance  $(1,  j)$,  and  applies the  following  \emph{squeezing}
procedure  to  $S$.   The  schedule  $S$ consists  of  a  sequence  of
\emph{blocks},  every block  spans  some time  interval  $[t, u)$  and
contains  a  sequence of  jobs  running  at  some constant,  but  block
dependent speed.

During the  procedure we keep track  of the first block which spans time interval
$[t,  u)$ and schedules the jobs $i,  \ldots,  b$ at  speed $s$.   Initially
$i=1$.  We consider the action  of squeezing the block to the interval
$[u   -    \ell,   u)$   by   increasing   the    speed   $s$,   where
$\ell:=u-(w_i+\ldots+w_b)/s$.

While $i\leq j$,  we decide which of the following events happens first, and
execute the corresponding actions.
\begin{description}
\item[unfeasibility event:]
  It  happens  when   $d_{i-1}=d_i$  or
  $r_j=r_{j-1}$.  Since  in  the  subinstance $(i,j)$  all  jobs  are
  restricted to the interval $[d_{i-1},r_{j+1}]$, it follows that one of
  the jobs  $i,j$ is  restricted to an  empty interval, and  cannot be
  scheduled  with  finite  speed.  In  this  case,  we  announce  that
  subinstance $(i,j)$ is  unfeasible, we remove job $i$  from $S$, and
  increase $i$.

\item[merge event:] It happens when the current speed
  $s$ equals $\text{speed} (u)$.  In this case we merge the first two blocks.
  (Note that  if $u=d_b$,  then this event  will immediately  be followed  by
  the next split event for the merged block.)

\item[split event:] At  some moment, a job $i\leq  k<b$ from the first
  block might  complete at its  deadline. This happens when  the speed
  $s$ reaches $\hat  s(k,b,u) := (w_{k+1}+\ldots+w_b)/(u-d_k)$. In this
  case the  block splits into  two new blocks  with the first  of them
  restricted to  the interval $[t, d_k)$  and to the  jobs $i, \ldots,
  k$.

\item[deadline   event:]  When   $s=(w_i+\ldots+w_b)/(u-d_{i-1})$,  the
  current  schedule $S$ is  the optimal  $c_\text{speed}$-schedule for
  the  subinstance $(i,  j)$. In this case we output  $S$ as  $Y_{i,  j}$, we
  remove job $i$ from $S$, and increase $i$.
\end{description}

\begin{figure}[ht]
\begin{picture}(0,0)%
\includegraphics{squeeze.pdf}%
\end{picture}%
\setlength{\unitlength}{3079sp}%
\begingroup\makeatletter\ifx\SetFigFont\undefined%
\gdef\SetFigFont#1#2#3#4#5{%
  \reset@font\fontsize{#1}{#2pt}%
  \fontfamily{#3}\fontseries{#4}\fontshape{#5}%
  \selectfont}%
\fi\endgroup%
\begin{picture}(7152,5715)(1486,-7414)
\put(4181,-2646){\makebox(0,0)[lb]{\smash{{\SetFigFont{9}{10.8}{\rmdefault}{\mddefault}{\updefault}{\color[rgb]{0,0,0}$u$}%
}}}}
\put(3676,-5836){\makebox(0,0)[lb]{\smash{{\SetFigFont{9}{10.8}{\familydefault}{\mddefault}{\updefault}{\color[rgb]{0,0,0}$d_k$}%
}}}}
\put(4201,-4261){\makebox(0,0)[lb]{\smash{{\SetFigFont{9}{10.8}{\rmdefault}{\mddefault}{\updefault}{\color[rgb]{0,0,0}$u$}%
}}}}
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}}}}
\put(1501,-5461){\makebox(0,0)[lb]{\smash{{\SetFigFont{9}{10.8}{\familydefault}{\mddefault}{\updefault}{\color[rgb]{0,0,0}split event}%
}}}}
\put(1501,-3961){\makebox(0,0)[lb]{\smash{{\SetFigFont{9}{10.8}{\familydefault}{\mddefault}{\updefault}{\color[rgb]{0,0,0}merge event}%
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\put(2701,-2386){\makebox(0,0)[lb]{\smash{{\SetFigFont{9}{10.8}{\familydefault}{\mddefault}{\updefault}{\color[rgb]{0,0,0}$i$}%
}}}}
\put(2626,-2686){\makebox(0,0)[lb]{\smash{{\SetFigFont{9}{10.8}{\rmdefault}{\mddefault}{\updefault}{\color[rgb]{0,0,0}$t$}%
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\put(3451,-5236){\makebox(0,0)[lb]{\smash{{\SetFigFont{9}{10.8}{\familydefault}{\mddefault}{\updefault}{\color[rgb]{0,0,0}$k$}%
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\put(3226,-6661){\makebox(0,0)[lb]{\smash{{\SetFigFont{9}{10.8}{\familydefault}{\mddefault}{\updefault}{\color[rgb]{0,0,0}$i$}%
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}}}}
\put(2926,-3811){\makebox(0,0)[lb]{\smash{{\SetFigFont{9}{10.8}{\familydefault}{\mddefault}{\updefault}{\color[rgb]{0,0,0}$i$}%
}}}}
\put(3076,-2386){\makebox(0,0)[lb]{\smash{{\SetFigFont{9}{10.8}{\familydefault}{\mddefault}{\updefault}{\color[rgb]{0,0,0}$i+1$}%
}}}}
\put(1501,-2461){\makebox(0,0)[lb]{\smash{{\SetFigFont{9}{10.8}{\familydefault}{\mddefault}{\updefault}{\color[rgb]{0,0,0}squeeze}%
}}}}
\put(2851,-4261){\makebox(0,0)[lb]{\smash{{\SetFigFont{9}{10.8}{\rmdefault}{\mddefault}{\updefault}{\color[rgb]{0,0,0}$u-\ell$}%
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\put(4051,-2386){\makebox(0,0)[lb]{\smash{{\SetFigFont{9}{10.8}{\familydefault}{\mddefault}{\updefault}{\color[rgb]{0,0,0}$b$}%
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\put(3151,-7336){\makebox(0,0)[lb]{\smash{{\SetFigFont{9}{10.8}{\familydefault}{\mddefault}{\updefault}{\color[rgb]{0,0,0}$d_{i-1}$}%
}}}}
\end{picture}%
\caption{Different events during the squeeze procedure}
\label{fig:squeeze}
\end{figure}

At  any  moment  the  algorithm  maintains  a  schedule  $S$  for  the
subinstance consisting  of all  jobs $i,\ldots,j$ with  release times and
deadlines restricted to the  interval $[u-\ell, r_{j+1}]$. We omit the
proof of optimality of $S$ which should be straightforward.

It remains to specify how the next event can be determined in constant
time. The  merge and deadline events,  are both specified  by a single
expression determining the value $\ell$  at which they occur. For the
split  event the  situation  is  more subtle,  since  there are  $b-i$
candidates $\hat s(k,b,u)$, one for each job $i\leq k<b$.  We handle this
by precomputing  $\hat s$. Note  that for a  given job $b$,  there are
only $O(n)$ different times $u$ to be considered, and they are of the form $d_b,r_{b+1}$
and $r_{j+1}$ for all $1\leq j \leq n$.  This is because every block of an optimal
schedule ends either at the end of the interval $I$ if it
is the  last block, or at  one of $d_b,r_{b+1}$,  depending on whether
the next block has lower or higher speed.

This means that there are  $O(n^3)$ values of the form $\hat s(k,b,u)$
to compute, and  this can be done for each pair  $b,u$ in linear time,
by iterating $k$ from $b-1$ to $1$.  In the procedure above we need to
determine the job $k,~ i\leq k<b$ minimizing $\hat s(k,b,u)$.
Clearly, such a job $k$ can  be computed in constant
time for each triplet $(i,b,u)$,  again by iterating $i$ from $b-1$ to
$1$ for each pair $b,u$.

In  the event  loop described  above every  job  is responsible  for  at most three
events. Therefore its complexity is $O(n)$ for fixed $j$, which yields to a
total running time of  $O(n^3)$.

\section{Conclusion}

We provided  a polynomial  time algorithm for  the speed  scaling with
power down scheduling  problem,  for the  special  case of  agreeable
deadlines.  This assumption leads to strong structural properties of optimal schedules,
which are non-preempted  and, moreover, permit a partitioning
leading  to a dynamic programming algorithm.  So the  proposed algorithm  could not
be generalized to instances with arbitrary deadlines. However, we believe that the squeezing
procedure could be of independent interest.

\bibliographystyle{elsarticle-num}

redpajama_set_name: RedPajamaArXiv


text:
Home Punditry	Cardinal McCarrick responds
Cardinal McCarrick responds
by Jeffrey Miller July 31, 2006
written by Jeffrey Miller July 31, 2006
Cardinal McCarrick responds to the Denver Catholic Register column by George Weigel. [Via Kevin Knight]
The cardinal says that Weigel is correct in his assertion that he often calls for "moderation and civility." However, McCarrick continues, "that doesn't mean compromising our faith and our teachings."
McCarrick, who said that through his column that Weigel is guilty of, "deceptive journalism, if not worse," wrote in his letter to the readers of Commonweal that people should, "avoid name calling and personal attacks and be careful that what we say is always true both in its expression and its implication." "Sometimes…it truly is important to set the record straight in the face of half-truths," McCarrick said.
I would be curious to exactly where George Weigel resorted to name calling or personal attacks. Re-reading the article I could find no signs of such behavior and wouldn't saying someone was guilty of "deceptive journalism" be a personal attack itself? The original article made no positive assertions against the Cardinal, but only wondered what he meant by moderation and whether it just meant being in the middle of issues. George Weigel also wondered what he meant by moderation when there were many issues he was not moderate on and was willing to lobby congress on.
The funniest part of the whole thing is that the Cardinal decided to make his reply via Commonweal a magazine not exactly noted for heterodoxy.
Similar things are done every day in the asylum
Mystification
Mr. Smith goes away f rom Washington
Marking Money
Disturbing the people
U.N. Termites
Teaching religious intolerance using religious intolerance
Vatican Wars
Psychic Liveblogging
Arian Adrian Dominican Sisters
He who hears you …
When reporters do theology
Fr. Philip, OP July 31, 2006 - 8:37 pm
Do you mean to say, "…Commonweal a magazine not exactly noted for orthodoxy"? Or perhaps, "…Commonweal a magazine noted for heterdoxy"?
Fr. Philip
BillyHW July 31, 2006 - 9:18 pm
Did he end the letter with an "Allah bless you"?
Janice August 1, 2006 - 7:31 am
I don't know who to cheer for here. I despise McCarrick and have for years (I live in D.C.) precisely for his "moderation" in the face of doctrinal orthodoxy (remember 2004?). On the other hand, Weigel (and his fellow traveller, Richard John Neuhaus) has his own agenda. While there are many things for which he could have criticized McCarrick, this column was fairly weak intellectually. The incident dates back to John Paul's reign. McCarrick has done many significantly heterodox things since then. Why didn't Weigel mention those? For instance, the lies McCarrick told about Cardinal Ratzinger's Worthiness to Receive Communion Letter of 2004? McCarrick didn't take a "middle ground" there. Or McCarrick support for "same sex" civil unions right before his tenure ran out? That wasn't a middle ground position either. In both of these incidents McCarrick wasn't worried about losing those on the right or the left. He was unambiguously supporting those on the left. That's where he's always been. Weigel himself seems very disingenous here by selecting a fairly innocuous incident and then building on it. Methinks there's more to this than meets the eye, but Weigel would have to write another column to explain it.
Thomas A. Gill August 1, 2006 - 10:41 am
In your second sentence, did you mean to type in disagree with and typed in despise by mistake?
Janice August 1, 2006 - 11:49 am
No, I typed in despise because I meant despise. McCarrick is the avatar for the type of bishop I despise. He is spineless when it comes to orthodoxy, never met a secular thought he couldn't endorse, never met a Church stand he couldn't sell out.
dan m. August 1, 2006 - 3:09 pm
"Weigel (and his fellow traveler Richard John Neuhaus) has his own agenda"
What's the agenda other than Catholicism?
Janice August 1, 2006 - 4:10 pm
Weigel and Neuhaus use "orthodox" Catholicism as a cover for very odd ideas about the relationship of church and state in the United States and for the way they evaluate what IS "orthodoxy." Both of them, it seems to me, have substituted John Paul II for Jesus Christ. Their notion of Catholicism is not predicated on the Gospel or on a personal relationship with Jesus Christ, but on a personal relationship with John Paul II. For both of them, it appears that Christianity began in 1978, rather than on Calvary.
dad29 August 1, 2006 - 5:27 pm
It's significant that the Weigel column was published by a Diocesan newspaper.
And you can now bet that McC. was the source of a lot of "anonymous" quotes in Commonweal before this.
Just as R. Weakland was the source of a lot of Steinfels' NYTimes comments…
michael hugo August 1, 2006 - 5:34 pm
Wiegel is a smart man. If he misunderstood the Archbishop's position on these issues, why did Abp. McCarrick not clarify them for Mr. Wiegel, and the millions of other Catholics left scratching their heads?
With all due respect, I do not think W and N are looking to 1978 as the beginning of the Church. I think they are speaking as men that know it didn't start in 1965.
Paul Smith Jr August 1, 2006 - 6:49 pm
"I would remind you that extremism in the defense of liberty is no vice! And let me remind you also that moderation in the pursuit of justice is no virtue!" – Barry Goldwater
We might say the same about God's will.
Fr. Chris Ciccarino August 2, 2006 - 7:06 am
Kind of interesting that the Weigel column ran in "The Catholic Advocate", the paper of the Archdiocese of Newark, the week that the Cardinal came to Seton Hall University for his first post-retirement visit.
Kevin Miller August 2, 2006 - 9:21 am
Jeff: Weigel accused McC of, e.g., "severe intellectual confusion." That isn't a positive assertion against the cardinal? That isn't an attack?
Also: The fact is that McC has been very forthright in teaching what the Church teaches about the evil of abortion, the unacceptability of same-sex "marriage," etc. And as he clarified more than once, he was not calling for "civil unions" as these are generally understood, i.e., as something that amounts to marriage in all but name, or that gives legal status to a sexual relationship as such.
McC hasn't been all good. He was, it seems pretty clear, wrong to misrepresent what Ratzinger had told him about communion for pro-abort pols.
But much of the criticism one hears of him is simply false.
McCarrick had to retract what he said about civil unions two days after he said it. At best, he's an incompetent, although I think he's been trying for years to sneak anti-Church teachings in under the radar. This last time, there was such a barrage of criticism he had to issue a "clarification." He's not "forthright," believe me.
lourdes August 2, 2006 - 2:54 pm
The "incident" referred to does not date back to JPII. The "incident" was a recent interview with Cardinal McCarrick in which he stated that his current method of "standing in the middle" was inspired by JPII's visit to Newark some years ago. So, while the visit may have been in the past, Cardinal McCarrick's response to it is very much in the present. Mr. Weigel and Fr. Neuhaus are referring to this very recent statement by Cardinal McCarrick.
Dim Bulb August 2, 2006 - 9:02 pm
Does Janice mean to suggest that her understanding of Church State relations, the Gospel, And Catholicism surpasses that of the two men she names; both of whom are rspected intellectuals, one of whom (Fr. RJN) is a respected theologian?
Yes, Janice does. Furthermore, Janice thinks Neuhaus distorts American history to get to his "understanding" of Church-State relations, the Gospel, and theology, with his disciple, Weigel, following close behind. By the way, Dim Bulb, since you don't know anything about me, how do you know I'm not just as intellectually prepared as both of these men?
EJ August 3, 2006 - 2:35 pm
All I can say is please pray for CHAPUT or BURKE for BALTIMORE – Lord knows many of us prayed for them for Washington to succeed Cardinal McCarrick. Many people here in DC have had enough American cardinals walking "in the middle" … which to me is a cop-out for an outright preference of the left. I've never seen Cardinal McCarrick on EWTN other than by non-preferential circumstance, or write for CRISIS, CWR, First Things or This Rock magazines – but have unfortunatley followed his courting of the Jesuits at Georgetown, his contributions to the Jesuit America magazine, and now his unfortunate choice of offering his viewpoint through Commonweal magazine, and the countless occasions he has given Holy Communion to pro-choice, Catholic politicians such as the current mayor of Washington, D.C., etc. etc. If His Eminence has ever walked "in the middle," he sure has taken some notable public breathers on the moderate and not so moderate left. His presence on the "right" side of the nave has been notably missing. I do not despise him, I pray for him and out of filial respect for his person and his office, I would readily bow and kiss his ring, but I cannot say that he has been "in the middle." I attend the monthly solemn Mass in the Tridentine rite celebrated in downtown Washington, and these faithful Catholics will sadly admit that their presence in the Archdiocese has been explicitly and implicitly ignored by their former cardinal- archbishop during his entire five year tenure in Washington. Not one word of support or concern, only a reluctant agreement to continue allowing Cardinal Hickey's indult. And how we miss the holiness and spiritual greatness of Cardinal Hickey, who with all his humility and meekness, made it clear he did not walk "in the middle," especially to Georgetown University and to local and national politicians. A dear friend and admirer of Mother Angelica, he courageously reminded his flock, in writing and in homilies during the 2000 presidential election, that in that election in particular – there was a clear Catholic, pro-life choice – and that choice won. We need another courageous voice who will stand on the shoulders of a holy giant like James Cardinal Hickey, may he RIP. And to conclude, I wonder how the late John Paul II would have provided the ideological, spiritual and political impetus to topple communism if he had "walked in the middle." Kudos to Mr. Weigel.
Perhaps McCarrick, in his desire for moderation and civility, should recall the words of Joseph Ratzinger:
"It is true that the Church may never simply align itself with the "Zeitgeist" [spirit of the times]. The Church must address the vices and perils of the time; she must appeal to the consciences of the powerful and of the intellectuals, not to mention of those who want to live narrow-minded, comfortable lives while ignoring the needs of the time, and so forth. As a bishop [of Munich] I felt obliged to face this task. Moreover, the deficits were too obvious: exhaustion of the faith, decline in vocations, lowering of moral standards even among men of the Church, an increasing tendency towards violence, and much else. The words of the Bible and of the Church Fathers rang in my ears, those sharp condemnations of shepherds who are like mute dogs; in order to avoid conflicts, they let the poison spread. Peace is not the first civic duty, and a bishop whose only concern is not to have any problems and to gloss over as many conflicts as possible is an image I find repulsive."
dan.m August 4, 2006 - 12:54 pm
With all respect, please help me out here. I just finnished readinf "Catholic Matters" by Fr.Neuhaus and it seems to me to be an orthodox account of his journey to Catholicism and the state of the Church today. I haven't read anything by him on the philosophy/history of Church/state relations but neither have I read anything indicating a distortion of facts. As far as George Weigel's writings, other that "Letters to a young Catholic" and "Witness to Hope" I havn't read much. He also seems to be pretty straightforward.
What distortions are you referring to that I can look up?
Tito August 7, 2006 - 10:43 am
Cardinal McCarrick is 'retired'.
Let us thank God for that.

redpajama_set_name: RedPajamaCommonCrawl


Individual was captured as early instar larva then reared in captivity.
Milne, Lorus and Margery Milne, 1980. National Audubon Society Field Guide to North American Insects and Spiders. Alfred A. Knopf, Inc., New York, NY, US.


text:
Q: CMake: how to get subversion revision but not to fail if we made an export? I retrieve the subversion revision this way :
include(FindSubversion)
IF(Subversion_FOUND)
    Subversion_WC_INFO(${CMAKE_SOURCE_DIR} MY)
    SET(SVN_REVISION "${MY_WC_REVISION}")
ELSE(Subversion_FOUND)
    SET(SVN_REVISION "-1")
ENDIF(Subversion_FOUND)

The problem is that when someone does "svn export" he can't compile :
-- Found Subversion: /usr/bin/svn (found version "1.6.11")
CMake Error at /opt/cmake-2.8.9-Linux-i386/share/cmake-2.8/Modules/FindSubversion.cmake:84 (MESSAGE):
  Command "/usr/bin/svn info /tmp/amore" failed with output:

  svn: '/tmp/amore' is not a working copy

Call Stack (most recent call first):
  CMakeLists.txt:32 (Subversion_WC_INFO)

How to solve this problem in an elegant way ?

A: I decided to simply test for the existence of the directory .svn in the sources :
# SVN revision
include(FindSubversion)
IF(Subversion_FOUND)
    if(EXISTS "${CMAKE_SOURCE_DIR}/.svn")
        Subversion_WC_INFO(${CMAKE_SOURCE_DIR} MY)
        SET(SVN_REVISION "${MY_WC_REVISION}")
    else ()
        SET(SVN_REVISION "-1")
    endif()
ELSE(Subversion_FOUND)
    SET(SVN_REVISION "-1")
ENDIF(Subversion_FOUND)

redpajama_set_name: RedPajamaStackExchange


Nice to see the dust blown of your fantastic blog. Happy new year Nilla😘. I hope your arse gets beaten soon.
Thanks darling! It's nice to be back!
Oh, so good to hear from you! I have more thoughts, and will write them later, but just wanted to say hi for now!
Hi blossom! Hugs gratefully accepted…and returned. Happy 2019!
Nice to see you're back…even if the content is sad (and if I am being 100% honest, kind of triggered my own dark day feelings). I mostly lurk, but enjoy your snark and humor. Sending positive thoughts your way!
Hi Jane, thanks for your comment, and I hope your dark day feelings have lightened up a bit. I come here to purge those feelings myself, so I get it. Sorry for adding to your sad. I hope ensuing posts will make your day brighter.
You aren't the only one who's been gone so long that you had to dig out the password and remove the dust covers. It was a rough year on many levels for many of us.


Post Graduate degree in Pharmacology or Life Sciences from a recognized university or Institution.
Interested candidates may attend the interview along with their bio-data, original certificates/ testimonials at Research Block-B, Room No 4043, Department of Pharmacology, PGIMER, Chandigarh.
Get more details PGIMER, vacancy details, qualification, experience, how to apply & other information click on the link given below….
Interested candidates may attend the interview along with bio data, documents/ certificates support of photocopies to the venue on 06/02/2017 at 02:30 PM.
Head, Department of Pediatrics, Advanced Pediatrics Centre, PGIMER, Chandigarh.
Date & Time of Candidates Interview: 06/02/2017 at 02:30 PM.
PGIMER Recruitment 2016 – Research Coordinator & Data Analyst Posts: Department of Community Medicine, School of Public Health, Postgraduate Institute of Medical Education and Research (PGIMER), Chandigarh has inform 02 vacant seats for Research Coordinator & Data Analyst posts for the project titled "Respectful Maternal Care in Punjab: A qualitative study for Advocacy" on contract basis. If you have a dream of join PGIMER. You can apply in prescribed format on or before 03/12/2016 at 12:30. Other details are mentioned below..
Post Graduation in Social Sciences (Social Work, Sociology, Anthropology, Psychology/ MPH) for S.No-01, Post Graduation in Social Sciences (Social Work, Sociology, Anthropology, Psychology/ MPH) and MBA (Finance) with relevant experience for S.No-02.
Interested candidates may send their application along with curriculum vitae with supporting documents to the Room No. 109, Office of School of Public Health, PGIMER, Chandigarh on or before 03/12/2016 at 12:30 PM.
Last Date for Submit of Application Form: 03/12/2016 at 12:30 PM.
Date & Time of Candidates Interview: 05/12/2016 (Monday) at 11:00 AM.
Address: Kairon Block, Sector 12, Chandigarh, 160012.
PGIMER Recruitment 2016 – Junior Research Fellow Posts: Department of Hematology, Post Graduate Institute of Medical Education & Research (PGIMER), Chandigarh has inform 01 vacant seat for Junior Research Fellow for the project entitled "Wilms' Tumor Gene 1 (WT1) in B-lineage Acute Lymphoblastic Leukemia: A study of its expression and utility as a prognostic and minimal residual disease marker" on adhoc basis. If you have a dream of join PGIMER. You can apply in prescribed format on or before 15/11/2016. Other details are mentioned below..
Post Graduation Degree in Basic Science/ PG/ Graduation Degree in Professional Course with NET qualification.
Interested candidates may send their application on plain paper, giving full details of their bio-data along with affixed passport sized photograph and attested copies of testimonials in support of their qualifications and experience to Hematology department office (H-1) to the venue on or before 15/11/2016.
Office of Dr. Neelam Varma, Professor & Head, Department of Hematology, Room No. 534/ H-2, 5th Floor, Research A-Block, PGIMER, Chandigarh.
Date & Time of Candidates Interview: 16/11/2016 at 11.45 am.
PGIMER Recruitment 2016 – Senior Research Fellow Posts: Department of Medical Microbiology, Indian Council of Medical Research (ICMR), Post Graduate Institute of Medical Education & Research (PGIMER), Chandigarh has inform vacant seats for Senior Research Fellow for the project entitled "Nodal Coordinating Centre for Surveillance of Antimicrobial Resistance (AMR) in members of family Enterbacteriaceae" on contractual basis. If you have a dream of join NIPHM. You can apply in prescribed format on or before 12/11/2016 by 01:00 pm. Other details are mentioned below..
M.Sc in Microbiology, Botany, Zooogy, Biotechnology, Molecular Biology or any other Biological Science allied field.
Interested candidates may send their application and bio data with relevant documents to the Dr Pallab Ray, Professor, Department of Medical Microbiology, Post Graduate Institute of Medical Education & Research, Chandigarh to the venue on or before 12/11/2016 by 01:00 pm.
Department of Medical Microbiology, Room No 228, Research Block A, FF, PGIMER, Chandigarh.
Last Date for Submit of Application Form: 12/11/2016 by 01:00 pm.


text:
Indian Armed Forces Pictorial Fortnightly...Sainik Samachar publishing since 1909.
Gorkhali
Photo Gallery Subscription PIB Releases Contact Us
"Sainik Samachar" published fortnightly in thirteen languages.
01-15 Dec
16-30 Nov
1-15 Oct
Ruby Thinda Sharma
A Bharat Bhushan Babu
ADG (M&C)
S Subramanian
Director, (PR)
South Block
New Delhi-110 011
President's Colour Awarded to Indian Naval Academy
Shri Ram Nath Kovind, the President of India and the Supreme Commander of Indian Armed Forces, awarded the President's Colour to Indian Naval Academy (INA) on November 20, 2019. The President's Colour - the highest honour that is bestowed upon a military unit - was received by Academy Cadet Captain Sushil Singh on behalf of the INA in an impressive parade .....
The last one hundred years have perhaps been the most momentous in the entire history of mankind, just as much as it has been for India. Two World Wars, the Freedom Movement, the emergence of India as a great nation, three wars, a near war and last but not the least, the growth of a thoroughly professional, apolitical Indian Armed Force, committed not only to protecting its territorial integrity under any circumstances but also coming to the aid of civil authorities in times of crisis and natural disasters, a magnificent force that each and every citizen of this country is justifiably proud of.
All such events and developments have been witnessed from close quarters and chronicled by Fauji Akhbar, rechristened as Sainik Samachar in 1954. The journey which started as an Urdu Weekly on January 2, 1909 continues, despite occasional setbacks in the past. In its chequered history, Fauji Akhbar moved from Shimla to Lahore and then to Delhi. Its editorial policy has also undergone many changes over the years. The publication had to be temporarily halted immediately after Independence due to a large scale migration of the staff and printer to Pakistan. It bounced back with renewed vigour and enthusiasm in no time. It is this magazine that the troops and officers look forward to for the last information that has a bearing on them. Sainik Samachar, a fortnightly now, is published in thirteen languages including English.
In this anthology, Soldiering On..., we have brought out a panoramic view of the major events in the life of the nation and to some extent, of the world, as reported by Fauji Akhbar / Sainik Samachar since its inception. We have embellished the reportage with rare pictures dug out from our archives, some of them for the first time. We have also included a comprehensive articles on the history and evolution of the Directorate of Public Relations of the Ministry of Defence, a unique inter-service organisation which has set benchmarks for PR activities over the years. We have included articles, features and short stories by writers, some of whom achieved eminence only in later years. In short, this volume not only provides a rare glimpse into the history of India in the last one hundred years but is also a collector's item.
Language Editions
The journal of India's Armed Forces published every fortnight in thirteen languages including Assamese, Bengali, English, Gorkhali, Hindi, Kannada, Malayalam, Marathi, Oriya, Punjabi, Tamil, Telugu & Urdu on behalf of the Ministry of Defence.
Inland (Ordinary) :
One year Rs.100.00
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*(Applicable for dependants of service personnel & ex-Servicemen.)
Please send your subscriptions to the Business Manager.
Money Order, IPO or Bank Draft should be drawn in favour of Editor-in-Chief, Sainik Samachar payable at Delhi.
All Subscribers must write their Subscription Number in all their correspondence.
Home l About us l English Edition l Hindi Edition l Photo Gallery l Subscription l PIB Releases l Contact us
Disclaimer: "The journal of Indian Armed Forces is published every fortnightly in thirteen languages including Hindi and English on behalf of the Ministry of Defence. It is not necessarily an organ for the expression of the Government's defence policy. The published items represent the views of respective writers and correspondents."


text:
This week in Motorsport history: April 13-19
in Features, News
With most of the world's motorsport on pause, we delve into a glance at some of the sport's archives to find the best bits that have occurred from yesteryear in this week of racing.
April 13 (1956) Rally icon Possum Bourne was born in Pukekohe, Auckland. Bourne won the NZ Rally Championship in 1991 and claimed the Australian Rally Championship an incredible seven consecutive years between 1996 and 2002. Bourne passed away on April 30, 2003 after a sustaining head injuries in a crash two weeks earlier while driving along the Race to the Sky track on Mount Cardrona.
April 14 (2018) The Ferrari Challenge Asia-Pacific series made its first (and only) pilgrimage to Hampton Downs. A weekend marred by torrential rain on Saturday and accidents aplenty on the Sunday, the event failed to stir interest amongst fans with only two hours of 'on-track' racing all weekend and has yet to return to New Zealand since.
April 16 (1942) Sir Frank Williams, founder and team principal of the Williams Formula One team, is born in South Shields, England. Williams has been home to many of the sport's greatest drivers, including Ayrton Senna, Alain Prost and Nigel Mansell. The team has won the second most constructors titles with nine.
April 17 (2018) Ford announce the return on the Mustang to the Supercars Championship for the 2019 season. It marked the first return of the Mustang to Australian Touring Car racing since 1986 with Dick Johnson's 'Greens-Tuf' challenger.
April 19 (1970) Bruce McLaren finished second at the Spanish Grand Prix from the Jarama Circuit in what would be his final Formula 1 podium. Before the race began, Grand Prix organisers restricted the number of starters to only 16 and annulled all lap times set on Friday, thus six cars who were already on the grid who forced to pack-up as they were classified as DNQ's (Did not Qualify). Jackie Stewart's March-Ford won the race lapping the entire field with McLaren and Mario Andretti rounding off the podium placings.
Bruce McLaren and Denny Hulme having a chat before the start of the 1970 Spanish Grand Prix
April 19 (2015) Scott Dixon wins his first and to date only IndyCar victory on the Streets of Long Beach. Capitalising on a slow pitstop from CHF Racing's Helio Castroneves, Dixon was able to leap into the lead with 44 laps remaining. The victory would be Dixon's first of four for the 2015 season but were crucial points as he would end the year tied for the points lead with Juan Pablo Montoya and only be awarded the championship on a countback.


Get detailed solutions to your math problems with our Basic Differentiation Rules step by step calculator. Sharpen your math skills and learn step by step with our math solver. Check out more online calculators here.


NHS staff took a record 3.9 million days off with stress and related conditions last year.
Almost 11,000 doctors, nurses and support staff were off work daily with stress, anxiety and depression, the latest NHS Digital figures reveal.
The biggest proportion of sick days triggered by stress was among lower ranked managers for whom it was one in three.
Across the NHS stress now accounts for 24% of all days lost to sickness. Five years ago it was 19%.
Sara Gorton, of Unison, said: "The huge shortage of staff is the biggest problem and Brexit uncertainty isn't helping.
"As pressure builds, stress soars, and a climate of bullying takes its toll.


text:
A  a Dragon Ball GT televíziós különkiadása, amit Japánban 1997. március 26-án mutattak be.

Az Egyesült Államokban 2004. november 16-án jelent meg DVD-n. Magyarországi premierje 2012. május 8-án volt az Animaxen.

Források

További információk

Dragon Ball
Japán animációs filmek
1997 filmjei
Japán kalandfilmek
Japán fantasyfilmek
Toei Animation-filmek
Mangából adaptált filmek

redpajama_set_name: RedPajamaWikipedia


There are a few things that really set Mighty Auto Parts apart from our competition. One is our inventory control methods and another is our programs designed to help our customers grow and succeed in business.
We strive to keep your inventory simple: Whatever you need will be there, when you need it. Our local Mighty representatives regularly visit each of their customers in order to maintain a proper inventory balance, so that when your customer asks for a particular service, you have the product available to perform that service on the same day. Mighty representatives will go over your shop's inventory to make sure that you are not only properly stocked, but also not overstocked. Our ultimate goal is for our partners to succeed in business.
In this video you will hear from one of our Mighty franchise owners, a car dealership, and a general repair service manager- All part of the Mighty Auto Parts extended family.


Measures to foster development of the agro-industrial sector and Russia as a whole. These measures were recommended to the federal authorities for further elaboration (the relevant methodological support and/or pilot testing may be carried out by "Governance in AIS and Rural Development" Department of VNIETUSH in cooperation with the corresponding authorities).
To strengthen local self-government in Russia. To deal with this objective it is recommended to devise and to implement a project to test the recommended self-government model in a specific locality.
To produce the Food Map of Russia. This will enable to assess the food production potential of the country and its regions and to rationalize the use of natural resources.
To create favorable conditions for agricultural marketing (gradual reduction of food imports, government procurement of over 50% of grain output of commercial farm operations, demonopolization of food markets, including Moscow market via their transfer to regions and districts).
To set up model large-scale farms (agricultural technological centers) to test and to disseminate the world best agricultural production practices.
To set up state-owned federal holdings specialized in seed growing and livestock breeding.
To create federal and regional clubs of the best agricultural workers.
To design large-scale farm models (including such characteristics as specialization, size, business management system, staffing, farm machinery, technologies, etc).
To determine managerial staffing standards and composition for large-scale farms.
To encourage socially-oriented integration model in the agro-industrial sector (when an enterprise-integrator enters into cooperation agreements with private farms, household farms and small-scale farms).
To encourage agricultural producer cooperation via creation of associations and unions.
To involve experienced professionals in management of lagging large-scale farms via transfer of farm shares.
According to the generally accepted interpretation of the manageability theory the average statistical manager of an enterprise or department is incapable to manage efficiently more than 8–12 people. If this standard is exceeded, the enterprise (and the whole industry) performance tends to decline. This statement reflects the core of the manageability theory. In our opinion, this is only one of the manageability theory elements.
We have proposed a different approach relating to this theory. A manager's potential capabilities are the main internal reserve of business development. The more people, who are capable to manage an enterprise, are vested with the right to conduct business independently, the more economic reserves are utilized.
The reduction of the economy efficiency, observed as the average enterprise size in the industry increases, is caused by two reasons: increased number of people, who are capable to lead the enterprise, but who work under someone else directions (since the number of enterprises tend to decrease as their size increases), reduced manageability of enterprises (there are not many people, who are capable to manage large-scale enterprises).
As the number of independently performing people having managerial skills grows, the amount of responsibilities and commitment tends to increase, and, consequently, the managerial potential strengthens. This leads to improved efficiency of an enterprise and of the industry as a whole.
In addition, we have arrived at a conclusion that enterprise manageability and performance efficiency depends on the number of management tiers. Two-tier enterprises are the most manageable and efficient.
An assumption is formulated that the competition in the national economy is the result of accumulation of the certain (critical) mass of realizable managerial potential.
Key factors, which constrain the agricultural development in Russia, have been identified (lack of favorable environment for farming, lack of self-government system in the country). The underlying principles for governance system formation have been formulated. In particular, it was established that the agricultural sector can develop only if the business environment (rules of play) created by the government are tailored to enterprises, headed by managers with average capabilities.
It has been revealed that the existing methodology for governance system establishment in the agro-industrial sector that predominantly relies on industry-specific approach is inefficient in the market environment. The new methodology has been recommended; it has been named the problem-focused functional approach to the management system design. The core of this approach is that the government authorities should focus on key problems of the sector, territory, enterprise. Individual researchers and practitioners from various regions (Oryol, Nizny Novgorod and other oblasts) have been already applying the methodology in their activities.
Using the above described methodology for management system establishment to be based on AIS state governance functions optimization the market-oriented model of the Russian AIS state governance structure has been recommended. The structure includes the federal, regional and local levels. The model is composed of 8 cross-cutting problem-focused functional blocks.
Institutional and economic measures aimed to establish efficient self-government system in Russia have been formulated. In particular, the model envisages building of inter-level (inter-budget) relationships based on territorial self-supporting principles (economic governance methods). The recommendations on local self-government improvement in Russia (including the mentioned model) were recognized as the best economic research results in Russia in 2004.
A conclusion has been made that Russia development is impossible without the decentralization of inter-budget relationships. To address this challenge it has been recommended to establish inter-budget relationships based on territorial self-supporting principle. For instance, it has been proved rational to distribute total tax revenues of a rural settlement in the following proportion among the settlement, the district, the region and the federal level: 60%, 20%, 10% and 10% correspondingly. The rural settlements contribute only 1.6% of the consolidated budget of the Russian Federation; therefore, the implementation of this approach will not substantially affect the budget expenses. The implementation of this approach will require to increase rural settlements expenses to 1% of the budget expenses. Taking into consideration that the recommended measure will enable to improve the social and economic conditions in the rural areas dramatically (covering 27% of population and 2/3 territory of Russia) these expenses are justifiable.
The expediency to replace three taxes (VAT, profit tax and gross income tax, including uniform agricultural tax) by the sale tax has been justified. This measure will add such merits to the national economy as liberalism, transparency, and will create favorable environment for business development. It is recommended to impose taxes only on three items in agriculture: outputs, land and labor. In this case farm enterprises will pay 3 taxes: the sale tax, the land tax and income tax.
The primary characteristics — blocks, which form the personality of each worker, have been identified (all other characteristics are synonyms or a result of synthesis of these primary characteristics). The characteristics are called basic, and they are used to elaborate models of manager, subject-matter specialist and other employees. A method to appraise staff conformity to these models has been elaborated. The methodology has been successfully tested in Moscow, Tula, Svedlovsk and in other oblasts. In 1989 the methodology was recognized by the RSFSR Ministry of Agriculture as the best one (out of all Russian and foreign methodologies translated into the Russian language) and was recommended for application in all Russian regions.
The methodology was based on the above mentioned worker's basic characteristics similar to the methodology for staff assessment and selection. The recommended approach enables to identify a business area, where a person will be able to demonstrate maximum of his capabilities. The methodology has been tested in a number of schools in Ryazan Oblast, as well as in selected military colleges (since it reveals the leadership capabilities) and has been highly appreciated by trainers and other participants.
The accepted approach to identification of the optimal size of the enterprise usually is limited to the size of cultivated area. The unsoundness of that approach has been demonstrated. It has been established that the number of farm personnel and management tiers should be the optimization factors. It has been determined that taking into account the manageability norms the optimal are large-scale farms with 2 management tiers and personnel number of 90–100 people. The expediency to increase the number of such enterprises is explained by the fact that in that case the sector structure would better match the social and psychological structure of workers.
The methodology comprises a package of measures to overcome crisis and to improve farm business performance using cost-efficient methods. The focus is to enhance farm business management system. The methodology has been tested on large-scale farms in Moscow, Samara, Oryol and other oblasts and proved to be highly efficient.
The expediency of relying on economic methods in farm business management has been justified. The methods envisage distribution of sale revenues between management tiers and farm units. This approach simplifies the relationship system; it does not require correction of business plans of the farm or its divisions during a year (due to the permanent input price growth) and offers other benefits.


text:
Q: Transform Form1 into Form2 I have a Form1 with a panel on the left side of the Window and I want to make Form2 appear when I click the button "Test" on the right side (where it is the Label "Test"). Is there any possibility or I have to write the code for each new thing I want to put on the right side?
Here is an image:
Image

A: Instead of using a second form, use a User Control.
If you are really determined to make a second form appear in your first form, try making the second form a child of the first form using this code inside of the first form's code:
  this.IsMdiContainer = true;
    Form2 form = new Form2();
    form.Parent = this;
    form.Show();


text:
Station Faulquemont is een spoorwegstation in de Franse gemeente Faulquemont.

Treindienst

Faulquemont
Faulquemont


text:
Typewritten extracts from 'The Ancient Coptic Churches of Egypt, Vol. 1', by Alfred J. Butler, late 1920s - early 1930s Digital
Typewritten extracts from 'The Ancient Coptic Churches of Egypt, Vol. 1', by Alfred J. Butler, late 1920s - early 1930s
late 1920s - early 1930s
Coptic, English, French, German, Greek, Russian, Turkish
Contains:"The Church of Burbarah, or St. Barbara"; "The Churches of Mari Girgis and Al'Adra", and "Coptic Art (Introduction)." Also includes a paper submitted to Professor Thomas Whittemore, "Coptic Art: Buildings in Ancient Egyptian Temples", by Bernard S, Myers, January 10, 1929.
Typewritten extracts from 'The Ancient Coptic Churches of Egypt, Vol. 1', by Alfred J. Butler, late 1920s - early 1930s. The Byzantine Institute and Dumbarton Oaks fieldwork records and papers, MS.BZ.004, Subgroup 2, Series 1, Box 1, Folder 8. Dumbarton Oaks Image Collections and Fieldwork Archives. https://id.lib.harvard.edu/ead/c/dca00003c00351/catalog Accessed January 22, 2020


The central Government has decided to extend the Pradhan Mantri Ujjwala Yojana (PMUY) to all poor households in the country.
Pradhan Mantri Ujjwala Yojana (PMUY) is the government's flagship programme to provide free cooking gas (LPG) connections. The PMUY scheme targets to reach out to provide free LPG connections to 80 million families by 2020.
With the expansion of the PMUY scheme, all the poor households can avail the benefit from PMUY and it will not be mandatory to be part of the Socio-Economic Caste Census (SECC) list or the seven identified categories under the programme to be eligible for the scheme.
Pradhan Mantri Ujjwala Yojana (PMUY) was launched in May 2016. The initial target set for the scheme was to provide 50 million LPG connections to below poverty line (BPL) families by 2019, by giving financial assistance of Rs 1600 per family. Till now, Under PMUY schemes 58.5 million connections have been given across 715 districts. As per the government data, About 80 per cent of the beneficiaries come back for a second refill and about 45 per cent take three or more refills annually. The government has also recently launched LPG Panchayats to promote the PMUY scheme.
The vision behind the scheme: The successful implementation of the scheme will ensure universal coverage of cooking gas in India, which will help in women empowerment and also will protect their health. The time spent on cooking and drudgery will reduce. Additionally, it will also generate employment for youth in the rural areas in the supply chain of LPG.


CITES will use big cats – broadly defined to include tigers, jaguars, leopards, cheetahs and lions - as the theme for World Wildlife Day (WWD) 2018.
The Snow Leopard Summit, which convened in August, concluded with a Ministerial Declaration.
The UN General Assembly passed a resolution (A/71/L.88) addressing wildlife crime.
IUCN downgraded the snow leopard's status on its Red List from "endangered" to "vulnerable".
October 2017: The Secretariat of the Convention on International Trade in Endangered Species of Flora and Fauna (CITES) has elected to use big cats – broadly defined to include tigers, jaguars, leopards, cheetahs and lions – as the theme for World Wildlife Day (WWD) 2018. WWD, held annually on 3 March, the day CITES was adopted, raises awareness and generates action on wildlife conservation. The announcement of the WWD theme came shortly after the conclusion of a 'Snow Leopard Summit' hosted by the Government of Kyrgyzstan and in concert with several other announcements of new snow leopard and wildlife conservation projects and initiatives.
The Snow Leopard Summit, which convened in August, concluded with a Ministerial Declaration, titled 'Caring for snow Leopards and Mountains – Our Ecological Future,' in which the 12 range States of Afghanistan, Bhutan, China, India, the Kyrgyz Republic, Kazakhstan, Mongolia, Nepal, Pakistan, the Russian Federation, Tajikistan and Uzbekistan agreed to intensify their conservation efforts, including through measures to address wildlife crime and reduce human-wildlife conflict.
In addition, the Snow Leopard Summit had a focus on ecosystem conservation. It held a symposium on science, conservation, and climate change in Central Asia that discussed the broad issues relevant to preserving the climate-sensitive mountainous areas snow leopards inhabit. Further, a main and overarching goal of the range States and one of the first steps of the Bishkek Declaration, is to secure 20 snow leopard landscapes by the year 2020. Issues such as transport, climate, mountains and land degradation all come into play with the achievement of this target.
These happenings were in-step with global momentum to address poaching and illegal trade. In early September, the UN General Assembly once again passed a resolution (A/71/L.88) addressing wildlife crime. The resolution calls for stronger national legislation, law enforcement, and enhanced technology to fight both the supply and demand of illicit wildlife products. These links were initially and strongly drawn for the cases of illegal trade in elephant ivory and rhino horn (see Fanning the Ivory Pyres). Speaking on the draft resolution, which connects illicit wildlife trade with peace and security, the representative of Gabon said that "poaching is currently the fourth most dangerous form of trafficking in the world after drug trafficking, counterfeiting, and trafficking in persons, generating almost $20 billion a year." Target 15.7 under the Sustainable Development Goal on life on land (SDG 15) also calls for stopping illegal wildlife trade and poaching.
Other initiatives were announced after the Summit. The UN Development Programme (UNDP), along with a coalition of partners, launched a regional initiative to protect snow leopards and their sanctuaries. It will be executed by the Snow Leopard Trust and the Secretariat of the Global Snow Leopard and Ecosystem Protection Programme. CITES also announced a partnership with the Jackson Hole Wildlife Film Festival, which will organize an international film festival on the world's big cats, to raise global awareness of the critical challenges facing these species. Finally, following on its commitments, the Range State of India, which hosted the October 2017 Global Wildlife Program (GWP) annual conference in New Delhi, announced, in concert with the UNDP, a Global Environment Facility (GEF)-funded project titled, 'Securing Livelihoods, Conservation, Sustainable Use and Restoration of High Range Himalayan Ecosystems project (SECURE Himalaya.' It will address wildlife tracking and ecosystem preservation to conserve snow leopards, including through securing community livelihoods, enhancing enforcement, strengthening community institutions, and improving knowledge, advocacy and information systems for landscape-based conservation strategies.


text:
MAR'S ROAD Mar's Road
Mar's Road
Mar's Road Revd [Reverend] Mr Ronald, Cabrach.
Revd [Reverend] John Minto, Clatt.
Mr Gordon, Farmer, Gordonstown 043 This road takes its name from its leading from Kildrummy Castle, the chief seat of the Earls of Mar and Garioch to the Garioch. It was at one time a main line of communication, but since the road by Auchindoir and Rhynie was properly constructed, it has in a great measure fallen into desuetude, though it may still be occasionally used as a shorter line by riders and foot passengers and so may in a certain sense be considered public.
R. Dickson
Sapper RE [Royal Engineers]


text:
Q: write five digits numbers using $0,0,0,1,1,2,2,2,2,3,3,3,4,4$. It is given that we want to write five digits numbers using $0,0,0,1,1,2,2,2,2,3,3,3,4,4$.
How many ways are there to write it $?$
My thought In the first place, it seems cumbersome question a little bit , because i think that we should write them separately in terms of the leading term such that firstly i check over $1$ as leading term , then $2$ so on. However , this process is exhaustive and i hope to find  elegant approach for this question.

A: Here is a method which still requires a bit of work, but which is still more efficient then naive brute force.
Start with a simpler question:

For each $k=1,2,\dots,5$, how many $k$ digit numbers can you make using $3, 3, 4, 4, 4$?

With a little work, the answers are

k
1
2
3
4
5

# numberss with k digits using 3s and 4s
2
4
7
10
10

Next....

For each $k=1,2,\dots,5$, how many $k$ digit numbers can you make using $2,2,2,2,3,3,4,4,4$?

The key is that we can leverage or work in the previous step to make this one easier. Take the summation of all ways to place the $2$'s, times the number of ways to fill in the rest of the empty spaces with $3$'s and $4$'s, the latter of which can be looked up in the previous table. For example,
\begin{align}
\text{# $5$-digit nums with $2$'s, $3$'s and $4$'s}
&= \binom{5}0\cdot \hspace{-1cm}
\overbrace{10}^\text{# 5 digit nums with 3,4}\hspace{-.1cm}
+ \binom{5}1\cdot \hspace{-1cm}\overbrace{10}^\text{# 4 digit nums with 3,4}\hspace{-1cm}
\\
&+ \binom{5}2\cdot \hspace{-1cm}\underbrace{7}_{\substack{\;\\\\\text{# 3 digit nums with 3,4}}}\hspace{-.1cm}
+ \binom{5}3\cdot \hspace{-1cm}\underbrace{4}_\text{# 2 digit nums with 3,4}\hspace{-.1cm}
\\&+ \binom{5}4\cdot \hspace{-1cm}\underbrace{2}_{\substack{\;\\\\\text{# 1 digit nums with 3,4}}}\hspace{-1cm}
\hspace{1.5cm}=\boxed{180}
\end{align}
You then have to do the same for the $1,2,\dots,4$ digit numbers, giving another row to the table. Then, use that row to calculate the number of numbers where you can use digits $1$ to $4$.

k
0
1
2
3
4
5

# numbers with k digits using 3s and 4s
1
2
4
7
10
10

# numbers with k digits using 2, 3, and 4
1
3
9
26
71
180

# numbers with k digits using 1, 2, 3 and 4
1
4
16
62
229
795

Finally, the number of five digit numbers using all available digits is found by summing over all ways to place the zeroes, times the number of ways to fill what remains with $1$ to $4$, which is in the last row of the table:
$$
\binom{4}0\cdot 795+\binom{4}1\cdot 229+\binom{4}2\cdot 62+\binom{4}3\cdot 16=\boxed{2147}
$$

A: Digits given: $0,0,0,1,1,2,2,2,2,3,3,3,4,4$ and we need to make five digit numbers from them. Removing bad cases seems to be a good choice here, even though there is a bit more work in the end for removing numbers with leading zeroes. The point to note is that you do not have any overlap between bad cases of two numbers or more, on other words, we cannot simultaneously have bad cases for two of them.
Number of bad cases for $0$ or $3 = \underbrace{5 \cdot 4}_{\text{Four 0's}} + \underbrace{1}_{\text{Five 0's}} = 21$
Number of bad cases for $1$ or $4 = {5 \choose 3} \cdot 4^2 + 5 \cdot 4 + 1 = 181$
Number of bad cases for $2 = 1$
Total number of bad cases $ = 2 \times 21 + 2 \times 181 + 1 = 405$
Subtract this from total number of unrestricted cases $ = 5^5 = 3125$ (if we had $5$ choices for each digit). That gives us an answer of $2720$.
Now as we need proper $5$ digit numbers where leading zeroes are not allowed,
Numbers with leading zeroes $ = 5^4$. Out of which below are already counted in above bad cases -
In bad cases for $0$, only $4$ start with another digit so $17$ duplicates.
In bad cases for $3$, numbers with leading zeros $ = 1$ (fix first digit as $0$, then remaining four digits are all $3$).
In bad cases for $1$ (or $4$), numbers with leading zeroes $ = 4 \cdot 4 + 1 = 17$ (first digit $0$, choose three out of four remaining digits as $1$ and the last remaining digit other than $1$ or all four digits as $1$).
So total five digit numbers without leading zeroes $ = 2720 - 5^4 + 52 = 2147$


CIOs need to establish themselves as a "disruptor CIOs" and wilfully disrupt their organizations and industries.
In 2012, American rapper Tupac took to the stage with Snoop Dogg to perform some of his best-known hits, more than 15 years after he died in a drive-by shooting in Las Vegas. He appeared as a kind of 'hologram', a projected re-creation developed by Hollywood visual effect experts.
That performance was more than five years ago, and "" has become much easier to create with new technology. Gartner defines counterfeit reality as the digital creation of images, video, documents, or sounds that are convincingly realistic representations of things that never occurred or never existed exactly as represented.
In the closing keynote at Gartner Symposium/ITxpo in Goa, Jenny Beresford, research director at Gartner, said technology that allows the creation of fake imagery or documents could be used for good or evil.
Position your organization to thrive in a connected world.
Andy Rowsell-Jones, research vice president at Gartner, said that while many CIOs are suffering from disruption fatigue, they need to look for opportunities they can grasp and "wilfully disrupt" their own businesses to overcome digital threats and operate at scale.
What's coming next? Gartner identified seven potential disruptions CIOs should consider.
Quantum computing. The ability to detect complex patterns in a matter of days or weeks instead of years represents both an opportunity and a threat. While it could be used to detect illness or design new drugs, it could also be used for cracking encrypted systems. CIOs are advised to explore quantum computing through online simulators or actual quantum computers offered "as a service".
"Counterfeit reality" detectors. Organizations will need to use technologies like artificial intelligence (AI) and quantum computing to create a "truth filter" to protect the corporate brand.
"Counterfeit reality" creators. Consider whether you could adopt AI-generated content, create artificial front-line agents or use avatars to enhance your corporate image.
Synthetic life. With the evolution of genetic modification, we may have the opportunity of re-engineering a replacement for useful organisms like bees. We also need to consider how we might counter use of the technology for evil, such as modified bacteria introduced into a public environment or workplace.
Magnetic and Quantum Levitation. You may have already experienced magnetic levitation, for example, on Shanghai's Maglev train. This technology also has the potential to change the way we move goods around, alter our industrial processes and change how we control the environment. Gartner advises CIOs to apply magnetic levitation in manufacturing processes and explore software for positioning and control.
Software distribution revolution. We are all familiar with changes in software distribution at a personal level, for example, through app stores. What if enterprise software was provided the same way, for example, through software marketplaces provided by Amazon or Alibaba? If there were no software updates , a single bill, simplified procurement, an explosion in the variety of tools available and easier backup and recovery, it could revolutionize IT.
Visual recognition and precognition. Visual and voice search is already becoming a reality, in apps like Tap Tap See, a mobile camera application designed to assist the blind and visually impaired. What if visual technology could be used for precognition, for example, to detect crowd control issues at public events before they become a problem, to know what we will need ahead of time, or in health, to detect underlying health conditions?
Gartner clients can read more in the report Willful Disruption: An Intent-Based Model for Analyzing Digital Disruption by David Mitchell-Smith et al.