text:
\section{Introduction}
\label{section:introduction}

\subsection{Motivation and Background}
\label{subsection:motivation_and_background}

Forward and inverse linear transport models find applications in many areas of science including neutron transport \cite{Dav-OX-57,spanier,Lux-Koblinger}, medical imaging and optical tomography \cite{Arridge99,B-IP-09}, radiative transfer in planetary atmospheres \cite{chandra,Liou-AP-02,MD-SP-05} and in oceans \cite{Mobleyetal93,ThomasStamnes02}, as well as the propagation of seismic waves in the solid Earth \cite{sato-fehler}.  In this paper, we focus on the solution of the forward transport problem by the Monte Carlo (MC) method with, as our main application, remote sensing (an inverse transport problem) of the atmosphere/surface system \cite{Schott07}.  In our demonstration, light is emitted from the Sun and propagates in a complex environment involving absorption and scattering in the atmosphere and reflection at the Earth's surface before (a tiny fraction of) it reaches a narrowband detector, typically mounted on a airplane or a satellite.

The integro-differential transport equation \eqref{align:RTE_differential} may be solved numerically in a variety of ways.  Monte Carlo (MC) simulations model the propagation of individual photons along their path and are well adapted to the complicated geometries encountered in remote sensing.  Photons scatter and are absorbed with prescribed probability depending on the underlying medium.  The output from the simulation, e.g., the fraction of photons that hit a detector, is the expected value of a well-chosen random variable.  These simulations are very easy to code, embarrassingly parallel to run, and suffer (in principle) no discretization error. The drawback is that they can be very slow to converge.  MC methods converge at a rate $(variance/N)^{1/2}$ where $N$ is the number of simulations, and the $variance$ is that of each photon fired.  In remote sensing, the (relative) variance is high in large part because the detector is typically small and thus most photons are not recorded by the detector.  In order to be effective, even in a forward simulation, MC methods must be accelerated.

One approach to speedup MC simulations is to use quasi-Monte Carlo methods, which steepen the convergence rate from $\sim N^{-1/2}$ to a more negative exponent.  However, most MC speedup efforts focus on reducing the variance of each photon.  See \cite{spanier,Lux-Koblinger} or the review of more recent work on neutron transport in \cite{Solomon,HagWag_ProNuclEn2003_Monte,Hoogenboom} and on 3D atmospheric radiative transfer in \cite{EvansMarshak05,BurasMayer11}.  See also \cite{Veach_Thesis1997} for a thorough introduction to the MC techniques, including variance reduction, used in computer graphics.  In problems with a small detector, this is achieved by directing photons toward that detector, and re-weighting to keep calculations unbiased.  When \emph{survival-biasing} is used, photons have their weight decreased rather than being absorbed \cite{spanier,Lux-Koblinger}.\footnote{
Note the somewhat confusing terminology:  On the one hand, a method is statistically biased if the expected outcome is not the intended one.  On the other, the practice of re-directing photons in favorable directions and/or reducing the number of scattering events is also called biasing.  In the latter case the photon has its weight adjusted so that the simulation is unbiased.}
Often, one uses some heuristic (such as proximity to the detector), or some function to measure the ``importance'' of each region of phase space.  In \emph{splitting methods} \cite{spanier,Lux-Koblinger}, the photon is split into two or more photons upon identifying that a photon is in a region of high importance.  The weight of each photon is then decreased proportionately.  Propagating many photons with a low weight is not desirable, therefore splitting is often accompanied by \emph{Russian roulette}.  Here, if a photon enters a region of low enough importance, then the photon is terminated with a certain probability, i.e., high chance of absorption if the weight is low; in the rarer alternative outcome of the Bernoulli trial, the weight is increased to keep the simulation numerically unbiased.  So there is typically a slight cost in variance to improve efficiency (by terminating low-weighted trajectories).  Typically a \emph{weight window} is used to enforce regions of low/high importance.  \emph{Source biasing} techniques change the source distribution in order to more effectively reach the detector.  More generally, the absorption and scattering properties at any point can be modified, provided photons are re-weighted correctly.

It has long been recognized that the adjoint transport solution is a natural importance function \cite{Kalos63,spanier,Lux-Koblinger,TurnerLarsen_NuclSciEng1997_Automatic1,TurnerLarsen_NuclSciEng1997_Automatic2,VanRiper_JointInterConf1997_AVATAR,
HagWag_ProNuclEn2003_Monte,DensmoreLarsen_JCompPhys2003_Variational,Hoogenboom}.
One can use approximations of the adjoint solution---typically a coarse deterministic solution---to reduce variance.  The result is a \emph{hybrid} method (deterministic \& MC).  The AVATAR method uses an adjoint approximation to determine weight windows \cite{VanRiper_JointInterConf1997_AVATAR}.  The CADIS scheme in \cite{HagWag_ProNuclEn2003_Monte} uses an adjoint approximation in both source biasing and weight-window determination.  An adaptive technique that successively refines the solution in ``important'' regions, using the adjoint to designate such regions, is described in \cite{Kong_Efficient_2008,Kong_ANewProof_2008}.  In \cite{Kalos63,spanier,Lux-Koblinger,TurnerLarsen_NuclSciEng1997_Automatic1}, a zero-variance technique is outlined that uses the true adjoint solution to launch photons that all reach the detector with the same weight ... which happens to be the correct answer.  This method is of course impractical since determining the exact adjoint solution everywhere is harder than determining some specific integral of that solution, which is usually the goal of a MC simulation.  The LIFT method \cite{TurnerLarsen_NuclSciEng1997_Automatic1,TurnerLarsen_NuclSciEng1997_Automatic2} therefore uses an approximation of the adjoint solution to approximate this zero-variance method.

We adapt the zero-variance technique to the particular problem we have at hand; see Fig.~\ref{fig:cos3boundary} for the type of geometry considered in this paper.  The problem we consider has a fixed, partially-reflective, complex-shaped lower boundary, and relatively large mean-free-path (MFP) in the sense that a large fraction of the photons reaching the detector have not scattered inside the (optically thin) atmosphere.  Calculation of the approximate adjoint solution used to emulate zero-variance techniques is difficult and potentially very costly.  What we demonstrate in this paper is that partial, ``localized'' (in an appropriate sense) knowledge of the adjoint solution still offers very significant variance reductions.  More specifically, we calculate adjoint solutions that accurately account for the presence of the boundary but do not account for atmospheric scattering (infinite MFP limit). The computation of the adjoint solution thus becomes a radiosity problem with much reduced dimensionality compared to the full transport problem.  This, of course, can only reduce variance in proportion to the number of ``ballistic'' photons that never interact with the atmosphere.  When combined with simple rules for allowing atmospheric scattering and sending some photons directly from the atmosphere to the detector, our hybrid method yields very significant variance reduction at relatively minimal cost.  Furthermore, the methodology studied is applicable whenever any method is available to deterministically pre-calculate flux over any subset of paths.  For instance, complex propagation of light in clouds and its importance could be pre-calculated locally and incorporated into the MC simulations in a similar fashion.  This ``modular'' approach to the description of the adjoint solution is well-adapted to the geometries of interest in remote sensing and avoids complicated, global (hence expensive) deterministic calculations of adjoint transport solutions.  Our treatment of the reflecting boundary described in detail in this paper is a first step toward modular adjoint transport calculations and their variance reduction capabilities in remote sensing.

\begin{figure}[ht!]
  \begin{center}
  \includegraphics[width=0.85\textwidth, clip=true, trim = 8cm 4cm 5cm 4.5cm]{tracers_cos3_06_annotated_02}
  \caption{Mountain ($1-\cos^3x$ shape), cloud, sky, and detector.  Dot size indicates relative adjoint flux strength.  Large dots on right-hand-side are the detector (dot size is down-scaled for detector).  Dot size on mountain indicates that portions of the mountain are shaded from the detector, and that the surface albedo is varying.  See section \ref{sec:numvol} for specifics, as used in the present study.}
  \label{fig:cos3boundary}
  \end{center}
\end{figure}

The rest of the paper is organized as follows.  In sections \ref{subsection:problem_setup} and \ref{subsection:statistical_formulation} respectively, the physical problem and statistical formulation are described.  In section \ref{subsection:standard_algorithms}, the analog and survival-biased MC algorithms are presented.  In section \ref{section:sai}, the surface adjoint importance (SAI) and regularized SAI methods are introduced.  These are the hybrid adjoint-based methods at the core of this work.  In section \ref{section:numerics}, numerical estimations of variance reductions and computational speedups are given.  For an expanded exposition of techniques and analyses from a mathematical standpoint, we refer the interested reader to \cite{BalImportanceArxiv}.  Finally, we summarize our findings in section \ref{section:conclusion} and conclude with thoughts about potential applications in remote sensing science.

\subsection{Problem Setup}
\label{subsection:problem_setup}

Our setup is photon transport in a domain $R\subset\Rd$ ($d=2,3$, with $d=2$ in our present demonstration) described in Fig.~\ref{fig:cos3boundary}.  The outward normal to the domain boundary $\pR$ at position $r$ is denoted $\nu_r$.  $R$ is the atmosphere, the sky/mountain/sides/detector constitute $\pR$.  We have one small detector located on the right-side of $\pR$, and the goal of simulations is to estimate the photon flux through the detector.  Since photons are monokinetic, propagation direction $v$ is a unit vector in the sphere $\dsphere$ embedded in $d$-dimensional space (unit circle for $d=2$).

We model radiance (a.k.a. specific intensity or angular photon flux density) $I(r,v)$ in our medium with a boundary source distribution $Q$.  $I$ obeys the following integro-differential transport equation and boundary condition:
\begin{align}
  \begin{split}
    v\cdot\nabla I(r,v) + \sigma(r)I(r,v) &= K I(r,v)\\
    I(r,v) &= \frac{K I(r,v)}{|\nu_r\cdot v|} + \frac{Q(r,v)}{|\nu_r\cdot v|},  \qquad r\in\pR,\mbox{ and } v\cdot\nu_r<0,
  \end{split}
  \label{align:RTE_differential}
\end{align}
the integral operators being defined by kernels
\begin{align}
   \begin{array}{rcll}
    Kf(r,v) &=& \displaystyle \sigma_s(r)\int_\dsphere \pfvol{r}{v'}{v}f(r,v')\dv', \quad &
    r\in R \\
    Kf(r,v) &=& \alpha(r)\displaystyle\int_{\nu_{r}\cdot v'>0}
    \PFsurf{r}{v'}{v}|\nu_r\cdot v'|f(r,v')\dv'\quad & r\in \pR,\mbox{ and } v\cdot\nu_r<0.
   \end{array}
\end{align}
The extinction coefficient, a.k.a. total cross section (per unit of volume) $\sigma(r)$ is the sum of the intrinsic absorption coefficient/cross-section $\sigma_a(r)$ and the scattering coefficient/cross-section $\sigma_s(r)$.  For the partially reflecting boundary condition (viewed here as a surface scattering), $\alpha(r)$ is the local value of the albedo.  Both volume ($\pfvol{r}{v'}{v}$) and surface ($\PFsurf{r}{v'}{v}$) phase functions are normalized ($\int p\dv'=1$).

Since the transport problem is linear, we use a normalized boundary source, i.e.,
\begin{equation}
  \int_\pR\int_{\nu_r\cdot v<0} Q(r,v) \d\mu(r) \dv = 1
  \label{eq:norms}
\end{equation}
where $\d\mu(r)$ is the appropriate measure on the $(d-1)$-dimensional boundary.

Our detector measures photon flux and is described by a ``response function,'' $g(r,v)|\nu_r\cdot v|$, where $g(r,v)$ is zero everywhere except when $r$ is in the physical detector (its aperture or ``pupil'') and $v$ points out of the boundary.  Where $g \neq 0$ it is constant and, furthermore, it is normalized so that $\int g(r,v)\d r\dv = 1$.  The goal of our Monte Carlo method is to compute the detector's signal
\begin{align}
  \int_\pR\int_{\nu_r\cdot v>0}g(r,v)|\nu_r\cdot v|I(r,v)\d\mu(r)\dv.
  \label{align:measurement}
\end{align}
In the present study, any $v$ can contribute to the radiometric signal measured at $r$.  To model an imaging detector, direction space would be limited to a finite field-of-view that would in turn be subdivided into individual ``pixels.''

For future use, we define the function
\begin{align*}
  E_\sigma(r,r') :&= \exp\left\{ -\int_0^{|r-r'|}\sigma(r+t\widehat{r'-r})\dt \right\},
\end{align*}
where $\widehat{r'-r} := (r'-r)/|r'-r|$.  Physically, it describes the probability of \emph{direct} transmission of light from point $r$ to point $r'$ (or vice-versa), that is, without suffering any collision.

\subsection{Statistical formulation/notation}
\label{subsection:statistical_formulation}

The measurement defined formally in \eqref{align:measurement} is approximated in a Monte Carlo simulation by estimating an average
\begin{align*}
  S_N :&= \frac{1}{N}\sum_{n=1}^N \one_D(\omega_n)
\end{align*}
where the $\omega_n$ are photon paths ($\omega=(r_0,r_1,\dots,r_k)$) generated by the ``analog'' chain (meaning analogously to real-life photon travel, cf. Algorithm \ref{alg:analog}), and the relevant indicator function is $\one_D(\omega) = 1$ if the path hits the detector (hence the subscript $D$), and $= 0$ otherwise.  The paths are random variables and, with $\Exp{\cdot}$ denoting statistical \emph{expectation}, we have
\begin{align*}
  \Exp{S_N} &= \Exp{\one_D} = \rmP[D],
\end{align*}
where the notation $\rmP[D]$ emphasizes that this is a probability of hitting the detector.  We also have $\rmP[D]$ equal to the desired measurement or signal in \eqref{align:measurement}.
For finite $N$, $S_N$ is not equal to $\rmP[D]$ exactly.  The mismatch is quantified in a statistical sense through the \emph{variance}
\begin{align*}
  \Var{S_N} :&= \Exp{\left( S_N-\rmP[D] \right)^2} = \frac{\Exp{\left( \one_D-\rmP[D] \right)^2}}{N} = \frac{\Var{\one_D}}{N},
\end{align*}
since all of the events $\omega_n$ contributing to the $S_N$ estimator are independently drawn.

Rather than $S_N$, one may generate paths according to some modification of real-life photon travel and then estimate
\begin{align*}
  \rmP[D] &\approx T_N := \frac{1}{N}\sum_{n=1}^N \one_D(\omega_n)\frac{\dPa\,}{\d\overline\rmP}(\omega_n),
\end{align*}
where the ratio $\dPa/\d\overline\rmP(\omega)$ is the ratio of the probability density of $\omega$ in the analog chain to that in the modified chain.  This \emph{importance sampling} technique is widely used in statistics since often times $T_N$ will have lower variance than $S_N$.  Indeed, most of the variance reduction techniques mentioned in the introduction are of this type.  In our algorithms we compute this ratio step-by-step and refer to it as a weight (modifier).  So, rather than counting photons, we count weighted photons.

For future use we define the following (standard) statistical notations and convention.  First, we write $u\sim\calU[0,1]$ to indicate that $u$ is a random variable uniformly distributed on the interval $[0,1]$.  Second, a probability density such as $\pi(x)$ can be denoted explicitly (e.g., $\pi(x) = (2\pi)^{-1/2}\exp\left\{ -x^2/2 \right\}$ in the case of the normal distribution with zero mean and unit variance), or it can be given up to a constant (since it must integrate to one).  In this last case, we would write $\pi(x) \propto \exp\left\{ -x^2/2 \right\}$.

\subsection{Standard Algorithms}
\label{subsection:standard_algorithms}

We present here two basic algorithms for Monte Carlo transport.  These are well known but we do this in order to demonstrate our notation.  Algorithm \ref{alg:analog} is often referred to as \emph{analog} since the photons follow a path analogous to photons in the real world.

\begin{algorithm}[H]
  \begin{algorithmic}[1]
    \caption{Analog Monte Carlo Transport}
    \label{alg:analog}
    \STATE Choose a starting position/direction $(r_0,v_0)$ according to the sun's source density $Q(r,v)$
    \STATE Draw $u\sim\calU[0,1]$ and cast the photon along the ray $r_0+tv_0$ until $E_\sigma(r_0+tv_0)<u$.  Call this point $r_1$.  If this does not happen before $\pR$ is reached then set $r_1$ to the boundary point at the intersection with the ray.
    \IF{$r_1\in R$}
    \STATE With probability $\sigma_s(r_1)/\sigma(r_1)$, the photon is not absorbed, and we select $v_1$ using the probability density
    \begin{align*}
      v_1&\mapsto \pfvol{r_1}{v_0}{v_1};
    \end{align*}
    otherwise the chain is stopped.
    \ELSIF{$r_1\in\pR$}
    \STATE With probability $\alpha(r_1)$ the photon is not absorbed, and we select $v_1$ using the probability density
    \begin{align*}
      v_1&\mapsto \PFsurf{r_1}{v_0}{v_1};
    \end{align*}
    otherwise the photon is absorbed and we stop the chain.
    \ENDIF
    \STATE Continue alternating casts and direction changes until either the photon is absorbed, escapes through the upper boundary (``sky+sides''), or the detector is reached.
  \end{algorithmic}
\end{algorithm}

For use in Algorithm \ref{alg:regularized_sai} further on, we will need to know the probability density of the analog chain producing a path $\omega$.  This is given by
\begin{align*}
  D_{analog}(r_0,r_1) &= Q(r_0,v_0)E_\sigma(r_0,r_1),\\
  D_{analog}(r_0,r_1,r_2) &= D_{analog}(r_0,r_1)K^{analog}(r_1,v_0\to \widehat{r_2-r_1})E_\sigma(r_1,r_2)
\end{align*}
and so on.  Above $K^{analog}$ is given by
\begin{align*}
  K^{analog}(r_1,v_0\to v_1) :&= \left\{
  \begin{matrix}
    \sigma_s(r_1)\pfvol{r_1}{v_0}{v_1},&\quad r_1\in R\\
    \alpha(r_1)\PFsurf{r_1}{v_0}{v_1},&\quad r_1\in\pR.
  \end{matrix}
  \right.
\end{align*}

Algorithm \ref{alg:survival_biased} uses a trick known as \emph{survival-biasing} since photons will survive (almost) any interaction with the media.  We do this by casting photons while ignoring intrinsic absorption.  So, e.g., if a patch of media has $\sigma_a$ large and $0<\sigma_s/\sigma\ll1$ the photon will almost never scatter there.  Our weight is then $E_\sigma/E_{\sigma_s}$.  When the photon interacts with the surface, then so long as $\alpha>0$, we do not absorb but multiply the photon weight by $\alpha$. Another, slightly different but also common, survival-biasing method would cast photons in the same manner as analog, but would eliminate absorption and re-weight by $\sigma_s/\sigma$.  So, e.g., if a patch of media has $\sigma_a$ large and $0<\sigma_s/\sigma\ll1$ the photon would likely interact with the media and scatter but not be absorbed there; its weight however would be reduced by a factor of $\sigma_s/\sigma$ (known in the radiative transfer literature as the ``albedo for single scattering'').

\begin{algorithm}[H]
  \begin{algorithmic}[1]
    \caption{Survival-Biased Monte Carlo Transport}
    \label{alg:survival_biased}
    \STATE Choose a starting position/direction $(r_0,v_0)$ according to the source density $Q(r,v)$
    \STATE Draw $u\sim\calU[0,1]$ and cast the photon along the ray $r_0+tv_0$ until $E_{\sigma_s}(r_0+tv_0)<u$.  Call this point $r_1$.  If this does not happen before $\pR$ is reached then $r_1$ is the boundary point we have reached.
        Since we paid no attention to intrinsic absorption during the cast, the photon picks up a weight equal to
        \begin{align*}
          E_{\sigma_a}(r_0,r_1) &= \frac{E_\sigma(r_0,r_1)}{E_{\sigma_s(r_0,r_1)}}
        \end{align*}
    \IF{$r_1\in R$}
    \STATE Select $v_1$ using the probability density
    \begin{align*}
      v_1&\mapsto \pfvol{r_1}{v_0}{v_1}.
    \end{align*}
    \ELSIF{$r_1\in\pR$ and $\alpha(r_1)>0$}
    \STATE Select $v_1$ using the probability density
    \begin{align*}
      v_1&\mapsto \PFsurf{r_1}{v_0}{v_1}.
    \end{align*}
    Since we had no chance of boundary absorption, the photon's weight is multiplied by $\alpha(r_1)$.
    \ELSIF{$r_1\in\pR$ and $\alpha(r_1)=0$}
    \STATE The photon is absorbed and we stop the chain.
    \ENDIF
    \STATE Continue alternating casts and direction changes until either the photon is absorbed, escapes, or reaches the detector.
  \end{algorithmic}
\end{algorithm}

\section{The Surface Adjoint Importance (SAI) Method}
\label{section:sai}

The SAI method uses an approximation to the surface reflection problem to reduce variance coming from surface interactions.  It ignores atmospheric effects and therefore, by itself, is statistically biased.  In section \ref{subsection:regularized_sai} we pair it with other methods to produce an unbiased estimate of the detected flux.

\subsection{Pure SAI}
\label{subsection:pure_sai}

Here we ignore atmospheric effects and demonstrate and develop a Monte Carlo method that sends photons from surface point to surface point and then to the detector.  If atmospheric effects are not present, and our deterministic solution was perfectly accurate, this method would have zero variance.

The adjoint solution to transport may be developed by considering the $L^2$ adjoint of the integral solution to transport and reversing the role of the source and detector.
Let $\Is$ be the adjoint solution when only surface effects are present.  We therefore have
\begin{align}
  \Is(r,v) &= \alpha(r)\int_{\nu_r\cdot v'<0}\PFsurf{r}{v}{v'}\Is(r_+(r,v'),v')\dv' + g(r,v).
  \label{eq:psis}
\end{align}
This adjoint solution corresponds (in a Monte Carlo viewpoint) to sending photons that start at the detector and travel backwards.  Therefore,
it will have its maximum at the detector.  It will be higher in places that have a clear path to the detector.  $\Is$ will be zero at places from which a photon cannot reach the detector.  Our numerical solution of \eqref{eq:psis} is described in the Appendix.

The pure SAI chain is defined by the steps described in the following Algorithm~\ref{alg:pure_sai}.

\begin{algorithm}[H]
  \begin{algorithmic}[1]
    \caption{Pure SAI}
    \label{alg:pure_sai}
    \STATE Choose a starting position/direction $(r_0,v_0)$ according to the modified source density
    \begin{align*}
     \Qsai(r,v) &\propto Q(r,v)\Is(r_+(r,v),v).
    \end{align*}
    The photon picks up a weight $Q(r_0,v_0)/\Qsai(r_0,v_0)$
    \STATE Cast the photon until it hits the opposing boundary at point/direction $(r_1,v_1)=( r_+(r_0,v_1),v_1)$.  The weight is multiplied by
    \begin{align*}
      \frac{E_\sigma(r_0,r_1)}{1}.
    \end{align*}
    \STATE Change direction according to the density
    \begin{align*}
      K^{sai}(r_1,v_1\to v_2)&=C_{sai}(r_1)\PFsurf{r_1}{v_1}{v_2}\frac{\Is(r_+(r_1,v_2),v_2)}{\Is(r_1,v_1)}
    \end{align*}
    where $C_{sai}(r)$ is a normalization factor depending only on $r\in\pR$.   Since we did not account for boundary absorption, the photon weight is multiplied by $\alpha(r_1)$.  The modified direction change must also be taken into account and therefore, in addition, the weight is multiplied by
    \begin{align*}
      \frac{K^{analog}(r_1,v_1\to v_2)}{K^{sai}(r_1, v_1\to v_2)}.
    \end{align*}
    \STATE Cast the photon until it hits the opposing boundary.  If it hits the detector, stop and record a hit.  Else, repeat step 3.
  \end{algorithmic}
\end{algorithm}
For use in Algorithm \ref{alg:regularized_sai}, we will need to compute the probability density of a path $\omega=(r_0,\dots,r_\tau)$ being generated by pure SAI.  This is simply the denominator in the corresponding weights.  Denoting this by $D_{sai}$ we have
\begin{align*}
  D_{sai}(\omega) &= 0,\qquad \mbox{if $r_j\in R$ for any $j$},
\end{align*}
and for paths such that $r_j\in\pR$ for all $j$, we define $D_{sai}$ recursively (with $v_j:= \widehat{r_{j+1}-r_j}$)
\begin{align*}
  D_{sai}(r_0,r_1) &= S^{sai}(r_0,v_0) \\
  D_{sai}(r_0,r_1,r_2) &= D_{sai}(r_0,r_1)K^{sai}(r_1,v_0\to v_1),\\
  D_{sai}(r_0,\dots,r_k) &= D_{sai}(r_0,\dots,r_{k-1})K^{sai}(r_{k-1},v_{k-2}\to v_{k-1}).
\end{align*}

\begin{remark}
  \label{remark:pure_sai}
  \mbox{}\\
  \begin{itemize}
    \item A discretized version of the density $\Qsai$ is pre-computed using the (discrete) solution $\Is$; see section \ref{section:numerics}.  This means that we can pre-compute the normalization factor $C_{sai}$.  The discrete density $\Qsai$ will be defined at a number of points $(r_i,v_0)$ where $v_0$ is the anti-solar direction.  We use the density to decide on a center point $r_i$, and then perturb the starting point by a small (random) amount to eliminate discretization effects in the final solution.
    \item The direction change pdf is also pre-computed and stored as a discrete pdf over angles.  We use the pdf to pick a direction center $v_j$ and then perturb to obtain the new direction.
    \item Up to numerical error one can see that $C_{sai}(r) = \alpha(r)$.  Indeed, dividing \eqref{eq:psis} through by $\Is(r,v)$ we have
      \begin{align*}
        1 &= \alpha(r)\int_{\nu_r\cdot v'<0}\PFsurf{r}{v}{v'}\frac{\Is(r_+(r,v'),v')}{\Is(r,v)}\dv' + \frac{g(r,v)}{\Is(r,v)}.
      \end{align*}
      So away from the detector $g(r,v)=0$ and the integral is therefore equal to $1$.
    \item That this method is biased is easy to see:  If a region of the atmosphere has non-zero scattering, then it would be possible (in the analog world) to scatter from that point to the detector.  This type of interaction is not allowed in a pure SAI world.
  \end{itemize}
\end{remark}

This is an implementation of the zero variance adjoint-based chains studied in \cite{spanier,Lux-Koblinger,TurnerLarsen_NuclSciEng1997_Automatic1} in the special case where atmospheric effects are not present.  Hence (disregarding numerical error), this would be a zero-variance method were atmospheric absorption/scattering absent.

We verify this claim numerically by testing the method in simulations without atmospheric effects.  See Fig.~\ref{figure:MFPinfinity_var_h} where this is tested with both a flat terrain and a curved ``$\cos^3$'' mountain.  The curved mountain increases variance since discretization does not allow the function $r_+(x,v)$ to be implemented perfectly.
\begin{figure}[ht!]
  \begin{center}
  \includegraphics[width=0.43\textwidth]{flat_MFPinfinity_var_h_BW}
  \includegraphics[width=0.43\textwidth]{cos3_MFPinfinity_var_h_BW}
  \caption{Left:  When a flat mountain is used, variance $\sim O(h^{1.5})$ where $h$ is the discretization parameter.  Right: On the curved boundary discretization effects are more prevalent and convergence is slower.}
  \label{figure:MFPinfinity_var_h}
\end{center}
\end{figure}

\subsection{Regularized SAI}
\label{subsection:regularized_sai}

Here we use the SAI chain as part of a larger unbiased chain. Since Algorithm \ref{alg:pure_sai} does not generate paths following all possible interactions, we must supplement it with an algorithm that does. We then use a number $q_s\in[0,1]$ to determine the fraction of photons that travel according to Algorithm \ref{alg:pure_sai} (this fraction $=1-q_s$), and what fraction according to the supplemental algorithm.

Before describing the regularized SAI algorithm, we present the supplemental Algorithm \ref{alg:heuristic} dubbed ``heuristic scattering adjustment.''  It is a survival-biased algorithm in the sense that no absorption occurs within the atmosphere, or at boundary points (unless the boundary point had $\alpha=0$, e.g. the sides/sky).  It also makes use of a simple scheme to direct a fraction of atmospheric interactions toward the detector.  No claim is made to the optimality of this re-direction (it is similar to the technique of \emph{local estimation} \cite{Marchuk_etal80,EvansMarshak05}).  We use Algorithm \ref{alg:heuristic} since it is simple to understand and illustrates the dramatic decrease in variance that can be achieved when two methods (SAI and heuristic) are used together in Algorithm \ref{alg:regularized_sai} (see also section \ref{section:numerics}).

\begin{algorithm}[H]
  \begin{algorithmic}[1]
    \caption{Heuristic Scattering Adjustment with Parameter $q_v\in[0,1]$}
    \label{alg:heuristic}
    \STATE Choose a starting position/direction according to the standard source density $Q(r,v)$
    \STATE Cast the photon as in Algorithm \ref{alg:survival_biased} until it hits the opposing boundary or interacts with the atmosphere at $r_1$.  The photon picks up a weight equal to $E_\sigma(r_0,r_1)/E_{\sigma_s}(r_0,r_1)$
    \IF{$r_1 \in R$}
    \STATE With $r_{d_0}=$``the midpoint of the detector'', compute
    \begin{align*}
      q_{heu}(r_1,v_0) :&= 1 - (1-q_v)\frac{\pfvol{r_1}{v_0}{\widehat{r_{d_0}-r_1}}}{\|\pfvol{r_1}{v_1}{\cdot}\|_{L^\infty}}
    \end{align*}
    With probability $1-q_{heu}$ draw $v_1$ from a uniform distribution of directions pointed toward the detector (we call this $f_V(r_1,v_1)$), and with probability $q_{heu}$ draw $v_1$ from $\pfvol{r_1}{v_0}{\cdot}$.  The weight is multiplied by
    \begin{align*}
      \frac{\sigma_s(r_1)\pfvol{r_1}{v_0}{v_1}}{(1-q_{heu})f_V(r_1,v_1) + q_{heu}\pfvol{r_1}{v_0}{v_1}},&\qquad\mbox{if $r_1\in R$}.
    \end{align*}
    \ELSIF{$r_1\in \pR$ and $\alpha(r_1)>0$}
    \STATE pick a new direction according to the density $\PFsurf{r_1}{v_0}{v_1}$.  The weight is multiplied by $\alpha(r_1)$.
    \ELSIF {If $r_1\in\pR$ and $\alpha(r_1)=0$}
    \STATE the photon is absorbed and we stop.
    \ENDIF
    \STATE Continue in this manner until absorption or the detector is reached
  \end{algorithmic}
\end{algorithm}

So at every scattering event, the weight is modified by a ratio of either $\alpha(r) P$ or $\sigma_s(r) p$ to $K^{heu}$ where
\begin{align*}
  K^{heu}(r,v\to v') :&= \left\{
  \begin{matrix}
    (1-q_{heu})f_V(r,v) + q_{heu}\pfvol{r}{v}{v'},&\qquad  r\in R\\
    \PFsurf{r}{v}{v'},&\qquad r\in \pR.
  \end{matrix}
  \right.
\end{align*}
For use in Algorithm \ref{alg:regularized_sai} we will need to compute the probability density of a given path generated by Algorithm \ref{alg:heuristic}.  This is simply the denominator in the corresponding weight.  Denote this by $D_{heu}(r_0,r_1,\dots,r_k)$, which we define recursively by (with $v_j:=\widehat{r_{j+1}-r_j}$)
\begin{align}
  \label{align:heuristic_density}
  \begin{split}
    D_{heu}(r_0,r_1) &= Q(r_0,v_0)E_{\sigma_s}(r_0,r_1),\\
    D_{heu}(r_0,r_1,r_2) &= D_{heu}(r_0,r_1)K^{heu}(r_1,v_0\to v_1)E_{\sigma_s}(r_1,r_2),\\
    D_{heu}(r_0,\dots,r_k) &= D_{heu}(r_0,\dots,r_{k-1})K^{heu}(r_{k-1},v_{k-2}\to v_{k-1})E_{\sigma_s}(r_{k-1},r_k),
  \end{split}
\end{align}
and so on.

We now present Algorithm \ref{alg:regularized_sai}, the regularized SAI algorithm that combines pure SAI (Algorithm \ref{alg:pure_sai}) with the heuristic scattering adjustment (Algorithm \ref{alg:heuristic}).  Note that any unbiased algorithm may be combined with pure SAI in a similar manner.

\begin{algorithm}[H]
  \begin{algorithmic}[1]
    \caption{Regularized SAI with parameters $q_s,q_v\in[0,1]$}
    \label{alg:regularized_sai}
    \STATE With probability $1-q_s$, generate a path according to Algorithm \ref{alg:pure_sai}.  With probability $q_s$ generate it according to Algorithm \ref{alg:heuristic}.
    \STATE The weight of the path $\omega=(r_1,\dots,r_\tau)$ is
    \begin{align*}
      \frac{D_{analog}(\omega)}{(1-q_s)D_{sai}(\omega) + q_sD_{heu}(\omega)}.
    \end{align*}
  \end{algorithmic}
\end{algorithm}

Algorithm \ref{alg:regularized_sai} uses SAI to produce paths that interact only with the surface.  One could easily devise other algorithms that send paths via the heuristic chain, and once paths interact with the surface they use the SAI chain.  This could reduce variance further, but we choose not to study this in order to simplify the presentation.

\section{Numerical Results}
\label{section:numerics}

\subsection{Parameter choices in numerical simulations}
\label{sec:numvol}

In the assumed $d=2$ transport space, we have $r=(x,y)$, where $x$ increases from left to right in Fig.~\ref{fig:cos3boundary} and $y$ increases from bottom to top; $r=(0,0)$ is the point at the bottom of the valley.  For directions, we have $v=v(\phi)=(\cos\phi,\sin\phi)$ where $\phi$ increases counterclockwise from the $x>0$ axis.

In the simulations performed with $\sigma=0$ (no atmospheric interactions), we used both a flat surface (so that our domain was $[-\pi,\pi]\times[2,4]$) and a ``$\cos^3$'' surface (Fig.~\ref{fig:cos3boundary}).  We swept $h$, with $0.002<h<0.2$.  We did not use any heuristic scattering adjustment ($q_v=1.0$).  In all cases, we assume an isotropic (Lambertian) redistribution by diffuse surface reflection.  This leads to the following surface scattering phase function and assumed surface albedo distribution:
\begin{align*}
  \PFsurf{r}{v}{v'} &\propto \left\{
  \begin{matrix}
    |\nu_r\cdot v'|,& \nu_r\cdot v'<0 \\
    0,&\mbox{ otherwise}
  \end{matrix}
  \right. ;\qquad
  \alpha(r)= \left\{
  \begin{matrix}
    1,& |x|<2.5\\
    0 ,& \mbox{ otherwise}
  \end{matrix}
  \right. .
\end{align*}
The cutoff $|x|<2.5$ was done to simplify the coding (allowed us to use one simple routine for all values of $h$), and has no theoretical consequence.  The source was mono-directional $\phi=-\pi/2$, and given by
\begin{align*}
  Q(r,v(-\pi/2)) &= \left\{
  \begin{matrix}
    1/5\quad& |x|<2.5,\, y=4\\
    0\quad& \mbox{ otherwise.}
  \end{matrix}
  \right.
\end{align*}

In the simulations involving atmospheric interactions ($\sigma>0$), we used a $\cos^3$ type surface.  We compute speedup in a variety of cases. The mean-free-path MFP$=\sigma^{-1}$ was varied as well as $q_s$, $h$, and $q_v$.  We swept $0.002<h<0.15$.  In all cases the atmospheric scattering coefficients were constant with $\sigma_s=2\sigma_a$ (hence $\sigma_s/\sigma = 2/3$).  The atmospheric scattering was given by
\begin{align*}
  \pfvol{r}{v}{v'} &\propto 1 + (v\cdot v')^2,
\end{align*}
which mimics a molecular (Rayleigh) in $d=2$.  The other coefficients were chosen to have features (in this case oscillations) on a scale coarser than the fine values of $h$, and finer than the coarse values.

The surface albedo was chosen to be quite complex (significantly different than the flat surface/constant reflection commonly used).  The phase function $P$ was as before (Lambertian), but $\alpha$ is given by
\begin{align*}
  \alpha(r)&=\left\{
  \begin{matrix}
    0& |x|>2.5,\\
    0.75 + 0.25\sin(2\pi x/0.05)& 1<x<2.5,\\
    0.35 + 0.25\sin(2\pi x/0.05)& -2.5<x<1,
  \end{matrix}
  \right.
\end{align*}
using the same inconsequential cutoff $|x|<2.5$.  Off the mountain there was no scattering (perfectly absorbing boundary).

The source was mono-directional $\phi=-\pi/2$ and given by
\begin{align*}
  Q(r,v(-\pi/2)) &\propto \left\{
  \begin{matrix}
    1 + 0.25\sin(2\pi x/0.07)\quad & |x|<2.5,\, y=4\\
    0& \mbox{ otherwise}
  \end{matrix}
  \right. .
\end{align*}

\subsection{Speedup (figure of merit)}
\label{subsection:fom}

We start by defining our figure of merit used to compare the different algorithms.  We take the viewpoint that each algorithm produces a sequence of paths $\left\{ \omega^n \right\}_{n=1}^N$ and corresponding random variables $\xi(\omega^n)$ equal to the product of $\one_D(\omega^n)$ times the weight that the photon picked up along the way.  To distinguish different methods we write $\xia$ for analog, $\xisb$ for survival-biasing, $\xisai$ for pure SAI, $\xiheu$ for heuristic scattering, and $\xiq$ for the regularized SAI method.

For all of these methods, define the approximation after $N$ random draws
\begin{align*}
  I_N(\xi) :&= \frac{1}{N}\sum_{n=1}^N \xi(\omega_n).
\end{align*}
For $\xi$ equal to any of the above methods, $I_N(\xi)$ is an unbiased estimator of $\Exp{\xi}=\rmP[D]$, i.e., the probability of a detector hit.

The RMS estimation error $\varepsilon$ is given by
\begin{align*}
  \varepsilon(\xi) :&= \sqrt{\Exp{|I_N(\xi)-\rmP[D]|^2}} = \sqrt{\frac{\Var{\xi}}{N}}.
\end{align*}
For a given error level $\varepsilon$, the required number of MC draws is then $N(\eps,\xi) := \Var{\xi}/\eps$.
The required simulation time $T(\varepsilon,\xi)$ for one estimation of $\rmP[D]$ is given by
\begin{align*}
  T(\varepsilon,\xi) :&= T_0(\xi) + \tau(\xi)N = T_0(\xi) + \frac{\tau(\xi)\Var{\xi}}{\varepsilon^2},
\end{align*}
where $T_0(\xi)$ is the time needed to compute the deterministic adjoint solution (e.g. at level $h$ when $\xi=\xih$), and $\tau(\xi)$ is the expected time for one draw using the appropriate measure for the random variable $\xi$.  We foresee the use of SAI in situations where the boundary remains fixed, but the atmosphere changes (due to, e.g., moving clouds over a fixed surface).  We therefore consider the time for $m$ simulations using one boundary,
\begin{align*}
  T(\varepsilon,\xi, m) :&= T_0(\xi) + m\tau(\xi)N = T_0(\xi) +m\frac{\tau(\xi)\Var{\xi}}{\varepsilon^2},
\end{align*}

Schemes may be compared with the ratio
\begin{align*}
  \frac{T(\varepsilon,\xi_1,m)}{T(\varepsilon,\xi_2,m)} = \frac{\eps^2T_0(\xi_1) + m\tau(\xi_1)\Var{\xi_1}}{\eps^2T_0(\xi_2) + m\tau(\xi_2)\Var{\xi_2}}.
\end{align*}

For a deterministic approximation of $\Is$, we expect $T_0(\xi)\approx C(\xi)h^{-2(d-1)}$.  We in fact measure (with $d=2$) $T_0(\xih)\approx 0.017h^{-2}$.  Our ``benchmark'' scheme is survival-biasing.  Since $\xisb$ requires no deterministic solution, the relevant ratio (and our figure of merit) is
\begin{align*}
  \mbox{Speedup}(\xiq,\eps,m) :&= \frac{m\tau(\xisb)\Var{\xisb}}{\left( \frac{\eps}{h} \right)^2C  + m\tau(\xiq)\Var{\xiq}}.
\end{align*}

We measured speedup when either $m=10$ or, formally, $m=\infty$ (``Ignoring deterministic solve'').

\subsection{Variance reduction}
\label{subsection:varred}

Here we analyze the variance of the SAI chain in the presence of atmospheric interactions.
Note that even when the error $|\rmP[D] - \ip{\Is}{S}|$ is high, we still get good variance reduction.  See Fig.~\ref{figure:deterministic_error}.  This emphasizes the point that the quality of the deterministic solve is not so important in a modular scheme.

\begin{figure}[h!]
    \begin{center}
  \includegraphics[width=0.43\textwidth]{cos3_MFP21_deterministic_error_BW}
  \includegraphics[width=0.43\textwidth]{cos3_MFP21_speedup_minfinity_BW}
  \caption{$|\rmP[D] - \ip{\Is}{S}|/\rmP[D]$ is generally lower for smaller $h$.  However, speedup is still very good even for large $h$.  Diam is the maximal diameter of the simulation domain $R$}
  \label{figure:deterministic_error}
  \end{center}
\end{figure}

Our implementation swept both $q_s$ and $q_v$.  As expected, we see
decreasing speedup with increasing atmospheric scattering strength $\sigma$.  See Fig.~\ref{figure:speedup_with_heuristic}.

\begin{figure}[h!]
    \begin{center}
  \includegraphics[width=0.43\textwidth]{cos3_MFP21_speedup_q_sai_q_0_m10_BW}
  \includegraphics[width=0.43\textwidth]{cos3_MFP10p9_speedup_q_0_q_sai_BW}\\
  \includegraphics[width=0.43\textwidth]{cos3_MFP4p07_speedup_q_0_q_sai_BW}
  \includegraphics[width=0.43\textwidth]{cos3_MFP2p35_speedup_q_0_q_sai_BW}
  \caption{Speedup when using both surface adjoint approximation $\Is$ (with parameter $q_s$) and heuristic atmospheric scattering (with parameter $q_v$)}
  \label{figure:speedup_with_heuristic}
  \end{center}
\end{figure}

It is important to note that use of adjoint-enhanced surface
scattering, and heuristic atmospheric scattering ($q_s<1$, $q_v<1$)
together is especially helpful.  In fact, even with a small
MFP = 1.3$\cdot$Diam (Diam is the maximal diameter of the simulation domain $R$), we realize good speedup when $q_s=0.9$, $q_v<1$.
Note that if either $q_s=1$ or $q_v=1$ (so no use of either SAI or
heuristic scattering adjustment), speedup almost
disappears.  This is slightly counter-intuitive but may be explained as follows:  Each method (SAI or heuristic) significantly increases the number of paths in two significant classes (surface-only and atmosphere-to-detector).  Therefore, variance from these path-classes is all but eliminated.  Supposing each of these path-classes accounts for $2/5$ of the total paths reaching the detector, by themselves they can only reduce variance by a factor of $1/(1-2/5)=5/3$.  However, together they can reduce variance by a factor of $1/(1-4/5)=5$.

As one can see, selection of the parameters $q_s$ and $q_v$ makes a significant difference in the resultant variance.  We provide some heuristics here and refer the reader to \cite{BalImportanceArxiv} for more details.  When $q_s\to0$ most of the photons will travel on the surface only.  The photons that take a route prescribed by the heuristic chain must then carry an additional weight $=1/q_s$ to compensate for this.  For this reason, picking $q_s$ too small results in increased variance.  A similar argument holds for $q_v$.  That the optimal $q_s$ is so close to $1$ (and greater than the optimal $q_v$) can also be explained by the fact that paths interacting exclusively with the surface are less likely to occur (in the analog world) than those interacting with the surface and atmosphere.

\section{Conclusion and Outlook}
\label{section:conclusion}

A novel method for Monte Carlo transport was presented that uses an approximation of the adjoint (ignoring atmospheric effects) to reduce variance in simulations, equivalently, accelerate convergence to a specified accuracy.  This algorithm, the Surface Adjoint Importance (SAI) method, may be combined with any unbiased method to significantly reduce variance coming from surface interactions when the overlaying atmosphere is optically thin.  If it is combined with a method that reduces variance coming from atmospheric interactions, significant overall variance reduction is achieved.  The implementation is relatively simple, requiring only an approximate adjoint transport solver for the boundary which adds virtually no overhead to the Monte Carlo computation time.

A possible application of this kind of accelerated Monte Carlo modeling in remote sensing is to address ``adjacency'' effects caused by highly variable terrain, including built environments (urban canyons).  The standard adjacency effect is observed when an aerosol layer of moderate optical thickness mixes in an imaging detector's pixel light that has been reflected off surface elements with contrasting albedos in neighboring pixels.  This is now a solved problem in the case of a variable-but-flat surface under a uniform atmosphere \cite{Lyapustin02}.  However, adjacency effects caused by non-flat terrain are only beginning to be explored, particularly in the thermal IR (where $Q(r,v)$ is determined by temperatures and emissivities).

On a broader scale, our work is an illustration of a modular approach to variance reduction whereby different interactions are handled separately and then pieced together in an unbiased manner.  Specifically, these different interactions could be pieced together as in Algorithm \ref{alg:regularized_sai}.

For instance one can envision a ``cloud'' module where radiation transport inside the cloud (dominated by multiple scattering) is treated off-line in some judicious approximation, and then incorporated into complex scene simulation.  In applications driven by surface property retrievals from remote sensing data, efficient modularized Monte Carlo modeling would open the door to advanced atmospheric compensation schemes with broken-cloud capability.  This is another wide open frontier recently explored in \cite{BartlettSchott2009}.

\section*{Acknowledgments}

This work was supported in part by DOE/NNSA Grant No. DE-FG52-08NA28779
and NSF Grants Nos. DMS-0804696 and PHY05-51164, as well as NSF Research Training Grant No. DMS-060DMS-0602235.  AD wishes to thank the Kavli Institute for Theoretical Physics at UC Santa Barbara for hospitality and stimulation while finishing this manuscript.

redpajama_set_name: RedPajamaArXiv


Jadon Sancho and Brahim Diaz have already left City for Borussia Dortmund and Real Madrid respectively after failing to break into Pep Guardiola's City squad, Riyad Mahrez's July 2018 arrival for a then club-record £60million pushing them down the pecking order.
"Before coming here I already knew a bit about Schalke: Mesut Ozil, Ivan Rakitic and Leroy Sane all took big steps in their careers here," said Matondo.
"As well as that, I had some good chats with the coach and my new team-mates only had good things to say. The Bundesliga is a great league too.
"Schalke is the right decision for my career and I'm happy to now be a part of this club and their future plans."
Schalke's 33-year-old coach Domenico Tedesco confirmed Matondo has been a target for some time.
"We have been interested in Rabbi for a long time, because we are impressed with his potential," he told Schalke's website.
"He is extremely quick and technically strong. We can't forget how young he is though.
"We will give him the time he needs to find his feet at Schalke and in the Bundesliga."


The Worthies Sports and Social Club is a friendly Members Club serving the Worthies in Winchester (Kings Worthy, Headbourne Worthy, Martyr Worthy and Abbots Worthy) and surrounding villages. Our premises offer a welcoming and comfortable environment for socaial activities. We have regular Saturday night entertainment making the Club a great meeting place for those who enjoy a relaxed and friendly atmosphere.
A well stocked bar with competitively priced drinks is available. The Club may also be able to help you with that special function by providing a venue and buffet facilities. We are open to enquiries and will be happy to give you a quote for the service you, or your organisation, may require.
If you have any questions, please feel free to contact us using the various methods available in our 'contacts' page. We will endeavour to provide a speedy and satisfactory response to all enquiries.


text:
Featured Stories South Africa
Limpopo Priest Fired for ANC Ties
By Oliver Ngwenya 06-Sep-2014 14:55 UTC+02:00
The URCSA church was not impressed that Timothy Xaba was Appointed ANC Chaplain. Image: Vgksa.org.za
A man of the cloth in Limpopo was reported to have lost his job as the priest of the local church because of his association with the ANC.
According to media reports, Reverend Timothy Xaba used to be the serving priest in the Uniting Reformed Church in Southern Africa (URCSA) until early July this year when he received communication from his employers advising him that his services were no longer required by the church organisation. Apparently, this started way back in 2013 when the former president of the republic, Nelson Mandela was still very ill in hospital. ThenANC approached several members of the clergy to organise their communities into prayer warriors for the then ailing former leader and statesman. Reverend Xaba did that with gusto and during the prayer sessions, he produced a moving prayer that had everyone in tears. He was subsequently appointed chaplain by the African National congress.
This would have signaled the beginning of a long and fruitful relationship with the ruling party as the revered member of the clergy was called upon to lead many ANC related religious functions in his new capacity. It appears that this did not please the powers that be in the URCSA, who quickly dispatched a letter to the priest which advised him that his contract had been terminated. In it, they informed him that it had been brought to their attention that the good priest had availed himself for functions that had to do with the ANC and that he had allowed himself to be appointed to the office of chaplain of the said party. This, they argue, meant that he was forfeiting his status as a minister of the "word" in the said church "with immediate effect". They also requested that he return his license to practise as a priest.
In response to questions put to him about the saga, Reverend Timothy Xaba could only state that he was not being paid for his role as the chaplain for the African Nationsl Congress.

redpajama_set_name: RedPajamaCommonCrawl


Northern Ireland dog trainers and behaviourists Robin Bates and Sandra Gilliland will be teaching a 10 week accredited 'Principles of Dog Training & Behaviour' course beginning Monday 24th September 2018.
Please email info@dog-training-ni.co.uk for more information and to register your place on the course.
Payment can be made in full through booking online here or we offer partial payment as detailed below.
£100 non refundable deposit to secure your spot and then remaining balance to be paid before course starts.


text:
A Tribute to Billie Holiday Featuring Karen Somerville July 20
July 12, 2019 by The Mainstay Leave a Comment
Karen Somerville
Join us at The Mainstay for day of nonstop music on a great sound system Saturday, July 13, 12 noon to 10pm. All tickets are $25 online or at the door.
A tribute to the quintessential voice of jazz, Billie Holiday, aka Lady Day, as celebrated by the Shore's own Lady K, Karen Somerville Saturday July 20 at 8pm. Tickets $20 online and $25 by phone reservation/at the door.Information and advance ticket sales are available on the Mainstay's website at www.mainstayrockhall.org
Ms. Somerville originated the show Just Call Me Billie in 2008 and since then the evening has taken on a life of its own. Somerville's vocal kinship with Holiday's timeless sound delights and pleases audiences everywhere garnering praise and rave reviews. The show depicts Billie's life story capturing her brilliance as well as the icon's true blues. It's an evening of passion comprised of a blend of anecdotes, poetry and songs composed by Holiday and those made popular by her renditions during the 1930 -1950s.
Join Somerville and her quartet in wearing black and white apparel to add a special sparkle as we delight to Billie's life of song in what would be her 104th year. Joe Holt on piano, Tom Anthony on bass, Seth Kibel on sax and Mike McShane on drums.
The Mainstay (Home of Musical Magic) is the friendly informal storefront performing arts center on Rock Hall's old time Main Street. It is a 501(c)(3), nonprofit dedicated to the arts, serving Rock Hall, MD and the surrounding region and is committed to presenting local, regional and national level talent, at a reasonable price, in an almost perfect acoustic setting. Information and advance ticket sales are available on the Mainstay's website http://www.mainstayrockhall.org.
Upcoming Mainstay performances include:
July 22 Joe Holt Welcomes Vaughan Bratcher and Dave Gladding
July 27 John Gorka returns to The Mainstay!
July 29 Joe Holt Welcomes Libby York
August 3 Bluegrass Supergroup Blue Highway!
August 5 Joe Holt welcomes Fred Hughes
August 9 Sue Matthews and the American Jazz Trio
August 12 Joe Holt welcomes Alex Lacquement
August 19 Joe Holt welcomes Pat Mercuri
Filed Under: Homepage Notes, Portal Notes
Vinyl Revival: The Mainstay Summer Fundraiser July 13
Join us at The Mainstay for day of nonstop music on a great sound system Saturday July 1312 noon to 10pm. All tickets are $25 online or at the door.Information and advance ticket sales are available on the Mainstay's website at www.mainstayrockhall.org
The Eastern Shore's best venue for live music is throwing the record party of the year! The Vinyl Revival is The Mainstay's summer fundraising event. We'll be spinning platters and raising money from noon until 10:00 p.m. As a special treat, the LPs will be played over an incredible sound system graciously provided by the Listening Room of Chestertown. The soundtrack of your life never sounded better! Bart's Records Chestertown will be on hand all day for those looking to buy that elusive, vintage vinyl LP.
Starting at noon, each hour of the 10-hour event will highlight a specific style of music. Come for the whole day or stop by or a few hours to hear your most beloved genres.
To keep the party going and, as part of your entrance fee, "Barbecue Sal" will be providing ribs and side dishes at two serving times- 2 and 6 p.m. The Byrd Room will be selling all your favorites beverages.
The schedule is as follows:
12:00 p.m. to 1:00 p.m. Bluegrass, NewGrass
1:00 p.m. to 2:00 p.m. Folk: Traditional, Celtic, Revival
2:00 p.m. to 3:00 p.m. Jazz: New Orleans, Dixieland
3:00 p.m. to 4:00 p.m. Classical: Symphonic, Chamber
4:00 p.m. to 5:00 p.m. Big Band Vocalists
5:00 p.m. to 6:00 p.m. Jazz: Latin
6:00 p.m. to 7:00 p.m. Blues: Traditional, Electric
7:00 p.m. to 8:00 p.m. Jazz: Bebop, Afro-Cuban
8:00 p.m. to 9:00 p.m. Jazz: Swing
9:00 p.m. to 10:00 p.m. Anything Goes
Do you have a favorite cut that belongs to one of these categories? Would you like to hear it played on the best sound system around? Bring your vinyl LP along and, for a mere $20 donation, you can share its magic with the crowd! This extra is offered first come, first served.
July 15 Joe Holt Welcomes Paul Midiri
July 20 "Just Call Me Billie" Featuring Karen Somerville
Tonight — June 24 — Peter Heck Joins Joe Holt for Mainstay Monday
June 24, 2019 by The Mainstay Leave a Comment
Peter Heck — guitar
Join us for another Mainstay Monday! These eclectic evenings happen every Monday night and are hosted by our own Joe Holt at the piano, partnering with a special guest. Each week is a unique, one of a kind show. Seating is casual and tables are available (bring your own dinner, if you like), along with a cash bar. Doors open at 6:30 p.m. with the show starting at 7:00. This 4th year of Mainstay Mondays is funded in part by Delmarva Power, an Exelon Company.
Our featured guest tonight, June 24, is Peter Heck. Peter is often seen on stage at the Garfield Center open mic, among, other area performance spaces. He was, for many years, a member of Col. Leonard's Irregulars, featuring our own Owen McCoy as lead vocalist. The band performed a wide range of styles including blues, folk, bluegrass, Irish music, and standards. Pete will revisit this varied repertoire, along with some of his own favorites, in a duo performance with Joe, dedicated to the memory of Owen McCoy.
Doors open at 6:30 p.m. The music fun starts at 7:00 pm. Admission $12 at the door.
Filed Under: Archives, Arts, Homepage Highlights, Peformance, Portal Highlights
The Mainstay at the Garfield Presents: Haint Blue in Concert
June 4, 2019 by The Mainstay Leave a Comment
This Friday, June 7th, Haint Blue is coming to the Garfield Center for the Arts from their native Baltimore. The Garfield has once again joined forces with Rock Hall's home for live music, The Mainstay, to bring this group to Chestertown for a night of Baltimore folk and Americana.
"There's folk music, and then there's Haint Blue. The local sextet's bold take on the Americana genre lands somewhere in the eye of the storm—between calm and chaos—a lilting chamber orchestra meets a holy roller gospel choir…. In the three years since the band's debut EP, their chemistry has coalesced into a crescendo of emotion and talent. You feel their rich harmonies, of voice and instrument, in your bones." -Baltimore Magazine
"Beyond the well-written folk tunes and catchy songs, there is something deeper and more complicated behind the inspirations for the band. Their vocal harmonies are seamless and the energy they bring to live performances cannot be denied. They transition well from entertaining a packed venue to filming in a small studio with ease; they have a familiar rapport with each other that is engaging and inviting. But driving these songs are deeply personal stories that carry a certain sadness. The lyrics tell stories of struggles with faith, family, addiction, and the achievement of moving forward… This multifaceted structure to their music makes Haint Blue not just a successful folk band but a welcome addition to the scene as a whole." -BMOREhush
"The seven-strong group artfully amalgamates poppy beats with Americana roots and instruments, producing a sound akin to Shovels & Rope or Avett Brothers, but still apart in its context and tonal shifts. Haint Blue has layers of pain and living in its lyrics, wrapped carefully in cheery beats and twangy harmonics." -Jonathan Goodwin, Deli Magazine
Co-sponsored by The Mainstay and The Garfield Center for the Arts, the concert on June 7th is at 7pm. Tickets are $15 and can be purchased online at www.garfieldcenter.org, over the phone by calling 410-810-2060, or in person at the Garfield Center box office. The theatre is located at 210 High Street in Chestertown.
Phil Wiggins and House Party at The Mainstay March 30
March 22, 2019 by The Mainstay Leave a Comment
Renowned blues harmonica player Phil Wiggins brings his amazing House Party show to The Mainstay. Admission is $22 online or $26 by phone reservation/at the door. Information and advance ticket sales are available at the Mainstay's website http://www.mainstayrockhall.org and reservations can also be made by calling 410-639-9133.
Washington, D.C. native Phil Wiggins, a Takoma Park, Maryland, resident, blues musician, teacher and artistic director, a two time winner of the prestigious WC Handy Blues Foundation awards, is only the third harmonica player to receive the lifetime honor of an NEA National Heritage Fellowship. Today he is the only living player of the instrument to hold the prestigious honor of being a "Master of Traditional Arts." Often referred to by its unofficial designation as "Living Cultural Treasure" award, the fellowship honors and preserves the diverse cultural heritage in the United States.
Phil Wiggins is a versatile traditional harmonica player, continuing the Piedmont blues tradition, a gentle and melodic blues style of the mid-Atlantic region. He plays the diatonic ten-hole harmonica in the country blues style, cupping both hands around the instrument and playing acoustically. His sound is not shaped by the gear, the microphone or amplifier when performing on stage, instead by his complex syncopated patterns, breath-control and rhythm, stylistic virtuosity and fiery solo runs.
Phil and partner John Cephas performed together for 32 years as internationally renowned stars of the country blues, and a staple on blues radio, ever present on the concert and festival. Cephas & Wiggins played Carnegie Hall, Royal Prince Albert Hall in London and the Sydney Opera House, as well as small venues worldwide, touring every continent except Antarctica. They recorded more than a dozen critically acclaimed albums, including on Flying Fish and Alligator Records. They even performed at the White House with B.B. King. Phil Wiggins has have been featured in major music magazines, including on the cover of Living Blues, and the Washington Post, the New York Times, the Chicago Tribune and many more.
Since the 2009 death of John Cephas, Phil has performed with numerous musicians including Nat Reese, Corey Harris, Australian guitarist Dom Turner, Ben Hunter and Joe Seamons, Sherman Holmes, the Rev. John Wilkins, Jerron Paxton, and longtime friends Eleanor Ellis and Rick Franklin. He fronts the acoustic swing/roots/blues ensemble, the Chesapeake Sheiks, and is actively engaged in reuniting the Piedmont blues with its origins of African American buck and tap dancing.
The House Party is an acoustic blues ensemble that reunites the dance tradition with the Piedmont and other country blues styles. Phil Wiggins is joined by the D.C. based Piedmont picker and longtime friend, guitar player Rick Franklin and Marcus Moore, a fiery jazz violinist steeped in the black string band tradition. They joined forces with urban dancer, Junious Lee Brickhouse, who understands the African American cultural reconnection of the act of dance with the dance music that is the blues.
April 1 Joe Holt welcomes Clark Bjorke and Johnson Fortenbaugh
April 6 Banda Magda
April 8 Joe welcomes Steve Giordano
April 14 The Hedgelawn Series presents Taylor Hillary Boykins
April 15 Joe Holt Welcomes Sue Matthews
April 20 Mainstay Scholarship Winner: The Zack Lambert Quartet
April 22 Joe Holt Welcomes Lester Barrett
April 27 The Mainstay Folk Series: Lula Wiles
April 29 Joe Holt Welcomes Paul Midiri
May 4 Keyed Up: Dick Durham and Stef Scaggiarri
Saxophonist Tae Ho Hwang at The Mainstay March 17
March 6, 2019 by The Mainstay Leave a Comment
The Hedgelawn Classical Series presents saxophonist Tae Ho Hwang at The Mainstay Sunday March 17 at 4:00 pm. Admission is $15 or by phone reservation/at the door.Information and advance ticket sales are available at the Mainstay's website http://www.mainstayrockhall.org and reservations can also be made by calling 410-639-9133.
The Hedgelawn Classical Series presents some of the most exciting young musicians at the Peabody Conservatory in a friendly interactive setting. The month we host saxophonist Tae Ho Hwang.
A passionate performer and educator, Tae is dedicated to advancing the saxophone repertoire by exposing new works to audiences and inspiring future generations. His remarkable technical capabilities combined with his inventively beautiful interpretation generate innovative performances and special experiences for the audience. An advocate of expanding the saxophone repertoire, Tae Ho Hwang commissions and performs music of living composers. Tae plans programs that integrate works of contemporary composers with masterworks of established composers. Actively collaborating with composers, Tae is developing concerts that spotlight the saxophone with new and significant works. Tae has performed the works of world-renowned composers such as William Albright, Luciano Berio, Edison Denisov, Michael Hersch, and Lori Laitman.
For one so young, Tae Ho Hwang has a deep background of performing experience. In 2015, Tae won the annual Concerto Competition at the University of Delaware and performed Alexander Glazunov's Concerto for Saxophone and Orchestra with the University's Symphony Orchestra. In recital, he has performed throughout the Mid-Atlantic area, in Philadelphia, Baltimore, and Annapolis since 2014. Presently, he is exposing diverse audiences to his music as he performs in coffee shops, art galleries, museums, and prominent concert series throughout the Mid-Atlantic. In addition, Tae has participated in master classes presented by distinguished saxophonists Claude Delangle, Timothy McAllister, Joseph Lulloff, Timothy Roberts, Ray Ricker, as well as saxophone quartets Musato Kumoi Quartet, Donald Sinta Quartet, and New Thread Quartet.
An advocate of education, Tae has been teaching music to students of different ages and backgrounds for some time. Tae earned a degree in Music Education from the University of Delaware in 2016. Tae has been teaching privately since 2012 and is currently in programs throughout Maryland.
Mr. Hwang recently earned a Master's Degree in Saxophone Performance and Pedagogy at the Peabody Conservatory of The Johns Hopkins University, where he studied with renowned saxophonist, Gary Louie.
March 18 Joe Holt Welcomes John Schratwieser
March 23 The Mainstay Tribute to Charlie Byrd featuring Chuck Redd
March 25 Joe Holt welcomes Dick Durham
March 30 Phil Wiggins and House Party
Juanito Pascual New Trio at The Mainstay October 20
October 13, 2018 by The Mainstay Leave a Comment
Flamenco guitar virtuoso Juanito Pascual brings his trio to The Mainstay on Thursday, October 18 at 8pm. Tickets are $22 in advance and at $25 by phone and at the door.
Lovers of great guitar can look forward to the Juanito Pascual New Flamenco Trio. For the first time ever, they'll appear at The Mainstay in Rock Hall, Maryland on Saturday, October 20. The Trio's sound is a truly masterful and organic blend of traditional and contemporary flamenco plus influences ranging from Jimi Hendrix and the Grateful Dead to Miles Davis and J.S. Bach, performed with virtuosity and passion.
A versatile guitarist and composer, Juanito Pascual has been called "one of the hottest flamenco guitarists in recent years" by National Public Radio, and "The Rye Cooder of Flamenco guitar" by music journalist Steve Morse.
Pascual's program is likely to include such tunes as "While My Guitar Gently Weeps" by George Harrison, "Afro Blue" by Mongo Santamaria, "Entre dos Aguas" by Paco de Lucia, and "All Blues" by Miles Davis, along with traditional and original compositions.
The Juanito Pascual Trio features two equally versatile and dynamic musicians, New York-based percussionist Guillermo Barrón (Jose Feliciano Band, John Benitez) and stunning bassist Brad Barrett (Jason Moran, Ran Blake). By combining their distinct musical backgrounds with a powerful personal chemistry, they have created a fresh, exhilarating, and constantly evolving sound, performing to enthralled audiences throughout the U.S. and abroad.
A Minnesota native, guitarist Pascual has logged countless miles as his career has taken him from the streets of Madrid to the hallowed halls of the New England Conservatory and concert stages around the world. Numerous appearances on radio, television and film have further widened his audience. He made a cameo performance with Steve Martin and Andy Garcia in the 2009 film Pink Panther 2 and performs much of the music in a film, TV and Netflix series about the life of Pope Francis.
Since the 2003 release of his debut solo recording Cosasen Comun, Pascual's international touring schedule has brought him to venues including the Tanglewood Jazz Festival, New York's Lincoln Center, and Blue Note Jazz Club, The Panama Jazz Festival, and Madrid's renowned Casa Patas. He has performed with top flamenco artists including a 2016 tour with Jorge Pardo of the legendary Paco de Lucia Sextet. Numerous collaborations include work with Grammy-winning soprano Dawn Upshaw, bassist John Patitucci, pianist Danilo Perez, percussionist Jamey Haddad and virtuoso guitarist Grisha Goryachev.
As a youth, Juanito Pascual studied with flamenco masters in Spain. He later earned a Bachelor of Music degree in contemporary improvisation from the New England Conservatory, where he directed the summer flamenco institute for five years. His book The Total Flamenco Handbook (with accompanying CD) was published by Alfred Press in 2011. He released Language of the Heart in 2009 and a self-titled album in 2014. A fourth recording is in the works.
October 22 – Joe Holt Welcomes Barbara Ferris
October 27 – Mainstay at The Garfield with the Eastport Oyster Boys
October 28 – Old Bay Brass Quintet
October 29 – Joe Holt Welcomes Jodie Littleton and Pres Harding
November 3 – Sue Matthews
November 9 – The Joey Calderazzo Trio
November 16 – Frank Vignola Returns to the Mainstay
November 24 – Karen Somerville
Decmber 1 – An Evening of Stories and Music with Tom Anthony
Low Lily at The Mainstay October 18
Americana folk trio Low Lily returns to The Mainstay on Thursday, October 18 at 8pm. Tickets are $15 in advance and at $18 by phone and at the door.
Start with excellently matched vocals, add some world-class playing, sprinkle with raised-off-grid Americana and you get Low Lily. Flynn's deft flatpicking on guitar and mandolin and Lissa's virtuosic fiddle-playing are grounded by Liz's percussive rhythm guitar playing, the sounds of which combine joyously in this stunning ensemble.
With a vocal blend that has been dubbed "outstanding" and "meticulous," Low Lily's cohesive sound comes naturally for musicians whose lives have been entwined on the road and onstage for almost two decades. Setting down roots in Brattleboro, Vermont, the band has crafted a signature sound which they have shared with enthusiastic audiences throughout North America and the UK, garnering two #1 songs on international folk radio and two New England Music Award nominations.
Chosen as Falcon Ridge Folk Festival's "Most Wanted Band" of 2016, Low Lily plays acoustic music that is deeply rooted in tradition yet sounds refreshingly contemporary. With their first full-album release, "10,000 Days Like These" (March 2018, following their 2015 self-titled EP release), Low Lily shares an intimate, no-tricks-involved, collection of songs that showcases their talents and proves them to be a formidable, ready-for-prime-time act. A first album this strong doesn't come from newbies–all the members have performed with numerous well-known names in folk and traditional music. Flynn has toured with Ruth Moody, John Whelan, Cathie Ryan and Aoife Clancy. Liz has toured with Tom Chapin, Livingston Taylor, Melanie, and Long Time Courting. Lissa has toured as a solo act as well as with Solas and Childsplay. The Mainstay (Home of Musical Magic) is the friendly informal storefront performing arts center on Rock Hall's old time Main Street. It is a 501(c)(3), nonprofit dedicated to the arts, serving Rock Hall, MD and the surrounding region and is committed to presenting local, regional and national level talent, at a reasonable price, in an almost perfect acoustic setting. Information and advance ticket sales are available on the Mainstay's website http://www.mainstayrockhall.org.
Megg Farrell and Friends at The Mainstay October 13
October 3, 2018 by The Mainstay Leave a Comment
Alt-country and Americana vocalist and songwriter Megg Farrell brings hers band, Megg Farrell and Friends to The Mainstay on Saturday, October 13 at 8pm. Tickets are $15 in advance and at the door.
Join us on the main stage at The Mainstay after Fall Fest as we welcome Megg Farrell and Friends. While previously known Mainstay audiences as a purveyor of quality classic jazz, this time Megg returns with her take on classic country and her own new country/Americana compositions.
Megg Farrell is quickly establishing herself as a voice to be heard in the Americana music scene. After paying her dues in the highly competitive New York City jazz world, she has cultivated a vocal style that is both moving and masterfully proficient. Taking cues from Emmylou Harris and The Hot Band, she has put together a group of musicians whose technical prowess is sure to excite any audience, without resorting to cheap tricks and flashy pyrotechnics. Equally impressive as the musicians she surrounds herself with, Farrell's original compositions truly shine. Her songwriting has been described as "the essence of folk story telling and organic musicianship."
October 15 Joe Holt Welcomes Vince Lardear
October 18 Low Lily
October 20 Juanito Pasucal Trio
October 22 Joe Holt Welcomes Barbara Ferris
October 27 Mainstay at The Garfield with the Eastport Oyster Boys
October 29 Joe Holt Welcomes Jodie Littleton and Pres Harding
November 3 Sue Matthews
November 9 The Joey Calderazzo Trio
November 16 Frank Vignola Returns to the Mainstay
November 24 Karen Somerville


text:
package org.gradle.api.internal.plugins;

import groovy.lang.MissingPropertyException;
import org.gradle.api.internal.BeanDynamicObject;
import org.gradle.api.plugins.ExtraPropertiesExtension;

import java.util.Map;

public class ExtraPropertiesDynamicObjectAdapter extends BeanDynamicObject {
    private final ExtraPropertiesExtension extension;
    private final Class<?> delegateType;

    public ExtraPropertiesDynamicObjectAdapter(Class<?> delegateType, ExtraPropertiesExtension extension) {
        super(extension);
        this.delegateType = delegateType;
        this.extension = extension;
    }

    public boolean hasProperty(String name) {
        return super.hasProperty(name) || extension.has(name);
    }

    public Map<String, ?> getProperties() {
        return extension.getProperties();
    }

    @Override
    public void setProperty(String name, Object value) throws MissingPropertyException {
        if (!hasProperty(name)) {
            throw new MissingPropertyException(name, delegateType);
        }

        super.setProperty(name, value);
    }
}

redpajama_set_name: RedPajamaGithub


Improving the effectiveness of Filipino science teachers - FlipScience - Top Philippine science news and features for the inquisitive Filipino.
Not all scientists started their quest for knowledge looking like Albert Einstein. They weren't wearing lab coats, spewing theorems and equations, or wielding flasks and beakers when they started.
Most of them were just precocious little boys and girls with an insatiable thirst for knowledge about the natural world and how it works. How and why does it rain? What pollutes water? How do we catch diseases? What's on the moon? They wondered a lot and asked questions which, when answered, prompted even more questions.
The magnanimous task of nurturing young minds and guiding them on the systematic process of discovery falls on the shoulders of science teachers.
In other words, if you happen to like or disdain science, chances are your elementary teacher greatly influenced how you regard it now.
After all, textbooks merely contain the facts. It's the teachers who link up these facts and transform them into something exciting and useful. They do this for students to gain a better understanding of the natural world, anchored with observable physical evidence.
Unfortunately, for professionals in the Philippines, the noble goal of empowering the youth may not be enough to persuade them to teach science here.
According to the Department of Education (DepEd), the country still needs "a huge army of teachers." Hiring Science and Math teachers is particularly challenging, according to Education Secretary Leonor Magtolis Briones.
In a bid to address this, the DepEd has allotted PhP15.5 billion for the hiring of 53,831 teachers out of its PhP567.56 billion total proposed budget this year. Support comes in the form of the PhP65.4 billion earmarked for the construction of 47,492 classrooms (including 10,000 classrooms for replacement); PhP43.9 billion for the construction of 17,562 laboratories; PhP7.3 billion for 7,260 TechVoc tools and equipment packages; PhP6.9 billion for 30,697 ICT packages ; PhP4.5 billion for 8,833 Science and Math equipment packages; PhP4 billion for hiring 13,266 non-teaching items; PhP3 billion for 55.8 million learning materials; and PhP2.5 billion for 51,492 school seat sets as additional basic resources in support of the K to 12 curriculum.
Above entry-level salary grades await graduates of Science and Technology courses under the Junior Level Science Scholarships (JLSS) of the Department of Science and Technology-Science Education Institute (DOST-SEI). As mandated by the Implementing Rules and Regulations of Republic Act 10612, s. 2014, qualified graduates are to be hired as Special Science Teachers with salary grade level 13. Scholar-graduates may also take part in a teacher training program that will qualify them to take the Licensure Examination for Teachers (LET).
DepEd also encourages graduates of Science, Math, or Engineering courses without LET certification, graduates of technical-vocational courses with TESDA certifications, and practitioners with expertise in specialized learning areas laid out in the K to 12 program to apply as part-time senior high school (SHS) teachers.
There's a sliver of hope, though, as long as there are teachers like Sandra Nequito and Maria Elena Pinlac, who had long ago answered the DepEd's call of duty for the simple joy and passion for teaching.
For more than 25 years, Teacher Sandra has been teaching Science to Grades 5 and 6 students at Santa Cruz Elementary School in Laguna, after obtaining her Bachelor of Elementary Education (BEED) and an MA in teaching Science.
She says "determination and dedication" drives her to continue teaching Science despite more lucrative opportunities. She also values excellence and continuous improvement in everything she does, citing constant observation audits and checks by school administrators which she actually welcomes.
Echoing the DepEd's earlier call for expert practitioners to teach, she explained that at PSHS, college graduates can teach as long as their course is related to the subject matter. PSHS teachers are also encouraged to take graduate studies and education units.
To become an effective science teacher, Teacher Elena emphasizes the following.
In 2011, the DOST-SEI and the University of the Philippines National Institute for Science and Mathematics Education Development (UP NISMED) published a "Framework for Philippine Science Teacher Education." This prescribing the following qualities of effective science teachers (Chapter 3): professional knowledge, professional practice, and professional attributes.
In Teacher Elena's case, a Science teacher's impact rests on these simple things — knowledge, creativity, and grit. Teaching is easy, said no one ever. Making sense of scientific facts to transform them into something useful and relevant to everyday life, and pushing on despite limitations, make teaching a noble profession.
"Kung minsan, mahirap makuha ang interes ng mga estudyante, lalo na't sanay sila sa constant sensory input na dulot ng teknolohiya. Isa ring hamon ay ang maturuan ang mga kabataan ng critical thinking, lalo na ngayong laganap ang fake news. Marami ring issue, katulad ng climate change, na kailangang gumawa ng informed and educated decisions ang mga tao.


text:
package com.alibaba.nacos.core.distributed.distro.component;

import org.springframework.stereotype.Component;

import java.util.HashMap;
import java.util.Map;
import java.util.Set;

/**
 * Distro component holder.
 *
 * @author xiweng.yy
 */
@Component
public class DistroComponentHolder {

    private final Map<String, DistroTransportAgent> transportAgentMap = new HashMap<>();

    private final Map<String, DistroDataStorage> dataStorageMap = new HashMap<>();

    private final Map<String, DistroFailedTaskHandler> failedTaskHandlerMap = new HashMap<>();

    private final Map<String, DistroDataProcessor> dataProcessorMap = new HashMap<>();

    public DistroTransportAgent findTransportAgent(String type) {
        return transportAgentMap.get(type);
    }

    public void registerTransportAgent(String type, DistroTransportAgent transportAgent) {
        transportAgentMap.put(type, transportAgent);
    }

    public DistroDataStorage findDataStorage(String type) {
        return dataStorageMap.get(type);
    }

    public void registerDataStorage(String type, DistroDataStorage dataStorage) {
        dataStorageMap.put(type, dataStorage);
    }

    public Set<String> getDataStorageTypes() {
        return dataStorageMap.keySet();
    }

    public DistroFailedTaskHandler findFailedTaskHandler(String type) {
        return failedTaskHandlerMap.get(type);
    }

    public void registerFailedTaskHandler(String type, DistroFailedTaskHandler failedTaskHandler) {
        failedTaskHandlerMap.put(type, failedTaskHandler);
    }

    public void registerDataProcessor(DistroDataProcessor dataProcessor) {
        dataProcessorMap.putIfAbsent(dataProcessor.processType(), dataProcessor);
    }

    public DistroDataProcessor findDataProcessor(String processType) {
        return dataProcessorMap.get(processType);
    }
}


Ebbsfleet United director Jessica McQueen says that playing staff are unlikely to be sold to cut costs at the Blue Square Bet Premier club.
However, Fleet have admitted that a sum of £50,000 must be generated before the end of the current campaign, and have appealed for investment.
"We're looking at every way we can to save money," McQueen told BBC Kent.
"The last thing we want to do is look at the team, which everyone thinks is the instant quick fix," she added.
"We're up to date with National Insurance, PAYE and VAT, so we are not in a dreadful position.
"But, as soon as the quality of football goes down, so do the gates."
On the pitch, Liam Daish's side, 16th in the Blue Square Bet Premier, have the 17th lowest average attendance in the division following the Boxing Day round of fixtures.
"Our gates are down, mainly because of the amount of home matches that have been scheduled for a Tuesday evening," said McQueen.
"Our advertising and promotions are also below the line we had hoped for and I can tell you it is not for the want of trying.
"Solutions need to be found to provide £50,000 between now and the end of the season. It's going to be a tall order."
Fleet are owned by members of a website called MyFootballClub, in which fans have bought shares to raise funds.


One fully feathered wing or head must be attached to the bird while in transit to Rocky Mountain Meats.
It is illegal to leave migratory birds anywhere other than your home or with someone picking, cleaning, processing or for taxidermy unless the birds or package of birds have a tag attached.
The required tag must include the hunter's address, total number and species of birds, date of kill, hunter's hunting license number and hunter's signature.


text:
The Vicar is a persona and multimedia project created by record producer, songwriter and Internet entrepreneur David Singleton. Since 2001, the project has produced music (singles and albums), a public diary, fictional stories (in blog, videoblog, print paperback and graphic novel form) and several culture-jamming initiatives.

The Vicar's identity remained secret until 2013. That year, Singleton revealed himself on the occasion of the release of the first Vicar album Songbook#1. Singleton has summarised the project ethos as being "that music and music alone should take centre stage without the current obsession with personality and celebrity, nor with the damaging thieving hand of the mainstream music business."

Concept
The core of the project is a semi-fictional/pseudonymous record producer referred to only as "The Vicar" (although over the course of the stories, his first name is occasionally revealed as "David"). In the Chronicles, novels and video blogs (presented as "surreal tales from the underbelly of the music industry") the Vicar is portrayed as a British eccentric who, in parallel to his production career, works as an industry troubleshooter and sleuth (aided and abetted by his rascally and long-suffering assistant Punk Sanderson). Although he is generally hired to solve the problems of senior industry executives the Vicar clearly has little respect for them, preferring to express a sardonic sympathy for exploited musicians and artists. On record, the Vicar's trademark sound is created by Singleton's own songwriting, production and arrangement talents, with guest appearances from some of the world's most outstanding musicians.

There is a clear overlap between the Vicar's fictional ethos and the actual campaigning ethos of Discipline Global Mobile (the record label run by Singleton in collaboration with Robert Fripp), and the character has been used as a method for protesting against corrupt practices within the recording business. Consequently, the Vicar has been described as being "a campaigner for artist rights and scourge of the evil empire of the record industry, both fictionally (in the stories) and in reality" while the stories have been described as "Sherlock Holmes meets Spinal Tap."

In an interview with the Salisbury Journal in 2013, Singleton commented on the multimedia nature of the project and its possible future expansion, explaining "in the past, a young writer would probably have just written a book – but nowadays people follow stories in all sorts of different ways, so the Vicar Chronicles have been released as physical books, ebooks, graphic novels, audiobooks and you can even see Punk Sanderson performing the whole book on YouTube... It's the first time to my knowledge that the same team have produced all the multimedia aspects of a project of this kind right from conception. We are also currently working on both a film script and a TV series."

History

1999–2003 (origins, "The Vicar's Diary", early production credits, speculations)
The concept for "The Vicar" emerged in 1999 out of a conversation between David Singleton and Robert Fripp (Singleton's creative and business partner in both the Discipline Global Mobile record label and the Ton Prob production team). When Singleton raised the question "why has no-one written whodunnits about the music industry?" Fripp replied, "because you haven't written them yet." This inspired Singleton to begin writing satirical mystery stories twisting true events into semi-fictional myths. Chief among the characters were the titular Vicar (an eccentric pseudonymous record producer and accidental sleuth) and his rascally assistant Punk Sanderson (ostensibly the narrator of the stories).

Both Singleton and Fripp disliked the cult of personality that was apparently inherent to rock music, and which was expressed in the behaviour and personas of performers, producers, executives and commentators alike. As a reaction to this, the Vicar persona was created as a virtual artist; a "man who isn't there."

From 8 January 2001, Singleton established a diary for the Vicar on the Discipline Global Mobile website, further developing the character. Diary notes generally represented Singleton's own working life and reflections, slightly fictionalised and with some identities and situations altered. Some aspects of the Vicar's personality were also drawn from Fripp's personal, philosophical and linguistic mannerisms.

From 2001 onwards, the Vicar was also given selected engineering and production credits on assorted Fripp or King Crimson recordings, beginning with the King Crimson live album Vrooom Vrooom. Regular diary readers began to enjoy speculating as to the Vicar's real identity. Suggested candidates included Fripp, Brian Eno, Bill Nelson, Peter Hammill, Anthony Phillips, Andy Partridge, Peter Gabriel, Sting, George Martin and Singleton himself. Various musicians wilfully added themselves to the "history" of the fictional Vicar, with Partridge's comment "since working with the Vicar, I can never feel the same about alpacas" or Nick Cave's "The Vicar? Half Buddha, half backstreet ****" being amongst the more memorable.

2003–2005 (first Vicar novel, School Aid single)
On 23 September 2003, the first Vicar novel Chronicle The First – The Mysterious Case of Billy's G String began to appear online on the Vicar's diary as a series of successive posts. The novel was an adventure ostensibly written and narrated by Punk Sanderson in which Punk and the Vicar attempted to track down the person or people involved in sabotaging the career of pop star Billy G. The stories, combining comedy and music have been described by The Cult Den as "the Airplane! of the music world" and "Monty Python's life of Punk", with the magazine also advising readers to "open your mind and enter into the irreverence of it all." Aficionados can again see Singleton mythologising true events – in this case the 1990s financial debacle at Lloyd's of London (which had engulfed Fripp's former managers at E.G. Records and which had led to the establishment and ethical policies of Discipline Global Mobile). The Mysterious Case of Billy's G String was followed by a second Chronicle, The Absurd Nonsense of The Orange Eyebrow, detailing further misadventures for Punk and the Vicar at the MIDEM music conference in the south of France (another merging of myth and reality).

On 29 November 2005, the Vicar produced and released a fundraising community single called "Where's the Money, Mr Blair?", performed by School Aid (various people from Singleton's hometown of Broad Chalke, including Robert Fripp). The single was intended to raise renovation money for Broad Chalke Primary School (attended by Singleton's children) and to embarrass the British government over their apparent reluctance to provide proper funding for dilapidated schools. The single was released nationally on both CD and download. Singleton identified himself as the songwriter (and was interviewed and named as producer of the single in the British national press) but did not, at that point, formally admit to being the Vicar.

2007–2012 (into multimedia – videoblogs, debut Vicar single, Facebook campaign, print novel)

In keeping with Singleton's ideas about "a single coherent multimedia future", the Vicar project now began to expand into other areas. On 30 April 2007 the first of a set of Vicar videoblogs was uploaded to YouTube, in which Punk Sanderson (appearing for the first time on camera) presented and narrated the first chapter of The Mysterious Case of Billy's G String. Further chapters followed at a regular rate, with thirty-six videoblogs shot in different locations telling the story of Chronicle the First (later included as a DVD extra with Songbook #1). The videoblogs were highly praised by Comic Spectrum which described them as "phenomenal" and advised "if you have any interest in music, comedy, or just plain great entertainment, click on the video and enjoy!"

On 18 November 2010, the debut Vicar single – "Count Your Blessings", sung by Andy Yorke of Unbelievable Truth – was released via iTunes.

On 6 September 2010, the Vicar project expanded to Facebook, setting up the "Free Punk Sanderson Campaign" and announcing that Punk Sanderson had been locked in there by the Vicar. The campaign backstory involved Punk being forced to stay within Facebook until he had "10,000 followers", at which point he would be set free and would be able to start broadcasting the second set of Vicar Chronicles videoblogs. A campaign video was released in which Punk attempted to force his way out of Facebook, followed by a series of teaser trailers for the new Chronicles. In the event, the second set of Chronicles videoblogs would not be broadcast for another two-and-a-half years.

In October 2012, The Mysterious Case of Billy's G String was compiled and released in two print versions, with authorship credited to Punk Sanderson. The first of these was a graphic novel released in October 2012 (and illustrated by Singleton's son Ben Singleton), which gained favourable reviews in the comics media. On 20 November 2012 The Mysterious Case of Billy's G String was published as a print novel.

2013 (Fart For Your Rights, debut Vicar album, more videoblogs)
On 13 January 2013, the Vicar launched the "Fart For Your Rights" campaign, a culture-jamming event and mock dirty protest aimed at Universal Music Group, who were at the time selling King Crimson's music without proper legal agreements or due remuneration). Via a series of video-recorded protests outside the Kensington headquarters of UMG (involving displayed-and-dropped cue-cards in the manner of Dont Look Back, plus flatulence and other pranks) Punk drew attention to this side of UMG's business practices.

On 26 February 2013, Discipline Global Mobile released the debut album by The Vicar, Songbook #1. Featuring a full set of fourteen songs written entirely by Singleton, the album featured multiple guest musicians including King Crimson members (Fripp, Tony Levin, Jakko Jakszyk) and associates (Theo Travis, Cathy Stevens of Europa String Choir, Chas Dickie, Tony Geballe, Geoff Nichols and Alex Mundy). The songs were sung by Andy Yorke, David Scott (of Pearlfishers), Lewis Taylor, Tim Elsenburg (of Sweet Billy Pilgrim), Mutch Katsonga (of The Indie Soul Movement), Steve Porter and Paul Ibberson. The formal launch was followed by a launch event at the Dolby Studios in London on 30 April 2013.

The album received good reviews, many of them focussing on Singleton's detailed chamber-music arrangements. Ludovic Hunter-Tilney of the Financial Times hailed Songbook #1 as "a highly engaging exercise in psychedelic chamber pop" while in Classic Rock Hugh Fielder described it as "continuing where 'Eleanor Rigby' left off... once you're past the novelty aspect, the album becomes compelling." Mediaversal described Songbook #1 as "one of the most intriguing and innovative records of our time. A throwback to the psychedelic sixties with an air of Beatles, King Crimson, and an edge of Philip Glass, the album traverses many musical styles while staying the course on its unique sound.... an engaging listen that will surely keep you coming back for more." and drew attention to its "truly spectacular" surround sound mix. Altrockchick.com described the record as "the most paradoxical and amazing album I have heard in years... a brilliant, courageous, convention-defying contribution to the art" and praised its avoidance of a standard rhythm section approach (as well as labelling the album as a whole as having "everything to do with talent, everything to do with musicianship and everything to do with artistic integrity."

The album was particularly well received by the Italian music press. DFB Musica suggested that the album was "an exquisite collection of songs in the Scott Walker tradition" (as well as citing Colin Blunstone as another comparison), while and JAM magazine suggested that the Vicar "recalls the elegance of the Penguin Café Orchestra in a work that could not be more English. Sometimes melancholy and dreamy, sometimes fast and light, but always substantial. Delicious." Rockerilla awarded Songbook #1 "Album of the Month" and hailed its "definitive pop arrangements with the harmonic and melodic genius of George Martin and Phil Spector. An incredible acoustic light orchestra."

Meanwhile, once Punk Sanderson had obtained the requisite number of Facebook followers, the second set of Vicar videoblogs (in which he presented and narrated "The Absurd Nonsense of The Orange Eyebrow") began to be broadcast on 23 March 2013.

2014–present (compiled novel, Drummer Jokes app, further initiatives)
In February 2014, both The Mysterious Case of Billy's G String and The Absurd Nonsense of The Orange Eyebrow were compiled into a single print novel, The Vicar Chronicles: Chronicle The First + 2nd.

On 20 August 2014, the Vicar website was revamped and relaunched. On 5 December 2014, the Vicar took on another aspect of multimedia with the release of a smartphone mobile app, The Vicar's Drummer Jokes and Celebrity Musician Guessing Game, developed by Flat Earth Studio LLC. It was later claimed that this was, in part, a humorous riposte to comments regarding the lack of drums (and drummers) within Songbook #1.

During this period, Singleton began work on the second Vicar album, Songbook #2, which will again feature guest singers. In 2015, the Vicar launched two further initiatives. "Be the Singer"/"V Factor" invited members of the public to record vocals to existing Vicar backing tracks, with the best performers to be invited to record material for Songbook #2. A simultaneous Instagram campaign, "#IamTheVicar", invited fans to photograph themselves obscuring their faces (a Vicar visual trademark) to appear on the cover of future Vicar releases. Both initiatives were intended to reinforce the underlying Vicar ethos of pure music made without a celebrity component.

Works

Ebooks, print novels
 The Vicar Chronicles: Chronicle the First – The Mysterious Case of Billy's Missing G-String (ebook, videoblog – text credited to Punk Sanderson)
 The Vicar Chronicles: Chronicle the Second – The Absurd Nonsense of The Orange Eyebrow (ebook – text credited to Punk Sanderson)
 The Vicar Chronicles: Chronicle the First & Second (paperback, text credited to Punk Sanderson) The Vicar Ltd.,

Graphic novels
 The Mysterious Case of Billy's Missing G-String (ebook, paperback – text credited to David Singleton and Punk Sanderson, art by Ben Singleton). The Vicar Ltd.,

Discography
 "Count Your Blessings" single (Discipline Global Mobile, 2010)
 Songbook #1 (Discipline Global Mobile, DGMSP1, 2013)
 Songbook #2 (Discipline Global Mobile, forthcoming)

Additional production credits
King Crimson: "Vrooom Vrooom" (2001) – production
School Aid, "Where's the Money, Mr Blair?" single, 2005 – production
King Crimson: 21st Century Guide to King Crimson, Vol. 2 (2005) – arrangement & production
Robert Fripp: Love Cannot Bear (2005) –  production
Robert Fripp: Exposure (2006 reissue) – production consultant

Mobile apps
 The Vicar's Drummer Jokes & Celebrity Musician Guessing Game (Flat Earth Studio LLC, 2014)

Notes

References
"Beatleg Magazine" (Japan), August 2013 – David Singleton interview
"Record Collectors' Magazine" (Japan), August 2013 – David Singleton interview
"Sound Designer Magazine" (Japan), August 2013 – David Singleton interview
"Player Magazine" (Japan), September 2013 – feature on The Vicar
"Euro-Rock Press" (Japan) 2013 vol 58 – "Interview: The Vicar"

External links
The Vicar's homepage
Discipline Global Mobile homepage
The Vicar's diary @ Discipline Global Mobile homepage

English record producers
English songwriters
Alter egos
English diarists
Pseudonymous writers
Absurdist fiction

redpajama_set_name: RedPajamaWikipedia


Craftin' Caro: A special "EAT CHOCOLATE" offer!
A special "EAT CHOCOLATE" offer!
During my Founders Circle trip last week, we attended a fabulous Stampin' Up! Regional event in St. George, Utah. As part of this event we were offered a Free Stamp Set incentive...and it's just for you!
It's a super sweet deal: receive a FREE "Eat Chocolate" Stamp Set when you purchase your Stampin' Up! Starter Kit through me by October 3.
* Get a gorgeous Free Greenhouse Gala Tote (valid thru Oct. 18). Value $49.95.
* Enjoy Demonstrator discounts and benefits whether you stamp for a hobby or prefer the Stampin' Up! business opportunity.
If you're in Canada, contact me to learn more about ordering YOUR kit today to take advantage of these great deals!