text:
\section{Introduction}
Recently we have seen enormous progress in the understanding of
critical phenomena in three dimensions by using the conformal
bootstrap approach \cite{Kos:2014bka,Gliozzi:2014jsa,Kos:2016ysd,Simmons-Duffin:2016wlq},
to give only a few references. For a recent lecture note on the subject see
\cite{Simmons-Duffin:2016gjk}.
In particular,  precise
numbers for scaling dimensions and operator product expansion (OPE)
coefficients  for the
universality class of the three-dimensional Ising model were
obtained. For a very detailed account see ref. \cite{Simmons-Duffin:2016wlq}.

The functional form of two-point
functions of primary operators is fixed by conformal invariance
\begin{equation}
\label{twopoint}
 \langle  \cO_1(x_1)  \cO_2(x_2)  \rangle =
  \frac{C_1 \delta_{\Delta_1,\Delta_2}}{|x_1 -  x_2|^{2 \Delta_1}} \;\;,
\end{equation}
where $\cO_i$ is the operator taken at the site $x_i$ and
$\Delta_i$ is its scaling dimension.
The scaling dimensions of the leading $Z_2$-odd scalar $\sigma$ and
the leading $Z_2$-even scalar $\epsilon$ for the three-dimensional Ising
universality class are
$\Delta_{\sigma} = 0.5181489(10)$ and $\Delta_{\epsilon} = 1.412625(10)$,
respectively \cite{Kos:2016ysd,Simmons-Duffin:2016wlq}.
The critical exponents that are usually discussed in critical phenomena
can be deduced from these two scaling dimensions. Let us consider two
examples:
The exponent $\eta= d + 2 -2 y_h = d + 2 -2 (d -\Delta_{\sigma})=
2 \Delta_{\sigma}-d +2 = 0.0362978(20)$
governs the decay of the spin-spin correlation function at the critical point,
 where
$y_h$ is the RG-exponent related to the external field and $d$ is the
dimension of the system.
The critical exponent of the correlation length is given by
$\nu=1/y_t=1/(d-\Delta_{\epsilon})=0.6299709(40)$, where $y_t$ is the
RG-exponent related to the temperature. In table 2 of
\cite{Simmons-Duffin:2016wlq} one finds
$\omega= \Delta_{\epsilon'}-3 = 0.82968(23)$  for the exponent of the
leading correction. These results are by far  more accurate than
previous ones obtained by other methods. For example using
Monte Carlo simulations of the improved Blume-Capel model
$\nu=0.63002(10)$, $\eta=0.03627(10)$, and $\omega=0.832(6)$ had been
obtained \cite{Hasenbusch:2011yya}. Results obtained from high-temperature
series expansions, see for example
refs. \cite{Campostrini:2002cf,Butera:2005zf}, are slightly less accurate
than those from Monte Carlo simulations.  Field theoretic methods,
see for example ref. \cite{Guida:1998bx}, give even less precise
estimates. In our numerical study, corrections caused by the breaking
of the rotational symmetry are an important issue. These are governed by
the correction exponent $\omega_{NR}$. In table I of ref.
\cite{Campostrini:2002cf} the authors quote $\omega_{NR}=2.0208(12)$,
which is in reasonable agreement with $\omega_{NR}=2.022665(28)$ that
follows from $\Delta=5.022665(28)$ for angular momentum $l=4$ given in
table 2 of ref. \cite{Simmons-Duffin:2016wlq}.
There is a very rich literature on critical phenomena, which
we can not recapitulate here. We refer the reader to reviews of the
subject \cite{Wilson:1973jj,Fisher:1974uq,Fisher:1998kv,Pelissetto:2000ek}.

Now let us turn to the OPE coefficients.
Also the form of three-point
functions is fixed by conformal invariance.
Normalizing the operators such that $C_i=1$, eq.~(\ref{twopoint}),
one gets \cite{Polyakov:1970xd}
\begin{equation}
\label{threepoint}
\langle  \cO_1(x_1)  \cO_2(x_2)   \cO_3(x_3) \rangle
= \frac{f_{123}}{
       |x_1-x_2|^{\Delta_1+\Delta_2-\Delta_3}
       |x_2-x_3|^{\Delta_2+\Delta_3-\Delta_1}
       |x_3-x_1|^{\Delta_3+\Delta_1-\Delta_2}
                } \;\;,
\end{equation}
where the OPE coefficients $f_{123}$   depend on the universality class.
Using
the conformal bootstrap method, highly accurate results for OPE coefficients
of the Ising universality class in three dimensions were obtained
\cite{Kos:2016ysd,Simmons-Duffin:2016wlq}:
\begin{equation}
\label{fbssse}
f_{\sigma \sigma \epsilon} = 1.0518537(41)
\end{equation}
and
\begin{equation}
\label{fbseee}
f_{\epsilon \epsilon \epsilon} = 1.532435(19) \;\;.
\end{equation}
Until recently, there had been no results obtained by other methods
that could be compared with eqs.~(\ref{fbssse},\ref{fbseee}). In particular
in Monte Carlo simulations of lattice models, it is unclear how an infinite
volume at the critical point could be well approximated.

In ref. \cite{Caselle:2015csa} the requirement of an infinite volume was
circumvented by studying two-point correlators at the critical temperature
applying a finite external field $h$. The OPE coefficients are obtained from
the $h$-dependence of the two-point correlators.
For details of the method we refer the reader
to ref. \cite{Caselle:2015csa}.  Simulating the Ising model on a simple cubic
lattice, the authors find
\begin{equation}
f_{\sigma \sigma \epsilon} = 1.07(3)  \;\;,\;
f_{\epsilon \epsilon \epsilon} = 1.45(30) \;\;.
\end{equation}
These estimates were improved by using a trapping potential in ref.
\cite{Costagliola:2015ier}:
\begin{equation}
f_{\sigma \sigma \epsilon} = 1.051(3)  \;\;,\;
f_{\epsilon \epsilon \epsilon} = 1.32(15)  \;\;.
\end{equation}

Very recently, Herdeiro \cite{Herdeiro:2017jmv} computed two- and three-point
functions for the Ising model on the simple cubic lattice at the
critical point, using the so called UV-sampler method.
The method had been tested at
the example of the Ising model on the square lattice \cite{Herdeiro:2016agy}.
Fitting his data for the three-point
function with a one parameter Ansatz,
fixing $\Delta_{\sigma}$ and $\Delta_{\epsilon}$ to their bootstrap values,
Herdeiro gets
\begin{equation}
f_{\sigma \sigma \epsilon} = 1.05334(203) \;\;,\;
f_{\epsilon \epsilon \epsilon}  = 1.578(27) \;\;.
\end{equation}

Here we shall follow a different strategy. We simulated the improved
Blume-Capel model at the critical point on a simple cubic lattice with
periodic boundary conditions. To keep finite size effects small,
we simulated  lattices of a linear size up to $L=1600$. Furthermore
an extrapolation in the lattice size is performed.
It turns out that finite size effects at the critical point are
$\propto L^{-\Delta_{\epsilon}}$ for all quantities that we study here.
We employ variance reduction as proposed in refs.
\cite{Parisi:1983hm,Luscher:2001up}. This is in particular helpful in the case
of the $\epsilon \epsilon \epsilon$ function.

The outline of the paper is the following: In the next section we recall
the definition of the Blume-Capel model and summarize briefly the results
of ref. \cite{Hasenbusch:2011yya}. Then we define the two- and three-point
functions that we measure. Then in section \ref{fse}
we discuss the finite size scaling
behaviour of the quantities that we study.
In sections \ref{variance} we discuss the application of the
variance reduction method to our problem. Next we discuss the simulations
that we perform. It follows the analysis of the data. Finally we conclude and
give an outlook.

\section{The model}
As in previous work,
we study the Blume-Capel model on the simple cubic lattice.
For a vanishing external field, it is defined by the reduced Hamiltonian
\begin{equation}
\label{BlumeCapel}
H = -\beta \sum_{<xy>}  s_x s_y
  + D \sum_x s_x^2   \;\; ,
\end{equation}
where the spin might assume the values $s_x \in \{-1, 0, 1 \}$.
$x=(x^{(0)},x^{(1)},x^{(2)})$
denotes a site on the simple cubic lattice, where
$x^{(i)} \in \{0,1,...,L_i-1\}$
and $<xy>$ denotes a pair of nearest neighbours on the lattice.
In this study we consider $L_0=L_1=L_2=L$ throughout.
The inverse temperature is denoted by $\beta=1/k_B T$. The partition function
is given by $Z = \sum_{\{s\}} \exp(- H)$, where the sum runs over all spin
configurations. The parameter $D$ controls the
density of vacancies $s_x=0$. In the limit $D \rightarrow - \infty$
vacancies are completely suppressed and hence the spin-1/2 Ising
model is recovered.

In  $d\ge 2$  dimensions the model undergoes a continuous phase transition
for $-\infty \le  D   < D_{tri} $ at a $\beta_c$ that depends on $D$, while
for $D > D_{tri}$ the model undergoes a first order phase transition,
where $D_{tri}=2.0313(4)$ for $d=3$, see ref. \cite{DeBl04}.

Numerically, using Monte Carlo simulations it has been shown that there
is a point $(D^*,\beta_c(D^*))$
on the line of second order phase transitions, where the amplitude
of leading corrections to scaling vanishes.
We refer to the Blume-Capel model
at values of $D$ that are good numerical approximations of $D^*$ as
improved Blume-Capel model.
 For a more general discussion of improved models
see for example section 3.5 of \cite{myhabil} or section 2.3.1 of \cite{Pelissetto:2000ek}.
In \cite{Hasenbusch:2011yya} we
simulated the model at $D=0.655$ close to $\beta_c$ on lattices of a
linear size up to $L=360$. We obtained $\beta_c(0.655)=0.387721735(25)$
and $D^*=0.656(20)$.
The amplitude of leading corrections to scaling at $D=0.655$ is at
least by a factor of $30$ smaller than for the spin-1/2 Ising model.

Here we simulate the Blume-Capel model at $D=0.655$.
Most of our simulations are performed at
$\beta=0.387721735$. In order to check the sensitivity of the results
on $\beta$, we performed in addition a few simulations
at $\beta=0.38772$ and $0.38772347$.
In order to check the effect of leading corrections to scaling we
also simulated the spin-1/2 Ising model on the simple cubic lattice
at $\beta=0.22165462$. Note that in eq.~(A2) of
ref. \cite{Hasenbusch:2012spc} we quote $\beta_c=0.22165462(2)$.

\section{The observables}
On the lattice we identify
\begin{eqnarray}
\label{epsi}
 \epsilon(x)  &=& s_x^2 - \langle s_x^2 \rangle + ... \\
\label{sigi}
 \sigma(x)   &=& s_x + ... \;,
\end{eqnarray}
where in our numerical study $\langle s_x^2 \rangle$ is replaced by
its estimate obtained from the given simulation at finite $L$.
Corrections are caused by fields with the same symmetry properties
but higher dimensions.

In the case of the Ising model, eq.~(\ref{epsi}) makes no sense. In the
literature $s_x s_{y}$, where $x$ and $y$ are nearest neighbours,
is used instead of $s_x^2$.  Here, motivated by eq.~(\ref{sum2}) below,
we used $S_x^2$, where $S_x = \sum_{y.nn.x} s_y$,
where $y.nn.x$ means that $y$ is a nearest neighbour of $x$.

In order to keep the study tractable, we have to single out
a few directions for the displacements between the points.
In the case of the two-point functions we consider displacements
along the axes
\begin{equation}
x_2-x_1 = (j,0,0) \; \;,\; x_2-x_1 = (0,j,0)  \; \;,\; x_2-x_1 = (0,0,j) \;,
\end{equation}
the face diagonals
\begin{eqnarray}
x_2-x_1 = (j,j,0) \; \;,\; x_2-x_1 &=& (j,0,j)  \; \;,\; x_2-x_1 = (0,j,j) \;,
\nonumber \\
x_2-x_1 = (j,-j,0) \; \;,\; x_2-x_1 &=& (j,0,-j) \; \;,\; x_2-x_1 = (0,j,-j) \;,
\end{eqnarray}
and space diagonals
\begin{equation}
x_2-x_1 = (j,j,j)  \; \;,\; x_2-x_1 = (j,j,-j)  \; \;,\; x_2-x_1 = (j,-j,j) \;,
\;\;x_2-x_1 = (j,-j,-j) \;,
\end{equation}
where $j$ is an integer.
In the following we shall indicate these three directions by axis ($a$),
face diagonal ($f$), and space diagonal ($d$), respectively.
In our simulation program we summed over all choices that are related by
symmetry to reduce the statistical error. In particular, we summed over all
possible choices of $x_1$. In the following we shall denote the two-point
function by $g_{r,\cO_1,\cO_2}(x)$, where $r \in \{a,f,d\}$ gives the
direction and $x=|x_1-x_2|$ is the distance between the two points.

In the discussion of our numerical results we are a bit sloppy with the
notation and
use $g$ also for the numerical estimates obtained from the
simulation. Hence there might be also a dependence on the linear
lattice size that is not indicated explicitly.

In the case of the three-point functions
\begin{equation}
G_{r,\cO_1,\cO_2,\cO_3}(x)=\langle \cO_1(x_1) \cO_2(x_2)
\cO_3(x_3) \rangle
\end{equation}
we study the two choices $\cO_1 = \cO_2 = \sigma$ and $\cO_3 = \epsilon$ and
 $\cO_1 = \cO_2 = \cO_3 = \epsilon$. Furthermore, we consider two different
geometries that are indicated by $r$. For $r=f$ the largest displacement
is along a face diagonal. For example
\begin{equation}
 x_3-x_1 = (j,0,0) \;\; , \; x_3-x_2 = (0,j,0) \;.
\end{equation}
Our second choice is indicated by $r=d$ and the largest displacement
is along a space diagonal.  For example
\begin{equation}
 x_3-x_1 = (j,0,0) \;\; , \; x_3-x_2 = (0,j,j) \;,
\end{equation}
where $j$ is integer and also here we sum in our simulation
over all choices that are related by symmetry to reduce the statistical
error. The argument $x$ of $G$ gives the largest distance between two points
$x=|x_1-x_2|$.

In order to eliminate the constants $C_i$, eq.~(\ref{twopoint}), and the power
law behaviour from the
three-point functions, we directly normalized our estimates of the
three-point functions by the corresponding ones of two-point functions.
For the direction $r=f$ we get
\begin{equation}
\label{f1}
f_{\sigma \sigma \epsilon} \simeq   2^{-\Delta_{\epsilon}/2 }
 \frac{<s_{x_1} s_{x_2} s^2_{x_3} >-<s_{x_1} s_{x_2} ><s^2> }
      {<s_{x_1} s_{x_2} > [<s_{x_1}^2 s_{x_3}^2> - <s^2>^2]^{1/2}}
\end{equation}
and
\begin{equation}
f_{\epsilon \epsilon \epsilon} \simeq
 \frac{<s_{x_1}^2 s_{x_2}^2  s^2_{x_3}>-[<s_{x_1}^2 s_{x_2}^2 >
                                       +<s_{x_1}^2 s_{x_3}^2 >
                                       +<s_{x_2}^2 s_{x_3}^2 >]<s^2>
 +2 <s^2>^3
}
      {  [<s_{x_1}^2 s_{x_3}^2> - <s^2>^2]  \;
      [<s_{x_1}^2 s_{x_2}^2 > - <s^2>^2]^{1/2} } \;,
\end{equation}
where we used that $|x_1-x_3|=|x_1-x_2|$.  For the direction $r=d$ we
get
\begin{equation}
f_{\sigma \sigma \epsilon} \simeq 3^{-\Delta_{\epsilon}/2}
 \frac{<s_{x_1} s_{x_2} s^2_{x_3} >-<s_{x_1} s_{x_2} ><s^2> }
      {<s_{x_1} s_{x_2} > [<s_{x_2}^2 s_{x_3}^2> - <s^2>^2]^{1/2}}
\end{equation}
and
\begin{equation}
f_{\epsilon \epsilon \epsilon} \simeq
 \frac{<s_{x_1}^2 s_{x_2}^2  s^2_{x_3}>-[<s_{x_1}^2 s_{x_2}^2 >
                                       +<s_{x_1}^2 s_{x_3}^2 >
                                       +<s_{x_2}^2 s_{x_3}^2 >]<s^2>
 +2 <s^2>^3
}
      {  [<s_{x_1}^2 s_{x_3}^2> - <s^2>^2]^{1/2}  \;
        [<s_{x_2}^2 s_{x_3}^2> - <s^2>^2]^{1/2}  \;
      [<s_{x_1}^2 s_{x_2}^2 > - <s^2>^2]^{1/2} } \;.
\end{equation}

\section{Finite size effects}
\label{fse}
Compared with the linear size $L$ of the lattice, the distances that
we consider for our two- and three-point functions are small. In that respect
they can all be viewed as operators in the even channel such as the energy density.
The free energy density on a finite lattice, for a vanishing external field
behaves  as \cite{Wilson:1973jj,Fisher:1974uq,Fisher:1998kv,Pelissetto:2000ek}
\begin{equation}
 f(\beta,L) = L^{-d} \; h(L^{1/\nu} t) + f_{ns}(t) \;,
\end{equation}
where $t=(\beta_c-\beta)/\beta_c$ is the reduced temperature,
$h$ and $f_{ns}$ are analytic
functions. Taking the derivative with respect to $t$ we arrive at
\begin{equation}
 E(\beta,L) =  L^{-d+1/\nu} \; \tilde h(L^{1/\nu} t) + E_{ns}(t) \;,
\end{equation}
where $\tilde h=- h'/\beta_c$. Setting $\beta=\beta_c$ we get
\begin{equation}
\label{finiteL}
 E(\beta_c,L) = L^{-d+1/\nu} \; \tilde h(0) + E_{ns}(0) \;\;,
\end{equation}
where $d-1/\nu=d-y_t=\Delta_{\epsilon}$.

Given the huge amount of data, we abstain from sophisticated fitting
with Ans\"atze motivated by eq.~(\ref{finiteL}).   Instead we consider pairs
of linear lattice sizes $L_1=L$, $L_2= 2 L$ and compute
\begin{equation}
\label{extrapol}
 G_{ex}(2 L) := G(2 L) + \frac{G(2 L) - G(L)}{2^{\Delta_{\epsilon}}-1} \;,
\end{equation}
where $G$ is the quantity under consideration.

\section{Variance reduction}
\label{variance}
Here we discuss the construction of variance reduced estimators of
$N$-point functions along the lines of refs.
\cite{Parisi:1983hm,Luscher:2001up} in a general setting.
Let us consider the $N$-point function
\begin{equation}
 \langle \cO_1(x_1) \cO_2(x_2) ... \cO_N(x_N) \rangle
 =
\frac{\int D[\phi] \exp\left(-H[\phi]\right) \; \cO_1(x_1) \cO_2(x_2) ... \cO_N(x_N)}
     {\int D[\phi] \exp\left(-H[\phi]\right)}  \;,
\end{equation}
where $[\phi]$ denotes the collection of all fields. In the case of the
Blume-Capel model that we simulate here, it is actually the collection of
the spins $s_x$ and  the integral becomes the sum over all configurations.
Let us consider  subsets $x_i \in \cB_i \subset \Lambda$ of sites for each $i$,
where $\Lambda$ is the set of all sites of the lattice. Typically one
 takes $x_k \in \cB_i$  if $||x_k-x_i||\le l_{max}$ for some norm $|| \;\; ||$.
The crucial requirement is that for any pair $i \ne j$,  no pair
of sites $x_k \in  \cB_i$ and $x_l \in  \cB_j$ exists such that
$x_k$ and $x_l$ are nearest neighbours. In Fig. \ref{sketch} we sketch an
implementation for a square lattice and three points. For simplicity, in the
sketch as well as in our simulations, we use
the Chebyshev distance. Let us denote the collection of fields living on
$\cB_i$ by $[\phi]_i$ and the collection of fields that are not associated
with any of the blocks by $[\phi]_R$.
 The reduced Hamiltonian can be written
as sum, where one summand  depends only on the fields on the remainder
and the others on the fields on the remainder and on one of the blocks:
\begin{equation}
 H[\phi] = h_R([\phi]_R) + \sum_i  h_i([\phi]_i,[\phi]_R) \;\;.
\end{equation}
This decomposition allows us to rewrite the expectation value in the
following way:
\begin{eqnarray}
 & & \langle \cO_1(x_1) \cO_2(x_2) ... \cO_N(x_N) \rangle \nonumber \\
 &=& \frac{\int D[\phi]_R \; \exp[-h_R([\phi]_R)] \;
\int \left(\prod_i D[\phi]_i \right)
  \left(\prod_i  \exp[-h_i([\phi]_i,[\phi]_R)] \right) \;
   \left(\prod_i  \; \cO_i(x_i) \right)}
{\int D[\phi]_R \;  \exp[-h_R([\phi]_R)] \; \int \left(\prod_i D[\phi]_i \right)
\left(\prod_i  \exp[-h_i([\phi]_i,[\phi]_R)] \right) } \;
      \nonumber \\
 &=& \frac{\int D[\phi]_R \; \exp[-h_R([\phi]_R)] \; \prod_i \left( \int D[\phi]_i \;
\exp[-h_i([\phi]_i,[\phi]_R)] \; \cO_i(x_i) \right)}
{\int D[\phi]_R \; \exp[-h_R([\phi]_R)] \; \prod_i \left( \int D[\phi]_i \;
\exp[-h_i([\phi]_i,[\phi]_R)] \right) }
      \nonumber \\
 &=& \frac{\int D[\phi]_R \; \exp[-h_R([\phi]_R)] \; (\prod_i z_i([\phi]_R) ) \;
      (\prod_i  \langle  \cO_i(x_i) \rangle_i([\phi]_R))}
{\int D[\phi]_R \;  \exp[-h_R([\phi]_R)] \; \prod_i z_i([\phi]_R) } \;,
      \nonumber \\
\end{eqnarray}
where we define
\begin{equation}
 z_i([\phi]_R) = \int D[\phi]_i \exp[-h_i([\phi]_i,[\phi]_R)]
\end{equation}
and
\begin{equation}
\langle  \cO_i(x_i) \rangle_i([\phi]_R)
= \frac{\int D[\phi]_i \exp[-h_i([\phi]_i,[\phi]_R)] \cO_i(x_i)}{z_i([\phi]_R)}
\;.
\end{equation}

\begin{figure}
\begin{center}
\includegraphics[width=14.5cm]{sketch.eps}
\caption{\label{sketch} Two-dimensional sketch of the decomposition of the
lattice
into blocks and the remained. The three points  $x_1$, $x_2$, and $x_3$
are represented by red squares. The blocks around these three points
are bordered by solid black lines. Lattice sites different from
$x_1$, $x_2$, or $x_3$ are given by solid black circles.
}
\end{center}
\end{figure}

Note that the variance of $\prod_i \langle  \cO_i(x_i) \rangle_i$ is smaller
than that of $\prod_i \cO_i(x_i)$, since degrees of freedom have been
integrated out. In our case we can perform an exact summation over all
configurations if $\cB_i$ is small. In particular if $\cB_i$ contains
only the site $x_i$ we can easily perform the summation over the
three possible values of $s_i$.

However it is also advantageous to perform the integration over the
variables on the blocks $\cB_i$ approximately by using a Monte Carlo
simulation. Let us denote the simulations restricted to field variables
on the blocks $\cB_i$ by baby simulations. These baby simulations are
started after the whole system is equilibrated. After the baby simulations
are finished, updates on the whole system are performed. Then again
baby simulations are started. This process is iterated.
During the baby simulations, we perform $n_B$ measurements of
$\cO_i(x_i)$ for all $i$. Let us define
\begin{equation}
 \bar{\cO_i(x_i)}_{\gamma} = \frac{1}{n_B} \sum_{\alpha=1}^{n_B}  \cO_{i,\gamma,\alpha}(x_i) \;\;,
\end{equation}
where $\alpha$ labels the measurements that are performed for a given
configuration on the remainder. The configurations on the remainder
are labelled by $\gamma$. We generate $n_R$ configurations on the
remainder after
equilibration. An estimate of the $N$-point function is obtained by
\begin{equation}
 \overline{ \overline{\cO_1(x_1)} \; \overline{\cO_2(x_2)} ...
\overline{\cO_N(x_N)}}
=
\frac{1}{n_R}
\sum_{\gamma=1}^{n_R} \bar{\cO_1(x_1)}_{\gamma} \bar{\cO_2(x_2)}_{\gamma}
 ... \bar{\cO_N(x_N)}_{\gamma} \;.
\end{equation}
Let us discuss the variance of $\prod_i \bar{\cO_i(x_i)}$.
The baby Monte Carlo simulations are independent of each other. Therefore
actually $n_B^{N}$ configurations are generated for the $N$-point
function.  Hence, at least for small $n_b$, we expect that the
variance of $\prod_i \bar{\cO_i(x_i)}$  behaves as $n_B^{-N}$.  As
$n_B$ further increases the variance of
$\prod_i \langle  \cO_i(x_i) \rangle_i$ is approached. Hence the
maximal efficiency is reached at some finite $n_B$ that in general
has to be determined numerically.

\section{The algorithm and our implementation}
As in our previous studies of the Blume-Capel model, for example
\cite{2016PhRvE..93c2140H}, we simulated the model
by using a hybrid of the local heat bath algorithm,
the local Todo-Suwa algorithm \cite{ToSu13,Gutsch},
and the single cluster algorithm \cite{Wolff:1988uh}.
The Todo-Suwa algorithm is a local algorithm  that does not fulfil
detailed balance but only balance. Since ergodicity can not be proved
for the Todo-Suwa algorithm, additional local heat bath updates are
needed to ensure ergodicity for the update scheme as a whole.
The advantage of the Todo-Suwa algorithm is that it reduces autocorrelation
times compared with the heat bath algorithm.

\subsection{Implementation}
We used the SIMD-oriented Fast Mersenne
Twister algorithm \cite{twister} as random number generator.  Our code
is a straight forward implementation of the algorithms in standard C.
We abstained from a parallelization of the algorithms, since in the case of the
single cluster update, a good scaling of the performance with the number
of processes is hard to achieve, see for example ref. \cite{KauRimMel10}.
We stored the value of the spins as character variable. For simplicity
we abstain from using a more compact storage scheme, using for example two
bits for a
spin only. With this setup, on the hardware that is available to us,
$L=1600$ is about the largest linear lattice size that can be simulated
efficiently. In order to extrapolate in $L$ and also monitor the dependence
of our results on the lattice size we performed simulations for the
linear lattice sizes $L=400$, $600$, $800$, $1200$, and $1600$.

A cycle of the update consists of one heat bath sweep followed by  $n_{cl}$
single cluster updates. Then follow $n_{ts}$ sweeps using the Todo-Suwa
algorithm.
For each of these sweeps $n_{cl}$ single cluster updates are performed.
Mostly $n_{cl}$ is chosen such that, very roughly, $n_{cl}$ times the
average cluster size equals the number of sites $L^3$.  For the range
of lattice sizes studied here $n_{cl}=L$ is a reasonable choice.

Let us summarize an update cycle with the following pseudo-C code:
\begin{verbatim}
  heat bath sweep
  for(icl=0;icl<ncl;icl++)  single cluster update
  for(its=0;its<nts;its++)
    {
    Todo-Suwa sweep
    for(icl=0;icl<ncl;icl++)  single cluster update
    }
  baby simulations for all blocks
  measure N-point functions
\end{verbatim}

We parallelized trivially by performing several independent runs. The
equilibration takes a significant amount of CPU-time for the larger lattices.
Therefore, in the case of the linear lattice sizes $L=800$, $1200$, and $1600$,
we first equilibrated a single Markov chain. We started
from a disordered configuration. Since in the initial phase of the simulation
clusters are small, we adapted the number of cluster updates for the first
few update cycles, such that the aggregate cluster size per local
update sweep is equal
to the lattice volume or larger. After this initial phase, we continued
with a fixed number of single cluster updates per local update sweep as
discussed above. We performed 1000 complete update cycles to equilibrate
the system. These update cycles are characterized by $n_{ts}=3$.
Here we only measured a few quantities like the energy density
and the magnetisation to monitor the equilibration.
We stored the final configuration to disc. Then we started several runs
using this configuration as initial one
and different seeds for the random number generator. In these runs we used
$n_{ts}=9$.  Since the baby simulations discussed below take a considerable
amount of CPU-time, we intend to essentially eliminate the correlation
between subsequent measurements by using such a large number for $n_{ts}$.
In the case of $L=800$, $1200$, and $1600$, starting from the configuration
written to disc, we performed four update cycles to
achieve a sufficient decorrelation between the branches of our simulation
before measuring the $N$-point functions.

\subsection{The baby Monte Carlos and the  measurements}
In our simulations we did not attempt to adjust the size of the
blocks to the distances between the points in the $N$-point functions.
Instead we determined the $N$-point functions for a certain range
of distances for a given decomposition into blocks.

In order to save CPU-time, we determined $\bar{s_x}$ and
$\bar{s_x^2}$ for a subset of the lattice sites only.
This subset is characterized by $x^{(i)} = 0, n_s, 2 n_s, ..., L-n_s$.
In our study we performed simulations for the strides $n_s=2$  and $4$.
We used blocks around these sites that are defined by $y \in \cB_i$ if
$|y^{(k)} - x_i^{(k)}|<n_s$ for $k=0$, $1$ and $2$.
This means that the linear size of these blocks is
$l_b=3$ and $7$ for $n_s=2$ and $4$, respectively. Before starting the baby
simulations we copied the spins of the block and its outer
boundary to an auxiliary array. Since for our choice nearest neighbour blocks
overlap, we can not write all the final configurations of the baby
simulations back to the main Markov chain. Only a subset with the larger stride
$2 n_s$ could be used to this end.
However, for simplicity we refrain to do so.
At the end of the baby simulations we only stored the results
$\bar{s_x}$ and $\bar{s_x^2}$ to compute the estimates of the $N$-point
functions.
We computed the two- and three-point functions for the distances
$j=2 n_s$, $3 n_s$, $...$,$9 n_s$. Note that for $j=n_s$ the blocks
overlap, and no valid result is obtained.

In the case of $n_s=2$, we performed $n_b$ sweeps over the block using the
Todo-Suwa algorithm. Note that in the case of the baby simulations
ergodicity is not needed.
In preliminary simulations we varied $n_b$. It turns out that the performance
maximum is not very sharp and  depends on the type of the
$N$-point function and on the distance $j$. Based on these experiments,
we decided to use  $n_b=10$ in our production runs.

We performed a measurement  for the starting configuration and after each
Todo-Suwa sweep.
We reduced
the variance by performing the sum over $s_x$ for fixed neighbours exactly:
\begin{equation}
\label{sum1}
 \tilde s_x = \frac{\sum_{s_x} \exp(\beta s_x S_x - D s_x^2) \; s_x }
                  {\sum_{s_x} \exp(\beta s_x S_x - D s_x^2)}
\end{equation}
and
\begin{equation}
\label{sum2}
 \tilde s_x^2 = \frac{ \sum_{s_x} \exp(\beta s_x S_x - D s_x^2) \; s_x^2 }
              {\sum_{s_x} \exp(\beta s_x S_x - D s_x^2)} \;,
\end{equation}
where
\begin{equation}
S_x = \sum_{y.nn.x} s_y \;\;,
\end{equation}
where $y.nn.x$ means that $y$ is a nearest neighbour of $x$.

In the case of $n_s=4$  we used two different updating schemes. Since the
measurement is performed  at the central site only, it might be useful to
update the spins at central sites more often than those at the boundary.
To this end, we performed one sweep using the Todo-Suwa algorithm over
the full $7^3$ block, then follows a sweep over the central $5^3$ and
finally a sweep over the central $3^3$ block. This sequence is repeated
$n_b$ times. A measurement using eq.~(\ref{sum1},\ref{sum2}) is performed
for the initial configuration and after each (partial) sweep. This means
that $3 n_b+1$ measurements are performed for each baby simulation.
After a few preliminary simulations we decided to take $n_b=30$.
We used this scheme for our
simulations of lattices of the linear sizes $L=400$ and $800$.

For $L=600$, $1200$, and $1600$ we performed  cluster
updates in addition to the sweeps with the Todo-Suwa update.
The cluster construction is started from the fixed boundary of
the block using the standard delete probability
$p_d=\mbox{min}[1,\exp(-2 \beta s_x s_y)]$, where $x$ and $y$ are nearest
neighbours. All spins that are not frozen to the boundary are flipped.
Here we used $n_b=20$. It turned out that the cluster update gives little
advantage. However it is likely that going to larger $n_s$ this will change.
We made no attempt to construct cluster improved estimators of $s_x$ and
$s_x^2$.

We performed simulations of the Ising model for $L=400$ and $800$ and $n_s=2$.
In the baby Monte Carlos, we replaced the Todo-Suwa update by the Metropolis
one. In the main Markov chain, we replaced the Todo-Suwa sweeps by
heat bath sweeps. Note that in the case of the Ising model, the single
cluster algorithm is ergodic and it is not necessary to add heat bath sweeps.

\subsection{Statistics of our simulations}
For a given set of parameters $n_s$ and $L$, we performed 8 up to 20
independent runs. Each running for a month on a single core of the CPU.
In table \ref{statis} we summarize the total number of update and measurement
cycles  performed for each stride $n_s$ and linear lattice size $L$.
We performed preliminary simulations without using
the variance reduction method. We abstain from discussing these
simulations in detail.

\begin{table}
\caption{\sl \label{statis}
Statistics of our simulations of the Blume-Capel model at $D=0.655$ and
$\beta=0.387721735$. For a discussion see the text.
}
\begin{center}
\begin{tabular}{rrr}
\hline
   $L$    &    $n_s=2$   &   $n_s=4$  \\
\hline
  400   &  239510 &  74270 \\
  600   &   93150 &  17810  \\
  800   &   39920 &  15670  \\
 1200   &   10300 &   1800  \\
 1600   &    4190 &   1630  \\
\hline
\end{tabular}
\end{center}
\end{table}
In  total our study took about 10 years on a single core of a recent
CPU.

\section{Numerical results}
Throughout we used the Jackknife method to compute statistical errors.

\subsection{The two-point functions}
First we extracted the dimension of the operators from the
two-point functions $g(x)$. To this end, we define an effective
exponent by
\begin{equation}
\label{effDim}
 \Delta_{eff}(x,\Delta x) = - \frac{1}{2}  \frac{\ln(g(x+\Delta x)/g(x))}
 {\ln((x+\Delta x)/x)}  \;\;,
\end{equation}
where $\Delta x=n_s$, $\Delta x= \sqrt{2} n_s$, and $\Delta x= \sqrt{3} n_s$
for $r=a$, $f$ and $d$, respectively.
Let us first discuss our results obtained for $g_{r,\sigma \sigma}$.
In Fig. \ref{plotDs} we plot results obtained for displacements along
the axis and the stride $n_s=2$. We give results for all linear lattice sizes
that we have simulated. Up to our largest linear lattice size $L=1600$ we
see a dependence on the lattice size.  In addition we give extrapolated
results using the pairs of lattice sizes $(400,800)$, $(600,1200)$, and
$(800,1600)$. The extrapolated results are essentially
consistent among
each other, confirming the validity of the extrapolation.  It seems
plausible that the extrapolated result approaches the bootstrap value as
$x$ increases.

In Fig. \ref{plotDsr} we give results for the extrapolation of the pair
$(L,2L)=(800,1600)$
for all three directions that we have studied.  The small $x$ deviations
are the largest for $r=a$. For  $r=f$ and $d$ they have the
opposite sign as for $r=a$. The amplitude of corrections is the
smallest for $r=f$.  Since the corrections depend strongly
on $r$, it is likely that they are dominantly caused by the
breaking of the rotational symmetry and fall off like $x^{-\omega_{NR}}$.

Here we make no effort to extract an optimal estimate for $\Delta_{\sigma}$
from our data.
Just looking at the figure, one might take the result for direction $f$ at
distance $x=10 \; \sqrt{2}$ as final estimate: $\Delta_{\sigma}=0.5177(3)$.
Using $\eta= 0.03627(10)$ \cite{Hasenbusch:2011yya},
we get $\Delta_{\sigma} =(1+\eta)/2=0.51814(5)$, which is consistent, but
clearly more accurate.  In the following analysis we shall use the
bootstrap value $\Delta_{\sigma} = 0.5181489(10)$, which outpaces the
Monte Carlo results by far.

\begin{figure}
\begin{center}
\includegraphics[width=14.5cm]{plotDs.eps}
\caption{\label{plotDs} We plot the effective dimension
$\Delta_{\sigma,eff}(x,s)$
of the field as defined by eq.~(\ref{effDim}) for various linear lattice
sizes $L$ and extrapolated estimates. The displacement between the points
is in direction $r=a$.
The dashed lines should only guide the eye.
We give only results obtained from our simulations with stride $n_s=2$
to keep the figure readable.  The horizontal solid line
gives $\Delta_{\sigma} =0.5181489$ obtained by the bootstrap method.
}
\end{center}
\end{figure}

\begin{figure}
\begin{center}
\includegraphics[width=14.5cm]{plotDsr.eps}
\caption{\label{plotDsr} We plot the effective dimension
$\Delta_{\sigma,eff}(x,s)$
of the field as defined by eq.~(\ref{effDim}) for the extrapolation obtained
for $L=800$ and $1600$. All results are obtained for the stride $n_s=2$. We
give results for all three directions of the displacement that we have studied.
The dashed lines should only guide the eye. The horizontal solid line
gives $\Delta_{\sigma} =0.5181489$ obtained by the bootstrap method.
}
\end{center}
\end{figure}

Let us look in more detail at the corrections at small distances. Since
we study an improved model, we expect that the numerically dominant
corrections are due to the breaking of the Galilean invariance by the
lattice.
In Fig. \ref{plotgss} we plot our extrapolated results for
$g_{\sigma \sigma} x^{2 \Delta_{\sigma}}$ with
$ \Delta_{\sigma} = 0.5181489$ for the three directions studied.
We have fitted these data with
\begin{equation}
\label{correctionsss}
 x^{2 \Delta_{\sigma}} g_{r,\sigma \sigma}(x) = c + a_r x^{-\omega_{NR}}
\end{equation}
with $\omega_{NR}=2.022665$.  For simplicity, we performed a naive fit of the
 data, not
taking into account the statistical correlation of the data for
different distances and directions. We fitted jointly the data for
the three different directions, requiring that the constant $c$ is the
same for all three directions.  The result is represented by the
solid lines in Fig. \ref{plotgss}.  Given the shortcomings of the
fit we do not give final results for the constants $c$ and $a_r$.
Our aim is to demonstrate that the Ansatz~(\ref{correctionsss}) indeed
describes the data well as can be seen in the plot.

\begin{figure}
\begin{center}
\includegraphics[width=14.5cm]{gss.eps}
\caption{\label{plotgss}
We plot $g_{\sigma \sigma} x^{2 \Delta_{\sigma}}$ with
$ \Delta_{\sigma} = 0.5181489$ for the three directions studied.
Most of the data are taken from the simulations with the stride $n_s=2$.
A few data
at small distances are taken from our preliminary simulations without
variance reduction. The solid lines give the result of the fit with the
Ansatz~(\ref{correctionsss}).
}
\end{center}
\end{figure}

Next we analysed the $\epsilon \epsilon$ function.
The findings are analogous to those of the $\sigma \sigma$
function. Therefore we refrain from a detailed discussion.  A main difference
is that the relative statistical error increases faster as for the
$\sigma \sigma$ function. In Fig. \ref{plotgee} we
have plotted the analogue of Fig. \ref{plotgss}.

\begin{figure}
\begin{center}
\includegraphics[width=14.5cm]{gee.eps}
\caption{\label{plotgee}
We plot $g_{\epsilon \epsilon} x^{2 \Delta_{\epsilon}}$ with
$ \Delta_{\epsilon} =1.412625$ for the three directions studied.
Analogous to Fig.~(\ref{plotgss}).
}
\end{center}
\end{figure}

\subsection{The three-point functions}

Let us first check that the extrapolation in the lattice size works. To this
end we plot in Fig. \ref{plotfsseE} our estimates of
$f_{\sigma \sigma \epsilon}$ for $r=f$, eq.~(\ref{f1}),
as a function of the distance $x$ for different linear lattice sizes $L$.
In addition we give the results obtained from the
extrapolation~(\ref{extrapol}). Note that we applied eq.~(\ref{extrapol})
to our estimates of $f_{\sigma \sigma \epsilon}$ obtained for given $L$.
For the results obtained for a given lattice size, we see a clear dependence
on the lattice size. In contrast, the extrapolated results are consistent
among each other.
\begin{figure}
\begin{center}
\includegraphics[width=14.5cm]{fsse.eps}
\caption{\label{plotfsseE}
We plot our estimates of $f_{\sigma \sigma \epsilon}$ for the direction $r=f$.
We give  results obtained for the linear lattice sizes $L=400$, $600$, $800$,
$1200$, and $1600$ and the
extrapolations for the pairs $(L,2 L)=(400,800)$, $(600,1200)$, and
$(800,1600)$. All data shown are based on our simulations with $n_s=2$.
The straight line gives the
bootstrap result.
}
\end{center}
\end{figure}

In Fig. \ref{plotfess}  we plot our results for $f_{\sigma \sigma \epsilon}$
obtained from the extrapolation using the lattice sizes $(L,2L)=(800,1600)$.
We give results for both geometries that we have implemented.
Here we use both the simulations with stride $n_s=2$ and $n_s=4$.  For
distances, where data from both strides are available, we give the
weighted average. Throughout, the estimates from $n_s=2$ are more
accurate than those obtained from $n_s=4$.  For example for $r=f$
we get for the distance $j=16$ the estimates $1.05322(59)$ and
$1.05242(88)$ from the simulations with stride $n_s=2$ and $n_s=4$,
respectively.
Also here we see corrections at short distances. We fitted with
the Ansatz~(\ref{correctionsss}). For simplicity we did not take into
account the cross correlations for different distances. We performed
independent fits for both directions.  Good fits are obtained starting from
$j_{min}=6$, where all  $j \ge j_{min}$ are included.
For example, for $j_{min}=8$ we find
$c=1.0513(3)$ and $c=1.0506(5)$ for $r=f$ and $d$, respectively.
The errors
give only an indication, since cross correlations of the data are not taken
into account in the fit.
In Fig. \ref{plotfess} results of these fits are given as solid lines.

It is hard to quote
a final value that is not biased by the knowledge of the bootstrap result.
But it is quite clear that our numerical data are consistent with the
bootstrap result. Looking at Fig. \ref{plotfess} we might read off
\begin{equation}
f_{\sigma  \sigma \epsilon}= 1.051(1)
\end{equation}
from the estimate of $f_{\sigma  \sigma \epsilon}$ at distances $x\approx 30$,
without relying on the fits discussed above.

\begin{figure}
\begin{center}
\includegraphics[width=14.5cm]{fess2.eps}
\caption{\label{plotfess}   We plot our estimates of
$f_{\sigma \sigma \epsilon}$ as a function of the distance $x$. These
estimates are obtained by the extrapolation of the pair of lattice sizes
$(L,2L)=(800,1600)$.  The solid lines represent the results of fits with
the Ansatz~(\ref{correctionsss}).
}
\end{center}
\end{figure}

Next we discuss our results obtained for $f_{\epsilon \epsilon \epsilon}$.
Here the statistical error increases faster with the distance than
for  $f_{\sigma \sigma \epsilon}$. Furthermore we find that our results
obtained for the simulations with the stride $n_s=4$ are more accurate
than those with $n_s=2$. For example for $r=f$ and $j=16$ we get
$f_{\epsilon \epsilon \epsilon} = 1.53089(85)$ and $1.53363(27)$ from
our simulations with $n_s=2$ and $n_s=4$, respectively.
Performing fits with the Ansatz~(\ref{correctionsss}) we get
for $j_{min}=8$ the results
$c=1.5312(14)$ and $c=1.5333(22)$ for $r=f$ and $d$, respectively.

In Fig. \ref{plotfess} the results of these fits are given as solid lines.
As final result we read off from  distances $x\approx 25$
\begin{equation}
 f_{\epsilon \epsilon \epsilon} = 1.533(5)
\end{equation}
not relying on the fits with Ansatz~(\ref{correctionsss}).

\begin{figure}
\begin{center}
\includegraphics[width=14.5cm]{feee.eps}
\caption{\label{plotfeee}   We plot our estimates of
$f_{\epsilon \epsilon \epsilon}$  as a function
of the distance $x$. The solid lines give the results of fits with the
Ansatz~(\ref{correctionsss}).
}
\end{center}
\end{figure}

\subsection{Statistical errors}
 We find that the relative statistical error of the two-point
 and three-point functions increases following a power law.
 The exponent is the same for $n_s=2$ and $n_s=4$ and for the
 simulations without variance reduction. The smallest exponent
 $\approx 1.36 $ is found for the $\sigma \sigma$ function and
 the largest $\approx 4$ for the estimate of
 $f_{\epsilon \epsilon \epsilon}$. This corresponds to the fact
that we see the largest gain by using the variance reduction method
in the case of $f_{\epsilon \epsilon \epsilon}$.

\subsection{Sensitivity on the value taken as estimate of $\beta_c$}
We performed simulations for $L=800$ with stride $n_s=2$ at $\beta=0.38772$ and
$0.38772347$ in order to estimate the dependence of the $N$-point
functions on $\beta$. For $f_{\sigma \sigma \epsilon}$ and
$f_{\epsilon \epsilon \epsilon}$, we find that the slope increases
with increasing distance. In the case of $f_{\sigma \sigma \epsilon}$
we find an exponent $\approx 1.25$, while for $f_{\epsilon \epsilon \epsilon}$
we get an exponent $\approx 1.38$. From the data it is not completely clear,
whether the exponents are different.
We estimate that the uncertainty of the estimate $\beta_c=0.387721735(25)$
used here results in  an uncertainty in the fourth digit of
$f_{\sigma \sigma \epsilon}$ and $f_{\epsilon \epsilon \epsilon}$  which
is negligible compared with the errors quoted above.

\subsection{Sensitivity on leading corrections}
Since we do not know the value of $D^*$ exactly, our results might be
affected by residual leading corrections to scaling.
In ref. \cite{Hasenbusch:2011yya}
we have demonstrated that the amplitude of leading corrections to scaling
should be at least reduced by a factor of 30 in the Blume-Capel model
at $D=0.655$ compared with the Ising model. Therefore we performed
simulations of the Ising model at $\beta_c$,
the pair of lattice sizes $L=400$ and $L=800$ and the stride $n_s=2$.
A bit to our surprise, it is hard to see a difference between the
results obtained from the Ising model and the improved Blume-Capel model.
We conclude that the effects of leading corrections to scaling can
be ignored at the level of our accuracy of our final results for
$f_{\sigma \sigma \epsilon}$ and
$f_{\epsilon \epsilon \epsilon}$.

\section{Summary and Conclusions}
We computed the operator product expansion coefficients
$f_{\sigma \sigma \epsilon}$ and
$f_{\epsilon \epsilon \epsilon}$ by using Monte Carlo simulations
of the improved Blume-Capel model at the critical point.
We simulated lattices with periodic
boundary conditions up to a linear size $L=1600$. We extrapolated our
results assuming that finite size corrections vanish
$\propto L^{-\Delta_{\epsilon}}$, where $L$ is the linear size of the
lattice.
An important ingredient of our study is the variance reduced estimator based on
 \cite{Parisi:1983hm,Luscher:2001up}.
In particular
$f_{\epsilon \epsilon \epsilon}$ could be determined accurately
due to the variance reduction.
The error of our results is smaller than that of previous estimates
obtained by Monte Carlo simulations of the three-dimensional Ising model.

Our results are fully consistent with the predictions obtained by the
conformal bootstrap method. These results are however by far more accurate
than ours. Our study still can be understood as preliminary. Easily
more CPU time could be used and the parameters of the algorithm could
be better tuned. However one would hardly reach the accuracy obtained
by using the conformal bootstrap method.  The fact that our results
agree with those of the conformal bootstrap method  confirm the
theoretical expectation that the RG fixed point that governs the
three-dimensional Ising universality class is indeed invariant under
conformal transformations.

The strategy used here seems to be applicable to other universality classes.
However in the case of $O(N)$-symmetric model with $N\ge 2$ more memory
per site is needed and therefore the linear lattice sizes that can be
reached are smaller. It is unclear, whether these lattice sizes allow
for a reliable extrapolation to the infinitely large system.

An interesting idea would be to combine the UV-sampler
\cite{Herdeiro:2016agy,Herdeiro:2017jmv}
or some similar method with the variance reduced estimator of $N$-point
functions discussed here.

\section{Acknowledgement}
This work was supported by the DFG under the grant No HA 3150/4-1.

redpajama_set_name: RedPajamaArXiv


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Skeletal Muscle Effects. Cases of myopathy and rhabdomyolysis with acute renal failure secondary to myoglobinuria have been reported with HMG-CoA reductase inhibitors, including CRESTOR® (rosuvastatin calcium). These risks can occur at any dose level, but are increased at the highest dose (40 mg).
CRESTOR should be prescribed with caution in patients with predisposing factors for myopathy (eg, age ≥65 years, inadequately treated hypothyroidism, renal impairment).
The risk of myopathy during treatment with CRESTOR may be increased with concurrent administration of some other lipid-lowering therapies (fibrates or niacin), gemfibrozil, cyclosporine, lopinavir/ritonavir, atazanavir/ritonavir, or simeprevir. Cases of myopathy, including rhabdomyolysis, have been reported with statins, including CRESTOR, coadministered with colchicine, and caution should be exercised when prescribing CRESTOR with colchicine.
CRESTOR therapy should be discontinued if markedly elevated creatine kinase levels occur or myopathy is diagnosed or suspected. CRESTOR therapy should also be temporarily withheld in any patient with an acute, serious condition suggestive of myopathy or predisposing to the development of renal failure secondary to rhabdomyolysis (eg, sepsis, hypotension, dehydration, major surgery, trauma, severe metabolic, endocrine, and electrolyte disorders, or uncontrolled seizures).
There have been rare reports of immune-mediated necrotizing myopathy (IMNM), an autoimmune myopathy, associated with statin use. IMNM is characterized by proximal muscle weakness and elevated serum creatine kinase, which persist despite discontinuation of statin treatment; muscle biopsy showing necrotizing myopathy without significant inflammation; improvement with immunosuppressive agents.
All patients should be advised to promptly report to their physician unexplained muscle pain, tenderness, or weakness, particularly if accompanied by malaise or fever or if muscle signs and symptoms persist after discontinuing CRESTOR.
Liver Enzyme Abnormalities and Monitoring. It is recommended that liver enzyme tests be performed before the initiation of CRESTOR, and if signs or symptoms of liver injury occur.
Increases in serum transaminases [AST (SGOT) or ALT (SGPT)] have been reported with HMG-CoA reductase inhibitors, including CRESTOR. In most cases, the elevations were transient and resolved or improved on continued therapy or after a brief interruption in therapy. There were two cases of jaundice, for which a relationship to CRESTOR therapy could not be determined, which resolved after discontinuation of therapy. There were no cases of liver failure or irreversible liver disease in these trials.
In a pooled analysis of placebo-controlled trials, increases in serum transaminases to >3 times the upper limit of normal occurred in 1.1% of patients taking CRESTOR versus 0.5% of patients treated with placebo.
There have been rare postmarketing reports of fatal and non-fatal hepatic failure in patients taking statins, including rosuvastatin. If serious liver injury with clinical symptoms and/or hyperbilirubinemia or jaundice occurs during treatment with CRESTOR, promptly interrupt therapy. If an alternate etiology is not found, do not restart CRESTOR.
CRESTOR should be used with caution in patients who consume substantial quantities of alcohol and/or have a history of chronic liver disease. Active liver disease, which may include unexplained persistent transaminase elevations, is a contraindication to the use of CRESTOR.
Safety and Side Effects
The most commonly reported adverse reactions (incidence ≥2%) in the CRESTOR controlled clinical trial database of 5,394 patients were1,2
Headache: 3.7%
Myalgia: 3.1%
Abdominal pain: 2.6%
Asthenia: 2.5%
Nausea: 2.2%
Adverse Reactions* Reported by ≥2% of Patients Treated With CRESTOR and Greater Than Placebo in Placebo-Controlled Trials (% of Patients)1
Adverse reactions reported in ≥2% of patients in placebo-controlled clinical studies and at a rate greater than placebo are shown below. These studies had a treatment duration of up to 12 weeks.1
*Adverse reactions by COSTART preferred term.
Adverse Reactions* Reported by ≥2% of Patients Treated With CRESTOR and Greater Than Placebo in the METEOR Trial (% of Patients)1
Adverse reactions reported in ≥2% of patients and at a rate greater than placebo in the METEOR trial are shown below.1
*Adverse reactions by MedDRA preferred term.
†Frequency recorded as abnormal laboratory value.
For more information concerning the METEOR trial, visit slowing atherosclerosis progression.
In the JUPITER study, 17,802 participants were treated with CRESTOR 20 mg (n=8901) or placebo (n=8901) for a mean duration of 2 years. A higher percentage of CRESTOR-treated patients versus placebo-treated patients, 6.6% and 6.2%, respectively, discontinued study medication due to an adverse event, irrespective of treatment causality. Myalgia was the most common adverse reaction that led to treatment discontinuation.
In JUPITER, there was a significantly higher frequency of diabetes mellitus reported in patients taking CRESTOR (2.8%) versus patients taking placebo (2.3%). Mean HbA1c was significantly increased by 0.1% in CRESTOR-treated patients compared to placebo-treated patients. The number of patients with an HbA1c >6.5% at the end of the trial was significantly higher in CRESTOR-treated versus placebo-treated patients.
Adverse Reactions* in the JUPITER Trial Reported by ≥2% of Patients Treated With CRESTOR and Greater Than Placebo (% of Patients)1
Adverse reactions reported in ≥2% of patients and at a rate greater than or equal to placebo in the JUPITER trial are shown below.1
*Treatment-emergent adverse reactions by MedDRA preferred term.
For more information concerning the JUPITER trial, visit primary prevention of CVD indication.
Eligible patients can pay as low as $3‡ for each prescription of CRESTOR‡
‡Subject to eligibility. Restrictions apply. Click here for eligibility information.
Help your patients reach LDL-C goal with CRESTOR
In the STELLAR trial, in patients with hyperlipidemia or mixed dyslipidemia
Nearly 9 out of 10
met their LDL-C goal with CRESTOR 20 mg.3
View the data
Next: Dosing and Administration
3143524-3097604 Last Updated 7/15
Important Safety Information for CRESTOR Tablets
CRESTOR is contraindicated in patients with a known hypersensitivity to any component of this product, in patients with active liver disease, which may include unexplained persistent elevations of hepatic transaminase levels, in women who are pregnant or may become pregnant, and in nursing mothers
Cases of myopathy and rhabdomyolysis with acute renal failure secondary to myoglobinuria have been reported with statins, including CRESTOR. These risks can occur at any dose level, but are increased at the highest dose (40 mg)
CRESTOR should be prescribed with caution in patients with predisposing factors for myopathy (eg, age ≥65 years, inadequately treated hypothyroidism, renal impairment). The risk of myopathy during treatment with CRESTOR may be increased with concurrent administration of some other lipid-lowering therapies (fibrates or niacin), gemfibrozil, cyclosporine, lopinavir/ritonavir, atazanavir/ritonavir, or simeprevir
Therapy with CRESTOR should be discontinued if markedly elevated CK levels occur or myopathy is diagnosed or suspected. There have been rare reports of immune-mediated necrotizing myopathy associated with statin use. All patients should be advised to promptly report unexplained muscle pain, tenderness, or weakness, particularly if accompanied by malaise or fever, and if muscle signs and symptoms persist after discontinuing CRESTOR
It is recommended that liver enzyme tests be performed before the initiation of CRESTOR and if signs or symptoms of liver injury occur. All patients treated with CRESTOR should be advised to promptly report any symptoms that may indicate liver injury, including fatigue, anorexia, right upper abdominal discomfort, dark urine, or jaundice. There have been rare postmarketing reports of fatal and non-fatal hepatic failure in patients taking statins, including CRESTOR. If serious liver injury with clinical symptoms and/or hyperbilirubinemia or jaundice occurs during treatment with CRESTOR, promptly interrupt therapy. If an alternate etiology is not found, do not restart CRESTOR
CRESTOR should be used with caution in patients who consume substantial quantities of alcohol and/or have a history of chronic liver disease
CRESTOR significantly increased INR in patients receiving coumarin anticoagulants. In patients taking coumarin anticoagulants and CRESTOR concomitantly, INR should be determined before starting CRESTOR and frequently enough during early therapy to ensure that no significant alteration of INR occurs
Dipstick-positive proteinuria and microscopic hematuria were observed among patients treated with CRESTOR. These findings were more frequent in patients taking CRESTOR 40 mg, though it was generally transient and was not associated with worsening renal function. Although the clinical significance of this finding is unknown, dose reduction should be considered for patients on CRESTOR therapy with unexplained persistent proteinuria and/or hematuria during routine urinalysis testing
Increases in HbA1c and fasting serum glucose levels have been reported with statins, including CRESTOR. Based on clinical trial data with CRESTOR, in some instances these increases may exceed the threshold for the diagnosis of diabetes mellitus
In the controlled clinical trials database, the most common adverse reactions were headache (3.7%), myalgia (3.1%), abdominal pain (2.6%), asthenia (2.5%), and nausea (2.2%)#,‡‡
Rare postmarketing reports of cognitive impairment (eg, memory loss, forgetfulness, amnesia, memory impairment, confusion) have been associated with statin use, including CRESTOR. These reports are generally nonserious and reversible upon statin discontinuation
CRESTOR 40 mg should be used only for those patients not achieving their LDL-C goal with 20 mg
Important Safety Information from the JUPITER Study
A higher percentage of rosuvastatin-treated patients vs placebo-treated patients (6.6% and 6.2%, respectively) discontinued study medication due to an adverse event, irrespective of treatment causality. Myalgia was the most common adverse reaction that led to treatment discontinuation
In JUPITER, there was a significantly higher frequency of diabetes mellitus reported in patients taking rosuvastatin (2.8%) vs patients taking placebo (2.3%). Mean HbA1c was significantly increased by 0.1% in rosuvastatin-treated patients compared to placebo-treated patients. The number of patients with HbA1c >6.5% at the end of the trial was significantly higher in rosuvastatin-treated patients vs placebo-treated patients
The most common adverse reactions reported were myalgia (7.6% vs 6.6%), arthralgia (3.8% vs 3.2%), constipation (3.3% vs 3.0%), and nausea (2.4% vs 2.3%) for CRESTOR vs placebo, respectively
CRESTOR is indicated as an adjunct to diet to reduce elevated Total-C, LDL-C, ApoB, non-HDL-C, and triglycerides, and to increase HDL-C in adult patients with primary hyperlipidemia or mixed dyslipidemia, and to slow the progression of atherosclerosis in adult patients as part of a treatment strategy to lower Total-C and LDL-C to target levels
CRESTOR is indicated to reduce the risk of myocardial infarction, stroke, and arterial revascularization procedures in patients without clinically evident coronary heart disease but with an increased risk of cardiovascular disease (CVD) based on age (men ≥50 and women ≥60), high-sensitivity C-reactive protein (hsCRP) ≥2 mg/L, and the presence of at least one additional CVD risk factor, such as hypertension, low HDL-C, smoking, or a family history of premature coronary heart disease
Read full Prescribing Information (PDF - 152k)
#Prescribing Information for CRESTOR. AstraZeneca Pharmaceuticals LP, Wilmington, DE.
‡‡Data on File, 268255, AstraZeneca Pharmaceuticals LP.
†Defined as covered without prior authorization on Commercial, Medicare Part D, and Medicaid formularies. "Patients without prior authorization" means covered lives at Tiers 1 to 7 calculated by Fingertip Formulary® as of March 4, 2015, that do not require additional information to the health plan in order for CRESTOR to be covered. Data include covered lives whose prescriptions may be subject to step-therapy requirements.
Prescribing Information for CRESTOR. AstraZeneca Pharmaceuticals LP, Wilmington, DE.
Data on File, 268255, AstraZeneca Pharmaceuticals LP.
Faergeman O, Hill L, Windler E, et al; on behalf of the ECLIPSE Study Investigators. Efficacy and tolerability of rosuvastatin and atorvastatin when force-titrated in patients with primary hypercholesterolemia. Cardiology. 2008;111(4):219-228.
LIPITOR is a registered trademark of Pfizer Inc.
Fingertip Formulary is a registered trademark of Fingertip Formulary, LLC.
You may report side effects related to AstraZeneca products by clicking here.
This product information is intended for US Health Care Professionals only.
CRESTOR is licensed from SHIONOGI & CO, LTD, Osaka, Japan. CRESTOR is a registered trademark of the AstraZeneca group of companies.
©2018 AstraZeneca. All rights reserved. 3143524-3097604 Last Updated 7/15

redpajama_set_name: RedPajamaCommonCrawl


Show Sheetal Dorby your appreciation by rating this post!
I like the day cream most. Himalaya launched good range. Like all the pics also.
Himalayas Youth Eternity Range has been very impressive.This is definitely my favorite from the skincare range and I feel with a regular use I can see visible difference in my fine lines and enjoy a firmer under eye area.
Thanks for detailed review. I am using Himalaya since ages but never tried this youth eternity range, would love to try it.
I have not yet tried Youth eternity. But this seems a great product I am a big fan of Himalaya products,..
I was on the lookout for a good night cream. This seems like the perfect choice. Himalaya products are always good.
This brand has been in my family for ages, the product has trust love from generations. I am a fan of Himalayas, this is a new range. Will check out these products soon.
Wow. This range can help reduce pigmentation! Looks like I could definitely give this a try. Would love to try the eye cream as well.
I am glad that Himalaya has introduced an anti ageing range. I can't wait to try out the products.
Undoubtedly this range from Himalaya is one of the most revolutionary ones in anti-ageing skincare today.
Hello my loves! Welcome to this space again! Today, I am going to talk about how to achieve younger and healthier looking skin. If you're following me on Instagram, you must be already knowing that few weeks back, I have attended the launch of #YouthEternity range from HimalayaPersonalCare.
I have been using this entire range since last 3 weeks and I can see significant reduction in my pigmentation. So, let's just start with the routine I've been following.
What it is? This is the lightest, fast-absorbing day cream is a powerful blend of botanical extracts and the formulation based on plant stem cell research. I use this day cream religiously under my makeup.
What it does? Edelweiss plant stem cells are power packed with antioxidants and cipadessa which regulate youth genes and work with your innate skin cell matrix.
Responsible for anti-aging mechanism of your skin.
Reduces age spot and pigmentation.
Prevents daily damage caused by PHOTOAGING.
Apply this day cream generously on cleansed face and neck, once or twice a day.
What it is? It's a night cream with special blend of exotic herbal actives which works overnight.
Provide intense hydration overnight with non-greasy effect.
leaves skin even-toned, healthy and visibly youthful.
Smoothens your skin and reduces fine lines.
Massage this night cream gently over cleansed face and neck at night before retiring.
It's s breakthrough anti-aging formulation under eye cream, rich in anti - inflammatory properties. Amla, rich and natural content of Vitamin C, possesses antioxidant properties is one of the key ingredient of this eye cream.
Reduces crow's feet and puffiness around eyes.
Nourishes and hydrates the tender skin around your eyes.
leaves your under eye area remarkably bright, healthy and youthful.
Visibly reduces the intensity of under eye dark circles.
Gently dab a dot of under eye cream around the eye area until the product is absorbed. Apply once or twice a day.
That's all pretty much about the easy steps to achieve youthful and healthier looking skin. For better results, use all three products of Himalaya #YouthEternity daily. I hope this is useful and do no forget to add or share if are on some similar routine.


text:
Q: FOR loops in MATLAB and numerical error I have a loop that sums the values of function called pdfomegat
omegat= -1.9999:0.01:+1.9999;
sum1=0;

for j=1:length(omegat)

   func(j)=pdfomegat(j)*0.01;
   sum1=sum1+func(j);
end

    c1=sum1;

My second loop is slightly different loop and is as follows
sum2=0;
syms t
for j=1:length(omegat)

   func2(j)=t*pdfomegat(j)*0.01;
   sum2=sum2+func(j);
end

    c2=sum2;

I know for fact that c1 is 1 .. However notice that in the second loop I change nothing but multiply by symbolic character t. Howver I get that
c2=0.99999464659732599597363744692302*t.
Why isn't c2=t?
Is there any ways I can fix it, I can't use the round function because it symbolic.. Any thoughts?

A: After your loop call the double() function on your symbolic number to convert it to a regular number and then call the round function.

redpajama_set_name: RedPajamaStackExchange


TalentReservoir | Lance A. Berger & Associates, Ltd.
TalentReservoir® is a significant breakthrough for all organizations, no matter how small or large, to implement a viable, cost-effective process for developing bench strength for key positions, cultivating and retaining the best people, allocating resources based on employee contribution, reducing turnover, and stimulating a performance oriented culture.
TalentReservoir® consists of a set of unique processes designed by experienced consultants and supported by a computer program that integrates diverse assessment and implementation systems into a single process that links employee capabilities and preferences to organizational needs. It identifies key areas of employee risk, organizational capability gaps and employee deficiencies to present clear options to address these issues.
What are the Benefits of TalentReservoir®?
What are the TalentReservoir® Sources of Uniqueness?


text:
Evolution of green shipping research: themes and methods
Shi, W and Xiao, Y and Chen, Z and McLaughlin, H and Li, KX, Evolution of green shipping research: themes and methods, Maritime Policy and Management, 45, (7) pp. 863-876. ISSN 0308-8839 (2018) [Refereed Article]
DOI: doi:10.1080/03088839.2018.1489150
Over the past 30 years, there have been growing concerns on the environmental impacts of maritime transportation, which have attracted great attention from both academia and practitioners. Understanding developments in this area can help guide future research. We conducted a comprehensive review of green shipping research, comprising 213 papers published in transportation journals in SSCI of 2017 over the period 1988�17. We find that research on green shipping has increased greatly since 2012, accounting for 77.5% of the reviewed papers. The main focus today on green shipping was on air pollution, and the classification of green shipping practice, such as technical measures, operational options, market-based measures, and recycling and reusing, is becoming clear. According to the existing studies, future research on green shipping must strengthen technology research to not only solve practical problems, but also to establish a theoretical green shipping system. Moreover, researchers from different countries could cooperate with each other to give effective suggestions on setting standards and laws of green shipping. Finally, we identify the future research themes will focus on setting up green shipping system and legislation and policy.
green shipping, green policy, pollution, air emissions, literature review
Transport economics
Shi, W (Dr Wenming Shi)
Maritime and Logistics Management


Get a Free Demo in our Redbird Flight Simulators!
Hummingbird Aviation is proud to announce that we have acquired two brand new Redbird flight simulators! These are not your typical stationary sims. Oh no, these incredible machines are full motion and will give you a realistic feel of what its like to be in an airplane. Both devices can be used for part 141 or 61 training!
Theres nothing better than the Redbird FMX. This simulator will let your practice nearly any aviation scenario in a safe environment. Whether its flying down the Hudson to the Statue of Liberty or practicing cold weather flying in the french alps, this sim can do it all.
Because of its full motion and realistic flight simulation, the FAA classifies it as an AATD or Advanced Aviation Training Device. What this means is that it can be used for nearly every stage of training from private pilot all the way through ATP and instrument currency. Another great advantage is that this device can count for twice the number of hours as a BATD (basic aviation training device). While a BATD can only count for 12.5 hours total for training, an AATD can be used for as much 97.5 hours! At nearly half the rental price of the airplane airplane, this cuts the cost of training down significantly for our customers.
Come visit us for a free demo flight!
One of the most critical and dangerous parts of aviation is during landing. The leading causes of accidents during this stage of flight are cross wind, turbulence, and gust. Until recently, there hasn't been a way to practice in these adverse conditions besides directly placing oneself in them. This is no longer the case thanks to the Redbird X-Wind. This cross-wind trainer eliminates the risk and lets both new and veteran pilots hone their skills while in a controlled environment. This is a great trainer for new pilots trying to get down the mechanics for landing. No other simulator can adequately help prepare someone for their first solo like the X-Wind can. Students can continuously shoot approaches without having to waste time taxing, taking off or circling back around. In the time a typical student would complete 4-5 landings, our students can complete 30 in the simulator. This helps us produce safe an proficient pilots.
In the X-Wind, you can manipulate the winds to be as strong as 30 knots direct cross wind, 15 knots gusting and two different severities of turbulence. There's a seatbelt in this thing for a reason. The wind will blow you on the tracks and off the runway. You can make it as difficult or as easy as you want as you fight the winds down to make a safe landing. The machine will even give you score on your landing. Pilots can score between Crashed to 1000. Come see if you can beat the top score!
© 2018 Hummingbird Aviation, LLC | All Rights Reserved.


text:
Q: What is the name of this property of a function I'm trying to find the right vocab word to describe a concept:
In computational geometry, there's a concept of a polygon "monotone" with respect to a line.  Which means that the polygon intersects the line and all lines parallel to it in at most two places.  I want to find the equivalent concept for real valued functions.  That is, I want a property that describes a function that intersects a given line and lines parallel to it (in this case I'm interested in lines of the form $f(x) = c$, for all values of $c$, ie: horizontal lines) in at most two places.
The obvious analog, monotone functions, isn't what I want at all, since it limits the first derivative to always have the same sign, and even allows it to go flat for a bit.
The most sophisticated example I can think of: $\sin(x)$ over the interval $[0, 2\pi)$.  If the interval was increased at all in either direction, there'd exist a horizontal line that intersects the function in 3 places.  But if it's limited to just $[0, 2\pi)$, $\sin(x)$ only ever crosses any given horizontal line twice or less.  From this example, there doesn't seem to be any rules you can impose on the first or second (or higher) derivatives, which was my initial thought.
Motivation: I'm thinking it's possible to decompose an oscillating (but not necessarily periodic) function in to chunks like this to help numerical root finders.  eg: $f(x)=\sin(x)+c$ (for all $c$) evaluated over all possible intervals exactly $2 \pi$ wide will have this property.  So if you break $\sin(x)+c$ in to $2\pi$ sized chunks, you know each chunk has at most two roots.  Smaller intervals (no matter how small) can still have up to two roots, so $2\pi$ is the largest interval that still guarantees this property.

A: Well, if what you're specifically interested in is horizontal lines, then if the function were to intersect each horizontal line exactly twice, it would be a 'two-to-one' function (i.e. for each $y$ value there are two distinct values of $x$ with $f(x) = y$).  I'm not sure whether there's a good name for 'at-most-two-to-one' functions.
As for conditions on derivatives: supposing your function is differentiable, surely you just want the first derivative (i.e. the slope) to change sign at most once in any 'piece'?

A: If a real-valued function $f$ is "quasi-convex", then the set $\{x: f(x) \le c\}$ is convex for each given $c$, and is therefore an interval. Similarly,  $f$ is said to be "quasi-concave" if the set $\{x: f(x) \ge c\}$ is convex for each given $c$. Taken together, I think these two classes of functions are pretty close to what you want. In computational geometry, you could also define a  polygon to be monotone if its intersection with every line is an interval.
Note that quasi-convex functions are not necessarily continuous. So, if you want a closer correspondence with polygons, you may want to focus on functions that are both quasi-convex (or quasi-concave) and continuous.


text:
Q: Overriding a master page function in ASP.net In my master page I have the line

<%= SitePath()%>

SitePath() involks a custom class that builds navigation elements based on the combination of the static sitemap and dynamically generated pages. It returns the html for a custom breadcrumb navigation element.
Here is the SitePath() code from my code behind
public string SitePath()
{
    BreadCrumbNav breadNav = new BreadCrumbNav();
    breadNav.divClass = ".dv";
    breadNav.homeTitle = "ABC Home";
    return breadNav.Build();
}

I'd like to be able to override this from my dynamic pages so I can add to the path. For Example...
public override string SitePath()
{
    BreadCrumbNav breadNav = new BreadCrumbNav();
    breadNav.divClass = ".dv";
    breadNav.homeTitle = "ABC Home";
    breadNav.AddPage("Cooking Equipment", "PathyGoodness/Cooking+Equipment.ASPX");
    breadNav.AddPage("Toasters", "PathyGoodness/Cooking+Equipment/Toasters.ASPX");
    return breadNav.Build();
}

Is there a way to bring the master page methods into scope so I can override them- or do I need to go about this in a different way? It feels like I'm missing something really obvious, but I seem to be stuck.
Thanks for your help!

A: Since the Master page is not actually inherited, but rather used as a template, this is not directly possible.
A few other approaches you could try:
Firstly, put this in a ContentPlaceholder and override it in the ASPX markup of your individual pages only where necessary.
A more complicated approach would be to create an interface for all your pages to inherit from that guarantees they have a SitePath() method. Call that method on the page instead, from the Master, and in those pages that do not "override" the behavior, simply call the Master. In others, add your specific implementation to that method, and voila! (I suppose you could also use an abstract BasePage-type class to call the Master from that method)

A: Generally im against putting page/context specific methods in the masterpage class. Why? Because, as Josh mentioned, Masterpages is just templates. You'll never inherit from a masterpage and you can't show a masterpage without also having access to a Page object. Therefor it makes more sense to put such methods in the Page class.

A: A much simpler way is to reference a master control directly from your child page.
In your master page, replace the sitepath() function with a literal control like so:

<asp:Literal id="litSitePath" runat="server" />

then in the code for the master page use this:
BreadCrumbNav breadNav = new BreadCrumbNav();
breadNav.divClass = ".dv";
breadNav.homeTitle = "ABC Home";
litSitePath.Text = breadNav.Build();

and in the child page you can override this by using the Master.FindControl method like this:
BreadCrumbNav breadNav = new BreadCrumbNav();
breadNav.divClass = ".dv";
breadNav.homeTitle = "ABC Home";
breadNav.AddPage("Cooking Equipment", "PathyGoodness/Cooking+Equipment.ASPX");
breadNav.AddPage("Toasters", "PathyGoodness/Cooking+Equipment/Toasters.ASPX");
Literal litSitePath = (Literal)Master.FindControl("litSitePath");
litSitePath.Text = breadNav.Build();

Easy peasy and no messing around with eventhandlers or interfaces or anything like that.


The weather's hot and this cool dessert is just as hot and sultry. This version of banana cream pie has a spicy kick as well as a nip of alcohol. Hints of curry flavor mingle in the sweet graham cracker crust and the cream of the pie is spiked with rum. Thin slices of ripe banana are layered in the cream too. I found this recipe on epicurious.com, and adapted it to my liking.
The curry flavor is subtle and works well with the other flavors of the pie. Don't expect the results to be your typical run of the mill, vanilla boxed pudding and whipped cream type of pie here ... this one is much, much better.
Stir together crumbs, butter, curry powder, cinnamon, and 2 tablespoons brown sugar in a bowl with a fork until combined well. Reserve 1 tablespoon crumb mixture for garnish and press remaining crumb mixture evenly onto bottom and up side of pie plate. Bake crust 10 minutes, then cool completely in pie plate on a rack, about 20 minutes.
Beat together cream cheese, zest, and remaining 6 tablespoons brown sugar in a bowl with an electric mixer at high speed until light and fluffy, about 1 minute.
Beat cream with rum in another bowl with cleaned beaters at medium speed until it holds soft peaks. Gently stir one third of whipped cream into cream cheese mixture to lighten, then fold in remaining whipped cream gently but thoroughly.


text:
Open-World Action RPG Elex Releases In October, Collector's Edition Revealed
By Mike Sousa on June 2, 2017, 8:28AM EDT
THQ Nordic announced that its upcoming science-fantasy, open world, action RPG ELEX will release on the 17th of October for PS4, Xbox One and PC. Along with the release date, the publisher also presented us with a new CGI trailer for the game, that establishes the heart of the player's journey on Magalan, a planet devastated after a meteor collision.
Being raised as an Alb and fed pure Elex to strengthen your body, which also stripped you of all emotions, your world of cold logic and military discipline were all you knew. Set to rise through the ranks, a scourge to your enemies, your destiny seemed certain. Now, as the smoke rises over the wreckage of your glider in the mountains of Edan, you are trapped far from your home Xacor. With no access to pure Elex, you are experiencing emotions for the first time in your life. Stranded amongst your enemies and outcast from your people, in front of you lies a new and open path, as heavily laden with magnificence as it is with ruin. The decisions you make will decide the fate of the world.
From swords and axes to bows, crossbows and harpoons, Elex offers one of the widest selection of weaponry in the history of role-playing. Pick up a shotgun, power up a plasma rifle or unleash a flame thrower – there's a weapon and combat style for every fighter out there. Be it a hammer, a rocket launcher or the power of magic, Elex balances science, fantasy and brute force to let you choose the combat style that fits your role best.
In Elex there is no traditional class system. Instead you must earn the trust of experienced teachers to develop the skills you select. But, skills alone won't be enough to survive in this harsh and challenging world. Your attitude towards the people you meet will influence those around you. Will you make an ally or an enemy? Is now the time to show emotion or take the course of logic? Every choice will forge the future of your game.
Thanks to the open world, players have access to all five regions of the game world right from the very start. You can go where you want, choose your battles and your allies. The only thing in the world that will stop you are the mutant creatures that live in Magalan's Elex-polluted landscapes.
THQ Nordic also announced a Collector's Edition for ELEX. This premium package includes the following:
A 10-inch-high figurine of an Alb Mage
A 2-inch amulet in the form of a combat drone
A cloth map, showing the world of Magalan
The original score on CD
An artbook
The game's manual
The game itself, obviously
A price for the Collector's Edition has yet to be revealed.


text:
H.R. 1029 - EPA Science Advisory Board Reform Act of 2015
Tuesday, March 3, 2015 - 3:00pm in H-313 The Capitol View Announcement »
Monday, March 2, 2015 - 3:00pm in H-313 The Capitol View Announcement »
Showing the text of the bill as ordered reported by the Committee on Science, Space, and Technology.
EPA Science Advisory Board Reform Act of 2015 (as reported)
:: H.R. 1029 (as introduced) PDF XML
Report from the Committee on Science, Space, and Technology
REPORTED BY RECORD VOTE of 7-4 on Tuesday, March 3, 2015.
Agreed to by record vote of 236-180, after agreeing to the previous question by record vote of 232-181, on Tuesday, March 17, 2015
MANAGERS: Burgess/Hastings (FL)
2. Provides one hour of general debate equally divided and controlled by the chair and ranking minority member of the Committee on Science, Space, and Technology.
4. Makes in order as original text for the purpose of amendment an amendment in the nature of a substitute consisting of the text of Rules Committee Print 114-10 and provides that it shall be considered as read.
5. Waives all points of order against that amendment in the nature of a substitute.
6. Makes in order only those further amendments printed in part A of the Rules Committee report. Each such amendment may be offered only in the order printed in the report, may be offered only by a Member designated in the report, shall be considered as read, shall be debatable for the time specified in the report equally divided and controlled by the proponent and an opponent, shall not be subject to amendment, and shall not be subject to a demand for division of the question.
7. Waives all points of order against the amendments printed in part A of the report.
10. Provides one hour of general debate equally divided and controlled by the chair and ranking minority member of the Committee on Science, Space, and Technology.
12. Makes in order as original text for the purpose of amendment an amendment in the nature of a substitute consisting of the text of Rules Committee Print 114-11 and provides that it shall be considered as read.
13. Waives all points of order against that amendment in the nature of a substitute.
14. Makes in order only those further amendments printed in part B of the Rules Committee report. Each such amendment may be offered only in the order printed in the report, may be offered only by a Member designated in the report, shall be considered as read, shall be debatable for the time specified in the report equally divided and controlled by the proponent and an opponent, shall not be subject to amendment, and shall not be subject to a demand for division of the question.
15. Waives all points of order against the amendments printed in part B of the report.
5 Version 1 Bonamici (OR) Democrat SUBSTITUTE Improves the selection of members for EPA's Science Advisory Board by increasing transparency and ensuring balance among board participants; Promotes public participation in the Board's review process. Made In Order
3 Version 1 Grayson (FL) Democrat Prohibits an EPA Science Advisory Board member from participating in any advisory action for which there is evidence that the action may involve a specific party in which the member has an interest. Made In Order
1 Version 1 McKinley (WV) Republican Withdrawn Ensures that the EPA considers adverse public health, welfare, social, economic and energy effects their regulations, guidance, and other documents and assessments have on the public. This language is derived from Section 109 of the Clean Air Act. Withdrawn
2 Version 1 McKinley (WV) Republican Prohibits an individual from sitting on the Board if they are currently receiving EPA contracts or grants; and then would prohibit them from being allowed to apply for, 3 years after serving as a Board member, for any EPA contracts or grants. Made In Order
6 Version 1 McKinley (WV) Republican Late Prohibits the consideration of specified assessments regarding climate change by the Board. Submitted
4 Version 1 Polis (CO) Democrat Requires the Administrator of the Environmental Protection Agency to solicit nominations for Advisory Board membership from (1) Institutions of Higher Education and (2) research institutions based in work relevant to that of the Board. Made In Order
Motion by Mr. Cole to report the rule. Adopted 7-4


You know you know this.
You have to plan your meals.
You have to plan your workouts.
You have to set your goals in stone.
You don't want to be the person that comes out of the holidays 5 to 10 pounds heavier, do you?
If you don't plan your strategy from preventing it, well, you can PLAN on getting some new clothes that fit your new size.
This is far from doom and gloom. You can still enjoy your favorite foods at parties. You can still have a great time.
But what you can't do is just free-for-all it and stuff your face with everything put in front of you. You know that.
Tell you what: Plan on taking a nice 30 minute walk this weekend and do some solid thinking about what your plan will be. And when you get back home, put it on paper and commit to it. Remember you don't have to wait till January, NOW is a good time to get started on your fitness goals.
And think about how great you'll feel about yourself when January comes after you've followed your plan. Oh, and be sure to reward yourself to by doing something special for yourself.
Hurry because this deal expires this Friday, December 11th at 11:59pm EST.


5th Annual WAMBO River Run! Race kit pickup will begin at 7:00am on race day, Saturday, August 12th, 2017 at the First Baptist Church. The race begins at 8:00am. Free coffee is available for runners/walkers and spectators at the church starting at 7:30am. There are 5 good reasons to do this run: 1. Cheapest entry fee in Southwestern Ontario. 2. We have a 5K walk-only division. 3. All participants, who register by midnight August 1st, receive a sweet duffle bag, with great swag and an awesome finisher's medal. 4. Water, cold cloths, fruit and cheesecake await runners at the finish line. 5. A scenic out-and-back course that follows the Sydenham River, with staggered starts to avoid crowding. There are water stations at the 2.5K, 5K and 7.5K markers. We will award a $50.00 cash prize and a $25.00 Black Goose gift card to the top male and female winners of each of the four races.
And, here is this year's version of the finisher's medal!
Good luck and have fun out there!!!!!
There will be an antique vehicles at the finish line. Cheesecake, fruit and cold beverages will await runners at the finish line.
Once the race is completed, we encourage all participants to enjoy the sights and sounds of WAMBO, located in the downtown core. Hundreds of antique cars, boats, and fire trucks are available for viewing. Plenty of delicious food and beverage options await you as well.
Here is a map of the area in Wallaceburg, where the race is. Parking is available at the church, but if you do not want to risk getting blocked in until after the run, there is plenty of parking at Steinhoff Park, a block away.
FROM CHATHAM: Follow Highway 40 into Wallaceburg. At the fork, stay to the right. You are now on Murray Street. Follow Murray Street to the bridge. You will cross the bridge and go straight through the lights. Steinhoff Park will be on your right. Turn right onto Mary Street. Turn left on Napier. Follow Napier to the end.
FROM DRESDEN: Follow Highway 78 to Wallaceburg. It will turn into Margaret Avenue at the hospital. Follow Margaret to Napier. Turn right on Napier and follow it to the end.
FROM SARNIA, SOMBRA, PORT LAMBTON: Follow Highway 40 into Wallaceburg. You will reach a set of lights at Dufferin. Turn left and follow Dufferin until you reach the lights at the CIBC. You will need to turn left here (Wellington) and follow Wellington as it curves around the downtown, which will be closed for WAMBO. Wellington ends at the Dundas Bridge. Cross the bridge and turn left on Napier. Follow Napier to the end.
August 12 8:00 AM EDT - Races Begin!


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The Taliban have attacked an army base in western Afghanistan, killing 17 Afghan soldiers and abducting 11 others, officials said Sunday.
Ghausuddin Noorzai, the district chief in Pusht Rod, said another four soldiers were wounded in the attack, which began late Saturday and continued into Sunday morning. He said the Taliban also overran two checkpoints near the base, seizing weapons and ammunition.
Abdul Samad Salehi, a member of the provincial council in Farah, confirmed the death toll and said the troops defending the base received no air support or reinforcements.
The Taliban claimed the attack, the latest in their near-daily assaults on Afghan security forces. The Taliban have seized a number of districts across the country in recent years as Afghan forces have struggled to hold rural areas and defend against coordinated attacks.
Elsewhere in Afghanistan, a young girl was killed and three others were wounded in the crossfire of a battle between Afghan forces and the Taliban in the western Herat province, according to Gelani Farhad, the spokesman for provincial governor.
Farhad said the main highway between the southern province of Kandahar and Herat was blocked for several hours.
The death toll from an attack on an election rally on Saturday in the northern Takhar province meanwhile climbed from 14 to 22, according to Jawad Hajri, a spokesman for the provincial governor.
He said another 36 people were wounded in the attack, in which a motorbike loaded with explosives exploded near the rally for Nazefa Yusoufi Beg, a female candidate running for parliament in the Oct. 20 elections.
No one immediately claimed responsibility for the attack, but the Taliban are active in the province and have claimed pervious attacks there.


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I took my kids to the pediatrician yesterday, and DS got bad news - he needs to lose weight and exercise. I'm trying to approach this as a "modern parent" and try to keep a balance between cutting out the junk food and not totally crushing his self-esteem or tying it to an unrealistic body image.
1. Extra-Special Grilled Cheese Toasts with Tomato. You would think they would like this because they love pizza, and it has the same basic ingredients. But this is reminiscent of the saying "like chalk and cheese:" two things that are superficially alike, but which are in fact totally different. The idea of an actual fresh tomato is not as appetizing as jarred tomato sauce that will probably last forever.
2. Cheesy Cinnamon Toast - another one that in theory should work because it would taste like a cheese danish, but again, cheese can only be on pizza, not mixed with anything else, and only accompanied by savory, not sweet spices.
3. Cheesy Quesadillas with Avocado. I, myself, am of the school that cheese tastes good on almost everything. In fact, it is the only way I can eat brussel sprouts. The only way my kids will eat avocado is in guacamole. I was thinking of spreading the guacamole on the tortillas, but they do not like green things with cheese.
4. Pan Fried Peanut Butter and Jelly - Okay, the pan frying is definitely out of the question, but I was looking for stuff for school, and there are no nuts allowed.
5. Super crunchy peanut butter and bananas. See #4.
6. Chicken nuggets with Honey-Lemon Dipping Sauce. My kids are suspicious of these because I thought kids would eat anything that was fried and dipped in batter, so I tried to feed them fish nuggets and soy nuggets, and now they won't eat any nuggets at all. The only sauce-like thing they will put on food is ketchup.
Is it just my kids, or is everyone challenged?


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