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

The enumeration of lattice polygons weighted by area
and perimeter arises in many physical systems, including
vesicles \cite{leibler87,fisher91},
cell membranes \cite{satyanarayana04}, emulsions
\cite{faassen98}, polymers \cite{privman} and
percolation clusters \cite{rajesh05}. A central quantity of interest is the
generating function
\begin{equation}
G(P,\mu,J)  = \sum_{A,t,b} C(A,t,b) e^{P A} \mu^t e^{-J b},
\end{equation}
where $C(A,t,b)$ is the number of self-avoiding polygons of area $A$,
perimeter $t$ and with $b$ bends. This is weighted by a pressure $P$
(conjugate to the area), a fugacity $\mu$ (conjugate to the perimeter)
and a bending rigidity $J$ (conjugate to the number of bends).

Exact solutions exist for
$G(P,\mu,0)$ when $C(A,t,b)$ is restricted to convex polygons
\cite{lin91,bousquet92a,bousquet92b} or to column-convex polygons
\cite{brak90a}. However, a general solution for self-avoiding polygons is
unavailable and even the exact solutions for these restricted polygons
are complex enough that extracting
the asymptotics is non-trivial. The properties of self-avoiding polygons can be
studied by enumerating the number of configurations that correspond to a
given area and perimeter. Exact enumeration results for self-avoiding polygons
exist for values of the area $A$ up to $A=50$ and for all $t$ for these values
of $A$ \cite{jensen03,jensensap}. The scaling function describing the scaling
behaviour near the
tricritical point $\lambda=0$ and $\mu=\kappa^{-1}$, where $\kappa$ is the
growth constant for self-avoiding polygons, is also known exactly
\cite{richard01,cardy01,richard02}.
A survey of different kinds
of lattice polygons and a review of related results
can be found in Refs.~\cite{bousquet96,rensburgbook}.

In an earlier paper \cite{mitra08}, we determined the
mean area of inflated convex and column-convex polygons of fixed
perimeter as a function of the pressure and bending rigidity.
This case relates
to the problem of two-dimensional vesicles, or equivalently, pressurised
ring polymers \cite{leibler87,rudnick91,gaspari93,haleva06,mitra07} on a
square lattice. We showed that in the limit of large pressure,
the expression for the average area was the same for convex and column-convex
polygons. We also verified numerically that the same result held for
the case of self-avoiding polygons.

In this paper, we consider the related problem of determining the mean
perimeter of a polygon of fixed area.
We calculate the mean perimeter for convex
[see Eq.~(\ref{convexasymp})] and column-convex
[see Eqs.~(\ref{eq:ccp_fullt},\ref{columnconvexasymp})] polygons exactly.
In the limit
$\mu \rightarrow 0$, corresponding to inflated polygons, we show that for
both convex and column-convex polygons, the perimeter is given by
\begin{equation}
\avg{t} = 4 \sqrt{A} \left[1 -
\frac{1}{2 (\ln \mu)^2} \int_{1-\alpha}^1 dx \frac{\ln (1-x)}{x} \right]
+ \mathcal{O}(\mu/\ln \mu) ,
\end{equation}
where $\alpha = e^{-2J}$.
Since this result is the same for both convex and row-convex polygons, we
argue that this result should therefore also extend to the self-avoiding
case.

In Sec.~\ref{sec2}, we outline the calculation scheme for determining the
mean perimeter. The results for convex polygons and column-convex polygons
are presented in Sec.~\ref{sec3a} and Sec.~\ref{sec3b} respectively.
In Sec.~\ref{sec4}, we generalise these results to the case of self avoiding
polygons and  compare the analytical results with results from exact
enumeration studies.

\section{\label{sec2} Outline of the calculation}

Convex polygons are those polygons that have exactly $0$ or $2$
intersections with any vertical or horizontal line drawn through the
midpoints of the edges of the lattice (Fig.~\ref{convexfig} (a)).
Column-convex polygons
are those polygons that have exactly $0$ or $2$ intersections with any
vertical line drawn through the midpoints of the edges of the lattice.
There is, however, no such restriction in the horizontal direction (Fig.~\ref{convexfig} (b)). Self avoiding polygons are polygons that have no
restrictions on overhangs.
\begin {figure}
\includegraphics[width=0.48\columnwidth]{Fig1a.eps}
\includegraphics[width=0.48\columnwidth]{Fig1b.eps}
\caption{\label{convexfig}
(a) Schematic diagram of a convex polygon.
Any vertical or horizontal line (thick dashed lines)
intersects the convex polygon at either
$0$ or $2$ points. (b) Schematic diagram of a column-convex polygon. Any
vertical line (thick dashed lines)
intersects the convex polygon at either
$0$ or $2$ points. }
\end {figure}

The shapes of convex and row-convex polygons are obtained by minimising
the free energy at fixed area, generalising the calculation presented in
Ref.~\cite{mitra08}. The equilibrium shape of convex polygons is
invariant under rotations by $\pi/2$. Let the shape in the first
quadrant be represented by a curve $y_1(x)$ with endpoints at
$(a\sqrt{A},0)$ and $(0,a \sqrt{A})$, where $A$ is the area of the
polygon (see Fig.~\ref{fig:shape}(a)). In the case of column-convex polygons,
the equilibrium shape is invariant under reflection about the x-axis.
Let $y_2(x)$ be the
shape of the column-convex polygon in the upper half plane with
endpoints at $(-b\sqrt{A},0)$ and $(b\sqrt{A},0)$ (see
Fig.~\ref{fig:shape}(b)). The free energy functionals for these shapes can
be written  as
\begin{eqnarray}
\mathcal{L}_1& =& \int_0^{a\sqrt{A}} \!\!\!\! dx \sigma_1(y_1')\sqrt{1+y_1'^2} -
\frac{\lambda_1}{\sqrt{A}} \int_0^{a\sqrt{A}} \!\!\!\!  y_1 dx ,
		\label{lagconvex}
\end{eqnarray}
for convex polygons and
\begin{eqnarray}
\mathcal{L}_2& =& \int_{-b \sqrt{A}}^{b\sqrt{A}} \!\!\!\!
dx \sigma_2(y_2') \sqrt{1+y_2'^2} -
\frac{\lambda_2}{\sqrt{A}} \int_{-b\sqrt{A}}^{b\sqrt{A}} \!\!\!\!  y_2 dx ,
\label{lagcolumn}
\end{eqnarray}
for column-convex polygons.
The subscripts $1$ ($2$) denote convex (column-convex) polygons,
$\sigma $ is the free energy per unit length associated with a slope
$y'$ and $\lambda$'s are Lagrange multipliers. The Lagrange multipliers have
been scaled by $\sqrt{A}$ so that they become intensive quantities.
\begin {figure}
\includegraphics[width=\columnwidth]{Fig2.eps}
\caption{\label{fig:shape} A schematic diagram of the equilibrium shape of
(a) convex polygon: the shapes in the other quadrants are obtained by
symmetry.
(b) column-convex polygons: the shape in the lower half plane is
obtained by reflection. }
\end {figure}

The angle dependent surface tension $\sigma$ was computed in \cite{mitra08}
using simple combinatorial arguments. For convex polygons $\sigma_1$ is given
by
\begin{equation}
\sigma_1(y') \sqrt{1+y'^2} = -f_1(\omega^*) - 2 \ln (\mu) ,
\label{convex_sigma}
\end{equation}
where
\begin{equation}
f_1(\omega) = y' \ln (\omega) + \ln [1-(1-\alpha)\omega] - \ln(1-\omega) ,
\end{equation}
and $\omega^*$ satisfies
\begin{equation}
\left. \frac{d f_1}{d \omega} \right|_{\omega^*} = 0 ,
\end{equation}
and $\alpha= e^{-2 J}$.

For column-convex polygons, the surface tension $\sigma_2$ is of the
form \cite{mitra08}
\begin{equation}
\sigma_2(y')  \sqrt{1+y'^2} = i B_0 y' -\ln \mu - \ln f_2(\mu,\alpha,B_0) ,
\label{column_sigma}
\end{equation}
where
\begin{equation}
f_2(\mu,\alpha,B) = \frac{1+(1-2\alpha)\mu^2 + \mu(\alpha-1)(e^{iB}+e^{-iB})}
{(1-\mu e^{iB})(1-\mu e^{-iB})} .
\end{equation}
and $B_0$ satisfies the equation,
\begin{equation}
\frac{d}{dB_0} \ln f_2(\mu,\alpha,B_0) = i y' .
\end{equation}
The equilibrium shape is obtained
from Eqs.~(\ref{lagconvex}) and (\ref{lagcolumn})  by solving the
Euler Lagrange equation \cite{rottmannwortis84},
\begin{equation}
\frac{d}{d x} \frac{d}{d y'} \left[ \sigma_{1,2}(y') \sqrt{1+y'^2} \right] =
-\frac{\lambda_{1,2}}{\sqrt{A}}.
\label{eq:euler}
\end{equation}

Using the above expressions for the surface tension $\sigma$, the
equilibrium shapes of convex and column-convex polygons were
computed exactly by solving the Euler Lagrange equations.
We reproduce the final results, which will be the starting point of the
calculations presented in the next section. For convex polygons, the
equilibrium shape is given by
\begin{equation}
y_1 = \frac{\sqrt{A}}{\lambda_1} \ln \left[ \frac{1-c_1 e^{\lambda_1 x/\sqrt{A}}}{
\left[1-c_1 (1-\alpha)e^{\lambda_1 x/\sqrt{A}} \right]  c_1}  \right],
\label{eq:convexshape}
\end{equation}
with the constant $c_1 $ being given by,
\begin{equation}
c_1  = \frac{(1+e^{\lambda_1 a}) - \sqrt{(1+e^{\lambda_1 a})^2 - 4
e^{\lambda_1 a} (1-\alpha)}}
{2 (1-\alpha) e^{\lambda_1 a}} .
\label{eq:cc1}
\end{equation}

The equilibrium shape for column convex polygons is given by
\cite{mitra08}
\begin{eqnarray}
\label{columnconvexshapeeq}
\lefteqn{y_2(x) = -\frac{\sqrt{A}}{\lambda_2} \times  }     \\ \nonumber
&& \!\!  \ln \left[ \frac{(1-\mu e^{\lambda_2 x/\sqrt{A}})
(1- \mu e^{-\lambda_2 x/\sqrt{A}}) e^{-c_2}}
{1+(1-2\alpha)\mu^2 +\mu (\alpha-1)(e^{\lambda_2 x/\sqrt{A}}+
e^{-\lambda_2 x/\sqrt{A}})}\right] ,
\end{eqnarray}
where the constant $c_2$ is given by
\begin{equation}
c_2 = \ln \frac{(1-\mu g_2) (1- \mu g_2^{-1})}
{1+(1-2\alpha)\mu^2 +\mu (\alpha-1)(g_2+g_2^{-1})} ,
\label{ccconstant}
\end{equation}
where, $g_2 = \exp (\lambda_2 b)$. The constants $a$ and $b$ (see
Fig.~\ref{fig:shape})  are
chosen so that the free energy is minimised.

\section{\label{sec3} Results}

Starting from the equilibrium shapes [Eqs. (\ref{eq:convexshape}) and
(\ref{columnconvexshapeeq})] described in Sec.~\ref{sec2}, we
now calculate the mean perimeter of convex and column-convex polygons
of fixed area $A$.

\subsection{\label{sec3a} Convex polygons}

The Lagrange multiplier $\lambda_1$ is determined by the constraint
that the area under the curve is $A/4$:
\begin{equation}
\int_0^{a\sqrt{A}} y_1 dx = \frac{A}{4} .
\end{equation}
Substituting for the form of the equilibrium curve as given by Eq.~(\ref{eq:convexshape}), we obtain,
\begin{equation}
\frac{\lambda_1^2}{4} = \int_0^{\ln g_1 } dz \ln \left[
\frac{1-c_1 e^z}{c_1  [1-c_1 (1-\alpha)e^z]} \right] ,
\label{eq:pt}
\end{equation}
where $g_1  = \exp (\lambda_1 a)$.

The free energy of the equilibrium shape is obtained by substituting
the expressions for the equilibrium curve Eq.~(\ref{eq:convexshape})
and the surface tension Eq.~(\ref{convex_sigma}), into
Eq.~(\ref{lagconvex}). Simplifying, we obtain
\begin{equation}
\mathcal{L}_1 = \frac{\lambda_1 \sqrt{A}}{2} + 2 a \sqrt{A} \ln c_1  - 2 \ln \mu~ a \sqrt{A} .
\end{equation}
The parameter $a$ is chosen to be that value that minimises the above
expression for the free energy, i.e. $a$ satisfies
$\partial{\mathcal{L}_1}/\partial{a} = 0$. This gives,
\begin{equation}
\frac{1}{2} \frac{d\lambda_1}{da} + 2 \ln c_1  +
\frac{2 a}{c_1 }\frac{dc_1 }{da} - 2 \ln \mu = 0.
\end{equation}
To calculate the first term, we differentiate Eq.~(\ref{eq:pt})
with respect to $a$ to obtain
\begin{eqnarray}
\frac{\lambda_1}{2} \frac{d \lambda_1}{d a} &=& \frac{1}{c_1 }
\frac{d c_1 }{d a}
\ln\!\! \left[ \frac{(1-c_1  g_1 ) (1-c_1)^{-1} g_1^{-1}}{[1-c_1 (1-\alpha)g_1 ]
[1-c_1 (1-\alpha)]} \right],
\label{eq:dpda}
\end{eqnarray}
where the constant $c_1 $ can be expressed in terms of $g_1 $ as
\begin{equation}
c_1  = \frac{1+g_1 -\sqrt{(1+g_1 )^2-4(1-\alpha)g_1 }}{2 (1-\alpha) g_1 } .
\label{eq:cofg}
\end{equation}

Substituting for $d\lambda_1/da$ from Eq.~(\ref{eq:dpda}) and using
Eq.~(\ref{eq:cofg}) and simplifying, we obtain the solution
\begin{equation}
c_1  = \mu .
\end{equation}
The expression for $g_1 $ for this value of $c_1 $ is obtained by
replacing $c_1 $ with $\mu$ in Eq.~(\ref{eq:cofg}) :
\begin{equation}
g_1  = \frac{1-\mu}{\mu+\mu^2(\alpha-1)}.
\end{equation}
Knowing $g_1 $, the parameter $a$ can  easily be obtained as
\begin{equation}
a = \frac{1}{\lambda_1} \ln g_1  = \frac{1}{\lambda_1} \ln
\big[ \frac{1}{\mu(1+\mu(\alpha-1))} \big] .
\end{equation}
The value of the mean perimeter is equal to
\begin{equation}
\avg{t} = 8 a\sqrt{A},
\end{equation}
where the factor $8$ accounts for all the four quadrants.

When $\mu \rightarrow 0$, the shape reduces to  a square and the perimeter
equals $4 \sqrt{A}$. We would like to find the corrections for small
values of $\mu$. For small $\mu$,
\begin{equation}
\ln g_1  = -\ln \mu - \mu (\alpha -1) + O(\mu^2) .
\end{equation}
Expanding the expression Eq.~(\ref{eq:pt}) for $\lambda_1$ for
small $\mu$, we obtain
\begin{equation}
\frac{\lambda_1^2}{4} = (\ln \mu)^2 \big[ 1 + \frac{1}{(\ln \mu)^2}
\int_{1-\alpha}^1 dx \frac{\ln (1-x)}{x} \big] +
O\left( \frac{\mu}{\ln \mu}\right).
\end{equation}
The parameter $a$ is then given by,
\begin{eqnarray}
a &=& \frac{1}{\lambda_1} \ln g_1   \nonumber \\
&=& \frac{1}{2} - \frac{1}{4 (\ln \mu)^2} \int_{1-\alpha}^1 dx \frac{\ln (1-x)}{x}
+ O\left( \frac{\mu}{\ln \mu}\right).
\end{eqnarray}
The total perimeter $t = 8a\sqrt{A}$ is then given by,
\begin{equation}
\frac{\avg{t}}{4 \sqrt{A}} = 1 -
\frac{1}{2 (\ln \mu)^2} \int_{1-\alpha}^1 dx \frac{\ln (1-x)}{x}
+ O\left( \frac{\mu}{\ln \mu}\right).
\label{convexasymp}
\end{equation}
The results for the mean perimeter for convex polygons are shown in
Fig.~\ref{perimeterplots}.

\subsection{\label{sec3b} Column-convex polygons}

In this section, we calculate the mean perimeter of column-convex
polygons of area $A$ for arbitrary $\mu > 0$. We start with Eqs.
(\ref{lagcolumn}), (\ref{column_sigma}),
(\ref{columnconvexshapeeq}) and (\ref{ccconstant}).

The Lagrange multiplier $\lambda_2$ is fixed by the constraint,
\begin{equation}
\int_{-b \sqrt{A}}^{b \sqrt{A}} y_2 dx = \frac{A}{2} .
\end{equation}
On simplifying, this gives,
\begin{eqnarray}
\label{eq:ccp_pt}
\lefteqn{\frac{\lambda_2^2}{4} =} \\ \nonumber
&& \int_0^{\ln g_2} dz \left[ \ln \frac{(1-\mu e^z)(1-\mu e^{-z})}
{1+(1-2\alpha)\mu^2 +\mu (\alpha-1)(e^z+e^{-z})} -c_2 \right] ,
\end{eqnarray}
where $\ln g_2 = \lambda_2 b$.

The total free energy of the curve with ends fixed as $(-b\sqrt{A},0)$ and $(b\sqrt{A},0)$
can be calculated by substituting the equation for the equilibrium curve
[Eq.~(\ref{columnconvexshapeeq})] into the expression for the
Lagrangian [Eq.~(\ref{lagcolumn})]and simplifying,  thus yielding
\begin{equation}
\mathcal{L}_2 = \sqrt{A} [ \lambda_2 + 2 b (c_2 - \ln \mu)].
\label{eq:ccp_lag}
\end{equation}

The parameter $b$ is fixed by the condition that the free energy
should be a minimum, i.e. $d \mathcal{L}_2/d b = 0$ :
\begin{equation}
\frac{d\lambda_2}{db}+2 (c_2-\ln \mu) + 2 b \frac{dc_2}{db} = 0.
\label{eq:dldb}
\end{equation}
The first term is calculated by differentiating Eq. (\ref{eq:ccp_lag})
with respect to b,
\begin{equation}
\frac{1}{2} \frac{d \lambda_2}{d b} = -b \frac{dg}{db} \frac{dc_2}{dg} .
\label{eq:dpdbeta}
\end{equation}

Substituting Eq. (\ref{eq:dpdbeta}) into Eq. (\ref{eq:dldb})
and simplifying, we obtain
\begin{equation}
c_2 = \ln \mu .
\end{equation}
This immediately allows the solution of $g_2$ by substituting for
$c_2$ in Eq.~\ref{ccconstant},
\begin{eqnarray}
\label{eq:ccp_g}
g_2 &=& \frac{1-\mu+\mu^2+\mu^3(2 \alpha -1)}{2 \mu [1+(\alpha-1)\mu]} \\
&+& \frac{\sqrt{(1-\mu^2)(1-2\mu+2(1-2\alpha)\mu^3-(1-2\alpha)^2 \mu^4)}}
{2 \mu [1+(\alpha-1)\mu]} . \nonumber
\end{eqnarray}

The average perimeter is related to the chemical potential $\mu$ by the
relation,
\begin{equation}
\avg{t} = - 2 \mu \frac{\partial{\mathcal{L}_2}}{\partial{\mu}} ,
\end{equation}
where the factor of two accounts for the equilibrium shape in the lower
half plane also. Substituting for the free energy, this implies,
\begin{equation}
\frac{\avg{t}}{4 \sqrt{A}} = -\frac{\mu}{2} \frac{\partial{\lambda_2}}{\partial{\mu}} .
\end{equation}
Now, using Eq.~\ref{eq:ccp_pt} for $\lambda_2$ and simplifying, we obtain,
\begin{eqnarray}
\label{eq:ccp_fullt}
\frac{\avg{t}}{4 \sqrt{A}} &=& -\frac{1}{\lambda_2} \ln
\left[ \frac{1-\mu g_2}{g_2(g_2-\mu)}\right] \\
&-& \left( \frac{1+\mu^2 (2 \alpha -1)}{\lambda_2 \sqrt{k_1^2 - k_2^2}}
\times \right. \nonumber \\
&& \left. \ln \left[
\frac{(k_1+k_2)(g_2+1)+\sqrt{k_1^2-k_2^2}(g_2-1)}{(k_1+k_2)(g_2+1)-
\sqrt{k_1^2-k_2^2}(g_2-1)} \right]
\right) ,
\nonumber
\end{eqnarray}
where $k_1$ and $k_2$ are given by,
\begin{eqnarray}
k_1 &=& 1+(1-2\alpha)\mu^2, \\
k_2 &=& 2 \mu (\alpha-1) .
\end{eqnarray}

We would now like to determine the small $\mu$ behaviour of the mean
perimeter. As in the case of  the convex polygon, Eq.~(\ref{eq:ccp_g}) reduces to
\begin{equation}
\ln g_2 = -\ln \mu -\alpha \mu + \mathcal{O}(\mu^2) .
\end{equation}
In this limit, we can expand the right hand side of Eq.~(\ref{eq:ccp_fullt}) as
\begin{equation}
\frac{t}{4 \sqrt{A}} = \frac{1}{\lambda_2} [-2 \ln \mu - \alpha \mu + \mathcal{O} (\mu^2 \ln \mu)] .
\label{eq:ccp_t}
\end{equation}

Finally, we require the expansion of $\lambda_2$ in terms of $\mu$ and
$\ln \mu$.
The equation for the Lagrange multiplier $\lambda_2$, Eq.~\ref{eq:ccp_pt}, can
be expanded as,
\begin{eqnarray}
\frac{\lambda_2^2}{4} &=& \int_{\mu}^{1-\alpha \mu} dx \frac{\ln(1-x)}{x}
+ \int_{\mu^2}^{\mu} dx \frac{\ln(1-x)}{x} -\ln g_2 \ln \mu \nonumber \\
&-& \int_0^{\ln g_2} dz \ln \left[ 1 + (1-2\alpha) \mu^2
+\mu(\alpha -1) (e^z + e^{-z}) \right] , \nonumber \\
&&
\end{eqnarray}
where we have used the identities,
\begin{eqnarray}
\int_0^{\ln g_2} dz \ln (1-\mu e^z) &=&
\int_{\mu}^{1-\alpha \mu} dx \frac{\ln(1-x)}{x} , \\
\int_0^{\ln g_2} dz \ln (1-\mu e^{-z}) &=&
\int_{\mu^2}^{\mu} dx \frac{\ln(1-x)}{x} .
\end{eqnarray}
On further simplification, this yields, in the limit $\mu \rightarrow 0$,
\begin{equation}
\lambda_2 = 2 \ln \mu \left[ 1 +
\frac{\int_{1-\alpha}^1 dx \ln(1-x) /x}{2(\ln \mu)^2} \right] .
\end{equation}
Substituting for $\lambda_2$ in Eq.~\ref{eq:ccp_t}, we obtain the average perimeter
for column-convex polygons as,
\begin{equation}
\frac{\avg{t}}{4 \sqrt{A}} \simeq 1 - \frac{1}{2 (\ln \mu)^2}
\int_{1-\alpha}^1 dx \frac{\ln (1-x)}{x} + \mathcal{O} (\mu/ \ln \mu) .
\label{columnconvexasymp}
\end{equation}
The column-convex polygon results, both for the general case and in the small
$\mu$ approximation, are shown in Fig.~\ref{perimeterplots}.

\section{\label{sec4} Self Avoiding Polygons}

In Sec.~\ref{sec3}, we calculated, as a function of the fugacity $\mu$ and
bending rigidity $J$, the
mean perimeter of convex and column-convex polygons of fixed area $A$.
For small $\mu$, the expression for the perimeter takes the form
\begin{equation}
\frac{\avg{t}}{4 \sqrt{A}} \simeq 1 - \frac{1}{2 (\ln \mu)^2}
\int_{1-\alpha}^1 dx \frac{\ln (1-x)}{x} + \mathcal{O} (\mu/ \ln \mu),
\label{periasymp}
\end{equation}
for both convex and column-convex polygons. This is similar to the case
of polygons with fixed perimeter, where the asymptotic expressions for
area match up to the second term as well \cite{mitra08}.
Introducing overhangs in one direction to
convert convex polygons to column-convex polygons does not affect the second
term in the expansion Eq.~(\ref{periasymp}). It is therefore plausible
that introducing overhangs in the vertical direction also
does not affect the above expression, and hence that
the mean perimeter of self-avoiding polygons should also be described by the
expression given in Eq.~(\ref{periasymp}), for small $\mu$.
\begin {figure}
\includegraphics[width=\columnwidth]{Fig3.eps}
\caption{\label{perimeterplots}
The mean perimeter for convex and column-convex polygons are compared with
the small $\mu$ expansion result and data from exact enumeration of self
avoiding polygons of area $A$ up to $A=49$.
}
\end {figure}

In order to test this conjecture numerically, we used exact enumeration data
for polygons on the square lattice for the case $J=0$. For self-avoiding
polygons, exact enumerations are available for areas up to $A=49$
\cite{jensensap}. The resulting plot for the average perimeter is shown in
Fig.~\ref{perimeterplots}. Unfortunately, with the data currently available
it is not
possible to extrapolate to infinite $N$, preventing an unambiguous
test of this conjecture. Also, we know of  no simple Monte
Carlo algorithm that preserves area while varying perimeter, by which one
could access higher areas.

\section{\label{sec5} Summary and conclusions}

We now summarise the basic results of this paper.
We  have  studied the variation of the perimeter, as a function of the chemical
potential $\mu$ and bending rigidity $J$, for fixed area,
for both convex and column-convex polygons. In each of these cases,  we
have calculated the perimeter exactly.
The asymptotic
behaviour in the limit $\mu \rightarrow 0$
coincides for both classes of polygons. We therefore
conjecture that overhangs are not important in the inflated regime, and hence
that self avoiding polygons should have the same asymptotic behaviour.
It is important to obtain a numerical confirmation or rigorous proof of this
conjecture.

\section*{References}


We are very actively investing in our HOSE DOCTOR mobile hose activity and we are constantly on the lookout for experienced engineers.
very high levels of support, so you can actually earn it!
If you are operating as a self-employed mobile engineer give us a call - the benefits of the security and support of being part of a larger team are very significant - maybe at last you could take a few days off!
kate.charles@lister.co.uk, or 0121 553 2411. No Agencies.
At the moment we have a full complement of great staff in other positions but please keep checking back in case an exciting opportunity opens up!
If you think you have something really special to offer us then send us your details anyway!


text:
"""
A basic test of the BFS path finding algorithm.
"""
from polaris.static.algorithm.map import Map
from polaris.static.algorithm.stop import Stop

ts = Stop(1, "Trafalgar Square", 0, 1, "ALL")
ws = Stop(2, "Wembley Stadium", 5, 1, "ALL")
tl = Stop(4, "Tower of London", 8, 2, "ALL")

ts.add_neighbor(ws, 5)

graph = Map()
graph.insert(ts)
graph.insert(ws)

print(graph.find_path(ts, ws))

redpajama_set_name: RedPajamaGithub


text:
An Outdoor Visit to Vermont's Black History
February 25, 2021 by Angie Hilsman Leave a Comment
Explore this historical site in Manchester, by skis. Photo courtesy: Hildene, the Lincoln Family Home
Did you know that Vermont was the first state to ban slavery, doing so in its 1777 Constitution? Despite being an early advocate of abolition, it's not inconceivable that this majority White state—with its 94 percent Caucasian population—may not be the most attractive to newcomers of color.
It's that image of Vermont that Curtiss Reed, Jr., executive director of Vermont Partnership for Fairness and Diversity and a Brattleboro resident, sought to reshape by recognizing both Vermont's Abenaki heritage and the state's growing diversity. When Peter Shumlin (D) won the 2010 gubernatorial election, he reached out to Reed for suggestions to better diversity, equity, and inclusion; one of those suggestions was backing Reed's brainchild, the Vermont African American Heritage Trail.
"The Agency [of Commerce and Community Development] saw the immediate benefit to the economy by drawing more tourists to the state, those that are interested in cultural tourism," said Reed in a Zoom interview. On January 15, 2013—Martin Luther King, Jr.'s birthday—the cultural trail was unveiled. It consisted of 10 historic sites illustrating Vermont's Black heritage and its contributions to modern society.
The Constitution House serves as a reminder of Vermont's evolution in the abolitionist movement. Photo courtesy: Vermont Vacation
Today, the heritage trail includes 30 sites around Vermont and the New York-side of the Champlain Valley, said Reed. Examples include the Old Constitution House, a tangible reminder that Vermont was the first state to prohibit slavery, located in Windsor; there's also the Rokeby Museum, previously home to four generations of the Robinson family, which served as a hideaway in Ferrisburgh for escaped slaves.
Reed will discuss the Vermont African American Heritage Trail in depth, along with challenges to attracting a more diverse tourism base, during his upcoming presentation in the Green Mountain Club's speaker series (March 4; register here).
In the meantime, we've compiled a few ways to explore the heritage trail now with nearby hikes, trails, and walking tours. Celebrate Vermont's Black history while also enjoying the outdoors and following COVID-19 safety precautions.
Interview with Curtiss Reed, Jr., via Zoom:
Reed's answers have been slightly edited for length and clarity. Reed was compensated for his time.
Curtiss Reed, Jr.
What inspired the idea of an African American Heritage Trail and moved you to initiate it?
At the 30,000-foot level, what we're working with is trying to make Vermont the most inclusive and equitable destination in the nation. And when we drop down to about 20,000 feet, our mission statement is how do we make Vermont the most desirable destination for People of Color?—be they tourists, convention goers, outdoor enthusiasts, [or] entrepreneurs. The full range of the experiences for folks of color could well find their way into Vermont if only they knew Vermont existed.
So the idea of the trail was as the bait… that would say to folks of color—around the country, if not around the world—that Vermont is a destination. There's a reason to come to Vermont and that reason is there is a lot of historical, cultural events and individuals that are steeped in Black culture.
What was the process like bringing the heritage trail to fruition?
They [Governor Shumlin and his team] loved the idea [of the Heritage Trail] because it meant dollars, [it] meant attracting a whole new demographic to the state, and that was 2010. So 2010, '11, and '12, the [Vermont] Department of Tourism and I worked on the trail, the contours. We had already identified 95 sites, but they were not all suitable for what we wanted to do, which was you needed to have something that you could touch, something that was documented. We started off with those 10 initial sites [in 2013], so that's the background story.
Learn more about how the Trail was developed at Curtiss's March 4 speaker session.
What's your favorite stop along the trail?
Daisy Turner. Photo courtesy: the Vermont Folklife Center Archive
Hands down, it is Grafton, Vermont. The Turner Wildlife Reserve and the Turner family's homestead—it is all the things that Vermont stands for. [There was] one woman with a strong voice, Daisy Turner. Her father, Alec, was a real, kind of grit, salt-of-the-earth guy; [he] eked out a living both as a logger, farmer, and hunter. The family was also really involved in local politics. They believed in the judicial system to defend their rights, and Daisy had gone to court a couple times and won cases. And you stand at the top of Journey's End and it's an absolutely gorgeous site.
What is your experience as a Black Vermonter?
I will give you my individual point of view. It's not a perspective that represents all Black and Brown Vermonters. I'm bullish on Vermont. I love Vermont. I've been here for 42 years, and it has afforded me a high quality of life in terms of outdoor recreation, although I'm aging out of that part of my life.
But in terms of living on a human scale, I feel like, when I'm walking around [Brattleboro], it's hard to make it from one stoplight to the other—there are only two stoplights in town—but it's a place that everyone sort of knows each other. I feel that I'm a member of this community. I feel like my voice is heard here in way that has changed our community for the better. I raised three kids here. They're all successful; they went through the schools here and are doing well in life. I love Vermont.
What can folks expect during your presentation?
You can expect me talking about my favorite sites. I will strongly encourage everyone to visit all sites on the trail. I'll also talk about the challenges of attracting a more diverse tourism base and how it's not as easy as it would appear to be. March 4; register here.
How has COVID-19 affected the experience of the heritage trail?
Because it's wintertime, [most] of the sites are all closed. But we will see this upcoming tourism season. Last season, no one traveled. All the sites were closed. This year we're expecting to see some more traffic.
Want to explore the Vermont African American Heritage Trail in a COVID-safe, outdoorsy way? Here are GMC's suggestions for family-friendly hikes and walks nearby or onsite at some of the heritage trail's premiere locations.
Trail Suggestions:
The Rokeby Museum
Photo courtesy: Rokeby Museum
The Rokeby property, located on Route 7 in Ferrisburgh, was home to four generations of the Robinson family. This family included Quaker farmers and abolitionists who opened their home to escaped slaves traveling north through the Underground Railroad. The home is now a museum and a National Historic Landmark.
While the museum is currently closed for the season, it offers virtual programs, a book group, and—our favorite—free walking trails. The trails and parking area are currently accessible and offer views of the two ponds and waterfall. Staff recommend snowshoes and/or Microspikes, and pets are welcome (but don't forget your poop bags!) You can also wander the 90-acre property and view the exterior of its 16 landmarks—including building foundations, a creamery, and a smokehouse.
Plan ahead: Bathroom facilities are closed. View the trail map here. The museum buildings will reopen May 9 through October 25. Find more information at rokeby.org.
Hildene, the Lincoln Family Home
Photo courtesy: Hildene, the Lincoln Family Home
In 1905, Robert Lincoln (son of Abraham Lincoln) built his home in Manchester while serving as president of the Pullman Palace Car Company. The train car manufacturer became the largest employer of African Americans in the country by the 1900s. Despite the exploitation of Black porters, the employer supported the rise of the Black middle class.
The 412-acre estate, which housed three generations of the presidents' descendants, includes 12-miles of walking trails that are available year-round. Visitors can explore 600 feet of floating boardwalk through the Battenkill wetland, an observation platform for the bobolink sanctuary, and the 1903 Pullman Car, Sunbeam. Staff recommend snowshoes and/or skis for your exploration around the trails and estate, but pets are not allowed. Download your map here.
Plan ahead: Pets are not allowed on the trails. Bring your snowshoes or skis for easier access on trails and around the estate; rentals available. Restrooms are accessible, and the museum is open for self-guided tours; face masks are required. Find more information at hildene.org.
Turner Hill Wildlife Management Area
Photo courtesy: Turn Hill Interpretive Center
Located on this 595-acre property are the homestead site and five acres that previously belonged to Alexander 'Alec' Turner. Turner, a former slave, moved to Grafton in 1892 and made a living as a logger and sawmill worker. On site, you'll find rock foundations and agricultural remnants, two cellar holes, and stone walls that remind us of Turner's accomplishments. Learn more about the Turner family at the nearby Grafton History Museum and Turner Hill Interpretive Center.
The landscape is comprised of a typical hardwood forest and a plateau that overlooks the Saxtons River. The wetlands surrounding the river include rare plants, a colony of herons, and beaver, making it a great vantage point for birding and wildlife watching.
There are no established trails on the property, but hiking, walking, and snowshoeing are popular activities. Because beavers are active under the ice, its thickness is unpredictable; for your safety, stay off the ponds and streams. Hunting is allowed in the fall, in accordance with state Fish & Wildlife regulations.
Plan ahead: Download a map here, and be sure to review authorized activities.
Marsh-Billings-Rockefeller National Historical Park
Photo courtesy: Marsh-Billings-Rockefeller National Historical Park
During the Civil War, 152 Black Vermonters served in the Union Army. That includes George Hart, a freed slave who joined the Massachusetts 54th Regiment, which is recognized as the first all-Black regiment formed for the Union Army. Hart settled in Woodstock after the war.
You can learn more about the home front, the broader social context of the Civil War, and Woodstock's abolitionist history with self-guided walking tours available for download as a PDF or iPhone app.
The national historical park also includes 12 miles of groomed trail as part of its Nordic trail network; you can purchase a ski or snowshoe pass at the Woodstock Nordic Center on Route 106. There are also four miles of multi-use trails available to walkers, free of charge. You'll also find more than 20 miles of hiking trails between the park and the abutting Billings Farm, appropriate for any season.
Plan ahead: Find your winter trail map here. Pets are allowed; pet waste must be carried offsite. All park buildings are currently closed, and no in-person programming is scheduled. Find more information at nps.gov/mabi.
Check out all the heritage trails sites, and look for the updated brochure ahead of the tourist season.
Filed Under: Education, Events, Hiking, History, News

redpajama_set_name: RedPajamaCommonCrawl


text:
Nueces County Business Lawyers
Nueces County Breach of Contract Attorneys
Find the right Breach of Contract attorney in Nueces County, TX
A contract is an agreement offered by one party and accepted by another. Contracts are almost always written documents in Texas, but it is not impossible to have an exclusively oral contract. If a contract is not fulfilled by one or more parties, there is a Breach of Contract. Parties occasionally choose not to honor their bargain during the course of business, or it may be unrealistic to perform. What happens after a breach of contract depends on the circumstances. The party that breached the contract might be ordered to pay for the other's loss, and this sometimes makes it necessary to bring the matter to court.
What If Someone Fails to Honor Their End of the Contract in Nueces County
When one party breaches a contract in Nueces County, they will typically pay the other party for the damage that resulted. However, there is often disagreement as to the exact amount. Disagreements not resolved privately might be taken to court. The courts will require you in the initial complaint to state the amount of damage that you suffered because of the breach.
If money cannot redress the harm suffered, courts in Nueces County,Texas might grant injunctions, which are orders for the party at fault to do what it agreed. If your concerns seem to fit this remedy, you must voice the complaint to the court properly so that it can consider the issue. A breach of contract does not always mean that someone did something wrong. Courts consider more then the question of whether a breach of contract truly occurred, but also Texas law looks to how and why the obligation went unfulfilled.
If a party intends to violate a contractual agreement, it must proceed cautiously in making its intention known to the other party. If voiced improperly, statements of intent to breach a contract might be taken as wrong doing. When fulfilling a contract becomes unrealistic, it is important to be aware of the unique ways that Texas law may impact your case. Nueces County, Texas If you believe a contract has been or may be violated, you should consult with an lawyer before proceeding. Contracts disputes almost always involve delicate issues of timing. A Nueces County, lawyer specializing in contractual breach may lend help when things go wrong.
Nueces County Business Law Attorneys
Nueces County Buying a Business Lawyers
Nueces County Contract Drafting Attorneys
Nueces County Entertainment Law Lawyers
Nueces County LLC Attorneys
Nueces County Business Dispute Lawyer
Nueces County Business Law Attorney
Nueces County Contract Review Lawyer
Nueces County Incorporation Attorneys
Nueces County Selling a Business Lawyers
Breach of Contract Lawyers in Hempstead
Breach of Contract Lawyers in Portland
Breach of Contract Lawyers in Rosenberg
Breach of Contract Lawyers in Denton County
Breach of Contract Lawyers in Del Rio
Breach of Contract Lawyers in Wylie
Breach of Contract Lawyers in La Grange
Breach of Contract Lawyers in Brownsville


Find it on the Number Line!
Big Idea:Before students can ADD on a number line, they need to be familiar with FINDING numbers on a line! This is especially helpful early in the year or with very beginning learners.
Big Idea:This lesson bridges addition with manipulatives and number line addition, so students combine what they know with a new tool for addition.
Big Idea:We use a well-known line dance song to help us remember the "rules" of adding on a number line.
Big Idea:Kids love toys and tend to be fascinated with driving, so we "drive" our transportation counters down the number line.
Big Idea:Free iPad apps are the best! This app utilizes sums to 5, perfect for beginning number line work, and kiddos transfer the problem to a page with a number line for practice.
Big Idea:Using super easy & inexpensive "tools," students get lots of interactive, fun practice using the number line to add.


The wait is over. 2 years have passed since the last episode of Star Wars and we are now halfway through the new trilogy. The Last Jedi picks up immediately after the events of The Force Awakens. Rey finds the estranged Luke Skywalker to ask for help against the First Order, Finn is in a coma after his injury from Kylo Ren and the First Order are gaining ground and strength on the Resistance. I'm very conscious on my wording in this review and it's intentionally shorter than normal as it is spoiler free.
Big questions were left on everyone's minds after watching The Force Awakens. Going into The Last Jedi, I had many thoughts going into it. The obvious ones come to mind; who are Rey's parents and who on earth is Snoke? I'm obviously not going into detail if they are answered or not. But personally, The Last Jedi does very well in carrying on straight from the events of the last film and carrying on even stronger. The Force Awakens was a very light-hearted movie that pulled at the nostalgia strings massively but Rian Johnson; director of The Last Jedi completely pulls you away from that environment and doesn't hold back. Twists galore throughout and it's never obvious to tell what is going to happen. The character development for Rey and Finn are well done, but it's the way that Kylo Ren completely comes into his own. By far and away the best character in the whole film, the conflicted villain is even angrier this time round.
Johnson does well though to keep some elements of humour to the film, especially with the Porg's relationship with Chewbacca. But when it goes dark, it goes dark. The tone of the film is perfect; nothing is hunky dory in the universe. Things are going down and no one is safe. Everybody has their purpose in the film and each character has their moment. Coming to the end of the film, I felt completely satisfied. The Last Jedi engrossed me from the opening crawl to the end credits. Being the longest film in the series, Rian Johnson does incredibly well to make sure it's an enjoyable ride.
In what direction episode 9 goes towards will be an interesting one. There are some open stories that are still yet to be closed, yet there are many more that I assume will be addressed further down the line. The Last Jedi is not without its faults, but they are very minimal. CGI at times was a little shaky, not absolutely stunning at times, but it's made up by the fantastic direction by Rian Johnson that made this epic blockbuster feel just like a drama. The excitement levels are there for future Star Wars films and for me, that's a job well done. 4.5 out of 5 stars.
Next Next post: Top 10 films of 2017 – The Big Dudes Perspective!


text:
SAUNDERS-ROE LTD.
In 1928 pioneer pilot/constructor A. V. Roe (later Sir) acquired an interest in S. E. Saunders Ltd and firm was reconstituted as above. First new product was Cutty Sark flying-boat, with Fokker-type wing, built in small numbers; also larger Cloud (1931) of which RAF had 16. Most successful product was twin-engined London biplane flying-boat of 1934 which served with RAF until 1941. Shrimp two-seat four-engined aircraft was built to serve as research vehicle for
A.27 London
larger types. Company built the Supermarine Walrus and Sea Otter in quantity. SR/A1 of 1947 was world's first jet-propelled flying-boat fighter, but was not ordered into service. Princess ten-turboprop commercial flying-boat of 1952 was a great technical achievment, but never entered service. SR.53, first flown in 1957, was experimental turbojet/rocket interceptor which demonstrated climb of about 15,240m/min. Promising SR.177 development was abandoned despite international interest. Company entered helicopter field in early 1950s with small Skeeter (originally Cierva), though in 1928 S.E. Saunders had made Isaaco Helicogyre (which never flew) for the Air Ministry. Five-seat P.531 built 1958, but in 1959 company was acquired by Westland Aircraft, which developed the P.531 as the Wasp/Scout.
Back to the letter S
A.17 Cutty Sark
A.19 Cloud
A.21 Windhover
S.36 "Lerwick"
SR.A/1
SR.45 "Princess"
SR.53


text:
Netflix's The Two Popes Trailer Doubles Down with Anthony Hopkins & Jonathan Pryce
Netflix has revealed the first trailer for The Two Popes. This comes from acclaimed director Fernando Meirelles (The Constant Gardener, City of God), as well as three-time Academy Award-nominated screenwriter Anthony McCarten (Darkest Hour, The Theory of Everything). The two have partnered with a couple of A-list stars in the form of Anthony Hopkins and Jonathan Pryce to tell the story of one of the most dramatic transitions of power in the last 2,000 years between Pope Benedict and Pope Francis.
The trailer, as anyone might expect, focuses heavily on the dynamic between the two stars. Anthony Hopkins and Jonathan Pryce have tremendous chemistry as they feel out the differences that exist between them. They amusingly discuss The Beatles, while also tackling heavier subjects, like the future of the Catholic Church. Regardless of one's personal religious beliefs, it's hard to deny the compelling nature of the stakes at play here, and the two performances at the center of that conflict. This looks stylish and like a surefire Oscar contender.
Related: Breaking Bad Movie Trailer Is Here
Netflix has truly ramped things up in their awards contention efforts in recent years. Last year, they scored a Best Picture nomination, and near win, with Alfonso Cuaron's Roma. This year, they've triple downed. Not only do they have this coming down the pipeline, but they've also got Martin Scorsese's The Irishman and Noah Baumbach's Marriage Story, amongst others. It's not at all hard to imagine the streaming service walking away with a few major wins come time for the Academy Awards next year with a lineup like that.
The Two Popes centers on Cardinal Bergoglio (Jonathan Pryce), who is frustrated with the direction of the church. He requests permission to retire in 2012 from Pope Benedict (Anthony Hopkins). Instead, faced with scandal and his own doubts, Pope Benedict calls upon his harshest critic and future successor to Rome and reveals a secret that sent shockwaves through the very foundations of the Catholic Church. Behind the walls of the Vatican, a struggle unfolds between these two very different men, as they tend with tradition and progress, guilt and forgiveness. They must both confront elements from their pasts in order to find common ground and forge a future for billions around the world.
A poster for the movie has also been released, which again focuses on the two leads. It also makes clear that this is inspired by a true story. The movie will have its premiere at the Telluride Film Festival later this week, so we should be getting our first wave of critical reactions and reviews on social media sooner rather than later. The Two Popes is set to arrive in select theaters on November 27 (most likely just so it will qualify for major awards later this year) before arriving for subscribers to stream on December 20 on Netflix streaming service. Be sure to check out the trailer and poster for yourself.
Topics: Netflix, Streaming
Writer of various things on the internet (mostly about movies) since 2013. Major lover of popcorn flicks. Avid appreciator of James Bond, Marvel and Star Wars. Has a tremendously fat cat named Buster and still buys CDs. I've got my reasons.


You probably know the classic game of Battleship, where two players take turns firing shots at "ships" that each player secretly places within their "territory".
The game encourages the players to think strategically and logically and is a great way for kids to learn how to use a coordinate system.
A while ago, I was looking at a chessboard, and I wondered if it would be possible to use the 8×8 coordinate system of this game for playing Battleship. I mean, you have a perfectly good coordinate system right there.
I quickly figured out that I would need to divide the chessboard in two halves – one for each player. This shrinks the number of coordinates in the game to 8×4 per player, but I think that might even be good for young, new players of the game. It makes the game faster to play, but still encourages the same strategic and logical thinking.
I tried a couple of variations with chess pieces used as ships and a book placed in the middle of the board to prevent the players from seeing the opponent's half.
I finally reached the conclusion that the best way to boil all the information from four coordinate systems used by a traditional battleship game into one single chessboard, would be to turn the game in to a, well, board game.
So here it is: The GrowUpSmart Battleship game.
Each player places all the cards facing down on his side of the chessboard.
On all other squares, he places the "miss" cards.
You might want to place something to block the view between the two halves of the board while setting up the game. You could e.g. use a large (but slim) book or a piece of cardboard.
Decide who goes first. Let's call him Player 1.
Player 1 starts by firing a shot at Player 2's side of the board by calling out a coordinate. Player 2 turns the called card around and reveals whether this is a hit or a miss.
Now the turn goes to Player 2 and he takes a shot at Player 1's ships. When a player hits a ship, the card reveals the type of ship and therefore how big it is.
The players must now use their logical sense to seek out and sink all the opponent's ships.
The winner is the first player to sink all his opponent's ships.
You can also play another variation of the game know as Salvo. The basic rules are the same as above, but in Salvo, each player fires three shots on every turn. If you lose a ship, you also lose a shot on your next turn. Therefore, if you lose one ship, you only get two shots when you fire your next salvo and if you only have one ship left, you can only fire one shot for the rest of the game.
You can create these cards yourself by cutting out 64 squares of paper or carton and draw the different ships on one side.
Or you could just download the file we prepared with all the cards you need. All you need to do is print it and cut out the cards.
The thicker paper you use, the better. It should obviously not be possible to see through the paper.
Click the image below to download your own printable Battleship cards and rules.


Description of Causal Ambiguity. Explanation.
Causal Ambiguity is the situation where it is hard or even impossible to relate the consequences or effects of a phenomenon to its initial states or causes.
One area were this phenomenon is well known is the development of the prices of shares, options, futures, and similar products on exchanges (picture).
But is phenomenon is also very common in strategy where it is often impossible to determine whether the success of a company is due to solid strategic thinking or due to sheer luck.
That is particularly relevant for the Resource-based View, because it is a condition that prevents both a firm and its rivals from determining the causes of the firm's above average performance. This may arise because a competence is complex, tacit, or firm specific; or because the causal path from the competence to performance is impossible to specify; or because a large number of competencies interact in ways that resist precise articulation and imitation.
Also causal ambiguity applies to leadership: are the actions, charisma or vision of the CEO the reason for the success of his corporation, or was he just at the right place at the right moment?
This ends our Causal Ambiguity summary and forum.


text:
Sun and clouds mixed. A stray shower or thunderstorm is possible. High 92F. Winds SW at 10 to 20 mph..
Partly cloudy. A stray shower or thunderstorm is possible. Low 77F. Winds SW at 10 to 15 mph.
Man requesting courtesy ride is caught riding dirty
North Royalton Police Department
June 28 – Two people were assaulting each other in a vehicle on Bennett Road around 9:44 a.m. Andrea Turk said she and Jeremy Dearth were at her house when they got into a verbal argument. Dearth collected his belongings, but Turk had to provide him a ride because he does not have a valid license. While on the road, the two began arguing again to the point they reportedly began to hit each other. Turk said she did not want to press charges, but wanted Dearth to stay away. Dearth said that while driving, Turk had started screaming and driving into oncoming traffic, then started hitting him in the face. He had a split lip and blood in his mouth. He did not wish to press charges, but wanted to collect his belongings and go home. The two were advised to go their separate ways and cease contact with each other. Dearth requested a courtesy ride, which requires a search of his belongings for weapons. When the officer picked up Dearth's bag, he reported a strong odor of burnt marijuana. Dearth said there was a pipe in the pocket, which the officer found to contain burnt residue and three small, clear plastic containers of marijuana. Dearth was cited for drug abuse and possession of drug paraphernalia.
June 26 – Dispatch received a complaint around 8:07 p.m. that a female appeared to be sleeping in a car, but the caller could not confirm if the woman was breathing. Officers responded to the Applewood Drive location to perform a welfare check. Ashley Wojtala – who is known to the department – reportedly was asleep with one foot up on the passenger's side dashboard – but she was breathing. After banging on the window, the officer was able to wake Wojtala, but she shouted an obscenity. The officer ordered her to open the door, which she did slowly. She allegedly admitted to drinking and smoking marijuana the night before, and had been up drinking since 6:30 a.m. that morning. The officer reported a strong odor of alcohol coming from Wojtala, and she had droopy eyelids and glossy eyes. She was allegedly defensive and offered no explanation as to how she ended up sleeping in her car, instead of just driving home. Field sobriety tests indicated possible intoxication, and Wojtala's breath sample registered a .017 BAC. She was arrested for OVI and her vehicle towed. During inventory, officers found both an unused and burnt chore boy, a burnt spoon with residue, a measuring cup with white residue suspected to be cocaine, a baggie of marijuana, and a baggie with white residue – all within reach of the driver's seat. A second breath sample at the station read .114 BAC at 9:37 p.m. and Wojtala's license was suspended. When asked her typical drug of choice, Wojtala reportedly said she is an equal opportunity user and uses whatever is available, but would not specify what she used last. She was cited for OVI, drug abuse/possession of marijuana, possession of drug paraphernalia, and more charges may be forthcoming pending item testing. Wojtala has one prior OVI conviction from 2012 and a reduced physical control conviction from another OVI charge.
June 28 – Around 1:10 a.m., an officer noticed a car driving over the segmented yellow and the white fog lines, nearly driving off the roadway. After pulling over the car, the driver, 18-year-old Seamus Kral, seemed confused and didn't realize he had driven over the marked lines. The officer detected a strong odor of alcohol coming from inside the car, and Kral reportedly had bloodshot eyes and slurred speech, but denied having alcohol that evening. Kral provided a breath sample of .135 BAC, appeared unsteady on his feet, and field sobriety tests indicated possible intoxication. He was placed under arrest and his vehicle towed. During vehicle inventory, police found a vape pen filled with THC oil, a glass pipe with burnt marijuana residue, a torch and six sealed vape cartridges labeled "Pineapple Express 91% 1g" which is a common name for a type of marijuana strain. Also located were a half-full bottle of Hennessy Cognac, three beers and a mason jar full of marijuana. All were seized as evidence. At the station, Kral produced a BAC sample of .131, his license was confiscated and he was placed under administrative license suspension. Kral reportedly admitted the contraband belongs to him and said he only sporadically smokes marijuana. He denied that he was trafficking in marijuana products, despite the large amount of cash he had on his person at the time of arrest. Kral was charged with OVI, driving within marked lanes, drug abuse, drug paraphernalia, open container in a motor vehicle and underage alcohol prohibitions.
June 28 – Patrol units were dispatched to Ridge and Tilby roads for an unconscious male who was punched in the face. The victim appeared highly intoxicated, had a mark on the side of his face, a bump on the back of his head, and was found carrying several unopened beers. A witness reported he heard the sound of the victim's head striking the concrete, and said another white male took off running toward Tilby. It was eventually determined that Jonathan Keating had been encouraged by Michael Benjamin Johnson to follow the victim across the street, Keating confronted him, and punched him in the face. The victim fell to the ground, striking his head on the concrete. Keating reportedly fled the scene. A formal complaint was written up for felony assault for Keating and a warrant issued. Johnson is being cited for inciting to violence. It was later reported the victim has a cranial fracture in the back of his skull, a cheek fracture, concussion and bleeding on the brain.
June 29 – The registered driver to a vehicle found to be swerving at 2:38 a.m. was shown to have an expired driver's license. After initiating a traffic stop, the driver said the car is registered to his brother, but the driver has failed the driver's test multiple times and did not have a driver's license of his own. He was identified as Hussein Maana, stating he used to have a Michigan driver's license, but it was suspended. Maana said he had no one to call for a ride, and his vehicle was ordered towed. Maana reportedly became argumentative, stating that he should not be getting a ticket because he has been driving without a license for over a year without an accident. He refused to exit the vehicle and had to be escorted out. He was placed under arrest for obstructing official business, driving with no driver's license and left of center at 3:03 a.m., and transported to the jail.
Who would you vote for today in a Democratic presidential primary?
Online reader poll; click here to vote!
Publisher's Notebook
What did we learn from Dem debates?
If we learned anything lately it is that the Democratic Party is an absolute mess, according to columnist Charles Lane from that other Post (the little Washington one). Click to read more
Cookin' with Karl
Patriots bourbon and cigar dinner
Chef Ryan Marino is hosting a very special dinner, which he is calling the Patriot's Bourbon and Cigar Dinner, on July 25. Click to read more


Xiaomi finally launched the Xiaomi Mi 4i at an event held in New Delhi on Thursday. The device is priced at Rs 12,999 and will go on sale on April 30. Registrations will start at 8 pm today on Flipkart. Initially, the device will be available on Flipkart, and later across all its channels including Mi website.
Xiaomi has given some serious thought to the new smartphone's display. The Mi 4i features a 5 inch HD display along with a pixel density that goes up to 441ppi. Xiaomi claims that the smartphone has a higher color saturation than iPhone 6. It is a fully laminated OGS. In other features, the Mi 4i comes with Sunlight Display, a technology which allows the phone to do dynamic tone mapping, which in turn, keeps the image quality balanced in bright sunlight.
if you have some suggestion, question, request on Xiaomi launches Mi 4i in India at Rs 12,999, to be available on 30 April via Flipkart.


Started this discussion. Last reply by Dennis AuBuchon Dec 29, 2018.
Started this discussion. Last reply by Peter N. Jones Sep 6, 2007.
I ran across this Washington Post article on Tumblr. It aptly describes book marketing in today's world. Enjoy!
Books are the trademark of civilization.
I was on the Coach Ron Tunick radio show today. Ron invited me to talk about the publishing industry and book shepherding. Ron published IN THE THINKING ROOM as a trade paperback and wants to publish it as a hard cover, too.


HDTV setup tips: So you have a new TV...now what?
CNET editors provide advice and tips on how to make the best use of your new HDTV.
You've just broken your new high-def TV out of the box, hooked it up to your cable box and fired it up. And chances are, you love the picture. But after the initial joy of seeing that screen in action wears off, you might be wondering: How can I get the most out of it? Here are a few tips.
The single most important thing you can do to get your new HDTV looking its best is to hook up an actual high-definition source. For television programming, that means an HDTV-capable cable box or satellite box--or an antenna. Ask your cable or satellite provider for a high-def box or DVR, and they'll hook it up for you (although it's a good idea to double-check their work; see below). If you don't have cable or satellite, try using an antenna to tune over-the-air HD stations, which are available in most areas.
Most TV services offer both standard-def and high-def channels, and if you have an HDTV you'll want to be watching (or recording) the HD versions. If your box allows it, you might be able to select a list in your programming guide that shows only HD channels.
You might also want to consider getting a Blu-ray player. The picture quality on standard DVDs looks very good on an HDTV, but Blu-ray discs look even better, especially on larger screens. Just don't expect the player to make regular DVDs look noticeably better on your TV--it can help, but usually not by much.
Other HD sources include game consoles like Xbox 360 and PlayStation3 (but not the Nintendo Wii, which is standard-def), media players like Roku and Apple TV, and even newer digital cameras, camcorders and computers.
The cable guy might connect your box using analog component-video cables, but HDMI is really the way to go. It's worth buying an HDMI cable to get the most out of your TV. HDMI cables are often quite expensive in stores, however, so we recommend buying a cable from an online vendor like Amazon, newegg.com or monoprice.com. For the vast majority of viewers, it's not worth spending extra for an HDMI cable.
More info: What HDMI cable should I buy?
Here's where a lot of even experienced HD owners (not to mention cable box installers) get confused. HD sources can have a lot of settings, and to take full advantage you'll want to match the resolution of the source as closely as possible to the capabilities of your TV. If you have a 1080p TV--the most common resolution among new models--you should set the source to 1080i or, if available, 1080p resolution. If you have a 720p (or 1366x768) TV, set the source to 720p resolution.
If the source lets you choose among other resolutions, check off every one that the TV can support. If there's a "native" option available, we recommend most users check that one off as well. These steps allow the TV to perform the video processing, and usually TVs do a better job of it than cable or satellite boxes. If you have a Blu-ray player and a TV that can handle 1080p/24 sources, we also recommend engaging that option. Computers should be set to output the native resolution of the display, as long as the TV can accept it. Check your manual if you're not sure what source resolutions your TV can support.
Now that you're watching HDTV, you might notice that the screen often isn't completely full. That's because the wide format of the screen doesn't always perfectly fit the source. The first step is to make sure your source is set to the wide-screen (or 16:9) format mode. The next is to adjust the aspect ratio control, which can zoom, crop, stretch or properly display the image. The confusing part, aside from the name "aspect ratio," is that such controls can be found on both the TV and the source.
In general we recommend setting the TV to the mode that fills the screen without distortion when fed a high-def source, yet preserves the full resolution of that source. Such modes can be called "Native," "Dot-by-dot," "Just Scan," "Full Pixel," or others. Some TVs have a secondary control to enable this native mode, then require you to select "Full" or a similar mode to fill the screen without zooming or stretching. Try cycling through the modes on your TV by pressing the button that controls aspect ratio repeatedly, just to get familiar. The manual will also have a section devoted to this control.
For TVs connected to cable boxes with their own aspect ratio controls, the least confusing route is to select the recommended TV mode as described above, then control aspect ratio using the box's own control. But results vary widely, and it's important to remember that some sources, like non-wide-screen TV shows and many movies, look best when you leave the bars on the screen.
If you thought the section on aspect ratio was confusing, brace yourself. The myriad picture settings available on many TVs can leave the most experienced techie baffled. Fortunately there are some shortcuts to adjusting your picture for optimal quality.
First try cycling through the presets. They have names like "Standard," "Movie" "Dynamic," and "Sports," and each typically delivers different brightness, color and other characteristics. Many TV watchers are content to choose a mode they like and leave it at that.
If you're not, it's time to dive into the individual controls. You can make basic adjustments by eye with the right program material, invest in a setup disc on DVD or Blu-ray, or even spring for a full-fledged professional calibration. You could also try using the picture settings we at CNET publish as a part of our TV review process.
Room lighting can have a big effect on picture quality, so when you can we recommend watching in a dim or dark room. When that's not possible, you should avoid letting a light source, such as a lamp or even a window, reflect from the TV screen. To avoid windows you might even want to consider moving your seating configuration to avoid reflections.
HDTVs can use a good deal of power, especially large models with bright picture settings, so if you want to be a greener TV watcher you can definitely take a few steps. Check out TV power saving tips for more info.
Still confused about how to get the most out of your new TV? Check out CNET's Home Audio and Video forums. Think you have a good tip I missed here? Leave a comment below.
Discuss: HDTV setup tips: So you have a new TV...now what?


text:
Clifton Collins Jr Movies
Hacker HD
With the help of his new friends Alex Danyliuk turns to a life of crime and identity theft.
Country: USA, Thailand, Kazakhstan, Hong Kong, Canada
Director: Akan Satayev
Actor: Callan McAuliffe, Lorraine Nicholson, Daniel Eric Gold, Clifton Collins Jr, Zachary Bennett, Kristian Truelsen, Vlada Verevko, Genadijs Dolganovs, Randy Thomas, Greg Hovanessian
M.F.A.
M.F.A. HD
An art student taps into a rich source of creative inspiration after the accidental slaughter of her rapist. An unlikely vigilante emerges, set out to avenge ..
Director: Natalia Leite
Actor: Francesca Eastwood, Clifton Collins Jr, Leah McKendrick, Peter Vack, Marlon Young, David Sullivan, Michael Welch, Mike C. Manning, David Huynh, Jess Nurse
Man Down HD
In a post-apocalyptic America, former U.S. Marine Gabriel Drummer searches desperately for the whereabouts of his son, accompanied by his best friend and a su..
Director: Dito Montiel
Actor: Shia LaBeouf, Jai Courtney, Gary Oldman, Kate Mara, Tory Kittles, Clifton Collins Jr, Charlie Shotwell, Jose Pablo Cantillo, Justin Smith, Paul Sado
Parker HD
A thief with a unique code of professional ethics is double-crossed by his crew and left for dead. Assuming a new disguise and forming an unlikely alliance wi..
Genre: Action, Crime, Romance
Director: Taylor Hackford
Actor: Jason Statham, Jennifer Lopez, Nick Nolte, Michael Chiklis, Clifton Collins Jr, Sala Baker, Carlos Carrasco, Wendell Pierce, Emma Booth, Daniel Bernhardt
Small Town Crime
Small Town Crime HD
An alcoholic ex-cop finds the body of a young woman and, through an act of self-redemption, becomes hell-bent on finding the killer but unwittingly puts his f..
Director: Eshom Nelms
Actor: John Hawkes, Octavia Spencer, Anthony Anderson, Robert Forster, Clifton Collins Jr, Michael Vartan, Caity Lotz, James Lafferty, Stefanie Scott, Daniel Sunjata
The Vault HD
Two estranged sisters are forced to rob a bank in order to save their brother. But this is no ordinary bank.
Director: Dan Bush
Actor: James Franco, Taryn Manning, Francesca Eastwood, Scott Haze, Q'orianka Kilcher, Jeff Gum, Clifton Collins Jr, Keith Loneker, Jill Jane Clements, Michael Milford
Transcendence HD
A scientist's drive for artificial intelligence, takes on dangerous implications when his consciousness is uploaded into one such program.
Country: UK, China, USA
Actor: Johnny Depp, Paul Bettany, Rebecca Hall, Kate Mara, Morgan Freeman, Cillian Murphy, Cole Hauser, Clifton Collins Jr, Falk Hentschel, Kristen Rakes
Triple 9 HD
A gang of criminals and corrupt cops plan the murder of a police officer in order to pull off their biggest heist yet across town.
Director: John Hillcoat
Actor: Casey Affleck, Chiwetel Ejiofor, Woody Harrelson, Kate Winslet, Anthony Mackie, Aaron Paul, Norman Reedus, Gal Gadot, Teresa Palmer, Clifton Collins Jr
Westworld - Season 2
Westworld - Season 2 HD
Set at the intersection of the near future and the reimagined past, explore a world in which every human appetite can be indulged without consequence.
Actor: Evan Rachel Wood, Thandie Newton, Jeffrey Wright, James Marsden, Ed Harris, Ben Barnes, Ingrid Bolsø Berdal, Clifton Collins Jr, Luke Hemsworth, Sidse Babett Knudsen


After multiple tests, I can happily say with out any doubt in my mind that 2008 server blows 2003 server in terms of web performance out of the water… How do I come to this conclusion you ask?
If you have been reading up on my partner in crime's Blog (Alan Lee) and Craig Baileys blog we have been performing some extensive bench testing on the servers. Alan within his blog describes the method that we have used to perform our testing, which in brief is a Linux command which does a simple WGET mirror of the home page this mirror copies all the contents locally and then removes it after the crawl is complete, within the mirror command it also copies all other associated links on the home page (there is roughly 13 links which means it copies another 13 pages and associated images).
One WGET, from the Elcom home page would receive a rough total of 6.4MB which with today's bandwidth speeds and abundance of images and multimedia everywhere we look this is not a huge number, its what we would call realistic.
The test, the script was set to run 20 concurrent connections 1,000 times. Again 20 concurrent connections is very realistic, if anything it may not be enough, however we though give the size and the connections this was a good benchmark.
JAW DROPPING isn't it, yes we ran the exact same tests, we had them configured the same, both out of the box with IIS installed as an additional component and installed .NET 2.0 on both machines nothing different.
However during these tests we could see for 2003 Server the bottleneck appeared to be the CPU as it was using everything it could get, so we thought ok let try something bigger.
Now that we had something bigger and better to test on, we thought ok lets compare something that is a little bit smaller in size, to speed the process up and also see what happens in terms of speeds.
2008 is still 4 times faster with something tiny and very manageable. There were no bottlenecks here are all, the CPU for 2003 was not varying between 70 and 80%. The memory was very, very much under utilized, it seemed to only use a lousy 350MB, when it had gigs to use.
Where as Server 2008, made much better use of the memory and left more CPU, See below for the stats yourself.
This shows that the SQLSVR is taking little resources, there is obviously not much for it to do there, are really no transactions of it to think about.
Here is how the network card was reacting to the masses of connections.
And here is the overview of all performance, as you can see the disk was getting a work out, but dosnt seem to be a bottle neck either.
To conclude… change all your servers to 2008, I know I cant wait to start implementing a few more 2008 Servers across our network at work.
This entry was posted on Tuesday, February 26th, 2008 at 1:51 am	and is filed under Microsoft, Server 2008, Software, Techie	. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.
I am often to running a blog and i really respect your content. The article has really peaks my interest. I am going to bookmark your site and hold checking for brand new information.


text:
Some uncomfortable questions about Eden's looming brewery closure
By Allan Freyer
- in Featured Articles, Progressive Voices
State Senate Leader Phil Berger has some questions about the news that MillerCoors is going to close its long-time facility in Eden, Rockingham County, laying off 520 people in the process. Last night, he and fellow Rockingham legislator Bert Jones sent a letter to the U.S. Senate Subcommittee on Antitrust, Competition Policy and Consumer Rights with a list of questions they urged the panel to pursue in an effort to determine whether the Eden brewery closure falls afoul of federal anti-monopoly regulations.
The Senator's efforts are admirable given the enormously negative impact the plant's closure would have on the rural community, which already has one of the state's highest unemployment rates. And we sincerely hope that the brewery remains open, staving off the kind of mass layoffs that proved so disastrous to the human and economic fabric in rural communities like Kannapolis.
But after years of watching the legislature systematically dismantle the very state investments that protect jobless workers and promote community resiliency in times of high unemployment, workers in Rockingham and across North Carolina have some questions for Senator Berger as well:
Why should Rockingham workers lose their unemployment benefits if they can't find a job after 12 weeks ? If the brewery closes, 520 workers will lose their jobs through no fault of their own. Given that there are already twice as many unemployed workers as available job openings in Rockingham County (according to NCWorks), it will be mathematically very difficult for most these laid off workers to find new jobs. Thanks to the policies enacted by the General Assembly in 2013, Rockingham County workers will only have 12 weeks to find a job before they lose their unemployment benefits—the lowest duration offered for temporary wage replacement in the nation.
Why should these laid off workers in Rockingham County lose food assistance after just three months if they can't find employment in a job market without enough jobs? Since welfare reform in 1990s, the federal government has required able-bodied adults with no dependents to find a job, be engaged in skills training, or participate in other qualifying activities after three months of receiving food assistance or lose this assistance altogether. At the same time, federal law allows states to request waivers from this time limit in economically distressed counties where jobs are not available. Unfortunately, the General Assembly banned the state from offering this waiver in 2015, despite the 77 counties that qualified due to weak labor markets. In effect this move will significantly reduce access to food assistance for workers living in those counties, including Rockingham, after July 1 when the prohibition goes into effect.
How will the Rockingham economy benefit from a system that provides workers with the lowest weekly unemployment benefits in the country? As part of unemployment insurance reform package enacted in 2013, the amount of unemployment insurance payments workers receive as a replacement to the wage they used to earn while employed was cut to an average of $233 a week— one of the lowest in the nation. This means that if Coors shuts down the Eden brewery, those 520 laid-off workers will almost certainly reduce their spending at local businesses. And given that employers need paying customers to stay in business, these unemployment benefit cuts will only make it harder for local businesses to survive.
Why didn't the North Carolina General Assembly expand Medicaid so that jobless workers in Rockingham County could have health coverage? As a union facility, the Eden brewery provides health insurance to most of its employees, insurance that laid-off workers will lose if the plant closes. In many other states, Medicaid expansion would provide these workers with the healthcare they would no longer receive through their job. Unfortunately, the General Assembly has refused to expand Medicaid in North Carolina, a decision that will likely leave hundreds of laid-off workers without access to affordable healthcare and add to the almost 3,000 county residents who already lack health insurance coverage. Moreover, a recent study showed expanding Medicaid would create 313 new jobs and $127 million in new business activity In Rockingham County by 2020—a crucial opportunity for reversing the job loss and local economic decline that would occur if the brewery closes.
Why has the state failed to invest state dollars in retraining and workforce development to ensure that workers in Rockingham County can gain the skills they need for new employment opportunities? Job training is a critical investment that gives unemployed workers the tools they need to retrain and gain the skills required to enter higher-wage occupations. Career pathway programs in particular create avenues for workers to build occupation-specific skills consecutively over the course of a career, creating stepping stones for long-term advancement within that occupation. But while the state has created successful programs like Basic Skills Plus and employer partnerships to provide workers with employment-ready skills in high-demand occupations, the General Assembly has repeatedly refused to adequately fund these programs. In fact, state commitment to workforce development has dropped by 10 percent since 2008 at the same time that the General Assembly has doubled the cost of community college tuition—putting retraining programs out of reach for many workers who would suffer from a Coors closure.
We wish Senator Berger well in his efforts to keep the Eden brewery open. But he needs to explain to his constituents why the legislature has been so comfortable dismantling the investments that would support unemployed workers and boost the Rockingham economy if the brewery ultimately closes.
Allan Freyer is the Director of the Workers' Rights Project at the North Carolina Justice Center. Alexandra Sirota of the N.C. Budget & Tax Center contributed to this commentary.
Governor quietly approves "Polluter Protection Act"
Grief at the heart of the Moral Movement
Help children's health by closing the Medicaid coverage gap
Duke Energy seeks to rig the system
Previous article Not much of a Carolina Comeback for low-income families
Next article Helping our economy by investing in high-quality Pre-K


text:
Yanjmaagiin Dorj (born 17 June 1954) is a Mongolian judoka. He competed in the men's extra-lightweight event at the 1980 Summer Olympics.

References

1954 births
Living people
Mongolian male judoka
Olympic judoka of Mongolia
Judoka at the 1980 Summer Olympics
Place of birth missing (living people)

redpajama_set_name: RedPajamaWikipedia


Renew! Renew! Renew! The AYC annual membership renewal season is well underway. Don't wait till the last minute…CLICK HERE to register now, or if you need some help come on down to the July membership meeting at Tempe Rolling Hills Golf Course (Tuesday, 7/12/11) and we'll get you signed up there and then!
We have a newly designed membership card in the works, which will be personalized in a batch run – make sure you get your renewal in before the end of July so that you don't miss out on the permanent annual card AND listing in the annual membership roster.
Prefer to use the good old US Mail and a pen or pencil? Drop an email to one of our "Ace" Membership Directors and they'll get you a hardcopy form to fill out and you can mail in your check. Time's a waistin! Renew your membership today!


Irene Mary Arends,nee Barry, 81, of Libertyville, Aug. 16, beloved wife of the late Edward; loving mother of Greg (Rosemary) Arends and Mary Catherine (Matt) Staley; dearest aunt of Nancy Meyer; proud grandmother of Nicholas, Alex, Danny, Chris, Michael and Mary Elizabeth; dear sister of Rita (Norbert) Mauch.
Funeral Service 9:30 a.m. Monday, Aug. 20 from McMurrough Funeral Chapel,101 Park Pl., Libertyville (Rt. 176, 1 blk E. of Milwaukee Ave.), to St. Joseph Church, 121 E. Maple Ave., Libertyville.
Mass 10 a.m. Interment Ascension Cemetery.
Visitation Sunday, 4 to 8 p.m. at the funeral chapel.
If desired memorials to the Alzheimer's Society, 4709 Golf Rd., Suite 1015, Skokie, IL 60076 would be greatly appreciated.


DANIEL Ricciardo has admitted he expected his relationship with now former-Red Bull teammate Max Verstappen to be a lot worse than it was.
The duo spent nearly three years together at the Milton Keynes-based outfit after Verstappen was promoted from Toro Rosso to replace Daniil Kvyat mid-season in 2016.
They have come across as good friends off the track but have shared some intense on-track moments, like battling for victory of the Malaysian Grand Prix in 2016 and their infamous crash in Baku earlier this year.
Verstappen's dad, Jos, also revealed his son was angry at Ricciardo Mexico this year following his celebrations after sealing pole at the expense of his teammate in a last-minute lap.
But with Ricciardo leaving for Renault in 2019, the Australian believes the two's relationship may actually improve as they will no longer be "direct competitors".
"Unless we're battling for the same bit of Tarmac," Ricciardo said on a Red Bull podcast. "That could always spice it up!
"I'd say the relationship with Max and myself went better than, I'll be honest, I thought it would go.
"Just our personalities and our self-belief. I really believe he thinks he's the best in the world and I believe I am.
"So, that can obviously clash. But we always managed at least 99% of the time managed to keep that in its own little place.
"It was cool, it was a good, hard fight with him and I enjoyed it."
Verstappen is widely tipped to be one of the closest challengers to Lewis Hamilton over the next few seasons, should Red Bull's partnership with Honda go well, and Ricciardo is predicted greatness for the Dutchman.
However, he did concede that Red Bull will have to match Verstappen's ambitions and that what he can achieve will be more down to being in the right car at the right time.
"There's a lot of potential, for sure some potential greatness for Max," Ricciardo added. "I think it's all about the trajectory. He was quick from day one but I'm convinced he's a lot quicker than his first win for Red Bull.
"So, I'm sure he'll keep improving, but it's probably going to be more of a scenario/situation if he's going to be in a car that's capable.
"That's probably going to dictate what levels of greatness he's going to achieve.
"He's obviously very talented and I've enjoyed the challenge with him, the rivalry. I think we've both grown as drivers - it's been beneficial to both of our careers."


text:
Pop Culture Media Arrow Down
Entertainment Arrow DownArrow Down Solid
TV Database
Celebrity Arrow DownArrow Down Solid
Lifestyle Arrow DownArrow Down Solid
Sports Arrow DownArrow Down Solid
Sports Drip
Comicbook Arrow DownArrow Down Solid
Gaming Arrow DownArrow Down Solid
or sign in with your PopCulture.com ID:
By creating an account, you verify that you are at least 13 years of age, and have read and agree to the PopCulture.com Terms of Service and Privacy Policy
Westworld: Understanding Maeve's Path Towards Self-Awareness
By Christian Hoffer - November 10, 2016 12:33 pm EST
In last week's episode of Westworld, we got a long glimpse into the mind and programming of the park hosts. When Maeve suddenly came to life in the bowels of Westworld's command center, a body shop employee showed her how different she was from a real human being. In addition to watching Maeve's actual "thoughts" (or in this case, a complex program that analyzes events and crafts responses) form on screen, the show also revealed that every host's personality was created via a complex and malleable chart of personality traits and attributes.
The host's personality chart wasn't that different from a Dungeons and Dragons character sheet, where players distribute points in certain attributes to help their character in certain situations. A host with a high "charm" rating might be able to talk and flirt her way out of trouble, but someone with a low self-preservation stat might wind up in the body shop getting bullets pulled out of their chest.
These personality charts are also changeable and are often edited by the programming team to give hosts new personalities when they take up new roles in the park. While someone else (heavily implied to be the mysterious Arnold) has been making major edits to the hosts' personalities, Maeve took the opportunity to make some changes to her own stats.
In addition to tweaking some of her other stats, Maeve had the techs up her "bulk apperception" stat to its maximum level. One of the techs briefly explained in the episode that apperception was a measure of intelligence, but it actually has much deeper implications for the show's slowly building plot of the hosts becoming truly self-aware.
Apperception actually has nothing to do with intelligence, but rather a person's ability to make sense of an idea or event in the context of past events in that person's life. In layman's terms, it's the ability to understand something by comparing it to past experiences. People appercieve things in different ways based on their experiences, which makes it a fundamental part of how humans think and process ideas.
A good example of apperception is watching how two people react to the same object. A 16 year old who gets a used car might see that car as a great gift because it enables them to drive, but a rich person given the same car could see at as insult because they're used to driving better.
Because apperception is a bit of a complex concept, it can be hard to grasp why that particular aspect is so important to the hosts of Westworld. In some philosophical circles, apperception is considered critical to self-consciousness, as it effectively controls how a person thinks and experiences life. Basically, apperception is one of the fundamental building blocks to self-awareness and it exists within the fundamental coding for every host inside of Westworld.
Maeve already had a high apperception skill because Westworld staff put her in a management position and wanted her to be able to understand and react to events inside her bordello. This could explain why she didn't have a meltdown when Felix gave a tour of the Westworld facilities, even as her entire reality was shown to be an illusion. But Maeve's apperception was still limited by a Westworld policy to prevent their hosts from understanding too much.
So now that Maeve's apperception is at its highest level, does that mean she's now self-conscious? Considering that Arnold never succeeded in creating an autonomously thinking host, it's unlikely that a maximum apperception is enough to make a host self-aware. But apperception is all about contextualizing experience. If Maeve returns to the park and continues to peel back at the layers of her false reality, it's possible that her high apperception will allow her to break free of her programming and form her own "real" thoughts.
Apperception isn't supposed to be self-awareness in Westworld, but it's definitely an important step for the hosts to gain it. We'll have to see if Maeve's modified personality will lead to her becoming a real independently thinking being.
MORE WESTWORLD: Mythology Of The Maze Revealed / What We Know About Dolores So Far / Angela Sarafyan On Host Evolution / The Man In Black Is Going To Free The Hosts / Who Is Arnold / The Man In Black's Backstory Revealed / What Planet Is Westworld On / Logos May Reveal Two Seperate Timelines
WestworldSunday at on HBO
ComicBook Composite NAAll-Time Comic TV Shows
3.75/5 from 8 usersNAAll-Time Rated
'13 Reasons Why': Netflix Finally Edits Suicide Scene After Years of Backlash
Jenelle Evans Going to 'Focus on the Positive' Amid E! News Host Feud, Dog Killing Fallout
Jason Aldean's Wife Brittany Reveals New Home Has a Concrete Safe Room
Watch the Moment A Documentary Film Is Held at Gunpoint for Sneaking Into Area 51
Emmys 2019 Nominations: 'Game of Thrones' Makes History With 32 Nods
Danielle Fishel Posts That Son Adler Is Finally out of the Hospital in New Photo
'Deadliest Catch' Earns 3 Emmy Nominations for Discovery Channel
YouTube Star PewDiePie Says Storming Area 51 'Actually Makes a Lot of Sense'
Entertainment Tonight/TV Guide Network. Copyright 2018 PopCulture.com. All rights reserved.


At this point in his career, Lil Yachty is a seasoned professional when it comes to not paying attention to what his haters (often older hip-hop heads) have to say about his music.
After admitting in an interview that he can't name five Tupac songs, the rapper was met with all sorts of criticism, some even calling into question his roots and how he was raised.
In a recent video interview, his father, Shannon McCollum, defends his son's honor, saying that his son isn't making music to win over the approval of older fans of rap music.
During the clip, McCollum says that the music his son making is geared towards attracting a fan base his own age, and that Lil Yachty's brand of rap is created by a teenager, made for teenage listeners.
"I would say to the older cats, because I'm an older cat, first off, I would say, it's not for you," his father says. "He calls himself king of the teens, not the king of the ole' heads, ya dig? It's not for you, it's for your kids. Let your kids rock with it."
He also excuses his son for not understanding the origins of hip-hop, saying that it comes with the territory of being a fresh high school graduate, while others firmly hold the argument that not knowing the history of the culture he's contributing to is inexcusable. His father also says that he, being older, doesn't know any of 21 Savage's songs because he's not really supposed to. He also adds that most people his son's age don't know the origins of hip-hop either.
At the end of the day, Lil Yachty was born in 1997, making him freshly 19 years old, and he's still accomplishing important career milestones regardless of his critics.
Take a listen to Lil Yachty's dad defending his son's music in the interview clip below.