text:
\section{Introduction}

Let $T \approx \mathbb{R}^2/\mathbb{Z}^2$ be the closed oriented surface of genus one.
We indicate the homotopy class of an embedding of $S^1$ briefly by `curve'.
By pulling a curve tight and lifting it to the universal cover, the collection of curves on $T$ is in one-to-one correspondence with slopes $\mathbb{Q} \cup \{\infty\}$.
From this vantage point, the \emph{intersection number} of a pair of curves on $T$ (that is, the minimum possible number of intersection points among representatives from the pair of homotopy classes) can be computed explicitly via
\[
\iota\left( \frac pq , \frac ab\right) = \ | \ pb-qa \ | \ ~.
\]
A collection of curves is called a \emph{$k$-system} when any pair of curves has intersection number at most $k$.

Let $\eta_S(k)$ equal the maximum size of a $k$-system on the closed surface $S$.
It was first shown by \cite{JMM} that $\eta_S(k)$ goes to infinity with $k$.
The determination of the growth rate of $\eta_S(k)$, as a function of both $k$ and the genus $g$ of $S$, is a subtle counting problem, about which much remains unknown \cite{Przytycki, Aougab, ABG, Greene1, Greene2}.
Notably, Greene has used probabilistic methods, leveraging the hyperbolic geometric bounds of Przytycki, to obtain $\eta_S(k) =O( g^{k+1}\log g)$, when $k$ is fixed and $g$ grows \cite[Thm.~3]{Greene2}.

For the study of $\eta_S(k)$ with $g$ fixed, the simplest nontrivial case is evidently $S=T$.
While studying Dehn filling slopes of 3-manifolds, Agol observed that $\eta_T(k)$ is at most one more than the smallest prime greater than $k$ \cite{Agol}, and via the Prime Number Theorem this implies $\frac{\eta_T(k)}k \to 1$ as $k\to \infty$ \cite{Agol-unpub}.

More can be said.
The size of prime gaps, large and small, is a major field of study.
The currently best upper bound is due to Baker-Harman-Pintz, which, together with Agol's observation, implies that $\eta_T(k) = k+O(k^{21/40})$ \cite{BHP}.
Cram\'er showed that a positive resolution of the Riemann hypothesis would provide $\eta_T(k) = k + O(\sqrt k \log k)$ \cite{Cramer1}, and he formulated a stronger conjecture that would imply $\eta_T(k) = k+O((\log k)^2)$ \cite{Cramer2}; although there seems to be general suspicion in the analytic number theory community that Cram\'er's error term should be replaced by $O((\log k)^{2+\epsilon})$ \cite{Granville, OSS}.

All of these estimates pass through Agol's remarkable prime number bound, but it is reasonable to be skeptical about whether estimation of $\eta_T(k)$ should depend on such notoriously subtle and difficult questions.
The purpose of this note is to sharpen currently available estimates, without reference to fine data about the distribution of the primes.
Our methods are elementary, combinatorial, and hyperbolic.

\begin{theorem}
\label{main thm}
There is a constant $C>0$ so that $\eta_T(k)\le k+C\sqrt k \log k$.
\end{theorem}

As for sharpness, it deserves remarking that there is a dearth of nontrivial lower bounds for $\eta_T(k)$.
In fact, we are unaware of any example of a $k$-system of size $k+7$ on the torus.

The function $\eta_T(k)$ admits a dual formulation: let $\kappa_S(n)$ indicate the minimum, taken over collections of $n$ curves on $S$, of the maximum pairwise intersection.
(For clarity, we will often use `$n$' to indicate the size of a set of curves and `$k$' for an intersection number.)
It is not hard to see that
\[
\eta_S(k) = \max \{ n: \kappa_S(n) \le k\} \ , \text{ and } \
\kappa_S(n) = \min \{k : \eta_S(k)\ge n\}~.
\]
Our path towards \autoref{main thm} will be to first estimate $\kappa_T(n)$ from below.

There is a kind of convexity to exploit in the study of $\kappa_T$, originally observed by Agol.
As remarked above, curves on $T$ are in correspondence with slopes $\mathbb{Q}\cup \{\infty\}$.
The latter form the vertices of the \emph{Farey complex} $\mathcal{F}$, in which a set of slopes form a simplex when they pairwise intersect once.
Any collection of $n$ curves that is maximal with respect to inclusion among $k$-systems determines a collection of vertices in $\mathcal{F}$ so that the induced simplicial complex is a triangulated $n$-gon (see \autoref{lem: convexity} for detail).

Conversely, any triangulation of an $n$-gon can be realized as a subcomplex of $\mathcal{F}$, in a way that is unique up to the action of $\mathrm{PSL}(2,\mathbb{Z}) \curvearrowright \mathcal{F}$ by simplicial automorphism. As $\mathrm{PSL}(2,\mathbb{Z})$ preserves the intersection form, the (multi-)set of pairwise intersection numbers is a well-defined function on the set of triangulations of an $n$-gon.
The set of triangulations of an $n$-gon forms the vertex set of a well-studied simplicial complex in combinatorics called the \emph{associahedron} $\mathcal{A}_n$
(there is a slight indexing issue; the object we refer to as $\mathcal{A}_n$ is the $(n-2)$-dimensional associahedron).
One obtains a `max intersection' function $\kappa: \mathcal{A}_n \to \mathbb{N}$ induced by the intersection form on $\mathcal{F}$,
and the above discussion leads to $\kappa_T(n)=\min \kappa$ (see \autoref{prop:kappa=kappa}).

\autoref{main thm} follows from the following:

\begin{theorem}
\label{thm: kappa}
There is a constant $C>0$ so that, for any $\tau\in \mathcal{A}_n$, we have $\kappa(\tau) \ge n - C \sqrt n \log n $.
\end{theorem}

We briefly describe the proof of this theorem.
The Farey complex $\mathcal{F}$ admits a natural embedding into a compactification of the hyperbolic plane $\mathbb{H}^2 \,\cup\, \partial_\infty \mathbb{H}^2$, so that the vertices of $\mathcal{F}$ embed naturally as $\mathbb{Q} \cup\{\infty\} \hookrightarrow \mathbb{R}\cup\{\infty\} \approx \partial_\infty \mathbb{H}^2$, with edges between vertices mapping to geodesics.
The hyperbolic plane $\mathbb{H}^2$ admits a maximal $\mathrm{PSL}(2,\mathbb{Z})$-invariant horospherical packing $\{H_{p/q}: \frac pq \in \mathbb{Q}\cup\{\infty\}\}$, where $H_{p/q}$ is centered at $p/q\in \mathbb{R}\cup\{\infty\}$, so that a set of slopes span a simplex in $\mathcal{F}$ precisely when the corresponding horospheres are pairwise tangent. (The horospheres $\{H_{p/q}\}$ are called \emph{Ford circles} in the literature \cite{Ford, ConwayGuy, BonahonVid}.)

A sketch of our proof of \autoref{thm: kappa} is as follows:
\begin{enumerate}
\item Locate a `nice horoball' $H$ for $\tau$, so that $\mathrm{ht}(\tau,H)$, the \emph{height of $\tau$ relative to $H$}, is $O\left(\sqrt{\kappa(\tau)}\right)$.
See \autoref{def:horoball height width} and \autoref{prop: exists horoball}.

\item Use $H$ to construct a convex combination of pairwise intersection numbers for $\tau$ whose sum is at least $n - O(h \log h)$, where $h= \mathrm{ht}(\tau,H)$.
It follows that there is a pair of horoballs of $\tau$ with intersection number at least $n-O(h \log h)$.
See \autoref{prop: control with height}.

\end{enumerate}
The proof of \autoref{thm: kappa} is now one line: if $\kappa(\tau)\le n$, then $\kappa(\tau) \ge n-C \sqrt n \log n$.

The first step above uses the hyperbolic geometry of $\mathbb{H}^2$ in an essential way, in which we exploit a simple relationship between intersection numbers, hyperbolic geometry, and Ford circles (see \autoref{lem:i vs d}).

\subsection*{Organization}
We describe the reduction from $\kappa_T(n)$ to $\kappa:\mathcal{A}_n\to\mathbb{N}$ in \S\ref{sec:prelim}, analyze several examples in \S\ref{sec:examples}, bound $\kappa(\tau)$ from below in \S\ref{sec:estimating kappa}, locate a good horoball for $\tau$ in \S\ref{sec:controlling height}, and prove \autoref{main thm} in \S\ref{sec:pf of main thm}.

\subsection*{Acknowledgements}
The authors thank Josh Greene and Ian Agol for valuable feedback on an early draft of this paper. We are especially grateful to Ian Agol for sharing with us an unpublished note that contained \autoref{lem: convexity}, and for suggesting an alternative to our proof of \autoref{prop: exists horoball} (see \autoref{rem: Agol proof}).

\section{Preliminaries}
\label{sec:prelim}

We collect here some useful facts about intersection numbers and the Farey graph $\mathcal{F}$.
For more of the beautiful connections between hyperbolic geometry, the Farey graph, continued fractions, and Diophantine approximation, we suggest the reader consult \cite{Hatcher, Series, Series2, Springborn}.

\subsection{Horoballs in trees, Farey labellings, and intersection numbers}
Dual to a triangulation of an $n$-gon $\tau\in\mathcal{A}_n$ there is a trivalent tree with $n$ leaves embedded in the plane, which we refer to as $\tau^*$.
Because $\tau^*$ is embedded in the plane, the three edges incident to vertices of $\tau^*$ are cyclically ordered.
Hence any non-backtracking path in $\tau^*$ induces a sequence of left-right turns.

The vertices of $\tau$ (that is, the slopes of the $k$-system) correspond to `horoball' regions in $\tau^*$:

\begin{definition}[`Horoballs in trees']
\label{def:horoball}
A \emph{horoball} of $\tau$ is a union of edges in a path of the dual tree $\tau^*$ that is composed of uni-directional turns (that is, only left or only right turns), which is moreover maximal with respect to inclusion among all such uni-directional subsets of $\tau^*$.
\end{definition}

For any triangulation $\tau$, the dual tree $\tau^*$ admits an orientation-preserving embedding to the regular trivalent tree dual to $\mathcal{F}$.
Any such choice of an embedding determines a map from horoballs of $\tau^*$ to $\mathbb{Q}\cup \{\infty\}$, by recording the center of the corresponding horoball in $\mathbb{H}^2$.

\begin{definition}[`Farey labellings and intersection numbers']
A \emph{Farey labelling} of $\tau$ is the map from horoballs to $\mathbb{Q}\cup\{\infty\}$ obtained from an orientation-preserving embedding from $\tau^*$ to the tree dual to $\mathcal{F}$.
The \emph{intersection number} $\iota(H_1,H_2)$ of a pair of horoballs $H_1$ and $H_2$ is given by the intersection number of the slopes corresponding to $H_1$ and $H_2$ in a Farey labelling of $\tau$.
\end{definition}
\noindent
We leave it as an exercise for the reader to show that intersection numbers in $\tau$ are well-defined.

Farey labellings are especially pleasant because the vertices spanning a simplex of $\mathcal{F}$ satisfy a remarkably simple relationship. Namely, if $\frac pq$ and $\frac ab$ span an edge of $\mathcal{F}$, then the two other vertices of $\mathcal{F}$ that span a triangle with $\frac pq$ and $\frac ab$ are $\frac{p+ a}{q+ b}$ and $\frac{p-a}{q- b}$; this is the `Farey addition' rule.
Farey addition can be used to construct a Farey labelling of $\tau$:
Choose labels $1/0$, $0/1$, and $1/1$ for the three horoballs incident to some vertex of $\tau^*$, and use Farey addition to successively add labels to neighboring horoballs.

\subsection{Monotonicity of intersection numbers and left-right sequences}
\label{subsec:monotonicity}
The intersection number $\iota(H_1,H_2)$ admits a description more intrinsic to the structure of $\tau^*$, which we now describe.
There is a unique (possibly degenerate) non-backtracking path $\sigma$ between the pair of horoballs $H_1$ and $H_2$, and this path determines a sequence of left-right turns $(\ell_1,\ell_2,\ldots,\ell_s)$, where $\sigma$ makes $\ell_1$ turns in the same direction, followed by $\ell_2$ turns in the opposite direction, etc.
The quantity $\iota(H_1,H_2)$ is given by the numerator of the continued fraction with coefficients $(\ell_1,\ell_2,\ldots,\ell_s)$ \cite[Thm.~5.3]{GLRRX}.

\begin{remark}
\label{rem:ambiguity}
Observe that there is ambiguity in this computation of $\iota(H_1,H_2)$.
For one, the non-backtracking path $\sigma$ may go either from $H_1$ to $H_2$, or from $H_2$ to $H_1$.
Moreover, one must declare that $\sigma$ is starting with either `left' or `right' at its origin vertex, so that it can be observed whether $\sigma$ is switching directions or not at later vertices.
These choices may be made arbitrarily and independently, and this ambiguity has no affect on the calculation of $\iota(H_1,H_2)$. See \cite[Fig.~3, Ex.~1]{GLRRX}.
\end{remark}

This viewpoint suggests a certain monotonicity.

\begin{lemma}[`Monotonicity of intersection numbers']
\label{lem:monotonicity}
Suppose that $\sigma$ and $\sigma'$ are non-backtracking paths with respective left-right sequences $(\ell_1,\ldots,\ell_s)$ and $(\ell_1',\ldots,\ell_{s'}')$.
If $s'\ge s$ and $\ell_i'\ge \ell_i$ for each $i=1,\ldots,s$, then the intersection number determined by $\sigma'$ is at least that determined by $\sigma$.
\end{lemma}

\begin{proof}
This lemma is almost exactly \cite[Lem.~5.5]{GLRRX}, with the sole difference that we may have $s'>s$.
Therefore to prove the claim we may assume that $\sigma'$ contains $\sigma$ as an initial subpath.

Choose a Farey labelling with label $1/0$ at the horoball forming the origin of $\sigma$ (and $\sigma'$), and labels $0/1$ and $1/1$ at the two neighboring horoballs that intersect $\sigma$.
Compare the denominators of the Farey labels of the horoballs at the terminuses of $\sigma$ and $\sigma'$; because these labels are computed using Farey addition, it is evident that the denominator of the horoball for $\sigma'$ is at least that of $\sigma$.
The intersection number of any horoball with $1/0$ is given by the denominator of its Farey label, so the claim follows.
\end{proof}

\subsection{Intersection numbers and hyperbolic distance}
The quotient of $\mathbb{H}^2$ by $\mathrm{PSL}(2,\mathbb{Z})$ is a hyperbolic orbifold with one cusp and two orbifold points, one of order $2$ and one of order $3$.
The preimage of the maximal horoball neighborhood of the cusp under the covering projection $\mathbb{H}^2 \to \mathbb{H}^2/\mathrm{PSL}(2,\mathbb{Z})$ is $\mathcal{H}=\{H_{p/q}:p/q\in\mathbb{Q}\cup\{\infty\}\}$,
a $\mathrm{PSL}(2,\mathbb{Z})$-invariant collection of horoballs centered at the completed rationals.
The following lemma is an exercise in hyperbolic geometry.

\begin{lemma}
\label{lem:distance from horoball}
Every point in $\mathbb{H}^2$ is within $\log\frac2{\sqrt 3}$ of a horoball in $\mathcal{H}$.
\end{lemma}

There is a simple fundamental relationship between intersection numbers of curves on the torus and hyperbolic distance between the corresponding horoballs.

\begin{lemma}
\label{lem:i vs d}
We have
$\
\displaystyle d_{\mathbb{H}^2}\left(H_{p/q},H_{a/b} \right) =
2 \log \iota\left( \frac pq , \frac ab \right) ~$
for any $\frac pq, \frac ab \in \mathcal{F}$.
\end{lemma}

\begin{proof}
Applying an element of $\mathrm{PSL}(2,\mathbb{Z})$, we may assume that $p/q=\infty$ in the upper half-plane model for $\mathbb{H}^2 \, \cup \, \partial_\infty \mathbb{H}^2$.
The horosphere $H_{a/b}$ is given by $\{z: \left| z-(\frac1b + \frac i{2b^2}) \right| = \frac1{2b^2}\}$ (see e.g.~\cite{Athreya}), so
\[
d_{\mathbb{H}^2}\left(H_{p/q},H_{a/b} \right) =
d_{\mathbb{H}^2}\left( a/b + \frac i{b^2} , a/b + i\right) = 2\log b = 2 \log \iota\left( \frac pq , \frac ab \right) ~. \qedhere
\]
\end{proof}

\subsection{Width and height for horoballs}\label{sec:width/height}
The interior of each edge of $\tau^*$ is incident to exactly two horoball regions.
Thus, for any choice of horoball $H$ in $\tau^*$, there are exactly two other horoball regions, distinct from $H$, that are incident to the interiors of the extreme edges of $H$. Call these $H_1$ and $H_2$.

\begin{definition}
\label{def:horoball height width}
The \emph{width of $\tau$ relative to $H$} is $w = \iota(H_1,H_2)$. The \emph{height of $\tau$ relative to $H$} is
\[
\mathrm{ht}(\tau,H) =
\max\, \{ \ \iota(H, H') \ : H' \text{ is a horoball of }\tau \ \}~.
\]
\end{definition}

For the remainder of this article, we will suppress the difference between the triangulation $\tau\in\mathcal{A}_n$ and its dual tree $\tau^*$.
The translation between them is quite natural, and the difference can henceforth be understood from context.

\subsection{The two kappas}
Recall from the introduction the quantity $\kappa_T(n)$, which is the minimum, taken over collections $\Gamma$ of $n$ curves on $S$, of the maximum pairwise intersection number of curves in $\Gamma$.
\begin{definition}[`Max Intersection Function']
\label{def:kappa}
The function $\kappa:\mathcal{A}_n\to \mathbb{N}$ is defined by
\[
\kappa(\tau) = \max\{\ \iota(H_1,H_2) : H_1 \text{ and }H_2 \text{ are horoballs of }\tau \ \}~.
\]
\end{definition}
\noindent As noted in the introduction, we claim that $\kappa_T(n)= \min \{ \kappa(\tau): \tau\in \mathcal{A}_n \}$.

That $\kappa_T(n)\le \min \kappa$ is easy: for any $\tau\in\mathcal{A}_n$, choose a Farey labelling.
The quantity $\kappa(\tau)$ is equal to the maximum pairwise intersection number of the $n$ slopes obtained in this Farey labelling, and $\kappa_T(n)$ is the minimum of the maximum pairwise intersection of any $n$ slopes, so $\kappa_T(n) \le \kappa(\tau)$ for each $\tau\in\mathcal{A}_n$.

The reverse inequality is slightly less obvious, and relies on a certain convexity of maximal $k$-systems in $\partial_\infty \mathbb{H}^2$.
The following lemma makes this precise.\footnote{We are grateful to Ian Agol for sharing an unpublished note with us which contained \autoref{lem: convexity} \cite{Agol-unpub}.}

\begin{lemma}
\label{lem: convexity}
If $\Gamma$ is a $k$-system on $T$ which is maximal with respect to inclusion among $k$-systems, then $\mathcal{F}$ induces a triangulation of the $n$-gon which forms the convex hull of $\Gamma\subset \partial_\infty \mathbb{H}^2$.
\end{lemma}

\begin{proof}
Let $g_{ab}$ indicate the geodesic in $\mathbb{H}^2$ with endpoints $a,b\in\partial_\infty \mathbb{H}^2$.
Suppose that $\alpha,\beta\in\Gamma\subset \mathcal{F}$, that $\Delta$ is a Farey triangle intersecting $g_{\alpha\beta}$, and that $\delta$ is a vertex of $\Delta$ (and, hence, of $\mathcal{F}$).
\autoref{lem:monotonicity} implies that both $\iota(\delta,\alpha)$ and $\iota(\delta,\beta)$ are at most $\iota(\alpha,\beta)$, which is at most $k$ by assumption.
For any $\gamma\in\Gamma$, either $g_{\alpha\gamma}$ or $g_{\beta\gamma}$ intersect $\Delta$, so it follows that $\iota(\gamma,\delta)\le k$ as well.
Maximality of $\Gamma$ implies that $\delta\in\Gamma$, so the convex hull of $\Gamma$ is equal to the union of Farey triangles spanning elements of $\Gamma$.
\end{proof}

This demonstrates that $\kappa_T(n) \ge \min \kappa$, so we may conclude:

\begin{proposition}
\label{prop:kappa=kappa}
We have $\displaystyle \kappa_T(n) = \min_{\tau\in\mathcal{A}_n} \kappa$.
\end{proposition}

\section{Illustrative examples}
\label{sec:examples}

There are several natural elements of $\mathcal{A}_n$ that we can use to observe $\kappa:\mathcal{A}_n\to \mathbb{N}$.

\begin{remark}
\label{rem:unlabelled}
Technically, the vertices of the associahedron correspond to triangulations of a \emph{labelled} convex polygon.
Notice however that the max intersection function $\kappa:\mathcal{A}_n\to\mathbb{N}$ is invariant under permutation of labels, so we can safely refer to $\kappa(\tau)$ for elements $\tau$ of $\mathcal{A}_n$ without reference to a particular ordering of the horoballs of $\tau$.
\end{remark}

\begin{itemize}

\item The element $\mathrm{ch}(n)\in\mathcal{A}_n$ (for `chain') contains a horoball of width $n$. We have $\kappa(\mathrm{ch}(n))=n$, and the height relative to the horoball of width $n$ is $1$.
\\

\item The element $\mathrm{ach}(n)\in\mathcal{A}_n$ (for `alternating chain') contains a path of length $n-3$ that switches direction $n-4$ times. Here we have $\kappa(\mathrm{ach}(n))=F_n$, the $n$th Fibonacci number, the largest width horoball of $\mathrm{ach}(n)$ is $3$, and the height relative to any horoball is at least $F_{\lfloor \frac n2\rfloor }$.
\\

\item The element $\mathrm{reg}(r)\in\mathcal{A}_n$ (for `regular'), with $n=3\cdot 2^{r-1}$, is formed by choosing the subtree of the homogeneous (infinite) trivalent tree that is induced on all vertices at combinatorial distance at most $r$ from a fixed vertex. The tree $\mathrm{reg}(r)$ contains the alternating chain $\mathrm{ach}(2r+1)$ as a subtree, and in fact we have $\kappa(\mathrm{reg}(r))=\kappa(\mathrm{ach}(2r+1))=F_{2r+1}$.
The largest width of a horoball of $\mathrm{reg}(r)$ is given by $2r-1$, and the height of $\mathrm{reg}(r)$ relative to this horoball is $F_{r+1}$.
\\

\item The element $\mathrm{Far}(h)\in\mathcal{A}_n$ (for the `Farey series'), with $n=2+\sum_{k\le h} \phi(k)$, is the subgraph of $\mathcal{F}$ induced on fractions in $\mathbb{Q}\cap [0,1]$ that can be written with denominator $\le h$, together with $1/0$.
Observe that $\kappa(\mathrm{Far}(h)) =h^2-2h$, the largest width of a horoball of $\mathrm{Far}(h)$ is given by $h$, while the height relative to this horoball is given by $h-1$. \\

\end{itemize}

We collect this information in \autoref{pic:elements} and \autoref{table}.

\begin{figure}
\centering
\vspace{1.5cm}
\begin{minipage}[t][3cm][t]{.2\textwidth}
\centering
\vspace{-.7cm}
\includegraphics[width=4cm]{pic-chain.png}
\vspace{1.5cm}
\subcaption{$\mathrm{ch}(n)$}
\label{pic:chain}
\end{minipage}\hfill
\begin{minipage}[t][3cm][t]{.2\textwidth}
\centering
\includegraphics[width=4cm]{pic-achain.png}
\vspace{1.5cm}
\subcaption{$\mathrm{ach}(n)$}
\label{pic:achain}
\end{minipage}\hfill
\begin{minipage}[t][3cm][t]{.2\textwidth}
\centering
\vspace{-2cm}
\includegraphics[width=4cm]{pic-reg.png}
\subcaption{$\mathrm{reg}(r)$}
\label{pic:chain}
\end{minipage}\hfill
\begin{minipage}[t][3cm][t]{.2\textwidth}
\vspace{-1.4cm}
\centering
\includegraphics[width=4cm]{pic-Farey.png}
\vspace{.6cm}
\subcaption{$\mathrm{Far}(h)$}
\label{pic:chain}
\end{minipage}\hfill
\caption{Several dual trees of elements in $\mathcal{A}_n$.}
\label{pic:elements}
\end{figure}

\renewcommand{\arraystretch}{1.5}
\begin{table}[]
\begin{tabular}
{|
>{\centering}p{.1\textwidth} |
>{\centering}p{0.2\textwidth} |
>{\centering}p{0.3\textwidth} |
>{\centering\arraybackslash}p{0.2\textwidth} |
}
\hline
$\tau$ & $\kappa(\tau)$ & Largest width horoball $H$ & $\mathrm{ht}(\tau,H)$ \\
\hline
\hline
$\mathrm{ch}(n)$ & $n$ & $n-2$ & $1$  \\
\hline
$\mathrm{ach}(n)$ & $ \Phi^n$ & $3$ & $\ge \Phi^{n/2}$  \\
\hline
$\mathrm{reg}(r)$ & $ n^{2\log_2\Phi}$ & $2\log_2n $ & $ n^{\log_2\Phi}$  \\
\hline
$\mathrm{Far}(h)$ & $ \frac{\pi^2}3 n $ & $\sqrt n$  &  $\sqrt n$ \\
\hline
\end{tabular}
\vspace{.5cm}
\caption{Some data for attractive elements of $\mathcal{A}_n$.
Some entries include only leading-order terms, ignoring multiplicative constants.
Note that $\Phi = \frac{1+\sqrt 5}2$.
}
\label{table}
\end{table}

\begin{remark}
\label{rem:An diameter}
Observe the large difference between $\kappa(\mathrm{ach}(n))\approx (\frac{1+\sqrt5}2)^n$ and $\kappa(\mathrm{ch}(n))=n$.
Though we have not discussed it, there is a natural simplicial structure on $\mathcal{A}_n$, with edges between triangulations of an $n$-gon that differ by a single diagonal flip.
It is not hard to see that the diameter of $\mathcal{A}_n$ is at most $2n$ (in fact, this quantity can be determined precisely \cite{STT, Pournin}), so it follows that the change in $\kappa$ across an edge of $\mathcal{A}_n$ can be arbitrarily large.
\end{remark}

\section{Estimating kappa using heights}
\label{sec:estimating kappa}

Let $\tau\in\mathcal{A}_n$.
The strategy to obtain a lower bound for $\kappa(\tau)$ is to find a set of pairwise intersection functions $\{I_\alpha\}$ for $\tau$, and estimate the convex combination
\begin{equation}
\label{eq:goal}
\sum_\alpha r_\alpha I_\alpha \ge n - \epsilon(n)~,
\end{equation}
for some set of non-negative weights $\{r_\alpha\}$ with $\sum r_\alpha =1$, and error term $\epsilon(n)$.
Of course, we have $\kappa(\tau)\ge I_\alpha$ for all $\alpha$, and by convexity we must have $I_\alpha \ge n-\epsilon(n)$ for some $\alpha$.

We will make use of three facts from classical analytic number theory, which we group together in a single lemma for convenience.
Below we indicate the interval $\{1,\ldots,m\}$ by $[m]$ and the subset of $\{1,\ldots,m\}$ relatively prime to $s$ by $[m]_s$, e.g.~Euler's totient function is $\phi(m) = \#[m]_m.$
The number of divisors of $n$ is indicated by $d(n)$.

\begin{lemma}
\label{lem:number theory}
We have the following estimates:
\begin{align}
\label{eq:euler count}
\#[m]_n & = \frac mn \phi(n) + O\left(d(n)\right)~, \\
\label{eq:dirichlet}
\sum_{k\le h} d(k)& = h \log h + O(h)~, \text{ and }\\
\label{eq:walfisz}
\sum_{k\le h} \frac {\phi(k)}k &= O(h)~.
\end{align}
\end{lemma}

The estimate \eqref{eq:euler count} is a standard application of M\"obius inversion \cite[Lem.~3.4]{Cohen}.
The second estimate \eqref{eq:dirichlet} is a weaker version of a famous theorem of Dirichlet \cite[Ch.~3]{Apostol}, and a more precise form of \eqref{eq:walfisz} can be found in \cite{Walfisz}.
(Note that the error term in \eqref{eq:euler count} is in fact $O(\vartheta(n))$, where $\vartheta(n)$ is the number of square-free divisors of $n$.
However, in the sum $\sum_{j\le h} \vartheta(j)$, one finds the same order of growth as $\sum_{j\le h} d(j)$ \cite{Mertens}, so in our application, \autoref{lem:count n}, this improvement is immaterial.)

In this section we will show:

\begin{proposition}
\label{prop: control with height}
Let $H$ be a horoball of $\tau\in\mathcal{A}_n$, and let $h = \mathrm{ht}(\tau,H)$.
There is a constant $C>0$ so that we have $\kappa(\tau) \ge n - C h \log h$.
\end{proposition}

As in \S\ref{sec:width/height}, let $H_1$ and $H_2$ be the two horoballs that are incident to $H$ along its two extreme edges.
By construction, the non-backtracking path $\sigma$ from $H_1$ to $H_2$ is contained in $H$; we indicate the vertices $\sigma$ passes through in order by $p_1,\ldots,p_w$.
See \autoref{fig:branches}.

\begin{figure}[h]
\centering
\includegraphics[width=10.5cm]{pic-branches2.png}
\caption{The horoball $H$ determines branches for $\tau$, and extreme horoballs $H_1$ and $H_2$.}
\label{fig:branches}
\end{figure}

For each $j$, the complement $\tau \setminus p_j$ consists of three components, and we indicate (the closure of) the unique such component that doesn't intersect $H$ as the $j$th \emph{branch} $B(j)$.

\begin{figure}
\centering
\includegraphics[width=10cm]{pic-numerators.png}
\caption{Each branch has minimal and maximal numerators at height $k$.}
\label{pic:numerators}
\end{figure}

Label $H$ with $1/0$, label the horoball neighboring $H$ along the edge $\overline{p_j p_{j+1}}$ with $0/1$, and label the horoball neighbor of $H$ along $\overline{p_{j-1}p_j}$ with $1/1$. Now Farey addition determines how to fill in labels for the remaining horoballs, and let $\mathrm{ht}_H \, B(j)$ indicate the maximum denominator among Farey labels for horoballs intersecting $B(j)$.
The vertices of $B(j)$ at height $k$ are given by $\frac {a_1}k, \frac{a_2}k,\ldots,\frac{a_{n_k}}k$. The \emph{minimum (resp.~max) numerator at height $k$} of $B(j)$, relative to $H$, is $\min a_i$ (resp.~$\max a_i$). See \autoref{pic:numerators}.

\begin{figure}
\centering
\includegraphics[width=10cm]{pic-heights.png}
\caption{The horoballs of $\tau$ may be filtered according to heights from $H$.}
\label{fig:heights}
\end{figure}

Observe that we may count the $n$ horoball regions of $\tau$ by filtering them according to their heights on the branches.
That is, for each $i\in \mathbb{N}$, let $X(k) = \{ j : \mathrm{ht}_H \, B(j) \ge k\}$ (that is, the set of indices $j$ where the $j$th branch has height at least $k$), and let $x_k = \#X(k)$.
See Figure~\ref{fig:heights}.

\begin{figure}
\centering
\includegraphics[width=10cm]{pic-function.png}
\caption{Extremal horoballs of $\tau$ at height $k$ from $H$.}
\label{fig:function}
\end{figure}

Consider $j_k^+$ (resp.~$j_k^-$), the maximal (resp.~minimal) index of $X(k)$. Let $\ell_k$ be the maximal numerator of $B(j_k^-)$ and let $r_k$ be the minimal numerator of $B(j_k^+)$.
See \autoref{fig:function}.

\begin{lemma}
\label{lem:count n}
We have
\[
\sum_{k=1}^h \phi(k)x_k \ge n + \sum_{k=1}^h \phi(k)
+ \sum_{k=1}^h \frac{\phi(k)}k (r_k - \ell_k)
- O\left( h \log h\right)~.
\]
\end{lemma}

\begin{proof}
Observe that the sum of the number of horoballs of $\tau$ at height $k$ relative to $H$, as $k$ goes from $1$ to $h$, is exactly $n-2$.

The horoballs of $B(j)$ at height $k$ relative to $H$ have size at most $\phi(k)$, so the total number of horoballs of $\tau$ at height $k$ from $H$ is at most $\phi(k) x_k$. Observe that we may count the vertices of $B(j_k^-)$ and $B(j_k^+)$ with slightly more care: When the maximal and minimal numerators of $B(j)$ at height $k$ are $\ell$ and $r$, the horoballs of $B(j)$ at height $k$ relative to $H$ are at most $\phi(k)-\#[r-1]_k$, and at most $\#[\ell]_k$.
Therefore the total number of horoballs of $\tau$ at height $k$ relative to $H$ are at most
\[
\phi(k)x_k - (\underbrace{\phi(k)-\#[\ell_k]_k}_{\text{overcount in }B(j_k^-)} ) - \underbrace{\#[r_k-1]_k}_{\text{overcount in }B(j_k^+)} ~.
\]
By \eqref{eq:euler count}, the latter is at most
\[
\phi(k)x_k   - \phi(k) + \frac{\ell_k}k \phi(k) - \frac{r_k-1}k \phi(k) + O(d(k))~.
\]
The sum of this expression as $k$ goes from $1$ to $h$ is at least $n-2$, so rearranging we find that
\[
\sum_{k=1}^h \phi(k)x_k \ge n +\sum_{k=1}^h \phi(k) + \sum_{k=1}^h \frac{\phi(k)}k (r_k-\ell_k) - 2- \sum_{k=1}^h \frac{\phi(k)}k - C\sum_{k=1}^h d(k)~.
\]
By \eqref{eq:dirichlet} and \eqref{eq:walfisz}, the last three terms can be replaced by $O(h\log h)$.
\end{proof}

The reader may observe how \autoref{lem:count n} is somewhat suggestive of \eqref{eq:goal}.

Given heights $k$ and $k'$, consider the intersection $I_{kk'}$ between the horoball of $B(j_k^-)$ with maximal numerator $\ell_k$ and the horoball of $B(j_{k'}^+)$ of minimal numerator $r_{k'}$.
We may compute:
\begin{equation*}
I_{kk'} = kk'
|j_{k'}^+ - j_k^-|
+ k'\ell_k - kr_{k'}~
\end{equation*}
Therefore, we have
\begin{equation*}
I_{kk'}+I_{k'k} = kk'\left( \big| j_{k'}^+-j_k^-\big| + \big| j_{k}^+-j_{k'}^-\big| \right) + (k'\ell_k - kr_{k'} + k\ell_{k'}-k'r_k)~.
\end{equation*}
Notice that $\big| j_{k'}^+-j_k^-\big| + \big| j_{k}^+-j_{k'}^-\big| \ge x_k+x_{k'}-2$, so dividing by $kk'$ we find
\begin{equation}
\label{eq:sum of Is}
\frac1{kk'} \left(I_{kk'} + I_{k'k}\right) \ge x_k+x_{k'} - 2 + \left(\frac{\ell_k}k- \frac{r_k}k\right) + \left(\frac{\ell_{k'}}{k'}  - \frac{r_{k'}}{k'}\right)~.
\end{equation}

With \autoref{lem:count n} in mind, we would like to choose pairs $\{k,k'\}\subset [h]$ so that the sum over the choices made of the terms `$x_k+x_{k'}$' on the righthand side of \eqref{eq:sum of Is} is equal to $\sum \phi(k)x_k$.
The following proposition makes this idea feasible.

\begin{proposition}
\label{prop:Gammas}
For each $h\in \mathbb{N}$, there is a graph $\Gamma_h$ satisfying:
\begin{enumerate}
\item
The vertex set of $\Gamma_h$ is given by $\{1,\ldots, h\}$.
\item \label{item:valence}
The valence of vertex $k$ is $\phi(k)$.
\item \label{item:weights}
The sum $\displaystyle \sum_{k\sim k'} \frac2{kk'}$ over the edges of $\Gamma_h$ is equal to $1$.
\end{enumerate}
\end{proposition}

See \autoref{pic:graph} for a picture of $\Gamma_6$.

\begin{proof}
Declare $k\sim k'$ when $\gcd(k,k')=1$ and $k+k'>h$.

For property~\eqref{item:valence}, choose a vertex $k$.
Each integer $i$ relatively prime to $k$ can be shifted by $k$ to $i+k$, another integer relatively prime to $k$.
For $1\le i\le k$, we may choose the maximum $n$ so that $i+nk\le h$.
The result is a bijection of $[k]_k$, the integers in $[k]$ relatively prime to $k$, with the set of integers $k'$, relatively prime to $k$, less than $h$, and so that $k+k'>h$. Therefore the valence of $k$ is $\#[k]_k=\phi(k)$.

For property~\eqref{item:weights}, observe that, to transform $\Gamma_h$ into $\Gamma_{h+1}$, the edges $k\sim k'$ with $k+k'=h+1$ are deleted and replaced by edges $k\sim(h+1)$ and $k'\sim(h+1)$. Because $k+k'=h+1$, the edge weight $\frac2{kk'}$ in $\Gamma_h$ is equal to the sum of edge weights $\frac2{k(h+1)}+\frac2{k'(h+1)}$ in $\Gamma_{h+1}$, so the sum $\sum_{k\sim k'}\frac2{kk'}$ is independent of $h$.
For the base case $h=2$, observe that $\frac2{1\cdot2}=1$.
\end{proof}

\begin{figure}
\centering
\includegraphics[height=7cm]{pic-graph.png}
\caption{The graph $\Gamma_6$ as described in \autoref{prop:Gammas}.
The sum of the edge weights is $1$.}
\label{pic:graph}
\end{figure}

Let $E$ indicate the set of edges of $\Gamma_h$. Now \autoref{prop:Gammas} and \eqref{eq:sum of Is} imply:

\begin{align*}
\sum_E \frac1{kk'} \left(I_{kk'} + I_{k'k}\right)
&\ge \
\sum_E  \ \left( x_k+x_{k'} - 2 + \left(\frac{\ell_k}k- \frac{r_k}k\right) + \left(\frac{\ell_{k'}}{k'}  - \frac{r_{k'}}{k'}\right) \right)  \\
&= \sum_k \phi(k) x_k \ -\  \sum_k \phi(k) \ + \ \sum_k \frac{\phi(k)}k \left( \ell_k  - r_k \right)
\end{align*}
Applying \autoref{lem:count n}, we find that
\begin{equation}
\label{eq:convex estimate}
\sum_E \frac1{kk'} \left(I_{kk'} + I_{k'k}\right) \ge n - O\left( h \log h\right)~.
\end{equation}
Because $\sum_E \frac2{kk'} =1$ by \autoref{prop:Gammas}, inequality \eqref{eq:convex estimate} proves \autoref{prop: control with height}.

\section{Finding a horoball of controlled relative height}
\label{sec:controlling height}

For many $\tau\in\mathcal{A}_n$, there exist $H$ so that the $\mathrm{ht}(\tau,H)$ is $O(1)$, so \autoref{prop: control with height} demonstrates that $\kappa(\tau)=n-O(1)$.
However, such a horoball need not exist, e.g.~every horoball of $\mathrm{ach}(n)$ has height at least $\approx (\frac{1+\sqrt 5}2)^{n/2}$.
Nonetheless, $\kappa(\mathrm{ach}(n))$ is quite large (on the order $(\frac{1+\sqrt 5}2)^n$), so one might hope that it is always possible to find horoballs of small height relative to $\kappa(\tau)$.
We show:

\begin{proposition}
\label{prop: exists horoball}
There exists a constant $C>0$ so that, for any $\tau\in \mathcal{A}_n$, there exists a horoball $H$ of $\tau$ so that the height of $\tau$ relative to $H$ is controlled as $\mathrm{ht}(\tau,H) \le C \sqrt{\kappa(\tau)}$.
\end{proposition}

\begin{remark}
\label{rem: sharpness heights}
The reader can observe that the conclusion above fits the data in \autoref{table}.
It is tempting to hope for an improvement of \autoref{prop: exists horoball} along the following lines:
as $\kappa(\tau)$ gets closer to $\min \kappa$ (e.g.~if $\kappa(\tau)\le n$), one should be able to find horoballs of $\tau$ with relative heights $\ll \sqrt n$.

On the other hand, the row containing $\tau=\mathrm{Far}(h)$, with $n\approx \frac3{\pi^2}h^2$, makes this hope seem quite remote.
Indeed, $\kappa(\mathrm{Far}(h))$ is greater than $n$ only by the innocuous looking linear factor $\frac {\pi^2}3 \approx 3.3$, and yet every horoball has relative height $\ge h \approx \sqrt n$.
\end{remark}

\begin{proof}
Let $K_1,K_2$ be horoballs of $\tau$ so that $\iota(K_1,K_2)=\kappa(\tau)$, and
let $r=\log \kappa(\tau)$.
By \autoref{lem:i vs d}, we have $d_{\mathbb{H}^2}(K_1,K_2) = 2r$.

Let $x\in \mathbb{H}^2$ be the midpoint of the geodesic from $K_1$ to $K_2$.
By \autoref{lem:distance from horoball} there is some Farey horoball $H$ so that $d_{\mathbb{H}^2}(H,x)\le \log \frac2{\sqrt3}$.
The Farey horoball $H$ is incident to the geodesic between $K_1$ and $K_2$, so by convexity it must be a horoball in $\tau$.

\begin{figure}
\centering
\includegraphics[height=10cm]{pic-thin-triangle2.png}
\caption{Hyperbolicity guarantees that a horoball $K$ far from $x$ is far from some $K_i$ as well.}
\label{fig:pic-thin-triangle}
\end{figure}

We claim that $H$ satisfies the requisite bound.
Let $K$ be any other horoball of $\tau$. Because $\mathbb{H}^2$ is $\delta$-hyperbolic, the point $x$ is within $\delta$ of the geodesic segment between $K$ and $K_i$ for $i$ equal to either $1$ or $2$.
A standard application of the triangle inequality (see \autoref{fig:pic-thin-triangle}) then yields
\[
d_{\mathbb{H}^2}(K,K_i) \ge d_{\mathbb{H}^2}(K,x) + d_{\mathbb{H}^2}(x,K_i) - 2\delta = d_{\mathbb{H}^2}(K,x) + r -2\delta~.
\]
Because $d_{\mathbb{H}^2}(K,K_i)\le 2r$, we conclude that $d_{\mathbb{H}^2}(K,x)\le r+2\delta$, and
\[
d_{\mathbb{H}^2}(H,K)\le d_{\mathbb{H}^2}(H,x) + d_{\mathbb{H}^2}(x,K) \le \log \frac2{\sqrt 3}+  r +2\delta~.
\]
By \autoref{lem:i vs d} we conclude that
\[
\iota(H,K) = e^{\frac12 d_{\mathbb{H}^2}(H,K) }
\le \frac2{\sqrt 3}e^{2\delta} \sqrt{\kappa(\tau)}~. \qedhere
\]
\end{proof}

\begin{remark}
\label{rem: Agol proof}
Ian Agol has suggested a slightly different version of the above proof: choose Farey labels for the horoballs in $\tau$, and enlarge the horoballs by $\log \kappa(\tau)+\log\frac2{\sqrt3}$.
A variation on \autoref{lem:distance from horoball} together with \autoref{lem:i vs d} implies that every trio of these horoballs mutually intersect, so by Helly's theorem there is a point $x$ in their common intersection \cite{Helly}, and one may finish as above.
\end{remark}

\section{From kappa to eta}
\label{sec:pf of main thm}

As stated in the introduction, it is an exercise to show that
\begin{equation*}
\label{eq:eta kappa}
\eta_T(k) = \max \{ n: \kappa_T(n)\le k\}~.
\end{equation*}
By \autoref{thm: kappa}, we may conclude $\eta_T(k)\le \max\{n: n-C\sqrt n\log n \le k\}$.

\autoref{main thm} now follows from the following lemma:

\begin{lemma}
\label{lem:functions}
Suppose that $C>0$ is a constant, and that $f:\mathbb{R}\to\mathbb{R}$ is an increasing, sublinear function, with $f(x)=o(x)$.
There is a $D>0$ so that for any $k\ge 1$ we have $\max\{ x: x- Cf(x)\le k\} \le k+ D f(k)$.
\end{lemma}

\begin{proof}
Because $f(x)=o(x)$, there is a $C_1>0$ large enough so that $C_1-1>Cf(C_1)$.
Because $f$ is sublinear, for any $k\ge 1$ we have
\[
(C_1-1)k > Ck \, f(C_1) \ge C \, f(C_1k)~.
\]
Adding $k$ to both sides and rearranging we find
\begin{equation}
\label{eq:too big}
C_1k-C\, f(C_1k) > k~.
\end{equation}

Let $F(k)=\max\{ x: x-Cf(x)\le k\}$.
By \eqref{eq:too big} we have $F(k) < C_1k$.
Of course, by definition of $F(k)$ we have $F(k) - Cf(F(k)) \le k$.
Because $f$ is increasing and sublinear, we find
\[
F(k) \le k+C f(F(k)) \le k+C f(C_1k) \le k+CC_1 f(k)~,
\]
as claimed.
\end{proof}

Because $\sqrt x\log x$ is increasing and sublinear, this completes the proof of \autoref{main thm}.

\begin{remark}
\label{rem:sloppy lemma}
The conclusion of \autoref{lem:functions} holds under much weaker assumptions. For instance, sublinearity of $f$ can be replaced by the assumption that there is some $C_2>0$ so that $f(x+y) $ is at most $C_2 f(x) + C_2 f(y)$.
\end{remark}

\bigskip

\bibliographystyle{alpha}
\newcommand{\etalchar}[1]{$^{#1}$}

redpajama_set_name: RedPajamaArXiv


text:
Q: Error: Adding WCS ( Web coverage Service ) into ArcMap 10.4.1 I am trying to publish some raster data sets as WCS using ArcGIS 10.4.1 (Desktop ArcMap and Server Manager), but have had little success. I've attempted to publish a data set stored as an ESRI Grid, a Geo-tiff, and a Mosaic data set. I am able to connect to the WCS image server, but when I try to add the image I get the following message:
"Could not add the specified data object to the map. Failed to open raster dataset."

Here are detailed steps:
First I created the shared folder to register my data source with ArcGIS server. Next in ArcMap Catalog I navigated to to the registered folder and selected the required raster data set ( Geo-tiff both geographic and sinusoidal ) also created a Geo-database ".gdb" for a list of mosaic data set.
Next using ArcMap publishing Wizard, I have published the Image services as WCS and WMS both. When publishing my dataset, I select the WCS and WMS capabilities along with the Image Service and verified on the Server Manager that the services I created are available on server along with under WMS and WCS tabs.
Next I needed to check if I can get these WMS and WCS links work in ArcMap. I am able to add the image as a Image Service when I connect to the ArcGIS Server just fine. I'm also able to add the published data as a WMS ( can see the image in Data view ). The WCS is the only service that fails. Does anyone know what would cause my WCS to fail, but allow my Image Service and WMS work.
There was a bug report of dragging the WCS layers in Data view of ArcMap might be issue so I tried the add layer button to select the WCS layers from WCS server connection but it still failed.
Below link, it seems like when we add WCS service in ArcMap it atleast gives a black layer which can be contrast stretched to get the right image. But in my case I am not getting any layer just the error mentioned above.
http://docs.gina.alaska.edu/ndvi/how_to.html
Also there seems to be not issue in my Geo-tiff's as when I add these files directly to ArcMap it will show up layers / images also using WMS it works.
Last, I also tried the same WCS service GET Coverage operation in browser and I got a Tiff Image downloaded. ( So same WCS service working in browser but not in ArcMap )
https://localhost:6443/arcgis/services/imageservicename/ImageServer/WCSServer?SERVICE=WCS&VERSION=1.1.1&REQUEST=GetCoverage&IDENTIFIER=1&FORMAT=image/GeoTIFF&BOUNDINGBOX=-124.45790612602009,40.000531011912074,-91.378950375060455,49.999999995506855,urn:ogc:def:crs:EPSG::4326

A: So after talking to ArcGIS team it comes out that only for "WCS server" inside ArcMap we have to use link with Qualified domain name instead of using localhost.
I tried with that link and it worked fine while bringing WCS Coverage in Arcmap.
https://serverqualifieddomainname:6443/arcgis/services/imageservicename/ImageServer/WCSServer?SERVICE=WCS&VERSION=1.1.1&REQUEST=GetCoverage&IDENTIFIER=1&FORMAT=image/GeoTIFF&BOUNDINGBOX=-124.45790612602009,40.000531011912074,-91.378950375060455,49.999999995506855,urn:ogc:def:crs:EPSG::4326

redpajama_set_name: RedPajamaStackExchange


text: <!DOCTYPE html>

redpajama_set_name: RedPajamaGithub


DuPont recently released its new flexographic printing plate technology platform, "DuPont Cyrel Easy®." This new technology platform is designed to simplify the prepress process by building the flat top digital dot directly into the plate, resulting in increased productivity and consistency (DuPont).
In typical Associated Labels and Packaging fashion, our research and development team jumped on board right away to make this technology available to all our customers. DuPont and Associated Labels and Packaging both speak the same language in wanting to improve quality, sustainability and productivity with this new product.
UPM Raflatac's VANISH™ range of clear PET films redefines how companies can maximize brand representation while boosting quality and performance to new levels. With a 0.92 mil film face stock, these thin, yet robust products are the perfect canvas for innovative imagery previously considered unattainable by creative designers.
The film's dimensional stability, excellent ink reception and dispensing properties simultaneously allow manufacturers to embrace new productivity gains and realize film packaging material reductions throughout their processes.
At Associated Labels, we are committed to delivering innovative decorating and flexible packaging solutions that fit our customers and their products perfectly. That's why we created our Flexible Packaging Division to handle the specialized requirements of specialty packaging and shrink sleeves; including offline lamination for all your laminating and slitting needs.


text:
Spotlight Records Nashville releases Kalysta's first single and lyric video off her debut CD
Spotlight Records is thrilled to announce the single release "Baby Girl" from the CD titled Kalysta, available everywhere. Baby Girl written by Dennis K Duff is a great country song about a momma concerned about her daughter's choice of boyfriends
Nashville, Tennessee Sep 22, 2021 (Issuewire.com) – Kalysta's CD consists of 11 country songs selected by Kalysta from Walton, Kentucky in cooperation with her record label Spotlight Records of Zanesville, Ohio, and Nashville, Tennessee. Her producer for 8 of the songs presented was John Pineiro of Perfect Image Recording Nashville, Tennessee. Three (3) of the songs selected were produced at Studio Q Nashville by Gary Sadker. Recordings will be released to radio starting in late August.
Kalysta signed a recording contract with Spotlight Records at the age of 14, and she was placed into the hands of the career development director, James Bruce. Bruce has been a talent agent and manager for over 33 years. Now four years later, Kalysta's dream is about to come true. She has completed her CD, which is about to be distributed to AM/FM and internet radio worldwide. The songs selected include country songs that the masses will like as suggested by Producers John Pineiro and Gary Sadker saying, "here we have selections for everybody."
In 2015 Darrel Riggs, agent for Access Entertainment Group the parent company for Spotlight Records discovered Kalysta at a Winterfest Event near Cincinnati. Darrel suggested to James Bruce owner "that we consider her talent for future projects." "She is an unbelievable talent for her age."
About Spotlight Records
Spotlight Records is a full-service talent, recording, and production agency founded in 1995 as an independent professional service firm for independent musicians, singers, songwriters, bands, entertainers, and their buyers. The firm and its founder Jim Bruce have demonstrated expertise in booking, recordings, career development, consultation, marketing, publicity, and talent management.
Spotlight Records
jamesbruce0927@gmail.com
209 Downing Drive
http://www.accessentertainmentgroups.com
Source :Spotlight Records
BIG GIRL : Web Series will be screening at Cinema Village for the Winter Film Awards
Bookmark.com launches their Marketplace with gang-lani media!

redpajama_set_name: RedPajamaCommonCrawl


text:
Labels: Happy Stuff
2010: Politics
Bossier and Caddo Parishes had a pretty interesting time politically in 2010.
The year started out with State Representative Barbara Norton's shameful behavior at the African American History Parade.
The Bossier Parish Police Jury outdid everyone by partying hearty at the D. C. Mardi Gras.
The Bossier Parish Police Jury paid for 9 people to attend the events. They were:
Bill Altimus, Rick Avery, Wanda Bennett, jury president Glenn Benton, Barry Butler, Paul Plummer, Joe E. Ford, Jr., parish engineer, Patrick R. Jackson, parish attorney & Craig Spohn, Cyber Innovation Center executive director all attended.
The cost to taxpayers: $22,809.56 and counting. According to the article "That total doesn't include the tab for a private dinner party for 75 guests (shared by Bossier & Caddo), mostly from Louisiana, at an Italian chain restaurant. Also missing are meals, cab fare and other expenses incurred by the nine officials the Bossier Parish Police Jury sent to the annual gala in the nation's capital."
The Cyber Innovation Center footed the bill for $2,000 worth of booze.
Robert Adley tried to notch up Nanny government a little in a failed attempt to ban the sale of energy drinks to kids under 16.
David Melville, Pastor of Fellowship Methodist Church on Barksdale Boulevard, threw his hat in the ring to take on John Fleming in the 4th District congressional race. He did about as well as we thought he would.
Larry Deen showed his disdain for his constituents when he held a short hearing for his increase in property taxes. Rather than providing a decent space and amount of time for the hearing, the sheriff crammed the people who attended into an office and then put an arbitrary time limit on the meeting.
He told the people at the meeting that 'state law' required that he could only give 15 minutes to public comments. Not true, he just pulled that one out of his hat.
This wasn't one of the sheriff's better moments.
We had a good school board race, with one incumbent being unseated. Several of the candidates actually answered my email about a tax 'roll-forward'. It was voted down.
Shreveport held city elections and the most interesting by far was the mayor's race.
Bryan Wooley pushed the envelope a little too hard and probably hurt himself so far as any future elections are concerned. Big Ced pulled it off with landslide numbers.
Then, of course, there was Chubbygate.
The arrest of Bossier City Council Member James "Chubby" Knight on charges of bank fraud has, needless to say, created a lot of conversation and speculation.
"I've never done anything illegal," Bossier City Councilman Chubby Knight told KSLA.
Not so, says the Bossier City Police Department and the 26th JDC District Attorney.
The Police Department began their investigation when the bank that cashed the bogus check for Knight filed a complaint.
Knight's attorney said that they know who is behind this 'political vendetta' to get Knight, but he's not telling. According to the Times, the attorney said "This is all driven by the Bossier power bosses . . . . that machine wants you to know if you cross it, ... it will erase you, even your memory."
To round out the year, Shreveport's Assistant CAO was summarily fired this week for having sex on Cedric's sofa with an 18 year old Georgia girl who was in town for the Independence Bowl.
No word as to whether the Mayor has a new sofa, but I'd bet on it.
Sam Wyatt
2011 will begin with a race for Bossier City Marshal in April. That one is shaping up between Lo Walker's right hand man, Lynn Austin, and former BCPD detective Sam Wyatt.
Later in the year we will see elections for all statewide offices, state representative, state senate and for a number of local positions.
Posted by Jim at 8:04 PM 16 comments:
Labels: Year in Review: 2010
Memorial to the Brave
Labels: Dakota Huse, Joshua Tomlinson, Roll of Honor, Wayne Culver
Seaton Sacked
I didn't rush into this one because I thought it was better to wait until more information was available.
Now it appears that Shreveport Assistant CAO Rick Seaton did indeed engage in sexual acts with an 18 year old high school student from Georgia who was in town for the Independence Bowl.
In the mayor's office, on the mayor's sofa. She later called police and told them that she had been raped. Mayor Glover fired Seaton.
The girl apparently was at the game where her boyfriend was arrested for creating a disturbance. Seaton heard her trying to get money to bail out her boyfriend, and since she didn't want to ride the shuttle bus downtown, he gave her a ride.
Shreveport police will complete their investigation and determine whether charges should be brought against Seaton.
What was he thinking?
The story is also hitting the media in other states, as well as throughout Louisiana. AP and CNN have picked it up.
Georgia Daily News
WXIA Atlanta
WBIR – Knoxville
Labels: Local Government
2010: Crime and Convictions
Several out of state men were arrested and charged with aggravated burglary, false imprisonment and simple battery of the infirmed for their part in a home invasion in Benton. The men broke in on a 68 year-old woman and robbed her.
Ricardo Aleman Palos, Juan Jose Martinez-Flores, Mark William McKinney
Gerardo Cortina & Miguel "Bear" Escutia are still incarcerated at Bossier Max awaiting trial.
The most heinous crime of 2010 was the murder of 12-year-old Justin Bloxom, whose body was found in the woods near Stonewall in March
A known sex offender, Brian Douglas Horn, is in custody awaiting trial.
Sheriff Rodney Arbuckle believes that the scenario that Horn played out was to tell Justin that if he wanted to meet in person, 'she' would send a cab to pick him up. Horn, a driver for Action Taxi, then drove to the residence were Justin was spending the night and picked him up.
Further evidence shows that the 12 year old was smothered to death, dying of asphyxiation, and then was left face down in about a foot of water. It appears that Justin was struggling for his life, but was overcome by the 34 year old Horn.
In March, Ronald Lee Broset robbed Citizens National Bank on Benton Road.
He returned two weeks later and robbed the same bank, but this time he was caught, with the money.
Charles Pilkinton entered a guilty plea to Negligent Homicide in May in the murder of 66 year old Raymond Tobin. Tobin was found slumped over the steering wheel of his car on Inda Drive shot twice in the back of the head. According to reports, when police arrived at the scene Pilkinton admitted to killing Tobin.
After explaining all of the rights and determining that the plea was voluntary, Judge Bolin accepted the plea and sentenced Pilkinton to 5 years at hard labor.
The prosecution was represented by Clifford Strider, Assistant Attorney General.
The body of 39 year old Nancy Miller was found in Red Chute Bayou. Miller had been missing since March 3rd.
A witness reported seeing Miller walk into Reflections on Hwy 80. She appeared to be confused and turned around and walked out across Hwy 80 toward the Westbound Lane. Canine trackers confirmed the story of the witness. At the time, investigators believed that she may have gotten into a car with someone.
The body was spotted by fishermen on Red Chute Bayou near Louisiana Downs
The Caddo Parish Sheriff's office arrested Bobbie Luttrell for paying to have her husband, Ernest Luttrell, killed. She was taken in and arrested right after his funeral and charged with 1st degree murder. Luttrell allegedly used a part time housekeeper and her acquaintance to carry out the crime.
In August, A 33 year old Shreveport man was arrested for gunning down 3 brothers, aged 20, 18 & 13 because he thought they stole an X-Box from his girlfriend. All three were dead at the scene.
Caddo Parish Sheriff Steve Prator said "You can have all the tent revivals you want and ask people to not be violent and go to classes, but you can't get through to some of these idiots. No amount of patrol cars could have stopped this. The only thing that could have stopped this is if he wasn't born.
I've been doing this 37 years and looking at bodies, and it gets old."
Marcus Donte' Reed is being charged with 3 counts of 1st degree murder.
The victims were identified as Jean Adams, Jarquis Adams & Jeremiah Adams.
Judge Jeff Cox accepted an amended plea in the Matthew Fite case. Fite pled guilty to Distribution of Methamphetines and was sentenced to 30 years, with no probation or parole for the first 2 years, subject to time served (which is just over 2 years).
To rehash the case a little, Fite bought drugs from Paul Martin and then gave Dorothy Gail Wilson some of the meth and a needle so she could shoot up. Wilson overdosed and died. An autopsy revealed that she had no other drugs in her system.
Martin pled guilty in March of last year and was sentenced to 25 years, all but 12 suspended, to run concurrent with sentencing from Caddo Parish.
Steven Rivers was charged in Caddo Parish for the murder of his ex-wife and her sister.
Two people have been arrested in another home invasion/robbery in Benton.
Randall Wayne Womack, Jr & Joshua Lopez & David Allen Weeks, Jr were charged with armed robbery.
The three entered (okay, I know 'allegedly'), anyway, the three entered a residence on Old Plain Dealing Road armed with a sword and a billy club and stole a whopping $132.
Womack and Weeks both have criminal history in Bossier Parish.
There has been a lot of speculation about the shooting of Vivian attorney John Morneau. Miller County Coroner Eddie Hawkins Jr first ruled that Morneau was shot in the back by a Miller County Deputy Sheriff.
He then changed his story to say that Morneau was shot in the chest.
Hawkins would not go into specifics about why that was done, except to say there was a mistake. The Miller County DA is supposedly investigating.
On November 16th Lance Thamm entered a guilty plea and was sentenced to life in prison for the murder of his 17 month-old daughter Isabella.
Thamm slammed Isabella's head into a doorjam when she wouldn't stop crying.
Thamm has a history of drug use and domestic violence. He and his wife lost a son in Texas because of abuse. That child, a boy, is being raised by an aunt.
Then, of course, there was Chubbygate
Labels: Crime, Year in Review: 2010
2010: Changes
Hell Froze Over
On February 7th, Louisiana's Team won the Super Bowl when Tracy Porter intercepted a Petyon Manning pass with 3 minutes remaining in the game and went all the way, making the final score 31-17.
A new Police Chief for Bossier City
Shane McWilliams started acting as police chief in April and was sworn in officially in July.
"We have an outstanding department and employees. We're going to strive to continue going in the right direction and work with other agencies as well as the people we have here. We're going to do better to make sure the residents feel safe and maintain the confidence of the residents of Bossier City."
The Cross on the Hill
The 199 foot cross at Central Assembly of God Church in Haughton was dedicated this year. A permit to build the cross was originally denied by the MPC because zoning regulations say that a structure in that area can't be taller than 45 feet.
The Church then appealed to the Police Jury for an exception, which was granted.
Bossier City Voters sent a message
Bossier City voters gave the public safety tax renewal proposition a landslide vote of 'yes'.
In 2000, when the city was not having financial problems, the tax was approved by 73% of the voters. This year, when the city was having budgetary problems, 80% of the people who voted said yes.
The people are saying 'we support our Firemen and Police officers and you'd better not mess with them'.
Shreveport Police Chief
Shreveport gained a new police chief, Willie Shaw, when Henry Whitehorn was appointed U.S. Marshal for the Western District.
New weather interruption policy from Channel 12
James Smith, Station Manager at KSLA, has announced via an email that the station will be changing its policy about interrupting progamming. This occurred after the brouhaha that arose during the LSU-Auburn game when most of the last half was interrupted for tornado warning coverage in Central Arkansas. No tornadoes touched down.
Smith announced that the station will do what all of the others do, run a small screen with warnings.
Jerry Springer tryouts at Haymeadow Trailer Park
Let me make one thing clear. The New Orleans Times-Picayune was somewhat misleading with its headline Woman, holding baby son, booked with hitting grandmother in Benton. She was booked in Benton, but that trailer park is NOT in Benton, it carries a Bossier City address.
Here's the sheriff's account.
A Bossier City woman was arrested on Christmas Eve for simple battery of the infirmed, cruelty to a juvenile, and simple battery, said Bossier Sheriff Larry Deen.
Sabra Nicole Tunstall, 32, of the 5200 block of John Wilson Drive, began a physical altercation with her 77-year-old grandmother and uncle while holding her child. The grandmother and uncle were trying to get the child away from Tunstall who had been drinking all day and was trying to leave the residence. Tunstall, while holding the child, began to hit both relatives. She caused a severe skin tear on the grandmother's right arm. When deputies arrived on scene, Tunstall was holding the child in her left arm and hitting her grandmother with her other arm.
Tunstall was arrested and transported to the Bossier Maximum Security Facility. Her bond was set at $7,000.
Labels: Crime
2010 in review: What we lost
A Bossier City legend passed away.
Joe Cobb, the owner of Cobb's Bar-B-Que in Bossier City since 1952, passed away in January. Who in Bossier City (or Shreveport for that matter) hasn't eaten one of those wonderful sandwiches topped off with coleslaw?
If you thought of barbecue in the last half century, you automatically thought of Cobb's.
Joshua Tomlinson
In May Army Spc. Joshua Tomlinson, 24, of Dubberly, was among five U.S. soldiers killed in May in Kabul. The Army said a bomber detonated a vehicle near a U.S. convoy. Funeral services were held in Minden.
Wayne Culver
Also in May, Major Wayne Culver of El Dorado, Arkansas, was killed in Numaniyah, Iraq. He grew up in Blanchard and was the brother of Bossier City Police Sgt. Shane Culver.
Major Culver was executive officer for the 2nd Squadron, 108th Cavalry Regiment, based in Shreveport.
Dakota Huse
On the day that the Marine Corps celebrated its 235th birthday the Pentagon announced the death of the 19 year old Marine from Greenwood while conducting combat operations in Helmand province, Afghanistan. He was assigned to 2nd Battalion, 9th Marine Regiment, 2nd Marine Division, II Marine Expeditionary Force, Camp Lejeune, N.C.
Johnny Wyatt
In October the popular Bossier City Marshal was killed in a one car crash. Wyatt took a very pro-active stand in the marshal's office, and was a leader in tracking online pedophiles in our area in conjunction with local law enforcement agencies.
A lot of people, of course, had individual losses and those were also losses to the entire community.
We will be looking at other events that affected us in 2010 in coming days.
St. Luke's Account
And it came to pass in those days that there went out a decree from Caesar Augustus that all the world should be taxed, everyone into his own city.
And Joseph also went up from Galilee, out of the city of Nazareth, into Judea, unto the city of David, which is called Bethlehem (because he was of the house and lineage of David) to be taxed with Mary his espoused wife, being great with child. And so it was that while they were there, the days were accomplished that she should be delivered.
And she brought forth her firstborn son and wrapped him in swaddling clothes and laid him in a manger because there was no room for them in the inn.
And there were in the same country shepherds abiding in the field, keeping watch over their flock by night. And lo, the angel of the Lord came upon them; and they were sore afraid.
And the angel said unto them: Ye shall find the babe wrapped in swaddling clothes, lying in a manger.
And suddenly there was with the angel a multitude of the heavenly host praising God and saying: Glory to God in the Highest, and on Earth peace, good will toward Men.
And it came to pass, as the angels were gone away from them into heaven, the shepherds said one to another, let us now go even unto Bethlehem, and see this thing which is come to pass, which the Lord has made known to us.
And they came with haste and found Mary, and Joseph, and the babe lying in a manger.
And when they had seen it, they made known abroad the saying which was told them by the shepherds. But Mary kept all these things and pondered them in her heart.
And the shepherds returned, glorifying and praising God for all the things they had heard and seen, as it was told unto them.
And when eight days were accomplished for the circumcising of the child, his name was called JESUS, which was so named of the angel before he was conceived in the womb.
Recorded by Thomas Edison in 1920
'Twas the Night Before Christmas
(or A Visit from St. Nicholas)
by Clement Clarke Moore
not a creature was stirring, not even a mouse.
in hopes that St. Nicholas soon would be there.
The children were nestled all snug in their beds,
while visions of sugar plums danced in their heads.
And Mama in her 'kerchief, and I in my cap,
had just settled our brains for a long winter's nap.
When out on the roof there arose such a clatter,
tore open the shutter, and threw up the sash.
gave the lustre of midday to objects below,
but a miniature sleigh and eight tiny reindeer.
I knew in a moment it must be St. Nick.
More rapid than eagles, his coursers they came,
and he whistled and shouted and called them by name:
"Now Dasher! Now Dancer!
Now, Prancer and Vixen!
On, Comet! On, Cupid!
On, Donner and Blitzen!
To the top of the porch!
To the top of the wall!
Now dash away! Dash away!
Dash away all!"
As dry leaves that before the wild hurricane fly,
when they meet with an obstacle, mount to the sky
so up to the house-top the coursers they flew,
with the sleigh full of toys, and St. Nicholas too.
As I drew in my head and was turning around,
and his clothes were all tarnished with ashes and soot.
and he looked like a peddler just opening his pack.
His eyes--how they twinkled! His dimples, how merry!
and the beard on his chin was as white as the snow.
and the smoke it encircled his head like a wreath.
and I laughed when I saw him, in spite of myself.
soon gave me to know I had nothing to dread.
and filled all the stockings, then turned with a jerk.
and giving a nod, up the chimney he rose.
But I heard him exclaim, 'ere he drove out of sight,
"Happy Christmas to all, and to all a good night!"
Northwest Louisiana Tea Party Alliance Announces Formation
The Mission Statement of the Alliance includes supporting the core principles of constitutionally limited government, fiscal responsibility, moral leadership, and individual liberty and responsibility. The Mission Statement additionally states that the focus of the Alliance is to ensure strict accountability of elected officials, to educate, and to encourage citizen involvement in the policy making process at all levels of government.
The Alliance is available to assist in building and training other citizen groups throughout Northwest Louisiana in policy advocacy on local, state and federal issues. Additionally, the Alliance will assist with training on candidate screening and campaign logistics in local and state races.
For more information, please contact Matt Sciba, or Evodna Springer at
http://nwlateapartyalliance.com/
Labels: Tea Party
Christmas week is on us. Got the tree up and nearly all of the shopping done. Now to share some Christmas with everyone. There will be more later in the week, some of it actually good music.
City Marshal Race: experience vs. experience
Now that Sam Wyatt has indicated that he will run for Bossier City Marshal, a race is beginning to shape up. Lynn Austin, who served at one time as police chief, has announced his candidacy. Austin served as interim chief for a couple of months after Mike Halphen retired and before Shane McWilliams was named chief. He also has served as Lo Walker's right hand man as the city's CAO.
Wyatt has more recent police experience, particularly in the area of sex crimes, which has been a project of the Marshal's office.
A couple of other people have expressed interest in the race, including Carl Richard, a Shreveport Deputy Marshal.
Posted by Jim at 11:53 AM 25 comments:
Labels: Bossier Parish/Bossier City, Local Politics
Police presence at Louisiana Boardwalk
In an earlier post about the proposed Bossier City budget, commenters got into a discussion about funding the police presence at the Boardwalk.
Councilman Don Williams talked to the Finance Director and to the Police Chief in an attempt to put this in perspective.
He found that there are seven officers assigned to the Boardwalk. Friday and Saturday nights see six officers per night while there are three to five working on weeknights. At times reserve officers are also used, as well as private security officers paid for by the Boardwalk and/or the businesses. The private officers, however, have no real authority and have to call on the police for assistance in some cases.
From January through the end of November of this year the city has collected $2,752,522 from the Boardwalk. That is just the city's 2.5%.
Although the Boardwalk wasn't fully leased out during the first couple of years of its existence, to date, through the end of November, the city has collected $16,839,822 in sales taxes.
I don't know what it costs to provide seven police officers for a year, but I think that considering insurance and retirement contributions, the figure would be less than $500,000 per year. That's just my guess, you can make your own guess.
I do believe the key question to ask is whether the Boardwalk would be as attractive as it is to families without the police presence.
Do you think that this is a legitimate expenditure for the city to make? Do you think the city should pull these officers and leave the Boardwalk to its own devices?
Labels: Bossier Parish/Bossier City
Vladmir Putin covers Blueberry Hill
Saw this in The Gambit, at a fundraiser in St. Petersburg. Who would have thought an old KGB guy would do this? Bizarre but entertaining.
Labels: Lagniappe
Deplorable Tragedy
On last Saturday evening Joe Patterson, colored, living on Mr. John A. Sewall's place, in this ward, shot & killed a colored man. His wife commenced to scream, when he shot her to death. He then went to Mr. James B. Lay's store, about a half mile distant, and entering it, without warning, shot and wounded Mr. Lay. Mr. David Wallace, who was at the store, was about to get into his jumper, when Patterson shot & fatally wounded him. Mr. Wallace died Saturday night at 12 O'Clock.
Steps were immediately taken to capture the murderer, and after trailing him over a long circuit, he was finally run to earth Sunday night in his own home, where he barricaded himself and defied arrest. Then the pursuers opened fire on the house with Winchesters. Two shots were heard within. On forcing an entrance, Joe's body was found near his wife's, with a bullet hole through his head. His body was dragged out; after removing the dead woman, his body was carried back into the building, which was set on fire and the fiend's corpse cremated.
Mr. Wallace was nominated at the parish primary election last Thursday for State Legislature. He was a farmer and a prominent and popular citizen – a man of sound practical sense, a sterling Democrat; a man of noble qualities of heart, and a citizen who was deeply and earnestly interested in the welfare of the parish. His sad and truly unfortunate death is universally deplored.
Bossier Banner Progress, December 17, 1891
David Wallace was my great-grandfather. My grandfather, Robert E. Wallace, was nine years old when his father was killed. He told me this story but never mentioned that his father was headed to the legislature. David Wallace had won the Democratic primary election, defeating W. B. Boggs, who was the first mayor of Plain Dealing. After Grandpa Wallace's death, Mr. Boggs got the nomination and served in the State House and in the State Senate.
Another interesting note is that my grandfather told me that the 'shootout' in which Joe Patterson was killed was at the site where the Palmetto Country Club is now located. Something to think about when you tee off next time.
The picture below is of the Wallace house, where David Wallace was taken after he was shot, and where he died that midnight, December 12, 1891. My grandfather grew up in this house with all of his siblings. The house burned down in 1920, so the picture below was taken sometime before that. Grandma Wallace had moved out years before, and although the house was lived in, it was in disrepair when this photo was taken.
The house was on Linton Road.
The bottom photo is of his widow, Louisa Wallace. She lived to the age of 93 and died in Benton in 1936.
Louisa Yarborough Wallace
Labels: Bossier History
Benton/Bossier Christmas Parade 2010
Biggest crowd I've seen for the festival so far, traffic and crowd seems well-managed by Benton PD.
Here are a few images I captured for you.
State Senator Robert Adley
Billy the Exterminator - I won't mention his close proximity to the politicians!
Nice Crowd
Bossier Sheriff Young Marines
No, he's not in trouble, just along for the ride.
I thought I had a good picture of Clerk of Court Cindy Johnston, but I cut off her head.
How about Deputy Clerk Sissy Crouch, her head is intact.
Labels: Benton, Bossier Parish/Bossier City
Councilman Don Williams responds
In a recent blog post I noted that the Bossier City Council had voted to restore funding for some non-profits while leaving the cuts for others intact. That brought on the following exchange in the comment section between Matt Sciba and Councilman Don Williams.
Matt Sciba said...
I don't see why Bossier funds the Robinson/RRFS. The Robinson is in Shreveport, and Shreveport receives the tax revenues. I can't even recall a single Film Society event in Bossier City.
Our City needs $100Million for a new sewerage system, and we laid off 40 police and fire a while back, but at least we have the film center! (Yeah, I know, it's all from the other budget.)
D. Williams said...
I didnt vote for funding the Robinson Film Center but you need to get a grip on yourself and figure out what your saying before you say it
I didn't say you voted for funding the Robinson.
What exactly am I missing?
This is how it appears to many in Bossier City:
1. BCC spends $50 Million on CyberCommand.
2. the next year there's a $6 Million deficit and BCC has to lay off 40 fire and police.
3. 2010 Budget lists a $6 million surplus.
4. Proposed 2011 budget, BCC is looking to cut spending. They cut spending on a business which isn't even located in the city, then reverse their decision, as "the economy worsens".
So please, explain to me where I have strayed. I welcome any and all clarification.
Dwilliams said...
Matt, I will call you and tell you where you have strayed. Thanks
DWilliams,
You could post where I have erred on this comment section so others of the same reasoning as me can also reach the same level of understanding.
Matt, I just e-mailed you a very long e-mail answering all of your questions and it is just to long to put on here. Maybe after you read it you can post what you wish.
As a followup, Matt sent the following email to Don Williams.
I responded to your post on MyBossier, but I have a couple other comments.
If I have misunderstood how things work in Bossier, it is not for lack
of trying. Currently, the proposed 2011 budget is not posted online, I
have not received any updates from my city councilman, we have no
assembly meetings, and very little news is reported by the Bossier Press
Tribune. Furthermore, the agenda and minutes for the BCC meetings
contain the least amount of detail possible to still comply with the
open meetings law. I'm not even sure yall keep minutes for the other
Tuesday meetings, the "agenda meetings" wherein you set the agenda for
the following Tuesdays. They are not posted online like the minutes for
the Regular Meetings (Yes, you are supposed to keep minutes for those
meetings too.) All of the meetings are during the workday. I can't
attend, my compatriots can't attend. We're all at work. David Jones
has refused to change the meeting times stating that it would be unfair
to the city workers to be at the office at night. Quite frankly, they
city workers are at the service of the citizens who pay their salaries.
There is almost no communication between Bossier City Council or the
Mayor and the citizens of Bossier. Even the most basic information
(items which Shreveport has posted online in great detail) seems to
warrant a public records request, and even then I have to find time
during the workday to make it to the BCC Clerk's office and make copies.
So if there is a misunderstanding, it is quite possibly the fault of the
Bossier City Council, for there is absolutely no effort to clearly
convey information to the citizens.
Matt Sciba
Williams' email to Matt is lengthy, so I'm just going to post a few points that the councilman made.
When we get he Proposed Budget we go thru it and make changes as we see fit. It would be hard to keep it updated online. We are probably on our 4th draft now so I hope you see my point. When we adopt the proposed budget, the Adopted Budget will be posted on-line and will appear in the Bossier Press. During this time the Proposed Budget is available for review in the Finance Directors office and the City Council office
When I was elected to the council coming from the Police Jury, I asked the council to have later meetings so the public would come. We did that for a period of time that I asked for and NO ONE showed up. You need to understand if we have later meetings then we pay overtime to all required city personnel to attend. And to be fair to David Jones, it's not his decision to change the meeting time.
Matt, if you tell me exactly what you want or expect from the council I will keep you posted as best I can.
As far as your post on My Bossier, let me answer those questions. David Montgomery made an amendment to the Non-Profit budget deleting the Robinson Film Center and changing some others. I requested ALL non-profits that received money from Bossier City to prepare a 3-5 minute presentation of exactly what they use the money for in Bossier City only. They all showed up and did what I asked. They presented the info along with paper copies of the info which I requested. I will tell you this. I believe we give too much away and stated that we need to ween some of these off our budget.
Bossier City didn't spend 50 million dollars on the Cyber Center. We spent 35 million and the Police Jury spent 15 million. That is how the 50 million was made up. Then the state kicked in 50 million. I will say I din't vote for this and you can verify that in my voting record. But as always 4 votes win. Now that it's up and going and the money is spent I still have questions about it and ask them quite often. We have to hope it suceeds now. I should have also said this money came from the 100 million bond issue in 2007 that we pay approximately 6.5 million yearly from our riverboat money that I disagreed with also. There was a 6.5 million deficit last year and that was from borrowing money from our General Fund balance over the last 3 or 4 years. Last year we got to the point that there was not enought money in the balance to transfer to cover the deficit. I voted against the prior budgets along with Mr. Darby. I told them we would be broke in 3 years. I missed it by 1 year. We were broke in 2 years. The Mayor's Proposed Budget last year cut 40 Police and 40 Firefighters. I didn't go for that and myself and Mr. Montgomery actually made the revised budget and finally got it adopted which the Mayor did not support. We actually only laid off 1 active duty police officer and the 8 or 10 in the academy and I believe 7 from the fire dept. and the guys in the academy. Of those 7 that were cut, 1 was a secretary, 1 a mechanic, 2 from comunications. So it was not as bad as it seemed. We let attrition take care of the rest thruout this year. There was NO 6 million surplus in 2010. That article in the Times was incorrect and when explained to the writer of the article he then understood.
It is good to see an exchange in the comments section of My Bossier between a citizen and an elected official taken to the next level, a serious exchange of ideas and views.
As a side note, Don Williams has always been very open and straightforward when I had questions of him, as has David Jones.
It is good to see people actually engaging our elected officials in a conversation, and it is good to see those officials striving to make their point of view understood.
Labels: Bossier Parish/Bossier City, Local Government
Willie Jones sentenced
Judge John Robinson sentenced Willie Jones, Jr. to two consecutive life terms. Jones was convicted on two counts of second-degree murder for killing Mark Lioy and Amy Lynn Foster.
City Council restores cuts
The Bossier City Council voted to restore funding to the Red River Film Society, and thus to the Robinson Film Center. Councilman David Montgomery had proposed a number of cuts to several local non-profits. Councilman David Jones has worked to restore some of the cuts, while leaving others in place.
Keep Bossier Beautiful will lose $46,000 in city funding. Jones says that they have not lived up to their promises.
The budget will be voted on at the December 21st meeting.
Sheriff presents awards
Bossier Sheriff Larry Deen presented the agency's commendation award during an awards ceremony Thursday afternoon at the Viking Drive Substation in Bossier City.
The honor went to Captain Charles Thomas, who currently supervises the patrol division. He has been with the agency 19 years and served as a patrol deputy, sergeant, lieutenant and now captain. In presenting the award, Deen said Thomas "serves in a quiet, humble, caring way but rises to the occasion with appropriate swift action when duty demands."
In addition, awards were given for Outstanding Performer of the Year in each division. In the Criminal Operations Division, the awards went to Deputy Dave Faulk and Deputy Josh Cathcart. In the Corrections Division, the awards went to Major Charles Gray, Sgt. Michael Glover, Deputy Joey Martin, Deputy Robert Maule. In the Support Services Division, the award went to insurance clerk Connie Myers.
Sheriff Deen with Capt. Thomas
I thought a commenter to KTBS said it best.
"There is so much bad in the best of us and so much good in the worst of us, that it ill behooves any of us to talk about the rest of us."
Update on Vernon case
This is a synopsis of what has transpired since the firing of Bossier City Police Officer Phillip Vernon last December. I am assuming that the readers of My Bossier are familiar with the arrest of Sherb Sentell, 26th JDC ADA and the subsequent firing of Reserve Officer Jared Fisher and Officer Phillip Vernon. The two officers were fired for filing false reports in backing up the charge of public intimidation.
Officer Vernon's report stated:
18. "C. Sentell refused to stop talking and he stated that he is friends with Ron Miciotto, a local attorney, and he was going to sue every officer involved.
19. He then advised me that he was going to see to it that officers were sued and that the officers were going to lose their jobs over this incident.
20. I advised C. Sentell that he could be charged for making the threats to the jobs of the Bossier City Police Officers involved in this arrest.
21. C. Sentell continued to curse and he continued to tell this officer to call Schuyler Marvin right now.
An in car video was operable in the patrol car. The remarks about Ron Miciotto were clearly audible, but there was no subsequent threat saying that officers were going to lose their jobs.
Reserve Officer Fisher was more specific, saying that the threat came as they were turning into the police station.
In an interview with Lt. Larry Stockton, after hearing the tape from the car, Vernon stated that it must have happened after they exited the car.
Reserve Officer Fisher did not change his statement, saying that it happened in the car.
Vernon appealed his termination to the Fire & Police Civil Service Board.
At the February hearing, according to Vernon's lawyer, the officer was 'shocked and dismayed' to find that former 26th JDC Judge Cecil Campbell was the board's attorney. Campbell currently prosecutes felony domestic abuse cases for the DA's office. "Not surprisingly", the lawyer continues in his brief, "the majority of rulings favored Sentell and/or the appointing authority. He went so far to say that some of the rulings were "absolutely contrary to law".
He doesn't bother to enumerate those adverse rulings, and indeed, the board ruled that the city had acted without just cause and changed the termination to a 90 day suspension.
A few days later the board met and changed the ruling to read that the city had acted with just cause. Board member Lt. Jimmie Stewart said that he misspoke when he made the motion and Board Chairman James Huckabay said that he misheard it.
On February 25th the City of Bossier City filed suit against Vernon and the Civil Service Board to overturn their ruling and enforce the termination.
On February 26th Vernon filed suit to overturn the decision of the Civil Service Board and for reinstatement.
The two suits were combined.
Various briefs and filings were made, among the notable claims by Vernon was that the Civil Service Board provided incomplete and spliced tape recordings and transcripts of the proceedings.
The City maintains that the ruling of the board stands on its own. The city offers state law in support.
La. R.S. 33:2478(A)(3): The board shall not be required to have the testimony taken and transcribed, but either the employee or the appointing authority may, at their own expense, make the necessary arrangements therefor. In such cases the board shall name any competent shorthand reporter as the official reporter. If the testimony is not taken or transcribed, then the board shall make a written finding of fact.
In other words, if Vernon's lawyer didn't arrange for a reporter to make a transcript, then none was made and the ruling of the board serves as official record.
There is an attempt by Vernon's lawyer to make a 'conspiracy' case, just as he is doing in the Chubby Knight case.
Chief Halphen, Lt. Stockton, Cpl. Murray Wells and Judge Campbell all were complicit in this conspiracy against his client. By extension, Reserve Officer Fisher would be too, since at the Civil Service hearing he did not change his statement that the alleged threat was made in the car.
[Disclaimer: Nearly everyone who reads the blog knows that Officer Murray Wells is my son. Despite that fact, and despite the fact that Vernon's lawyer has made statements to the media and in court filings that my son is not being truthful, I am trying to present this in as factual a manner as possible.]
In another brief, the lawyer waxes eloquent, describing the actions of the Bossier City Fire & Police Civil Service Board in what he says are the words of Nazi henchman and Propaganda Minister Josef Goebbels.
"If you tell a lie big enough and keep repeating it, people will eventually come to believe it. The lie can be maintained only for such time as the State can shield the people from the political, economic and or military consequences of the lie. It thus becomes vitally important for the State to use all of its powers to repress dissent, for the truth is the mortal enemy of the lie, and thus by extension, the truth is the greatest enemy of the State."
As I stated in a previous post, Judge Parker Self will issue a ruling on the merits of the above case within the next couple of weeks.
In the meantime, Vernon has filed another suit for reinstatement and compensatory damages. The main difference in the suits is that the new one includes all attorney fees and costs.
Phillip Vernon sues Bossier City for damages
Bossier City Police Officer Phillip Vernon has filed a lawsuit against The City of Bossier City and former Chief Mike Halphen for damages, wrongful termination & retaliatory discharge.
The City terminated Vernon last December saying that he had filed a false incident report. The Bossier City Fire & Police Civil Service Board resinstated Vernon and changed the termination to a 90 day suspension.
At first the board said the firing was 'without just cause' and then reversed that to say it was 'with just cause'. The City sued in District Court to overrule the board and to terminate Vernon; a few days later Vernon filed to overturn the 90 day suspension. The two suits were combined. Just this week Judge Parker Self took all the pleadings under advisement and will issue an opinion within 30 days.
This weekend I will post a detailed account of the goings on to this point. It will be quite lengthy.
Use the "I forgot" defense
A Bossier City woman was arrested Tuesday afternoon on two counts of bigamy, said Bossier Sheriff Larry Deen.
Bridget K. Mize, 35, of the 200 block of Adair Street, was taken into custody after she admitted to a Bossier Sheriff's investigator that she is married to three different men at the same time. Mize also admitted she never divorced any of the men.
Mize married for the first time in Dallas County, Texas, on September 24, 1993. She married for the second time in Caddo Parish, Louisiana, on December 28, 2005. Mize married for the third time in Columbia County, Arkansas, on August 13, 2007. She married her third husband when her second husband was incarcerated at the Bossier Maximum Security Facility.
Mize, who told the investigator she knew she was not divorced from her first and second husbands, was transported to the Bossier Maximum Security Facility and booked. Her bond is pending.
Who but Elton could express it better?
Posted by Jim at 12:35 PM 10 comments:
Northwest Louisiana Tea Party Alliance Announces F...


Multifamily owners are always anticipating the needs of our changing demographics. Whether it's swimming pools for families, gyms for millennials, or dog parks for pet owners, we always want to be one step ahead. Unfortunately, these groups are always changing. Families move to the suburbs, millennials grow up and want different things, and even pet owners—who will almost always own a pet—don't necessarily want to be renting forever. There's only one demographic in which a large number of people will always want rented accommodation in the same area, and it's often an overlooked group: seniors. In areas like Riverside County that have significant senior populations, multifamily owners need to consider how to renovate and appeal to this demographic.
With LA's senior population expected to surge in the next 15 years to 40% of the population as baby boomers hit 65, renovating your multifamily with the elderly in mind could mean high occupancy rates, impressive, stable income, and an end to second-guessing the next on-trend amenities only to see them wane in popularity as different varieties of residents come and go.
These guidelines are merely a start, however. If you want to make your property a safe and comfortable place for senior residents, consider the following renovation options.
First things first—look at the journey your residents have to take from the sidewalk, through the grounds, inside your property, and to their front door. Is the building easy for seniors to approach? Can they get inside easily? Is it safe and convenient for them to walk along corridors and reach their apartments? This all might sound very straightforward and obvious, but it's easy to miss something small that can make a significant difference, especially for someone who may have mobility issues.
Make sure there is a stepless entry from the sidewalk to the front door of your apartment block. If there are currently a few steps that need to be climbed to access the entrance, consider installing a ramp for those in wheelchairs. If there isn't enough room for a ramp or the ramp risks being too steep, consider a chair lift instead. But getting to the doorstep is only the first factor to consider—you must also ensure that your front doors are wide enough. Ideally, all doors throughout your multifamily should be 36 inches or wider to allow for wheelchair access.
A landscaped garden can help set you apart from competitors, but not if it's inaccessible. Common dangers here are paths that are too thin or unsuitable for wheelchairs, or both. Lighting is also important; seniors with vision issues need more light to see, so ensuring that your garden is well lit at night is crucial for their safety. An abundance of light will also help seniors to feel more secure about their surroundings.
While getting the communal areas of the property right is important, the real difference (and benefit) of a multifamily designed for seniors will be experienced in the apartments themselves.
Install a curbless shower system with a bench and removable shower head so that seniors can wash themselves sitting down if they wish.
Raise the height of the sink and leave open space underneath. As a result, seniors won't have to bend down to wash their hands, and those in wheelchairs can position themselves directly under the sink without having to lean over to reach the basin and tap.
Raise the height of the toilet, as well, and install safety railings on the surrounding wall space.
Surface the bathroom in a non-slip material to prevent falls.
Never skimp on safety measures. Traditional bathrooms are the most inaccessible part of the house for seniors, and they require the most renovation work, but knowing they have been designed with safety at the forefront will give both you and your senior residents peace of mind.
Focusing on bathroom safety doesn't mean that other parts of the house can't also be made a tad more accessible. Take the kitchen for instance. The main issues here are reaching up for cupboards (tricky for most, impossible if you're in a wheelchair) and bending down to use the oven, dishwasher and washing machine. Undercounter cabinets are an excellent way to make your kitchen friendly to seniors, whether they are in or out of wheelchairs. So are sinks with shallow basins. To avoid difficulties using the oven and other appliances typically placed on the floor, position them higher than you would normally. What's more, if your tabletops are particularly high, you may want to consider lowering them to increase general accessibility, as well as wheelchair accessibility.
When it comes to flooring, there are two different schools of thought. The first recommends vinyl or laminate flooring to make it easy for wheelchairs to maneuver. These types of flooring provide an even surface without any bumps or loose threads that could get stuck in wheels.
The second school of thought recommends carpet. The belief here is that carpet can still be relatively flat, but it also provides warmth (both underfoot and through insulation) and a soft surface in case residents have a fall. Regardless of which side of the coin you fall on, remove rugs and anything else on the floor that can be viewed as a tripping hazard, including electrical wiring.
Bear in mind when finalizing renovation plans that, while added safety and accessibility are the primary goals, the aim shouldn't be to turn apartments into hospital wards. You don't have to forgo aesthetic design choices; the apartment should still feel like a home and should be one that the resident can live in comfortably and safely in for many years to come.
As baby boomers continue to get older, they'll continue to need accessible housing options, and renovating to appeal to their particular needs is a wise choice. Make a start on these renovations now so you're already seen as a reputable and sought-after multifamily as this demographic continues to age. Our consultants are on-hand to discuss your renovations today. Just pick up the phone or leave them a message below to get in touch.


text:
Odorrana trankieni, also known as Trankien frog or Tran Kien's odorous frog, is a species of frogs in the family Ranidae. It is endemic to northern Vietnam. Its natural habitats are montane evergreen forests and secondary mixed evergreen bamboo forests at elevations of  above sea level.

References

trankieni
Frogs of Asia
Amphibians of Vietnam
Endemic fauna of Vietnam
Amphibians described in 2003
Taxa named by Nikolai Loutseranovitch Orlov
Taxonomy articles created by Polbot

redpajama_set_name: RedPajamaWikipedia