text:
\section*{Abstract}
{\bf
In Kontsevich's graph calculus, internal vertices of directed graphs are inhabited by copies of a given Poisson structure;

the Nambu\/-\/determinant Poisson brackets
are differential polynomials in the Casimir(s) and
density~$\varrho$ times
Civita symbol.
We
resolve the old vertices into
subgraphs such that every new internal vertex contains one Casimir or one Civita symbol${}\times\varrho$.
Using this micro\/-\/graph calculus, we show
that Kontsevich's tetrahedral $\gamma_3$-flow on the space of Nambu\/-\/determinant Poisson brackets over~$\mathbb{R}^3$ is a Poisson coboundary: we realize the trivializing vector field~$\smash{\vec{X}}$ over~$\mathbb{R}^3$ using micro\/-\/graphs.

This~$\smash{\vec{X}}$
projects to the known trivializing vector field for the $\gamma_3$-flow over~$\mathbb{R}^2$.%
}

\subsection*{Introduction

Kontsevich introduced~\cite{Ascona96} a universal --\,for any affine Poisson manifold of dimension~$d$\,-- construction of infinitesimal symmetries for the Jacobi identity: for suitable cocycles~$\gamma$ in the graph complex, one obtains bi\/-\/vector flows $\dot{P} = Q_{\gamma}([P])$ with differential\/-\/polynomial right\/-\/hand sides (with respect to components~$P^{ij}({\boldsymbol{x}})$ of Poisson structures~$P \in \Gamma(\bigwedge^2 TM^d_{\text{aff}})$).
We detect in~\cite{skew21} that for the tetrahedral graph cocycle~$\gamma_3$ from~\cite{Ascona96} and for the pentagon\/-\/wheel graph cocycle~$\gamma_5$ (see~\cite{JNMP2017}), the corresponding flows (see~\cite{f16,sqs17,OrMorphism2018}) have a well\/-\/defined restriction to the subclass of Nambu\/-\/determinant Poisson brackets\footnote{\label{FootFormulaNambu}%
The Nambu\/-\/determinant Poisson brackets (with $\varrho \not\equiv 1$ and Casimir(s)~$a_\ell$) of $f,g \in C^1(\mathbb{R}^d)$ are, e.g.,
\[
\{f,g\}_{P(\varrho,[a])} = \varrho(x,y,z) \cdot \left|\begin{smallmatrix}a_x & f_x & g_x \\ a_y & f_y & g_y \\ a_z & f_z & g_z\end{smallmatrix}\right|\quad\text{ on }\mathbb{R}^3\ni{\boldsymbol{x}} = (x,y,z);
\]
likewise $\{f,g\}_{P(\varrho,[a_1],[a_2])} = \varrho(x^1,x^2,x^3,x^4) \cdot \det\bigl(\partial(a_1,a_2,f,g)/\partial(x^1,x^2,x^3,x^4)\bigr)$ on~$\mathbb{R}^4$, and so on; all such formulas are coordinate free
(as
$\varrho({\boldsymbol{x}}) \cdot \partial_{x^1} \wedge \ldots \wedge \partial_{x^d}$
is a top\/-\/degree multivector on~$\mathbb{R}^d$).}
$P(\varrho, [{\boldsymbol{a}}])$ on~$\mathbb{R}^d$ at least in the following three cases:
(\textit{i}) $\gamma_3$-\/cocycle flow $\dot{P} = Q_{\gamma}([P])$ for $P(\varrho,[a])$ over~$\mathbb{R}^3$,
(\textit{ii}) the same $\gamma_3$-\/cocycle and the flow of $P(\varrho,[a_1],[a_2])$ over~$\mathbb{R}^4$, and
(\textit{iii}) the next, $\gamma_5$-\/cocycle flow for $P(\varrho,[a])$ over~$\mathbb{R}^3$.

To study universal --\,for all~$d \geqslant 3$\,-- or incidental --\,at fixed~$d$\,-- (non)\/triviality of Kontsevich's graph flows in the second Poisson cohomology for Nambu\/-\/determinant brackets $\{\cdot,\cdot\}_{P(\varrho,[{\boldsymbol{a}}])}$, we consider the coboundary equation,
\begin{equation}\label{EqCoboundaryInPoly}
	Q_{\gamma}([P])([\varrho],[{\boldsymbol{a}}]) = \schouten{P(\varrho,[{\boldsymbol{a}}]), \smash{\vec{X}}([\varrho],[{\boldsymbol{a}}])},
\end{equation}
upon the trivializing vector field solution(s) $\smash{\vec{X}}([\varrho],[{\boldsymbol{a}}])$ with differential\/-\/polynomial coefficients over~$\mathbb{R}^d$.
We discovered in~\cite{skew21} that the $\gamma_3$-\/flow over~$\mathbb{R}^3$ is trivial w.r.t.\ a unique solution~$\smash{\vec{X}}$;
we found it by using \emph{micro\/-\/graphs} that resolve $\varrho({\boldsymbol{x}}) \cdot \text{Civita symbol}$ against the Casimir(s)~$a_\ell$ within copies of Nambu\/-\/determinant Poisson brackets $\{\cdot,\cdot\}_{P(\varrho,[{\boldsymbol{a}}])} = \varrho({\boldsymbol{x}}) \cdot \sum_{i_1,\ldots,i_d=1}^d \varepsilon^{\vec{i}} \cdot \partial_{i_1}(a_1)\cdot$
$\ldots\cdot\partial_{i_{d-2}}(a_{d-2}) \cdot \partial_{i_{d-1}} \otimes \partial_{i_d}$ in the vertices of Kontsevich's directed graphs for $Q_{\gamma}([P])
$.

Within the differential calculus of (multi-)\/vectors $\smash{\vec{X}}$,\ $P$,\ $Q_{\gamma}$,\ and $\schouten{P,\smash{\vec{X}}}$ with differential\/-\/polynomial coefficients over~$\mathbb{R}^d$, the Poisson (non)triviality problem for the $\gamma_3$-\/flow in dimension $d=4$ is computationally hard.
Yet the dimension\/-\/specific micro\/-\/graphs offer us a much more economical way to encode and process all such differential\/-\/polynomial structures over~$\mathbb{R}^d$.
At the same time, at the level of micro\/-\/graphs before they are projected to polynomials, the cocycle equation acquires a previously invisible right\/-\/hand side:
\begin{equation}\label{EqCobundaryInMicroGraphs}
	Q_{\gamma}([P]) - \schouten{P,X^\gamma} = \Diamond([\varrho],[{\boldsymbol{a}}],\tfrac{1}{2}\schouten{P,P}) + \langle\text{zero micro-graphs}\rangle + \cdots.
\end{equation}
Now its r.-h.s.\
contains differential consequences of
Jacobi identity for
Nambu bi\/-\/vector $P(\varrho,[{\boldsymbol{a}}])$, as well as can it contain non\/-\/empty micro\/-\/graphs that encode identically zero bi\/-\/vectors.

This text is a sequel to~\cite{skew21}, which we refer for motivation, notation, and details.
The present paper is structured as follows: in~\S\ref{SecFindX}, we explain how, for $\gamma=\gamma_3$ and $d=3$, a solution of~\eqref{EqCoboundaryInPoly} was constructed using micro\/-\/graphs, and we discuss its properties.
In~\S\ref{SecTetraFlow4D} we explore the composition
of both sides in~\eqref{EqCobundaryInMicroGraphs} for larger problems:
$\gamma=\gamma_5$ or~$d\geqslant 4$.

\subsection*{Preliminaries}

Kontsevich's directed graphs are built of $n \geqslant 0$~wedges $\smash{\xleftarrow{L}\!\!\bullet\!\!\xrightarrow{R}}$, usually drawn in the upper half\/-\/plane~$\mathbb{H}^2$, over $m \geqslant 0$~ordered sinks along~$\mathbb{R} = \partial \mathbb{H}^2$; tadpoles are allowed.
Leibniz graphs are akin: the out\/-\/degrees of all but one (or more) vertices equal~$2$ yet there is (at least) one aerial vertex of out\/-\/degree~$3$ and its outgoing edges are ordered $\text{Left} \prec \text{Middle} \prec \text{Right}$.\footnote{\label{FootExJacLeibnizGraph}
For example, the tripod is a Leibniz graph; like every Leibniz graph, it expands to a linear combination of Kontsevich's graphs, namely to the Jacobiator $\tfrac{1}{2}\schouten{P,P}$ for a bi\/-\/vector~$P$ whose copies are realized by wedges.}

We shall study only those flows $\dot{P} = Q([P])$ on spaces of bi\/-\/vectors $P \in \Gamma(\wedge^2TM^{d<\infty}_{\text{aff}})$ which are encoded by Kontsevich's graphs.
From~\cite{Ascona96} (cf.~\cite{OrMorphism2018}) we know that from suitable \emph{cocycles}~$\gamma$ in the Kontsevich graph complex,
one obtains the flows\footnote{\label{FootFlowDependsOnMarkerGraphCocycle}
The formula of Kontsevich's graph flow $\dot{P} = Q_{\gamma}([P])$ can depend on a choice of representative~$\gamma$ for the graph cohomology class~$[\gamma]$. Fortunately, the vertex\/-\/edge bi\/-\/gradings $(4,6)$ for~$\gamma_3$ and $(6,10)$ for two graphs in~$\gamma_5$ are not yet big enough to provide room for any nonzero coboundaries (from nonzero graphs on $3$~vertices and $5$~edges or on $5$~vertices and $9$~edges, respectively). In other words, the known markers for~$[\gamma_3]$ and~$[\gamma_5]$ are in fact uniquely defined modulo constant;
we prove this by listing all the admissible (non)zero ``potentials'' and by taking their vertex\/-\/expanding differentials in the graph complex.
This is why, in our present study of the $\gamma_3$-{} and $\gamma_5$-\/flows on the spaces of Nambu\/--\/Poisson brackets, we do not care about a would\/-\/be response of trivializing vector fields~$X^\gamma$ in~\eqref{EqCobundaryInMicroGraphs} to shifts of the marker cocycle~$\gamma$ within its graph cohomology class~$[\gamma]$.}
$\dot{P} = Q_{\gamma}([P])$ which preserve the (sub)\-set of \emph{Poisson} bi\/-\/vectors on~$M_{\text{aff}}^d$.

The tetrahedron~$\gamma_3$ and pentagon-wheel cocycle $\gamma_5$, see \cite{OrMorphism2018, sqs17}, are examples of graph cocycles giving such flows
)

\begin{define}
The \emph{Nambu\/-\/determinant Poisson bracket} on~$\mathbb{R}^{d \geqslant 3}$ is the derived bi\/-\/vector $P(\varrho, [a])$
$\stackrel{\text{def}}{=} \schouten{\ldots \schouten{\varrho \cdot \partial_{x^1} \wedge \ldots \wedge \partial_{x^d}, a_1}, \ldots ]\!], a_{d-2}}$,
where $\varrho({\boldsymbol{x}})\cdot \partial_{{\boldsymbol{x}}}$ is a $d$-\/vector field and scalar functions~$a_{\ell}$ are Casimirs ($q \leqslant \ell \leqslant d-2$).
In global (e.g., Cartesian) coordinates $x^1,\ldots,x^d$ on~$\mathbb{R}^d$, the Nambu bracket of $f,g\in C^1(\mathbb{R}^d)$ is expressed by the formula
\begin{equation}
	\{f,g\}_{P(\varrho,[{\boldsymbol{a}}])} = \varrho({\boldsymbol{x}}) \cdot \sum\nolimits_{i_1\ldots,i_d=1}^d \varepsilon^{\vec{\imath}} \cdot \partial_{i_1}(a_1) \cdots \partial_{i_{d-2}}(a_{d-2}) \cdot \partial_{i_{d-1}}(f) \cdot \partial_{i_{d}}(g),
\end{equation}
where $\varepsilon^{i_1,\ldots,i_d}$ is the Civita symbol on~$\mathbb{R}^d$: $\varepsilon^{\sigma(1,\ldots,d)} = (-)^\sigma$ for $\sigma \in S_d$, otherwise zero.
\end{define}

\begin{rem}\label{RemReduceDimInNambu}
Nambu\/--\/Poisson brackets on~$\mathbb{R}^{d \geqslant 3}$ can be obtained from Nambu\/--\/Poisson brackets on~$\mathbb{R}^{d+1}$ by taking $a_{d-1} = \pm x^{d+1}$
on~$\mathbb{R}^{d+1}$ and by excluding the last Cartesian coordinate~$x^{d+1}$ from the list of arguments for~$\varrho({\boldsymbol{x}})$ and $a_1,\ldots,a_d({\boldsymbol{x}})$.
$\bullet$\ By doing the above for $d+1=3$, one obtains a generic bi\/-\/vector $P = \varrho(x^1,x^2) \partial_{x^1} \wedge \partial_{x^2}$, which is Poisson on~$\mathbb{R}^2$, and the (Nambu--)\/Poisson bracket $\{f,g\}(x,y) = \varrho(x,y)\cdot(f_x \cdot g_y - f_y \cdot g_x)$.
\end{rem}

\begin{define}\label{DefMicroGraph}
Fix the dimension~$d \geqslant 2$.
A \emph{micro\/-\/graph} is a directed graph built over $m \geqslant 0$~sinks, over $n \geqslant 0$~aerial vertices with out\/-\/degree~$d$ and ordering of outgoing edges, and over~$n$ $d$-\/tuples of aerial vertices with in\/-\/degree~$1$ and no outgoing edges.
$\bullet$\ The correspondence between micro\/-\/graphs and differential\/-\/polynomial expressions in $\varrho,a_1,\ldots,a_{d-2}$ and the content of sink(s) is defined in the same way as the mapping of Kontsevich's graphs to multi\/-\/differential operators on~$C^\infty(M^d_{\text{aff}})$, see~\cite[\S 2.2]{skew21} or~\cite{Ascona96}.
\end{define}

\begin{example}\label{ExNambuByMicroGraphs}
Nambu\/--\/Poisson brackets $P(\varrho,[a_1],\ldots,[a_{d-2}])$ on~$\mathbb{R}^d$ are realized using micro\/-\/graphs, namely by resolving $\varrho({\boldsymbol{x}}) \cdot \varepsilon^{i_1,\ldots,i_d}$ in one vertex against $d-2$ vertices with the Casimirs $a_1,\ldots,a_{d-2}$.
The out\/-\/degree of vertex with $\varrho({\boldsymbol{x}}) \cdot \varepsilon^{\vec{\imath}}$ equals~$d$; the in\/-\/degree of each vertex with a Casimir equals~$1$ and its out\/-\/degree is zero: the Casimir vertices are terminal (not to be confused with the two sinks, of in\/-\/degree~$1$, for the Poisson bracket arguments).
The ordered $d$-\/tuple of edges is decorated with summation indices:
for the Civita symbol $\varepsilon^{i_1,\ldots,i_d}$
in their common arrowtail vertex, the range is $1 \leqslant i_{\ell} \leqslant d$ for~$1 \leqslant \ell \leqslant d$.
\end{example}

\begin{rem}\label{RemExpandMKgraphToMicro}
If the wedge tops contain Nambu\/--\/Poisson bi\/-\/vectors $P(\varrho,[a])$ on~$\mathbb{R}^d$, every Kontsevich graph expands to a linear combination of micro\/-\/graphs: the arrow(s) originally in\/-\/coming to an aerial vertex with a copy of~$P$, now work(s) by the Leibniz rule over the $d-1$ vertices, with $\varrho \cdot \varepsilon^{\vec{\imath}}$ and with $a_1,\ldots,a_{d-2}$, in the subgraphs $P(\varrho,[a_1],\ldots,[a_{d-2}])$ of the micro\/-\/graph.%
\footnote{But not every micro\/-\/graph is obtained from a Kontsevich graph by resolving the old aerial vertices into subgraphs.}
\end{rem}

\begin{example}\label{ExTrivVF3D2Dsunflower}
If $d=2$ and
(Nambu\/--)\/Poisson brackets on $\mathbb{R}^2$ are $\{f,g\}(x,y) = \varrho \cdot (f_x \cdot g_y - f_y \cdot g_x)$ as in Remark~\ref{RemReduceDimInNambu}, the only possible Kontsevich graph, `sunflower' built with tadpoles
from $n=3$ wedges over one sink (see~\cite[Appendix F, Remark 13]{f16}) tautologically expands to a nontrivial linear combination of nonzero micro\/-\/graphs on three aerial vertices with $\varrho(x,y)\cdot \varepsilon^{i^\alpha j^\alpha}$, $1 \leqslant \alpha \leqslant 3$.
Independently, the linear combination~$X^\gamma$ of micro\/-\/graphs that encode the trivializing vector field $\smash{\vec{X}}([\varrho],[a])$ for Kontsevich's $\gamma_3$-\/flow for Nambu bi\/-\/vectors $P(\varrho,[a])$ on~$\mathbb{R}^3 \ni (x$, $y,z)$, see~\cite{skew21} and~\S\ref{SecFindX} below, under the reduction $a \mathrel{{:}{=}} z$ and $\varrho = \varrho(x,y)$ becomes a well\/-\/defined vector field on the plane $\mathbb{R}^2 \subset \mathbb{R}^3$:
the $z$-\/component of $\smash{\vec{X}}([\varrho(x,y)],[z])$ vanishes.

Let us compare the two vector fields on~$\mathbb{R}^2$.
\end{example}

\begin{proposition}\label{PropDim3Down2trivVFtetra
The old `sunflower' vector field which trivializes the tetrahedral $\gamma_3$-\/flow for {all} Poisson brackets on~$\mathbb{R}^2$
\emph{coincides} with
the new vector field $\smash{\vec{X}}([\varrho(x,y)],[a=z])$ from the trivialization of $\gamma_3$-\/flow for the Nambu brackets $P(\varrho,[a])$ on~$\mathbb{R}^3$
(both viewed as $1$-\/vector fields on~$\mathbb{R}^2$ with differential coefficients in~$[\varrho]$).
\end{proposition}

\begin{lemma}\label{LemmaLeibnizMicroGraphExist}
If $d=3$ and $P(\varrho,[a])$ is Nambu, the Jacobiator tri\/-\/vector graph $\Jac(P)$ remains a nontrivial linear combination, $\Jac(P)([\varrho],[a])$, of $3$ or $6$ nonzero micro\/-\/graphs, each on $m=3$ sinks of in\/-\/degree~$1$, on two trident vertices with $\varrho \cdot \varepsilon^{i_1^\alpha i_2^\alpha i_3^\alpha}$, and on two terminal vertices of in\/-\/degrees~$1$ and~$2$ (if $\varrho \equiv \text{const}$) or $(1,1)$ and $(1,2)$ if~$\varrho \not\equiv \text{const}$.
\end{lemma}

This is why linear combinations of Leibniz micro\/-\/graphs $\Diamond([\varrho],[{\boldsymbol{a}}],\tfrac{1}{2}\schouten{P,P})$
can contribute nontrivially to the right\/-\/hand side of~\eqref{EqCobundaryInMicroGraphs}.

\section{Trivializing vector field~$\smash{\vec{X}}$ for $\gamma_3$-flow over~$\mathbb{R}}\newcommand{\BBC}{\mathbb{C}^3$}
\label{SecFindX}

\noindent%
We recall from~\cite[\S 4.1]{skew21} that, given a suitable graph cocycle~$\gamma$ (e.g., $\gamma_3$ which we take here), Kontsevich's $\gamma$-\/flow $\dot{P} = \Or(\gamma)(P^{\otimes \#\text{Vert}(\gamma)})$ restricts to the set of Nambu\/--\/Poisson bi\/-\/vectors $P(\varrho,[a])$ such that the velocity of a Casimir~$a_\ell$ is still encoded by Formality graphs~\cite[Proposition 2]{skew21}: $\dot{a}_\ell = \Or(\gamma)(P\otimes \cdots \otimes P \otimes a)$, whence the velocity $\dot{\varrho}([\varrho],[{\boldsymbol{a}}])$ is expressed from the known~$\dot{{\boldsymbol{a}}}$ and~$\dot{P}$ (see~\cite[Corollary 3]{skew21}).
The Leibniz rule, balancing $\dot{P}$~with $\dot{\varrho}, \dot{{\boldsymbol{a}}}$ for $P$~linear in~$\varrho$ and the first jets of all~$a_\ell$, is then a tautology.

Independently, if $\smash{\vec{Y}}$ is any $C^1$-\/vector field on~$\mathbb{R}^d$ with Nambu\/--\/Poisson bi\/-\/vectors $P(\varrho,[{\boldsymbol{a}}])$, then the evolution $L_{\vec{Y}}(a_\ell) = \schouten{\smash{\vec{Y}},a_\ell}$ of scalar functions and $L_{\vec{Y}}(\varrho \cdot \partial_{{\boldsymbol{x}}}) = \schouten{\smash{\vec{Y}}, \varrho \cdot \partial_{{\boldsymbol{x}}}}$ of $d$-\/vectors
correlates, by the Leibniz\/-\/rule shape of the Jacobi identity for the Schouten bracket $\schouten{\cdot,\cdot}$, with
evolution $L_{\vec{Y}}(P) = \schouten{\smash{\vec{Y}}, P}$ of Nambu bi\/-\/vector $P = \schouten{\varrho \cdot \partial_{{\boldsymbol{x}}}, \cdots {\boldsymbol{a}} \cdots }$, see~\cite[\S 2.1]{skew21}.

Our finding in~\cite[Theorem~8]{skew21} is that for the graph cocycle~$\gamma_3$ and $d=3$, the action of vector field~$\smash{\vec{X}}$ (which trivialzes the $\gamma_3$-\/flow $\dot{P} = Q_{\gamma_3}([P]) = \schouten{P, \smash{\vec{X}}}$ of Nambu brackets~$P$ on~$\mathbb{R}^3$) upon $P(\varrho,[a])$ factors through the initially known --\,from~$\gamma_3$\,-- velocities of~$a$ and~$\varrho$: having solved~\eqref{EqCoboundaryInPoly} for~$\smash{\vec{X}}$, we then verified that $\dot{a} = \schouten{a,\smash{\vec{X}}}$ and $\dot{\varrho}\,\partial_{{\boldsymbol{x}}} = \schouten{\varrho \cdot \partial_{{\boldsymbol{x}}}, \smash{\vec{X}}}$.

By using this factorization --\,i.e.\ the lifting of the sought vector field's action on the elements of~$P(\varrho,[a])$\,-- the other way round, we create an economical scheme to inspect the \emph{existence} of trivialzing vector field~$\smash{\vec{X}}$ for larger problems (i.e.\ for bigger graph cocycles or higher dimension $d \geqslant 3$).
When this shortcut works, so that $\smash{\vec{X}}$~is found, it saves much effort.
Otherwise, to establish the (non)\/existence of~$\smash{\vec{X}}$ one deals with a larger PDE, namely Eq.~\eqref{EqCoboundaryInPoly}.

\begin{open}\label{OpenPrbAlwaysCanSeekARhoDotFirst}
Are Nambu\/--\/Poisson bi\/-\/vectors $P(\varrho,[a])$ such that the action of trivialzing vector field(s) $\smash{\vec{X}}$ (when such exist(s) for a Kontsevich graph flow) always lifts to the Casimir(s)~$a_\ell$ and $d$-\/vector field $\varrho\cdot\partial_{{\boldsymbol{x}}}$, so that $\dot{a}_\ell = \schouten{a_\ell, \smash{\vec{X}}}$ and $\dot{\varrho}\cdot \partial_{{\boldsymbol{x}}} = \schouten{\varrho \cdot \partial_{{\boldsymbol{x}}}, \smash{\vec{X}}}$\,?
\end{open}

Let us illustrate how the shortcut scheme works.
We now tune a $1$-\/vector field $\smash{\vec{X}}(\varrho,[a])$ for the flow $\dot{P} = Q_{\gamma_3}([P])$ of $P(\varrho,[a])$ over~$\mathbb{R}^3$ such that $\dot{a} = \schouten{a,\smash{\vec{X}}}$ and $\dot{\varrho}\cdot \partial_{{\boldsymbol{x}}} = \schouten{\varrho \cdot \partial_{{\boldsymbol{x}}}, \smash{\vec{X}}}$, whence we verify that $\dot{P} = \schouten{P, \smash{\vec{X}}([\varrho], [a])} \in \operatorname{im} \partial_P$ for the Nambu\/-\/determinant class of Poisson brackets on~$\mathbb{R}^3$.

The micro\/-\/graph expansion of $Q_{\gamma_3}(P)$ for $P(\varrho,[a])$ over~$\mathbb{R}^3$ consists of directed graphs on $2$~sinks for~$f$ and~$g$, on four terminal vertices for Casimirs~$a$ without outgoing arrows, and on four vertices for~$\varrho \cdot \varepsilon^{ijk}$ with three ordered outgoing edges.
In every micro\/-\/graph in bi-\/vector $Q_{\gamma_3}(P)$ there are $12$~edges, with exactly two going
towards~$f$ and~$g$ in the sinks.
To have a solution~$\smash{\vec{X}}$ of the equation $Q_{\gamma_3}(P(\varrho,[a])) = \schouten{P,\smash{\vec{X}}}$ using micro\/-\/graphs that encode $\smash{\vec{X}}([\varrho],[a])$ we thus need micro\/-\/graphs on one sink, three terminal vertices with~$a$,
and three trident vertices for $\varrho \cdot \varepsilon^{ijk}$.
Of the nine edges in each micro\/-\/graph, exactly one goes to the sink, so that $\smash{\vec{X}}$~is a $1$-vector.

We first generate all suitable unlabeled micro\/-\/graphs (i.e.\ without distinction which sinks are for Casimirs) without tadpoles and with exactly one tadpole.
Next, by deciding on the run which of the four sinks is the argument of $1$-\/vector, we produce $366$ $1$-\/vector fields with differential polynomial coefficients in~$\varrho$ and~$a$, encoded by micro\/-\/graphs.
Some of the coefficients are identically zero when the sums over three triples of indices in Civita symbols are fully expanded; there remain $244$~nonzero marker micro\/-\/graphs in the ansatz for the trivializing vector field~$\smash{\vec{X}}$.
Now, we do not attempt solving the big problem $Q_{\gamma_3}(P) = \schouten{P,\smash{\vec{X}}}$ directly with respect to the $244$~coefficients of nonzero marker micro\/-\/graphs.
Instead, let us find a vector field~$\smash{\vec{X}}$, realized by $1$-vector micro\/-\/graphs~$X^\gamma$, which reproduces the known velocities~\cite[Eq.\:(11)]{skew21}
of~$\varrho$ and Casimir~$a$, that is, we solve the equations $\dot{a} = -\schouten{\smash{\vec{X}},a}$ and $\dot{\varrho}\, \partial_x \wedge \partial_y \wedge \partial_z = \schouten{\varrho\, \partial_x \wedge \partial_y \wedge \partial_z, \smash{\vec{X}}}$ with respect to the coefficients in the micro\/-\/graph ansatz for~$X^\gamma$.
To determine exactly the number of equations in either linear algebraic system we keep track of the number of differential monomials appearing when $\smash{\vec{X}}$~acts on either~$a$ or~$\varrho $ as abov
, and we recall also the differential monomials which already appeared in~$\dot{a}$ and~$\dot{\varrho}$ in the left\/-\/hand sides, that is in~\cite[Eq.\:(11)]{skew21
.
In this way, we detect that the linear algebraic system for~$\dot{a}$ contains $2961$~equations and the system for~$\dot{\varrho}$ contains
$6679$~equations.
Each equation is a balance of the coefficient of one differential monomial.
We now merge these two systems of linear algebraic equations upon the coefficients of micro\/-\/graphs in the ansatz for the trivializing vector field~$\smash{\vec{X}}$,
and we find a solution.
Only $11$~coefficients are nonzero.
The analytic formula of this vector field was reported in~\cite[Theorem~8]{skew21}.
The three equalities, namely $\dot{a} = -\schouten{\smash{\vec{X}},a}$ and $\dot{\varrho}\, \partial_x \wedge \partial_y \wedge \partial_z = \schouten{\varrho \partial_x \wedge \partial_y \wedge \partial_z, \smash{\vec{X}}}$ implying $Q_{\gamma_3}(P) = \schouten{P,\smash{\vec{X}}}$, are verified immediately.
Here is the encoding of the weighted sum~$X^\gamma$ of these $11$ micro\/-\/graphs which realize the trivializing vector field~$\smash{\vec{X}}$ for the tetrahedral flow $Q_{\gamma_3}(P) = \schouten{P,\smash{\vec{X}}}$ on the space of Nambu\/--\/Poisson structures over~$\mathbb{R}^3$:

{\tin
\begin{verbatim}
 16 * [(0,4), (0,5), (0,6), (5,0), (5,1), (5,6), (6,0), (6,2), (6,3)]
 24 * [(0,4), (0,5), (0,6), (5,0), (5,1), (5,6), (6,1), (6,2), (6,3)]
 16 * [(0,4), (0,5), (0,6), (5,0), (5,1), (5,2), (6,1), (6,3), (6,5)]
-16 * [(0,4), (0,5), (0,6), (5,0), (5,1), (5,2), (6,1), (6,3), (6,5)]
 12 * [(0,4), (0,5), (0,6), (5,1), (5,2), (5,6), (6,1), (6,2), (6,3)]
-12 * [(0,4), (0,5), (0,6), (5,1), (5,2), (5,6), (6,1), (6,2), (6,3)]
 24 * [(4,0), (4,1), (4,6), (5,0), (5,1), (5,2), (6,0), (6,2), (6,3)]
-24 * [(4,0), (4,1), (4,6), (5,0), (5,2), (5,4), (6,0), (6,1), (6,3)]
  8 * [(4,0), (4,1), (4,5), (5,0), (5,2), (5,6), (6,0), (6,3), (6,4)]
 -8 * [(4,0), (4,1), (4,5), (5,2), (5,3), (5,6), (6,0), (6,1), (6,4)]
  8 * [(0,4), (0,5), (0,6), (5,0), (5,1), (5,6), (6,2), (6,3), (6,6)]
\end{verbatim}

}

\begin{rem}\label{RemTadpoleInXonR3must}
At the level of micro\/-\/graphs, the
solution $X^{\gamma_3}$ contains a tadpole, i.e.\ a $1$-cycle, in the last graph.
In terms of differential polynomials this means the presence of a deriative~$\partial_{x^i}$ acting on the coefficient~$\varrho({\boldsymbol{x}})$ near the Civita symbol $\varepsilon^{ijk}$ containing the index~$i$ of the base coordinate~$x^i$ in that derivative; that is, the last term in the vector field~$\smash{\vec{X}}$ contains $\partial_{x^i}(\varrho({\boldsymbol{x}})) \cdot \varepsilon^{ijk}$.
\end{rem}

\begin{proposition}
Without tadpoles in the micro\/-\/graph ansatz $X^{\gamma_3}$, there is no solution~$\smash{\vec{X}}$ to the trivialization problem $Q_{\gamma_3}(P(\varrho,[a])) = \schouten{P, \smash{\vec{X}}}$ at the level of differential polynomials.
\end{proposition}

\begin{rem}\label{RemRHSabsorbsTadpoles}
The tadpole from~$X^\gamma$ survives into the l.-h.s.\ of Eq.~\eqref{EqCobundaryInMicroGraphs} because there is no solution without tadpoles, so the 11th graph cannot be in the kernel of~$\schouten{P, \cdot}$.
There must be Leibniz graph(s) with tadpole in the r.-h.s.\ to balance the equality.
\end{rem}

\begin{rem}\label{RemG3R3ansatzDiamond}
Over~$\mathbb{R}}\newcommand{\BBC}{\mathbb{C}^3$, to generate an ansatz for the part of~$\Diamond$ \emph{without} tadpoles in the r.-h.s.\ of~\eqref{EqCobundaryInMicroGraphs}, it suffices to take
Leibniz micro\/-\/graphs on two sinks (receiving exactly one edge into either sink), with one trident Jacobiator vertex, with two trident vertices for $\varrho(x,y,z)\times{}$Civita symbol, and with two terminal vertices for copies of the Casimir~$a$.
There are $96$ isomorphism classes of directed graphs with the above out\/-\/degree profiles; by filtering them w.r.t.\ the in\/-\/degree~$1$ of tri\/-\/vector's sinks, we keep~$45$.

Likewise, to generate the other part --\,with one tadpole\,-- of~$\Diamond$ in the r.-h.s.\ of~\eqref{EqCobundaryInMicroGraphs} for the $\gamma_3$-flow $\dot{P}([\varrho],[a])$ over~$\mathbb{R}}\newcommand{\BBC}{\mathbb{C}^3$, we artificially decrease by one the number of edges in the graphs to generate --\,specifically, one of the ``Civita'' tridents becomes a wedge; the Jacobiator remains a trident that does not produce a tadpole\,-- and, as soon as these new directed graphs are produced, we by hand add a tadpole at the lonely
Civita vertex.
\end{rem}

To conclude this section, we note
that existence of a micro\/-\/graph solution~$X^\gamma$ for~\eqref{EqCobundaryInMicroGraphs} in a fixed dimension $d \geqslant 2$ implies the existence of a solution~$\smash{\vec{X}}$ with differential\/-\/polynomial coefficients for problem~\eqref{EqCoboundaryInPoly}
of triviality of Kontsevich's tetrahedral flow $\dot{P} = \Or(\gamma)(P^{\otimes n})$ on the space of Nambu\/-\/determinant Poisson structures $P(\varrho,[a])$ over~$\mathbb{R}^d$.
The vector field~$\vec{X}([\varrho],[a])$ trivializing the tetrahedral flow $\dot{P} = \Or(\gamma_3)(P^{\otimes 4})$ over~$\mathbb{R}^3$ can be
derived
in precisely this~way.

\section{(Non)triviality of $\gamma_3$-flow for Nambu\/--\/Poisson brackets on~$\mathbb{R}}\newcommand{\BBC}{\mathbb{C}^4$}
\label{SecTetraFlow4D}

\noindent%
From~\cite{skew21} we know
that Kontsevich's tetrahedral $\gamma_3$-flow restricts to the space of Nambu\/-\/determinant Poisson bi-\/vectors $P(\varrho,[a_1],[a_2])$ over~$\mathbb{R}^4$:
the differential\/-\/polynomial velocities~$\dot{\varrho}$ and $\dot{a}_1, \dot{a}_2$ inducing the
graph cocycle evolution $\dot{P}([\varrho],[a_1],[a_2])$ are stored externally.\footnote
\texttt{https://rburing.nl/gcaops/adot\_rhodot\_g3\_4D.txt}}

Recall that the evolutions $\dot{a}_1,\dot{a}_2(\varrho,[a_1],[a_2])$ are realized by
Kontsevich graphs $\Or(\gamma_3)(P\otimes P\otimes P$ $\otimes a)$, hence they are immediately expanded to micro\/-\/graph realizations.
The evolution $\dot{\varrho}([\varrho]$, $[a_1],[a_2])$ can then be expressed by using micro\/-\/graphs with minimal effort.

The problem of Poisson (non)\/triviality of the tetrahedral $\gamma_3$-flow for Nambu brackets in dimension $d=4$ is \textit{a priori} independent from the similar problem in dimension three (the solution of which has been discussed in the preceding section).

\begin{open}
Is the restriction of Kontsevich's tetrahedral $\gamma_3$-flow on the space of Nambu\/-\/determinant Poisson structures $P(\varrho,[a_1],[a_2])$ over~$\mathbb{R}^4$ trivial or not in the second Poisson cohomology\,?
That is, at the level of differential polynomials in~$\varrho$ and~$a_1,a_2$ in (multi\/-)\/vector coefficients,
is there a vector fiel
~$\smash{\vec{X}}([\varrho],[a_1],[a_2])$ satisfying the equation

\begin{equation}\label{EqTetra4DTrivial}
Q_{\gamma_3}([P])([\varrho],[a_1],[a_2]) = \schouten{P,\smash{\vec{X}}}\text{\,?} \tag{\ref{EqCoboundaryInPoly}$'$}
\end{equation}
\end{open}

\begin{rem}
Solving equation~\eqref{EqTetra4DTrivial} can be attempted, first, strictly at the level of differential polynomials by generating all the homogeneous differential monomials in $\varrho$,$a_1$,$a_2$ for the $d=4$ coefficients~$X^i$ of the sought vector field~$\smash{\vec{X}}([\varrho],[a_1],[a_2]) = \sum_{i=1}^d X^i$. For the graph cocycle~$\gamma_3$, every such monomial contains $\varrho^3=\varrho\cdot\varrho\cdot\varrho$, $a_1^3$, $a_2^3$ and $11$ derivatives falling on these nine factors; the 12th derivative makes the 1-vector~$X^i\,d_i$. These twelve derivations $\partial_{x^{i_1}}$, $\ldots$, $\partial_{x^{i_{12}}}$ are such that $\{x^{i_1},\ldots,x^{i_{12}}\} = \{x^1,\ldots,x^4\} \sqcup \{x^1,\ldots,x^4\} \sqcup \{x^1,\ldots,x^4\}$.
Another constraint --\,upon the derivative order profiles in~$X^i([\varrho],[{\boldsymbol{a}}])$, hence in $[\![ P,\smash{\vec{X}} ]\!]$\,-- comes from the bi\/-\/vector $Q_{\gamma_3}(P(\varrho,[{\boldsymbol{a}}]))$ with known differential\/-\/polynomial coefficients.
In effect, terms in~$X^i$ can contain only those orders of derivatives which, under $[\![ P,\cdot]\!]$, reproduce the actually existing profiles of derivatives in~$Q_{\gamma_3}([\varrho],[{\boldsymbol{a}}])$. (This technique was illustrated for Eq.~\eqref{EqCoboundaryInPoly} with~$\gamma_3$ over~$\mathbb{R}}\newcommand{\BBC}{\mathbb{C}^3$ in~\cite[\S7.1.5]{BuringDisser}.)

At the level of micro\/-\/graphs and Nambu\/-\/determinant Poisson structures $P(\varrho,[a_1],[a_2])$ over~$\mathbb{R}^4$,
a solution~$X^\gamma$ of~\eqref{EqCobundaryInMicroGraphs} for the graph cocycle~$\gamma_3$ would be realized by micro\/-\/graphs
possibly with tadpoles, on one sink of in-degree $1
, three vertices of out-degree~$4$, and two triples of terminal vertices for
Casimirs $a_1,a_1,a_1$ and $a_2,a_2,a_2$.
Expanding just one such micro\/-\/graph into a 1-vector on~$\mathbb{R}}\newcommand{\BBC}{\mathbb{C}^4$ means taking $n=3$ sums with $d=4$ indices in each sum, every index running from~$1$ to $d=4$; this gives us $4^4\cdot 4^4 \cdot 4^4 = 2^{24}\approx 16\cdot10^6$ terms.
From Proposition~\ref{PropCountMicroG3R4} below we read
that there are ${}\approx 20,000$ micro\/-\/graphs in the ansatz for~$X^\gamma$. This totals with ${}\approx 320\cdot 10^9$ differential monomials in the ansatz for
trivializing vector field~$\smash{\vec{X}}$ on~$\mathbb{R}}\newcommand{\BBC}{\mathbb{C}^4$.

So, to solve equation~\eqref{EqCoboundaryInPoly}, let us try solving equation~\eqref{EqCobundaryInMicroGraphs} at the level of micro\/-\/graphs, i.e.\ without projecting down to differential polynomials.
\end{rem}

\begin{open}\label{OpenPrbG3triv4Dgraphs}
Is there a vector field~$X^\gamma$ (realized by micro\/-\/graphs
as above)
satisfying the micro\/-\/graph equation
\begin{equation}\label{EqG3triv4DusingGraphs}
Q_{\gamma_3}(P(\varrho,[a_1],[a_2])) - \schouten{P, X^\gamma} = \Diamond([\varrho], [{\boldsymbol{a}}], \Jac(P)([{\boldsymbol{a}}],[\varrho])) + \langle\text{zero micro\/-\/graphs}\rangle\,\text{?}
   \tag{\ref{EqCobundaryInMicroGraphs}$'$}
\end{equation}
\end{open}

\begin{rem}
In the right\/-\/hand side of~\eqref{EqG3triv4DusingGraphs} the term $\Diamond([\varrho], [{\boldsymbol{a}}], \Jac(P)([{\boldsymbol{a}}],[\varrho]))$ can, firstly, be a linear combination of \emph{Leibniz graphs}, that is, $\Diamond_1(P(\varrho,[{\boldsymbol{a}}]), \Jac(P))$, built from the micro\/-\/graph realizations of the Nambu\/--\/Poisson structure $P(\varrho,[a_1],[a_2])$ over~$\mathbb{R}^4$ and then expanded into the linear combination of micro\/-\/graphs: the Leibniz graphs expand to Kontsevich graphs (by expanding the Jacobiator and Leibniz rules in each graph) and each Kontsevich graph expands to micro\/-\/graphs.
Secondly, for a solution~$X^\gamma$ to appear, the right\/-\/hand side may need a term $\Diamond_2([\varrho], [{\boldsymbol{a}}], \Jac(P(\varrho, [{\boldsymbol{a}}]]))$ with a linear combination of \emph{Leibniz micro\/-\/graphs}, which by definition contain a micro\/-\/graph expansion of the Jacobiator, same as above, but also other micro\/-\/graph vertices with~$\varrho$ and Casimirs~$a_\ell$ that do not merge into subgraphs realizing copies of the Nambu\/-\/-Poisson bi-vector over~$\mathbb{R}^4$.
To make equation~\eqref{EqG3triv4DusingGraphs} a strict equality of left- and right\/-\/hand sides, its right\/-\/hand side could require addition of zero micro\/-\/graphs with outgoing edge ordering (which equal minus themselves under an automorphism).
\end{rem}

\begin{proposition}\label{PropCountMicroG3R4}
$\bullet$\ There are $1,079$ isomorphism classes of directed graphs on one sink,
three vertices of out-degree four, six terminal vertices, and at most one tadpole (of them, $352$~are without a tadpole and $727$ have one tadpole).\\
$\bullet$\ Taking those graphs containing a vertex of in-degree one (for the sink), and dynamically appointing the Casimirs from the multi\/-\/set $\{a_1,a_1,a_1,a_2,a_2,a_2\}$ to the six terminal vertices of the above graphs, we obtain $38,120$ micro\/-\/graphs.\\
$\bullet$\ Excluding repetitions in the above set of micro\/-\/graphs (e.g., if those micro\/-\/graphs are isomorphic), still not excluding micro\/-\/graphs which equal minus themselves under a symmetry (automorphism of micro\/-\/graph with outgoing edge ordering and known location of~$a_1$'s and~$a_2$'s) we obtain $19,957$ micro\/-\/graphs in the ansatz for~$X^\gamma$ that would encode the trivializing vector field solutions, if any, of coboundary equation~\eqref{EqTetra4DTrivial}.\\
$\bullet$\ Of these $19,957$ micro\/-\/graphs, one tadpole is present in $13,653$ micro\/-\/graphs, and there are no tadpoles in $6,304$ micro\/-\/graphs.
\end{proposition}

\begin{proof}[Construction sketch]
The representatives of isomorphism classes of graphs without tadpoles are generated by the \textsf{nauty}~\cite{nauty} command-line call \texttt{geng 10 9:12 | directg -e12 | pickg -d0 -m7 -D4 -M3}.
Likewise, the graphs with one tadpole are generated by first producing graphs with one edge fewer, using \texttt{geng 10 0:12 | directg -e11 | pickg -d0 -m7 -D4}, and adding a tadpole to the lonely vertex of out-degree $3$ in each graph.
For the appointment of Casimirs to $6$ vertices in all \emph{different} ways, one uses an efficient algorithm to generate the $20$ permutations of the multi-set $\{a_1,a_1,a_1,a_2,a_2,a_2\}$.
\end{proof}

\begin{rem}
The \textsf{gcaops} software~\cite{gcaops} for calculus in Kontsevich's graph language (see~\cite{f16,OrMorphism2018,BuringDisser}) so far does not support the generation and manipulation of directed graphs with tadpoles~--- which, we expect, are essential for a solution~$X^\gamma$ of~\eqref{EqTetra4DTrivial} to appear.
\end{rem}

Finally, let us examine how an unknown solution of~\eqref{EqCobundaryInMicroGraphs} in high dimension $d\geqslant4$ can be constrained by using the known solution(s) for similar problem with the same graph flow but in lower dimension~$d-1$.

\begin{rem}
There is no known natural procedure to extend a given micro-graph realization $X^\gamma_d$ of trivializing vector field $\smash{\vec{X}}_d$ on~$\mathbb{R}^d$ (for $d \geqslant 2$) to a larger micro-graph realization $X^\gamma_{d+1}$ of some solution(s) $\smash{\vec{X}}_{d+1}$ (if any) for Kontsevich's graph flow (non)triviality problem over~$\mathbb{R}^{d+1}$.
Note that in the next dimension $d+1$, Civita symbols are
realized by micro-graph vertices with $d+1$ outgoing edges, instead of the vertices with $d$~outgoing edges in a given solution~$X^\gamma_d$.

Conversely, the \emph{reduction} $d+1\mapsto d$ of dimension for the Nambu-determinant Poisson structures amounts to setting the last Casimir $a_{d-1} =\pm x^{d+1}$ and excluding the last coordinate $x^{d+1}$ from the list of arguments in either $\varrho(x^1,\ldots,x^d)$ or any of the remaining Casimirs $a_1,\ldots,a_{d-2}$.
The (un)known trivializing vector field $\smash{\vec{X}}_{d+1}$ then provides a known solution $\smash{\vec{X}}_{d}$ and its micro-graph realization~$X^\gamma_d$.
By tracking backwards the correspondence of micro-graphs under the dimensional reduction, when the $(d+1)$th edges are essentially removed from the Civita symbol vertices, one can conjecture the shape of many micro-graphs in a sought solution $X^\gamma_{d+1}$ of the larger problem.
\end{rem}

\subsection*{Conclusion}
We conjecture that over all~$\mathbb{R}^{d\geqslant 3}$, Kontsevich's $\gamma_3$-flows of Nambu\/--\/Poisson brackets are coboundaries; the trivializing vector fields then project down under $\mathbb{R}^{d} \to \mathbb{R}^{d-1}$.

{\small
\subsubsection*{Acknowledgements}
The authors thank the organizers of~\textsc{Group34} colloquium on group theoretical methods in Physics on 18--22 July 2022 in Strasbourg for a very warm atmosphere during the meeting.
This paper is a follow-up to \cite{skew21}; the authors are grateful to the anonymous referee for useful comments and suggestions.
The research of R.B.\ is supported by project~$5020$ at the Institute of Mathematics,
Johannes Gutenberg\/--\/Uni\-ver\-si\-t\"at Mainz and by CRC-326 grant GAUS ``Geometry and Arithmetic of Uniformized Structures''.
The travel of A
K.\ was partially supported by project 135110 at the Bernoulli Institute, University of Groningen.
A part of this research was done while A.K.\ was visiting at the $\smash{\text{IH\'ES}}$ in Bures\/-\/sur\/-\/Yvette; A.K.\ thanks the $\smash{\text{IH\'ES}}$ for hospitality and financial support.

}

redpajama_set_name: RedPajamaArXiv


text:
Twitter slams top five spammers with legal suit
Big bird gets busy
Iain Thomson in San Francisco Fri 6 Apr 2012 // 23:45 UTC
Twitter has filed a legal suit against five entities for selling tools that send out spam tweets and clog up its network.
The suit names TweetAttacks, TweetAdder, and TweetBuddy, plus James Lucero of Justinlover.info and Garland Harris of Troption.com as its targets. In the legal filing, Twitter says that it has had to pour resources into its Trust and Safety team to try to stop spam, and has spent nearly a million dollars to counter the effects of the five defendants.
"With this suit, we're going straight to the source. By shutting down tool providers, we will prevent other spammers from having these services at their disposal. Further, we hope the suit acts as a deterrent to other spammers, demonstrating the strength of our commitment to keep them off Twitter," the company said on its blog.
The filing points out that all of the accused have signed up for a Twitter account, which involves signing the terms of service that specifically prohibit spam generation, as well as selling software that also breaks Twitter's terms. Furthermore, they market their code specifically as being able to circumvent existing spam controls.
As for the goal of the suit, Twitter wants the defendants to be shut down and claims damages equal to the amount it estimates they have cost the company. That works out at $300,000 for TweetBuddy , $150,000 for TweetAttacks, a $100,000 bill for James Lucero, and for TweetAdder and Garland Harris, $75,000 apiece.
Twitter made clear that it wasn't just relying on the legal system in its anti-spam campaign, but is beefing up security-engineering efforts as well. Just how successful it is will depend upon the ability of spammers to react technologically, and whether or not they are worried about their legal position. ®
Broader topics

redpajama_set_name: RedPajamaCommonCrawl


Previous Article Next Article Building Blocks: What makes a good EVM package?
Building Blocks: What makes a good EVM package?
A mental shortcut for thinking about EVM packages is to compare them to a package manager such as NPM. Package managers serve as convenient repositories for code that you can easily reuse and share with others. Indeed, when you use zos link <<packageName>>, ZeppelinOS will actually download code from NPM and save it directly into your node_modules folder. This is similar behavior to npm install, which is how you would install the openzeppelin-solidity smart contracts.
The difference when using zos link <<packageName>> to install EVM packages rather than npm install is that after downloading the package, ZeppelinOS checks the zos.<<network-name>>.json files to see if and where the code is already deployed on-chain. If the bytecode is already deployed, the zos create command will link it to your project by creating a transparent proxy. In other words: instead of having to upload the logic contract's code to the blockchain, ZeppelinOS will reuse the existing instance, and just spin up a proxy that delegates all logic to it. Linking to on-chain code, rather than deploying entirely new contracts, can be a vastly less expensive operation, especially for cases that might end up deploying hundreds of instances of the same contract.
Note that if you decide to write your own contracts extending from a base contract in an EVM package, ZeppelinOS will need to compile a completely new contract, extended from the downloaded Solidity source code. Publishing this code will essentially create a completely new logic contract that is now linkable itself. However, the gas savings from linking to an on-chain implementation during deployment will be lost.
When considering what makes a good EVM package, it helps to first clarify what your goals are. In keeping with DRY programming principles, we want to avoid rewriting code as much as possible to avoid the introduction of errors and improve code maintainability. Considering the level of danger that an error in smart contracts can expose users to, breaking a program down into smaller, isolated pieces of code can reduce a program's attack surface area, improve readability/maintainability, and, if individual pieces are themselves upgradable, create more robust and less brittle software.
With DRY programming, we generally turn each particular task into its own function, and then rather than rewriting tasks, we reuse code via functions. When these functions are audited and well-tested, reusing them, rather than writing new implementations each time, allows developers to craft their contracts in a secure way. While theoretically, you could create an EVM package from a single function, in most cases this won't end up being very efficient in terms of gas deployment savings or for the organization of code. Instead, EVM packages are best built out of collections of functions that form a standalone contract.
As you can rarely complete complicated tasks with a single function (we coding mortals anyway!), by grouping these functions together based on cohesive areas of functionality, you can build modular building blocks that can be used standalone or linked to as a part of something yet larger.
As an example, Zeppelin's OpenZeppelin-eth implementation of the ERC20 standard is a concise collection of the functions and data definitions required to implement the functionality described by the EIP-20. Standards such as this make good candidates for EVM packages, and they gather all of the functionality required for a particular goal into a concise collection. Functions related to the implementation requirements of ERC20 tokens can be found inside the ERC20 EVM package, and any project wishing to incorporate ERC20 tokens need only link to the deployed on-chain contract to implement a standards-compliant and secure ERC20 token.
When building your own EVM packages, keep in mind how you might bundle together all the related functionality for a task, or implement a standalone standard by itself. The goal is to create a package that you might reuse any number of times for your own project and, optionally, share with a wider community of users. EVM packages should be self-contained, ready-to-go packs that don't need external supporting code to make them work.
In building EVM packages, you may also find yourself wondering, "Is this a Solidity library?" Generally, we use libraries to help keep our code DRY, and the OpenZeppelin-Solidity SafeMath library is a good example of this. SafeMath allows us to safely perform arithmetic operations repeatedly but using a "safe" implementation that protects us from things like overflow, which can be exploited to do some nasty things. As SafeMath is currently written, it is a library that has only internal functions, and as such will be embedded within the contract. At compile time, the SafeMath code is directly inserted into the user's Solidity code and compiled together as if it were one large contract, while EVM packages are designed to be used as external bytecode.
While it is certainly possible to craft an EVM package that offers the functionality of a standard Solidity library, generally an EVM package will have its own storage and keep its own state. Contracts that make use of embedded libraries rather than link to them as an EVM package will also have an advantage in terms of gas cost: it is cheaper to call functions directly inside a contract than to call them externally. Thus, modifying SafeMath to work as an EVM package might save deployment gas costs (if you need to deploy many contracts), but the resulting smart contract could be significantly more expensive to interact with.
For developers working on private networks or sidechains with different gas-cost dynamics, this may or may not be a relevant concern. Certainly, a theoretical use case for libraries as EVM packages could be a private network where gas costs are not a concern and smart contract libraries are required to use singular approved implementations.
On a higher level, EVM packages are great for solving commonly occurring problems and simplifying the software development process. If you find yourself creating or using the same code over and over, or thinking, "Hasn't someone already built this?", then your code might be a good candidate for creating an EVM package. Thoughtful developers may also want to include documentation in their EVM packages or tests, to clarify what behavior is expected from the code and to make it easier and safer for the community to build on it. If you are developing your EVM package primarily for the community, nice documentation, sample usages, and a clear readme with a quick-start guide are always highly appreciated.
Have a look at what some noteworthy projects are building with EVM packages to get inspiration.
*Solidity libraries that are deployed separately and then linked at compile time (rather than having their code inlined by the compiler) or are linked manually after the compile process, are also not ideal EVM packages, as the ZeppelinOS system does not currently support linking to a Solidity library in an EVM package, although this will change in the future.


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text:
Police release 911 call of kayak rescue
Kayaker rescued Sunday
Updated: 4:56 PM EDT May 16, 2016
A kayaker is thanking two Martin County Sheriff's Marine Deputies after being rescued Sunday.Anthony Prezioso, of Port St. Lucie and Juan Aguia, of Palm City set out to go fishing in Stuart. Shortly into their trip, Prezioso's kayak began to take on water. Aguia immediately called 911.Dispatch: 911. Do you need police, fire or medical?Caller: I need. My buddy flipped off his kayak...in Stuart.Download app: iOS | AndroidDispatch: I'm sorry. I can't hear anything you're saying where are you?Caller: We're in Stuart. Watch out behind you. We're about a mile out on kayak. My buddy's kayak is taking on water and he just flipped his kayak over.Prezioso was clinging to the side of the kayak waiting for help."I was really worried for my life at the moment, just not. Just helpless. Helpless out in the middle of the water not knowing what was going to happen," said Prezioso.The U.S. Coast Guard sent out a helicopter and the Martin County Sheriff's Office Marine Unit hit the water in search for the pair.Deputies Jeff Read and Michael Libasci eventually located the two kayakers about two miles off shore near the House of Refuge and bring them ashore.They were absolutely incredible. They were very friendly. They were up on us in 35-45 minutes," said Prezioso.Prezioso's fishing trip ended abruptly, but knows things could have ended differently."I'm thankful that we were both prepared in the respect that we had waterproof phones. We had whistles, first aid kits, we had ropes. We had dozens of different things that some people would not bring with them because they think, 'Oh it's not going to happen to me,'" said Prezioso.
STUART, Fla. —
A kayaker is thanking two Martin County Sheriff's Marine Deputies after being rescued Sunday.
Anthony Prezioso, of Port St. Lucie and Juan Aguia, of Palm City set out to go fishing in Stuart. Shortly into their trip, Prezioso's kayak began to take on water. Aguia immediately called 911.
Dispatch: 911. Do you need police, fire or medical?
Caller: I need. My buddy flipped off his kayak...in Stuart.
Download app: iOS | Android
Dispatch: I'm sorry. I can't hear anything you're saying where are you?
Caller: We're in Stuart. Watch out behind you. We're about a mile out on kayak. My buddy's kayak is taking on water and he just flipped his kayak over.
Prezioso was clinging to the side of the kayak waiting for help.
"I was really worried for my life at the moment, just not. Just helpless. Helpless out in the middle of the water not knowing what was going to happen," said Prezioso.
The U.S. Coast Guard sent out a helicopter and the Martin County Sheriff's Office Marine Unit hit the water in search for the pair.
Deputies Jeff Read and Michael Libasci eventually located the two kayakers about two miles off shore near the House of Refuge and bring them ashore.
They were absolutely incredible. They were very friendly. They were up on us in 35-45 minutes," said Prezioso.
Prezioso's fishing trip ended abruptly, but knows things could have ended differently.
"I'm thankful that we were both prepared in the respect that we had waterproof phones. We had whistles, first aid kits, we had ropes. We had dozens of different things that some people would not bring with them because they think, 'Oh it's not going to happen to me,'" said Prezioso.


Whether we like it or not, men, we are in a fight. You have an enemy that is coming for you. His name is Satan. The word Satan means adversary. He will do anything and everything to knock you down. He is coming for you whether you are ready for it or not. So be ready. Get in the fight. Because it is a grudge match…and this time it's personal.


Faith needs to head down towards the rail system; however the Blues are already waiting. Wall Run to the two red pipes, and slide down them to ground level. Leave the alleyway and hop the fence, climb the red pipes to get on top of the blue catwalk.
Continue up the blue stairs to the top of the building, jump from the plank over the fence, and move left.
It's safer to deal with one enemy at a time, than take them all at once.
Climb over the duct to the far left and disarm each Blue one at a time. After the coast is clear, move up the pipe and take the zipline to the next area.
On the next roof will be a red door into the building. Enter the the door, and inside will be an open elevator shaft with red pipes. Jump to the pipes and slide down below.
Down the hall will be another red door, move through it to an exterior stairwell.
You'll need to get on top of the roof on the right. Wall running is the only option of getting across.
The shotgun is far too deadly to confront both of these enemies at once.
Use the zipline to reach the fans on the next building. Be careful to not let go early, as it is easy to fall to your death.
You can use these air-conditioners to get on top of the roof.
Move forward and into the alley to the far left. Use the trash pile to jump up and cling to the ledge above, the jump to the bar behind and swing to the duct. After climbing through the duct, move through the next two red doors and into the mall. Follow the Mystery Runner into the mall's main area, that will be filled with Blues.
The window can only block a few shots before breaking.
Once the elevator jams, break the glass if it's still intact, then leap out and into the hall to the right. At the end of this hall hop the rail to the area below and up the escalators.
Climb the lockers on the left to enter the duct above.
Use the duct as a bridge to get to the other side.
The box ahead can be used to cling to the ledge.
Use the button to turn of the e large fan.
Once safe, move into the duct to the left, then drop down, and take the stairs up. Climb the red pipe in the next room, and through the red door to finish the chapter.


text:
Volume 41 - Article 2 | Pages 37–52
The geography of changing fertility in Myanmar
By Anne Schuster, Sabu S. Padmadas, Andrew Hinde
Date received: 14 Apr 2018
Date published: 03 Jul 2019
Keywords: access, fertility decline, Myanmar
DOI: 10.4054/DemRes.2019.41.2
Background: Between 1983 and 2014, the total fertility rate in Myanmar declined from 4.7 to 2.3 children per woman. Previous analyses of fertility decline in the country suggest that the decline varied regionally, but the geography of the decline has not been formally assessed.
Methods: Using data from the 1983 and 2014 censuses, we examine fertility trends and geospatial patterns in fertility decline in Myanmar during the intercensal period, and investigate the aggregate socioeconomic factors underlying fertility decline at subregional levels.
Results: Between 1983 and 2014, fertility change at subregional level was characterised by a precipitous decline in fertility rates in the broad central valley areas and a much weaker decline in remote, peripheral areas. Regression analysis of the 2014 census data, adjusting for state/region level variances, reveals a strong negative correlation between fertility and access to modern communication technologies. District-level female education and road connectivity were also associated with fertility.
Conclusions: The geographical diversity in Myanmar's fertility transition has intensified over time, as fertility decline is concentrated in areas with greater development, higher socioeconomic status, and better connectivity to information networks.
Contribution: A district's digital connectivity, measured through access to communication technologies, was a better predictor of fertility than other traditional measures. There is a need to explore to what extent digital connectivity is a proxy indicator for levels of modernisation and access to family planning and reproductive health services, and the extent to which it measures the intensity of social networks and the diffusion of information.
Anne Schuster - University of Southampton, United Kingdom [Email]
Sabu S. Padmadas - University of Southampton, United Kingdom [Email]
Andrew Hinde - University of Southampton, United Kingdom [Email]
» On the pace of fertility decline in sub-Saharan Africa
» Gender Inequalities in Employment and Wage-earning among Economic Migrants in Chinese Cities
» An editorial on plagiarism
» Does early childbearing and a sterilization-focused family planning programme in India fuel population growth?
» Unusually small sex differentials in mortality of Israeli Jews: What does the structure of causes of death tell us?
» Fertility and union dissolution in Brazil: an example of multi-process modelling using the Demographic and Health Survey calendar data
» The proximate determinants of fertility and birth intervals in Egypt: An application of calendar data
» Measuring and explaining the baby boom in the developed world in the mid-twentieth century
Volume 38 - Article 40 | Keywords: fertility decline
» Cohort fertility decline in low fertility countries: Decomposition using parity progression ratios
» The impact of kin availability, parental religiosity, and nativity on fertility differentials in the late 19th-century United States
» Economic crisis promotes fertility decline in poor areas: Evidence from Colombia
»Articles by Anne Schuster
»Articles by Sabu S. Padmadas
»Articles by Andrew Hinde


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Three epic North American trips
By Chris Leadbeater
Photography by Feng Wei Photography/Getty Images
With awe-inspiring landscapes, exciting cities, and wide, open roads made for driving, the world's third-largest continent delivers adventures of all kinds at every turn. Travel writer Chris Leadbeater picks three epic itineraries that you'll want to add to your bucket list.
East coast city hopping
Best for... city-breakers with an intrepid spirit
Boston – New York – Philadelphia – Washington DC
The journey: 450 miles
One of the joys of America's northeast is that it offers four of the country's major cities in a close-knit cluster. This is a legacy of the way in which the fledgling USA developed in the 18th and 19th centuries. And it makes for an unforgettable road trip in the 21st century.
Begin in Boston. The Massachusetts capital was at the centre of the colonization of America in the 1620s. The Freedom Trail cuts a 2.5-mile path across the centre, connecting 16 prime sites, which played a prominent role in the breaking away from Britain in the 1770s and 1780s.
One of the joys of America's northeast is that it offers four of the country's major cities in a close-knit cluster
But there's more to Boston than its yesterdays. In summer, visit Fenway Park, home of the Boston Red Sox. And the city revels in good food, whether it is the pizza and pasta joints of Little Italy, or top-notch fish restaurants such as Legal Sea Foods
Once you've had your fill, hire a car and hit the road in search of New York, which lies 215 miles southwest. You could spend a lifetime sampling its delights, from the cityscape visible from the roof of the Empire State Building to the gilded department stores of Fifth Avenue. Burnish your evenings by discovering the chic bars of Brooklyn – or the superb culinary scene that dominates West 46th Street in Hell's Kitchen.
Philadelphia is an easy drive through New Jersey and into Pennsylvania. Priding itself as being the birthplace of American democracy, this underrated metropolis tells its tale in Independence National Historical Park, a cornucopia of the past where Independence Hall witnessed the debating of the Declaration of Independence in 1776. The brilliant Museum of Art has works by Picasso and Dali, while Pat's King of Steaks serves that meat-heavy sandwich and city signature – the Philly Cheesesteak.
The seats in Fenway Park stadium are all green, apart for one solitary red seat in the right field bleachers. According to the Baseball Almanac, seat 21 in section 42, row 37 marks where the longest home run ever hit in the stadium – by Boston Red Sox's Ted Williams in 1946 – fell.
Search flights to Boston
Catch a baseball game at Boston's Fenway Park © Alamy
An Empire state of mind
Every year on Valentine's Day, couples who marry on the 80th floor become members of the Empire State Building Wedding Club. They receive free admission to the observatory each year on 14 February (their anniversary) thereafter.
Head to lofty heights at the top of New York's Empire State Building © Maico Presente/Getty Images
Though efforts to create a tribute to Abraham Lincoln began immediately after his assassination in 1865, it took more than 50 years to get the memorial built and open to the public. Due to delays in the project's planning and construction, as well as World War I, the memorial didn't open until 1922.
Fly to Washington DC
Washington's Lincoln Memorial honours the 16th President of the United States, Abraham Lincoln © Trevor Carpenter/Getty Images
From here, Washington DC is 140 miles southwest. Little needs to be said by way of introduction to the American capital. But if the Washington Monument and Lincoln Memorial are celebrated slabs of political tribute, and the Smithsonian Institution is arguably the planet's greatest clutch of museums in one place (notably the National Air and Space Museum), then DC also has its "secrets". U Street is a rich mixture of African-American heritage and stylish bars, while 14th Street NW has some of the city's most alluring restaurants – including Lupo Verde and its menu of delicious Southern Italian fare.
Each of these four fantastic cities is alive with exciting accommodation options. Boston has the Omni Parker House, a five-star pile which has been an upmarket presence in the Massachusetts capital since 1855. New York displays its hip side at the four-star McCarren Hotel, which is nestled in Brooklyn's trendy Williamsburg. The Loews Philadelphia revels in Art Deco flourishes and black-granite floors to such an extent that it is listed as a National Historic Landmark. And the Washington Hilton is perfectly positioned for a break in the capital – located close to the central Dupont Circle.
May, when New York and Boston have both shaken off their winter chills, and Washington DC is yet to embrace the mugginess which can grasp it in high summer.
The best of the west (and beyond)
Best for fans of the American landscape
Los Angeles – Honolulu – Phoenix
The journey: 5,700 miles (mostly by air
Los Angeles is a city, which could easily snare your attention for an entire holiday. Always set in sunshine, it promises splendid slices of seafront galore, not least Santa Monica Beach. Throw in A-list notes of culture such as the Museum of Contemporary Art, and the razzle-dazzle mixture of theme park thrills and cinematic folklore that is Universal Studios Hollywood – plus the eateries of resurgent Downtown – and you have an urban adventure playground.
Hawaii is the only US state that still honours a monarch. Locals celebrate King Kamehameha Day on 11 June to celebrate the man who united the Hawaiian islands in 1810 and became the archipelago's first leader.
Discover Hawaii
Paradise found: Hawaii's Oahu © Robert Cravens/Getty Images
But if the beaches of LA are photogenic, spare a thought for the powdery crescents that decorate the edges of Hawaii. Spare five hours too, and you can glimpse them yourself. British Airways' oneworld partner American Airlines flies direct from LAX to Honolulu, the glittering Hawaii state capital, on the south coast of the island of Oahu. Here, you can doze on the shore where the famous Waikiki Beach is kissed by the blue Pacific, or take in the sombre history of Pearl Harbor and the sunken memorial of the USS Arizona in World War II Valor in the Pacific National Monument. Or you can hike up the flanks of Diamond Head State Monument, the volcanic monster that frames the city.
You could, of course, retrace your jetstream trail to Los Angeles. But American Airlines also flies from Oahu to Phoenix. Like Philadelphia, the capital of Arizona is a little underappreciated – Phoenix Art Museum is a treasure trove of visual creativity, boasting works by Georgia O'Keeffe. Better still, the city is also a gateway to Grand Canyon National Park, the greatest geological scar in the soil of the American West.
Enticing accommodation is as much a part of this journey as the places you may encounter. The Andaz West Hollywood delivers a dose of unbridled luxury (and a heated rooftop pool) to Los Angeles' most coveted area. As its name hints, the Hilton Hawaiian Village Waikiki Beach Resortheads straight for the sand in Honolulu. And the Westin Kierland Resort and Spa proffers four-star relaxation near to Phoenix in Scottsdale.
April. LA and Oahu are always sunny, the Grand Canyon is a joy in spring.
Canada's mighty National Parks
Best for… road-trippers who want something different
Calgary – Banff – Jasper
Lake Louise in Canada's Banff National Park © jlazouphoto/Getty Images
Toronto is a loud bubble of big-city buzz, and Vancouver a sophisticated sliver on the lip of the Pacific. But there is much to be said for a Canadian road trip, which charts the mountainous westerly province of Alberta. Here, Calgary is an obvious start-point. The cosmopolitan enclave soothes its soul to the classical music of its Philharmonic Orchestra, and obeys its stomach at fine restaurants such as carnivore heaven Charcut. It's also worth climbing to the top of the Calgary Tower for sky-high vistas.
Add a hire car to your booking and venture west. Almost as soon as the city vanishes in your mirrors, the Rockies appear in the windscreen. You could pause to take in the raw beauty and forested slopes of Kananaskis Country. Or you can forge on into the maw of Banff National Park whatever the season – it's renowned for its ski runs in winter, while in summer, it's a wonderland for hiking.
Continue northwest along the Icefields Parkway, which passes the enormous Athabasca Glacier. It also clips through the town of Lake Louise, where the water feature of the same name is a turquoise jewel. Finally, the road drops you into Jasper, another feted ski destination, where you can pass autumn nights star-gazing under the clear skies of Jasper National Park.
The temperature in the canyon can vary greatly depending on the time of year and location. In the winter months, the North Rim can drop to -23˚C, while the inner canyon can reach 47˚C in the height of summer. At any given time of year, the North Rim will be 1-2˚C cooler than the South Rim.
The Grand Canyon at sunset © SumikoPhoto/Getty Images
Don't look down
As well as providing 360-degree views of the city and the Rocky Mountains from its 191m observation deck, there is also a section of glass floor off the deck that allows visitors to stand over 9th Avenue SW and Centre Street North.
The vertiginous view from Calgary Tower © frankreporter/Getty Images
Though the Fourth of July marks Independence Day in America, most of the delegates didn't actually sign the Declaration of Independence until August 1776. However 4 July 1776 marks the date that Congress officially adopted the Declaration.
Philadelphia's historic Independence Hall © Travelif/Getty Images
The Fairmont Palliser is a four-star slice of tradition and atmosphere at the very core of Calgary, while its sibling retreat the Fairmont Chateau Lake Louise supplies a dash of country-house majesty and Gallic refinement to Banff National Park.
February to catch the best of the ski season, June to take to the hiking trails.
You might like some of these articles
Classic New York: a weekend guide
Five ways to experience California
Epic three-week adventures


Home Articles Did You Personally Choose Your line of Profession?
Have you ever ask yourself some questions like, why do some people choose professions that help only themselves while others choose professions that help those in need? We almost all think we are masters of our own fate. While it is true that we all make our own choices there are many things that influence what we choose.
Health and wellness professionals all share the desire to help others. Our work is commendable and very important, but why do we choose the profession we're in?
Professionals in the "caring jobs" share some unique qualities. We're almost always creative, sensitive and nurturing. We also almost all share a willingness help others in every way possible and suffer pangs of guilt if we say "no." Our willingness to help sometimes comes with a price. It leaves us vulnerable to burn out.
Burnout is often the result of a professional feeling overwhelmed with his or her job responsibilities. Let's face it, caring for others can be a burden. Even if you love your job facing unmotivated, clients can be draining to even the most enthusiastic wellness professional. Add to this any inside pressure from trying to make a decent living, dealing with negative attitudes of co-workers or pressure with sales commissions and you're on the road to feeling more negative yourself.
Caregivers tend to burn out more quickly than others because we typically put the needs of those around us first. By the time we are through dealing with the issues of our clients, families and friends we have little left for ourselves.
So how do you deal effectively with those clients who seem to have a "seek out and destroy" personality? Simple, you learn to develop your own "repair and replenish" skills now and make them an important part of your everyday routine.
Make it a point to be more aware of your surroundings. Try to notice the little things that bring joy to your life and take a moment to reflect on them.
Learn to say "no" – not all the time but some time. When someone asks for another piece of your time, a little more of your energy, or is looking for you to commit to their newest project, take the time to know if it's the right choice for you. Make it your personal policy to never give an answer that you haven't had at least 24 hours to think about: there's much to be said for the adage of let me sleep on it.
Talk, talk and then talk some more. Find peer professionals that share similar values and goals and talk about work. Some think it's taboo to talk about work on your days off but in reality it is important to be able to share your feelings and frustration with someone who understands how you feel and their feedback can be very helpful.
Vacations aren't just what other people do. You earn the time too. Take your vacation time all together or in shorter bursts. Whatever works for you is fine – just take those days and forget about work for awhile.
Sometimes a nurturing personality can open the door for our own wellness to suffer and it is up to each person to find the tools that help to keep them on track and healthy. By learning to say no, nurturing yourself, becoming more aware of your surroundings, talking to a trusted people and taking a break when you can, you'll be able to find a healthy balance in your professional and personal life leading to greater business success and fulfillment.


Welcome to the second installment of the Wimpy Trilogy – 3 books written to help you find your missing confidence, to inspire you to reach your goals and to make you laugh and cry along with my journey.
Here you will be regaled with tales of sadness, of utter joy and pure elation as I gallop through my first ever eventing season.
We delve deeper into the reasons why you cannot let fear win and hopefully enlarge the balls that the first book, 'How to get your leg over' helped you to find.
Love this book as much as the first! Can't wait for the third and hopefully more! Really gave me the kick up the bum that I can do what iv always wanted to do and to never give up! Lots of love for you Vic! ??
A brilliant follow on from the first book, with its fantastic blend of humour and inspiration.
Can't wait for number 3 !
Loved this even more than the first book! So so easy to read, really well written and hilarious!!!
This will be one I treasure personally. I was lucky to receive a signed copy of the book which unfortunately was damaged in a serious car accident. When Vic heard about this I was sent a bundle of gifts personally from her!! Including a signed copy. Thank you! Bring on the next book!!
Couldn't wait for this book to come out and wasn't disappointed, laughed, cried, laughed some more. Absolutely inspiring!
full of excitement, humour and positive energy for anyone needing a boost.
This book is as amazing as the first one. I could never put hem down. I have read these books crying my eyes out at my lowest as a way to pick myself up and also they have had me crying with laughter. Vics books reflect her personality beautifully. Such and inspiration and what a great price for both books what more could you ask for!
Love it, so funny, and so relatable. Waiting patiently for the next installment!
As amazing and funny as the first book, Can't wait for the third!
Loved book 1, couldn't wait to read book 2 & did so practically in one go! Highly recommend!
Loved this book even more than the first! Loved hearing the stories of Vics younger days and the continuing successes of her and Pat!
How to get yourself off!! The Final One!


A good restaurant that serves exceptionally good meals is offered. There's service and repair available in case you have mechanical problems. A store is offered for your convenience, and Port of the Island Marina is a great location for boating. There are boats for rent here at Port of the Island Marina, and bait and tackle is offered at this marina. With such a vast number of things to do in Florida you'll never get bored.
this is a magnificent choice.
The helpful operators of the marina and all the fun things makes the journey here worthwhile. Park your boat in a pleasant wetslip; there is dry storage here.
a good fishing trip at Satisfaction Guaranteed Fishing Charters is always enjoyable. Port of the Island Marina gets a lot of water. The wettest month of the year is frequently June, that's the one that rains the most while December is ordinarily the driest month. Through the summer months at Port of the Island Marina temperatures are frequently in the 90's while night lows are typically in the 70's.
AMENITIES: A good restaurant that serves exceptionally good meals is offered. There's service and repair available in case you have mechanical problems. A store is offered for your convenience, and Port of the Island Marina is a great location for boating. There are boats for rent here at Port of the Island Marina, and bait and tackle is offered at this marina. With such a vast number of things to do in Florida you'll never get bored.
You can play golf here, and don't forget your fishing pole given that fishing here at Port of the Island Marina is glorious . Quite a lot of fun things to do in the vicinity of Port of the Island Marina, and if you're trying to locate a great place to go boating, this is a magnificent choice.
There are good tent sites here where you may raise that tent of yours, and this marina is equipped with a pumpout station. A day of fishing at Double Rs Fishing & Tour Co. is always a nice idea, and while here here do take a look at nearby Morgan Beach. Lots of folks from Naples-Marco Island come to Port of the Island Marina; time spent at Marco Beach is always great. It's always enjoyable to go for a fishing trip and an excellent location to do that is Fins & Grins Charter Fishing. Going for a good fishing trip at Satisfaction Guaranteed Fishing Charters is always enjoyable. Port of the Island Marina gets a lot of water. The wettest month of the year is frequently June, that's the one that rains the most while December is ordinarily the driest month. Through the summer months at Port of the Island Marina temperatures are frequently in the 90's while night lows are typically in the 70's.
These outdoors activities are available near Port of the Island Marina.


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Format: Trade Paperback
The Life and Times of Jann Wenner and Rolling Stone Magazine
Joe Hagan
Tr. Paperback
Over the course of five decades, founding editor of Rolling Stone Jann Wenner has put an indelible stamp on American culture. A nuanced portrait of a man who helped define a generation, and provides an explosive chronicle of an era.
Sticky Fingers: The Life and Times of Jann Wenner and Rolling Stone Magazine is the story of how one
man's ego and ambition captured the 1960s youth culture of rock and roll and turned it into a hothouse of fame, power, politics, and riches that would last for fifty years.
Drawn from dozens of hours of interviews with Wenner, who granted Joe Hagan exclusive access to his
vast personal archive, this biography tells the story of how Wenner partnered with rock luminaries like John Lennon, Mick Jagger, and Bob Dylan to manufacture an unforgettable cultural mythology in story and image every other week for five decades.
Featuring on-the-record interviews with Mick Jagger, Bruce Springsteen, Paul McCartney, Elton John, Keith Richards, Pete Townshend, Yoko Ono, Billy Joel, Tom Wolfe, Cameron Crowe, Lorne Michaels, David Geffen, Dan Aykroyd, Bette Midler, and dozens of others, Hagan captures Wenner with intimacy, nuance, and complexity—his marksmanship as an editor, his extraordinary understanding of the zeitgeist, his endless pursuit of fame and power, and his capacity for betrayal that would earn him as many enemies as friends.
"I'll tell you what Jann did. He put together a really good gang of writers, nice kids. Not afraid to go and ask questions. And turned something that could have just been a fan magazine into a real piece of journalism. That's what I think Jann did."
"I was intimidated by Jann . . . Not because he was a nasty or snobbish person, but because he founded something so great."
"It was clear to me that Jann, like myself, was growing up in a world surrounded by people who were often out of their minds on drugs, and equally out of their minds on conspiracy theories and rhetoric. All we had to do was enjoy the company and carefully steer the journey, and we might survive; standing on a pile of corpses perhaps, but having survived."
"Jann likes sexual power, and if you're doing what he's doing, and you're in this business, how could you not be interested in that?"
"He's a huge music fan. That's something that has never changed. It's
a big part of who he is. And that's at the basis of our relationship. He still gets into the records like we used to get into the records."
"What a fuckin' editor. He's crazy, but he's got a dream."
Pub date: 13 November 2017
Joe Hagan has written for Rolling Stone and also for New York, The Wall Street Journal, and many other publications. He has published long-form profiles and investigative exposés of some of the most significant figures and subjects of our time, including Hillary Clinton, in her first post-Secretary of State interview, Karl Rove, the Bush family, Henry Kissinger, Dan Rather, Goldman Sachs, The New York Times, and Twitter.
Rock'n'Roll Lives
Jump on the tour bus with the music idols you love.
Peter FitzSimons
Wham, George and Me
Andrew Ridgeley
How to Make Gravy
The Diary Of A Young Girl
Anne Frank, Anne Frank And Elie Wiesel
The Tall Man
Chloe Hooper
Strange Fascination
David Buckley
Elizabeth Kleinhenz
Mr Showbiz
Stephen Dando-Collins
Grant & I
It's All Going Wonderfully Well
Rosa Hoskins
Nicholas Foulkes
Orson Welles, Volume 3
Hockney: The Biography Volume 2
Christopher Simon Sykes
Breakfast with Lucian
Geordie Greig
Brian Jay Jones
Boy About Town
Tony Fletcher


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You are in: NSF Home > Speeches > Speeches by the Rita Colwell > Dr. Colwell's Remarks
Dr. Colwell's Remarks
Dr. Rita R. Colwell
Remarks to American Meteorological Society
2003 Summer Policy Colloquium
See also slide presentation.
If you're interested in reproducing any of the slides, please contact
The Office of Legislative and Public Affairs: (703) 292-8070.
Greetings to all of you. I commend your courage in coming to visit Washington, the city where the sun hardly ever shines.
As climatologists and meteorologists, I hope you don't mind if I share the tale of the meteorologist who was waiting at the Pearly Gates for judgment, was it going to be heaven or hell. It was a very long line. He could see that some in the line were chosen to proceed through the gates of heaven; other unfortunates, however, were shuffling along in the other direction. Now, the meteorologist was observant-he quickly noted a small group of the unfortunates who were roped off to one side. Curious, he went up to them and asked why they had been singled out. "Oh," came the answer, "we're Washingtonians--these days, we're too wet to burn."
I certainly hope you can stay dry while you're here; I also hope that you may conclude after the policy colloquium that there really is a category of Washingtonians who pursue science policy as a worthy and lofty goal.
I've been asked to speak introspectively today--rather than giving an overview of the National Science Foundation, to convey my personal perspective on executive leadership. The reality is that I have never experienced some "Eureka!" moment of transition from research scientist to administrator, because I never really made that transformation from one to the other; for me, being a scientist in itself has also meant being a leader.
Looking back, I realize that it has been a progression, beginning with running a small laboratory that grew into a large one-in the 1970s my laboratory was populated with 25 or 30 students, technicians and post-docs, at the University of Maryland, all working in a lab with a budget equivalent to $2 million in today's figures. It was all cumulative training in managing resources and keeping accounts, with grants over the years from NSF, NIH, NOAA, EPA, DOE, NASA, FDA and the Navy, even some from private foundations. All of it brought valuable administrative experience-succeeding and being called upon to assume ever-more-responsible positions, from founding a Sea Grant college at the University of Maryland-College Park to eventually becoming academic vice president for an entire university system. Founding a biotechnology institute in Maryland also expanded my experience to include industry.
At the same time, active participation in scientific societies throughout my career has been a sort of career incubator, although I did not necessarily see it that way at the time. It was simply interesting and fun. Work on scientific society committees eventually poised me for further leadership roles, whether as president of the American Society of Microbiology or the American Association for the Advancement of Science or the International Union of Microbiological Societies.
Even today, there has been no clear break in the progression of my life from working scientist to administrator. In fact, since I've been director of NSF, I've been averaging about 17 scientific papers a year (of course, that work has to be done at night and on weekends). I've also continued to mentor graduate students, post-doctoral fellows and visiting foreign scientists.
Looking back, I've been involved with the Foundation one way or another over my entire professional life. Of course there was my experience as an NSF grantee, but over the years I also served on many panels and committees, from advising on science and engineering education in the 1970s to helping to decide who would get the next ship in the UNOLS fleet (that's the University-National Oceanographic Laboratory System) to evaluating our infrastructure for supporting Antarctic science. The result is that I have gotten to know to know NSF very well from many angles, and becoming director really has been the career-crowning step.
What about some of the personal attributes that contribute to leadership? Whether in scientific research or administration, I believe that mental toughness, or perseverance in the face of obstacles, has been fundamental to success. I have said more than once that I believe I got my start in science out of sheer stubbornness-during an era when girls simply were not allowed to take physics. I recall that in high school my chemistry teacher told me I'd never make it in chemistry, because women could not. That angered me but also galvanized me. I had already begun to see science as both a way to understand the world and a way to make my way in the world. That duality still plays out today in both my research and administration activities.
Yet it's not only mental toughness--it's also flexibility, the versatility to seize an opportunity when offered. When I moved out to Washington State as a young wife with my husband, Jack (who is also a scientist), I was intent on going to medical school. I had already been accepted at several medical schools in the East, including Yale, but gave up those opportunities to be with my husband who had been accepted at the University of Washington Department of Chemistry. Then I discovered that the medical school at the University of Washington would admit students only from the Northwest. That door did close, but another opened--I took a fellowship to study microbial genetics. Then, I met a newly arrived faculty member, a Scotsman named John Liston, and ended up with a doctorate in oceanography--and became a pioneer in the nascent field of marine molecular microbiology.
Another critical attribute for scientific leadership, I believe, is actively tapping into the global network of science. As a researcher investigating the ties between climate and cholera, my career has connected me to colleagues around the world, from Europe to Bangladesh to Japan and beyond. Working collaboratively across the globe was critical to tracing the ecology of the cholera bacterium, showing that it lives naturally in the marine environment and that fluctuations in climate increase the incidence of cholera-fluctuations also linked to cholera epidemics, whether in Bangladesh or Peru.
This worldwide network of research--it exists, of course, in every field of science and engineering--is a tremendous resource for all of us. In fact, my work at NSF continues to span the globe; I spent a recent weekend at a G-8 meeting in London with science leaders from Europe, the next at a gathering of agricultural ministers from many nations. The international perspectives on science are essential; here is an area where U.S. leadership has much room for growth.
I find that I spend a great deal of my time as NSF director speaking to groups large and small, explaining what NSF does. I try to convey the excitement of discovery to a variety of audiences, and to explain how investing in fundamental research pays off in economic and educational terms for our nation, and, more recently, in national security. One take-home lesson is that making a concerted effort to hone one's communications skills--whether in dealing effectively with the media, or learning to speak more persuasively--has huge dividends.
My research career prepared me in another way to lead an institution of such great breadth as NSF. As a biologist I have always been intrigued by how it all comes together--fascinated by the mixture, by the froth that makes life bubble. Reductionist science, dissecting the world into the smallest parts, seemed to me like clear-cutting a forest in order to study one tiny seedling.
[First slide: Dr. Colwell with a group of villagers and fellow researchers in Bangladesh]
(Use "back" to return to the text.)
I still work closely with a lab in Bangladesh and still have my lab in Maryland. This image depicts our trials in Bangladeshi villages of a simple filter to remove disease-causing cholera bacteria from drinking water. The filter is simply an old sari cloth. We have found out that cholera bacteria in the water, attached to plankton, are efficiently sieved out with this readily available material. My own research has ranged from testing such humble solutions to using sophisticated tools, and has touched upon a wide array of fields, from remote sensing to sociology to medicine, oceanography, genomics, mathematics and physics. It has combined the sophisticated with the basic.
[turbulence backdrop with the priority areas cited]
In fact, much of the excitement of discovery today ignites at the interfaces of disciplines. As an oceanographer I draw a metaphor for this from the sea, where water masses of different temperatures converge; gyres form, polynyas appear, upwelling occurs, and nutrients collect at the interfaces.
Convergence zones in the ocean may shift, appear and disappear, but they are often where the nutrients concentrate and where the fish and seabirds up the food chain gather to feast. Just as enriched are the interfaces between physical science, engineering and biology, and now the social sciences: discovery foments in these "hyphenated" zones. We see a few of the converging areas listed here that NSF has chosen for special investment--biocomplexity, nanotechnology, information technology, mathematics, the 21st century workforce, and human and social dynamics. The convergence of disciplines holds a compelling lesson for science policy--that all of science and engineering, now so interdependent, must now advance as one enterprise.
[South Pole Station]
As someone who loves every aspect of science, serving as director of the National Science Foundation has provided an exciting and very broad vantagepoint. It has literally taken me to the ends of the Earth. Here we see South Pole Station, on its way to being realized as a facility fit for 21st century science. You are no doubt aware that it hosts year-round measurements of weather and climate, but you may not know that it is a world-class astronomy observatory as well. Just one example is the array for neutrino astronomy, a cutting-edge field taking off using a detector buried in the ice at the South Pole. It has been of great personal satisfaction to preside over NSF while a new discipline is literally being launched.
[series of shots of sub surfacing]
In the Arctic, where an ice-covered ocean covers the highest latitudes, access for science has been a challenge. I had the opportunity to ride aboard one of these Navy submarines employed for scientific cruises, a joint effort between NSF, the Navy and the Office of Naval Research. The subs have been able to explore parts of the Arctic where ships simply cannot go. This one is punching up through the sea ice from below. These subs have served as a unique research platform to explore the Arctic Ocean ice from beneath, as well as to chart the seafloor. Such cruises, along with U.S. Navy submarine data, show that ice in the central Arctic Ocean has thinned an average of 43% over the past 20 years. Congress actually held a field hearing in Alaska where I was summoned to testify about the importance of Arctic science.
[Dr. Colwell in Alvin/ undersea life]
Quite a different experience, but just as awesome, was to descend in the scientific submarine, Alvin, off the coast of the Northwest U.S. This was a fantastic experience, gliding soundlessly along volcanic eruptions, amongst swarms of luminescent animals and strange communities of tubeworms and other sea creatures. However, human-piloted submarines are only one component as we look ahead to remote, multidisciplinary ocean observatories.
[Seafloor observatory]
Seafloor observatories such as the one depicted here will employ new technical capabilities to detect and forecast environmental change. Instruments will be turned on and off remotely, and monitoring could trigger rapid deployment of a submersible in response to climate or geologic events. Even portable observatories will be employed, based around a system of large, instrumented buoys. They will collect important climate data in remote areas such as the Southern Ocean-exploring many issues related to climate. Again, it's been my own research experience that made clear to me the compelling need to instrument our environment to understand the complexity of how our planet operates.
[Internet and USA]
Another priority at NSF has been imagining and creating the cyberinfrastructure that 21st century science and engineering require. This virtual frontier is one of the most exciting-again, I think back to using a computer at the beginning of my own career. (I used it to develop an identification system and a taxonomy of marine bacteria--it was an IBM 650, and one of that model is now in the Smithsonian Institution.) Certainly understanding the power of computing in my own research set the stage for my strong support for information technology during these years at NSF. Today we are taking steps toward a terascale facility that will demonstrate the first widely distributed grid-computing platform. This will be the most advanced computing facility available for all types of research in the United States--exceptional not just in computing power but also as an integrated facility, offering access to researchers across the country, merging of multiple data resources, and visualization capability.
[human face and ray coming out]
Another frontier that has been extremely important at NSF is advancement of the mathematical sciences. Given that NSF supports all of science and engineering, and that mathematics is the ultimate cross-cutting discipline, vigorous support for mathematics is one of our most vital responsibilities. Again, my personal conviction about this truth in strongly rooted in my research experience. My background as a bioscientist who has worked on biological systems of great complexity brought a firsthand appreciation of the power of mathematics in discovery.
[Gemini North]
NSF is dedicated to pushing the frontiers, and some of those frontiers extend beyond the bounds of our own planet. The dedication of the Gemini North telescope in Hawaii has been one of my most moving experiences as NSF director. The staff even set up the inauguration quite dramatically so that with a wave of the hand, the doors of the telescope dome slid open, with the background music of Handel's Messiah! Looking down on the clouds from the summit of Mauna Kea and up into the endless space of the universe, we celebrated the launch of a telescope whose images in the infrared will surpass those gathered from space. In many instances the Gemini telescopes outperform even the Hubble Space Telescope in both clarity and data collection.
[spiral galaxy]
Not too long after that dedication, Gemini North captured this image of the "Perfect Spiral Galaxy," called such because of its nearly ideal form.
[Gemini South]
Gemini, as its name denotes, is really two telescopes, and here is the partner observatory, located in Chile. The two telescopes, working together, constitute an astronomical partnership between north and south, among seven nations. Together they provide a sweeping and very sharp view of both northern and southern hemisphere skies. The project is a model for engaging our younger generation of scientists and engineers throughout the world to form closer bonds through research and education, something our world so desperately needs.
[running the race]
In reality, of course, I do not spend my bulk of my time as director at the ends of the earth, but in interacting with people. I use this shot, from the recent Capital Challenge Race, in which a number of us from NSF competed, to depict another truth about leadership. Those who work at NSF continue to teach me many lessons about leadership, including the truth that the troops need to be with you, not behind or ahead.
Still, whether running a race or running NSF, leadership does require having a sense of direction, an intuitive sense of where the new developments will happen. Leadership, whether in science or administration, is really about nurturing the spark of discovery.
I wish you well in using your days in Washington to explore how the world of science policy connects to the world of scientific exploration. At least in my career, there's been a very happy convergence between them. Now I'd very much like to hear your questions and comments.
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