text:
\chapter*{Preface}
This textbook is intended for use by students of physics, physical
chemistry, and theoretical chemistry. The reader is presumed to have a
basic knowledge of atomic and quantum physics at the level provided, for
example, by the first few chapters in our book {\it The Physics of Atoms
and Quanta}. The student of physics will find here material which should
be included in the basic education of every physicist. This book should
furthermore allow students to acquire an appreciation of the breadth and
variety within the field of molecular physics and its future as a
fascinating area of research.

\vspace{1cm}
\begin{flushright}\noindent
June 2016\hfill Walter Olthoff\\
Program Chair\\
ECOOP 2016
\end{flushright}
\chapter*{Organization}
ECOOP 2016 is organized by the department of Computer Science, Univeristy
of \AA rhus and AITO (association Internationa pour les Technologie
Object) in cooperation with ACM/SIGPLAN.
\section*{Executive Commitee}
\begin{tabular}{@{}p{5cm}@{}p{7.2cm}@{}}
Conference Chair:&Ole Lehrmann Madsen (\AA rhus University, DK)\\
Program Chair:   &Walter Olthoff (DFKI GmbH, Germany)\\
Organizing Chair:&J\o rgen Lindskov Knudsen (\AA rhus University, DK)\\
Tutorials:&Birger M\o ller-Pedersen\hfil\break
(Norwegian Computing Center, Norway)\\
Workshops:&Eric Jul (University of Kopenhagen, Denmark)\\
Panels:&Boris Magnusson (Lund University, Sweden)\\
Exhibition:&Elmer Sandvad (\AA rhus University, DK)\\
Demonstrations:&Kurt N\o rdmark (\AA rhus University, DK)
\end{tabular}
\section*{Program Commitee}
\begin{tabular}{@{}p{5cm}@{}p{7.2cm}@{}}
Conference Chair:&Ole Lehrmann Madsen (\AA rhus University, DK)\\
Program Chair:   &Walter Olthoff (DFKI GmbH, Germany)\\
Organizing Chair:&J\o rgen Lindskov Knudsen (\AA rhus University, DK)\\
Tutorials:&Birger M\o ller-Pedersen\hfil\break
(Norwegian Computing Center, Norway)\\
Workshops:&Eric Jul (University of Kopenhagen, Denmark)\\
Panels:&Boris Magnusson (Lund University, Sweden)\\
Exhibition:&Elmer Sandvad (\AA rhus University, DK)\\
Demonstrations:&Kurt N\o rdmark (\AA rhus University, DK)
\end{tabular}
\begin{multicols}{3}[\section*{Referees}]
V.~Andreev\\
B\"arwolff\\
E.~Barrelet\\
H.P.~Beck\\
G.~Bernardi\\
E.~Binder\\
P.C.~Bosetti\\
Braunschweig\\
F.W.~B\"usser\\
T.~Carli\\
A.B.~Clegg\\
G.~Cozzika\\
S.~Dagoret\\
Del~Buono\\
P.~Dingus\\
H.~Duhm\\
J.~Ebert\\
S.~Eichenberger\\
R.J.~Ellison\\
Feltesse\\
W.~Flauger\\
A.~Fomenko\\
G.~Franke\\
J.~Garvey\\
M.~Gennis\\
L.~Goerlich\\
P.~Goritchev\\
H.~Greif\\
E.M.~Hanlon\\
R.~Haydar\\
R.C.W.~Henderso\\
P.~Hill\\
H.~Hufnagel\\
A.~Jacholkowska\\
Johannsen\\
S.~Kasarian\\
I.R.~Kenyon\\
C.~Kleinwort\\
T.~K\"ohler\\
S.D.~Kolya\\
P.~Kostka\\
U.~Kr\"uger\\
J.~Kurzh\"ofer\\
M.P.J.~Landon\\
A.~Lebedev\\
Ch.~Ley\\
F.~Linsel\\
H.~Lohmand\\
Martin\\
S.~Masson\\
K.~Meier\\
C.A.~Meyer\\
S.~Mikocki\\
J.V.~Morris\\
B.~Naroska\\
Nguyen\\
U.~Obrock\\
G.D.~Patel\\
Ch.~Pichler\\
S.~Prell\\
F.~Raupach\\
V.~Riech\\
P.~Robmann\\
N.~Sahlmann\\
P.~Schleper\\
Sch\"oning\\
B.~Schwab\\
A.~Semenov\\
G.~Siegmon\\
J.R.~Smith\\
M.~Steenbock\\
U.~Straumann\\
C.~Thiebaux\\
P.~Van~Esch\\
from Yerevan Ph\\
L.R.~West\\
G.-G.~Winter\\
T.P.~Yiou\\
M.~Zimmer\end{multicols}
\section*{Sponsoring Institutions}
V. Meyer Inc., Reading, MA, USA\\
The Hofmann-International Company, San Louis Obispo, CA, USA\\
Kramer Industries, Heidelberg, Germany
\tableofcontents
\mainmatter
\part{Hamiltonian Mechanics}
\title{Hamiltonian Mechanics unter besonderer Ber\"ucksichtigung der
h\"ohereren Lehranstalten}
\titlerunning{Hamiltonian Mechanics}
\author{Ivar Ekeland\inst{1} \and Roger Temam\inst{2}
Jeffrey Dean \and David Grove \and Craig Chambers \and Kim~B.~Bruce \and
Elsa Bertino}
\authorrunning{Ivar Ekeland et al.}
\tocauthor{Ivar Ekeland, Roger Temam, Jeffrey Dean, David Grove,
Craig Chambers, Kim B. Bruce, and Elisa Bertino}
\index{Ekeland, I.}
\index{Temam, R.}
\index{Dean, J.}
\index{Grove, D.}
\index{Chambers, C.}
\index{Kim, B.}
\index{Bertino, E.}
\institute{Princeton University, Princeton NJ 08544, USA,\\
\email{I.Ekeland@princeton.edu},\\ WWW home page:
\texttt{http://users/\homedir iekeland/web/welcome.html}
\and
Universit\'{e} de Paris-Sud,
Laboratoire d'Analyse Num\'{e}rique, B\^{a}timent 425,\\
F-91405 Orsay Cedex, France}

\maketitle

\begin{abstract}
The abstract should summarize the contents of the paper
using at least 70 and at most 150 words. It will be set in 9-point
font size and be inset 1.0 cm from the right and left margins.
There will be two blank lines before and after the Abstract. \dots
\keywords{computational geometry, graph theory, Hamilton cycles}
\end{abstract}
\section{Fixed-Period Problems: The Sublinear Case}
With this chapter, the preliminaries are over, and we begin the search
for periodic solutions to Hamiltonian systems. All this will be done in
the convex case; that is, we shall study the boundary-value problem
\begin{eqnarray*}
  \dot{x}&=&JH' (t,x)\\
  x(0) &=& x(T)
\end{eqnarray*}
with $H(t,\cdot)$ a convex function of $x$, going to $+\infty$ when
$\left\|x\right\| \to \infty$.

\subsection{Autonomous Systems}
In this section, we will consider the case when the Hamiltonian $H(x)$
is autonomous. For the sake of simplicity, we shall also assume that it
is $C^{1}$.

We shall first consider the question of nontriviality, within the
general framework of
$\left(A_{\infty},B_{\infty}\right)$-subquadratic Hamiltonians. In
the second subsection, we shall look into the special case when $H$ is
$\left(0,b_{\infty}\right)$-subquadratic,
and we shall try to derive additional information.
\subsubsection{The General Case: Nontriviality.}
We assume that $H$ is
$\left(A_{\infty},B_{\infty}\right)$-sub\-qua\-dra\-tic at infinity,
for some constant symmetric matrices $A_{\infty}$ and $B_{\infty}$,
with $B_{\infty}-A_{\infty}$ positive definite. Set:
\begin{eqnarray}
\gamma :&=&{\rm smallest\ eigenvalue\ of}\ \ B_{\infty} - A_{\infty} \\
  \lambda : &=& {\rm largest\ negative\ eigenvalue\ of}\ \
  J \frac{d}{dt} +A_{\infty}\ .
\end{eqnarray}

Theorem~\ref{ghou:pre} tells us that if $\lambda +\gamma < 0$, the
boundary-value problem:
\begin{equation}
\begin{array}{rcl}
  \dot{x}&=&JH' (x)\\
  x(0)&=&x (T)
\end{array}
\end{equation}
has at least one solution
$\overline{x}$, which is found by minimizing the dual
action functional:
\begin{equation}
  \psi (u) = \int_{o}^{T} \left[\frac{1}{2}
  \left(\Lambda_{o}^{-1} u,u\right) + N^{\ast} (-u)\right] dt
\end{equation}
on the range of $\Lambda$, which is a subspace $R (\Lambda)_{L}^{2}$
with finite codimension. Here
\begin{equation}
  N(x) := H(x) - \frac{1}{2} \left(A_{\infty} x,x\right)
\end{equation}
is a convex function, and
\begin{equation}
  N(x) \le \frac{1}{2}
  \left(\left(B_{\infty} - A_{\infty}\right) x,x\right)
  + c\ \ \ \forall x\ .
\end{equation}

\begin{proposition}
Assume $H'(0)=0$ and $ H(0)=0$. Set:
\begin{equation}
  \delta := \liminf_{x\to 0} 2 N (x) \left\|x\right\|^{-2}\ .
  \label{eq:one}
\end{equation}

If $\gamma < - \lambda < \delta$,
the solution $\overline{u}$ is non-zero:
\begin{equation}
  \overline{x} (t) \ne 0\ \ \ \forall t\ .
\end{equation}
\end{proposition}
\begin{proof}
Condition (\ref{eq:one}) means that, for every
$\delta ' > \delta$, there is some $\varepsilon > 0$ such that
\begin{equation}
  \left\|x\right\| \le \varepsilon \Rightarrow N (x) \le
  \frac{\delta '}{2} \left\|x\right\|^{2}\ .
\end{equation}

It is an exercise in convex analysis, into which we shall not go, to
show that this implies that there is an $\eta > 0$ such that
\begin{equation}
  f\left\|x\right\| \le \eta
  \Rightarrow N^{\ast} (y) \le \frac{1}{2\delta '}
  \left\|y\right\|^{2}\ .
  \label{eq:two}
\end{equation}

\begin{figure}
\vspace{2.5cm}
\caption{This is the caption of the figure displaying a white eagle and
a white horse on a snow field}
\end{figure}

Since $u_{1}$ is a smooth function, we will have
$\left\|hu_{1}\right\|_\infty \le \eta$
for $h$ small enough, and inequality (\ref{eq:two}) will hold,
yielding thereby:
\begin{equation}
  \psi (hu_{1}) \le \frac{h^{2}}{2}
  \frac{1}{\lambda} \left\|u_{1} \right\|_{2}^{2} + \frac{h^{2}}{2}
  \frac{1}{\delta '} \left\|u_{1}\right\|^{2}\ .
\end{equation}

If we choose $\delta '$ close enough to $\delta$, the quantity
$\left(\frac{1}{\lambda} + \frac{1}{\delta '}\right)$
will be negative, and we end up with
\begin{equation}
  \psi (hu_{1}) < 0\ \ \ \ \ {\rm for}\ \ h\ne 0\ \ {\rm small}\ .
\end{equation}

On the other hand, we check directly that $\psi (0) = 0$. This shows
that 0 cannot be a minimizer of $\psi$, not even a local one.
So $\overline{u} \ne 0$ and
$\overline{u} \ne \Lambda_{o}^{-1} (0) = 0$. \qed
\end{proof}
\begin{corollary}
Assume $H$ is $C^{2}$ and
$\left(a_{\infty},b_{\infty}\right)$-subquadratic at infinity. Let
$\xi_{1},\allowbreak\dots,\allowbreak\xi_{N}$  be the
equilibria, that is, the solutions of $H' (\xi ) = 0$.
Denote by $\omega_{k}$
the smallest eigenvalue of $H'' \left(\xi_{k}\right)$, and set:
\begin{equation}
  \omega : = {\rm Min\,} \left\{\omega_{1},\dots,\omega_{k}\right\}\ .
\end{equation}
If:
\begin{equation}
  \frac{T}{2\pi} b_{\infty} <
  - E \left[- \frac{T}{2\pi}a_{\infty}\right] <
  \frac{T}{2\pi}\omega
  \label{eq:three}
\end{equation}
then minimization of $\psi$ yields a non-constant $T$-periodic solution
$\overline{x}$.
\end{corollary}

We recall once more that by the integer part $E [\alpha ]$ of
$\alpha \in \bbbr$, we mean the $a\in \bbbz$
such that $a< \alpha \le a+1$. For instance,
if we take $a_{\infty} = 0$, Corollary 2 tells
us that $\overline{x}$ exists and is
non-constant provided that:

\begin{equation}
  \frac{T}{2\pi} b_{\infty} < 1 < \frac{T}{2\pi}
\end{equation}
or
\begin{equation}
  T\in \left(\frac{2\pi}{\omega},\frac{2\pi}{b_{\infty}}\right)\ .
  \label{eq:four}
\end{equation}

\begin{proof}
The spectrum of $\Lambda$ is $\frac{2\pi}{T} \bbbz +a_{\infty}$. The
largest negative eigenvalue $\lambda$ is given by
$\frac{2\pi}{T}k_{o} +a_{\infty}$,
where
\begin{equation}
  \frac{2\pi}{T}k_{o} + a_{\infty} < 0
  \le \frac{2\pi}{T} (k_{o} +1) + a_{\infty}\ .
\end{equation}
Hence:
\begin{equation}
  k_{o} = E \left[- \frac{T}{2\pi} a_{\infty}\right] \ .
\end{equation}

The condition $\gamma < -\lambda < \delta$ now becomes:
\begin{equation}
  b_{\infty} - a_{\infty} <
  - \frac{2\pi}{T} k_{o} -a_{\infty} < \omega -a_{\infty}
\end{equation}
which is precisely condition (\ref{eq:three}).\qed
\end{proof}

\begin{lemma}
Assume that $H$ is $C^{2}$ on $\bbbr^{2n} \setminus \{ 0\}$ and
that $H'' (x)$ is non-de\-gen\-er\-ate for any $x\ne 0$. Then any local
minimizer $\widetilde{x}$ of $\psi$ has minimal period $T$.
\end{lemma}
\begin{proof}
We know that $\widetilde{x}$, or
$\widetilde{x} + \xi$ for some constant $\xi
\in \bbbr^{2n}$, is a $T$-periodic solution of the Hamiltonian system:
\begin{equation}
  \dot{x} = JH' (x)\ .
\end{equation}

There is no loss of generality in taking $\xi = 0$. So
$\psi (x) \ge \psi (\widetilde{x} )$
for all $\widetilde{x}$ in some neighbourhood of $x$ in
$W^{1,2} \left(\bbbr / T\bbbz ; \bbbr^{2n}\right)$.

But this index is precisely the index
$i_{T} (\widetilde{x} )$ of the $T$-periodic
solution $\widetilde{x}$ over the interval
$(0,T)$, as defined in Sect.~2.6. So
\begin{equation}
  i_{T} (\widetilde{x} ) = 0\ .
  \label{eq:five}
\end{equation}

Now if $\widetilde{x}$ has a lower period, $T/k$ say,
we would have, by Corollary 31:
\begin{equation}
  i_{T} (\widetilde{x} ) =
  i_{kT/k}(\widetilde{x} ) \ge
  ki_{T/k} (\widetilde{x} ) + k-1 \ge k-1 \ge 1\ .
\end{equation}

This would contradict (\ref{eq:five}), and thus cannot happen.\qed
\end{proof}
\paragraph{Notes and Comments.}
The results in this section are a
refined version of \cite{smit:wat};
the minimality result of Proposition
14 was the first of its kind.

To understand the nontriviality conditions, such as the one in formula
(\ref{eq:four}), one may think of a one-parameter family
$x_{T}$, $T\in \left(2\pi\omega^{-1}, 2\pi b_{\infty}^{-1}\right)$
of periodic solutions, $x_{T} (0) = x_{T} (T)$,
with $x_{T}$ going away to infinity when $T\to 2\pi \omega^{-1}$,
which is the period of the linearized system at 0.

\begin{table}
\caption{This is the example table taken out of {\it The
\TeX{}book,} p.\,246}
\begin{center}
\begin{tabular}{r@{\quad}rl}
\hline
\multicolumn{1}{l}{\rule{0pt}{12pt}
                   Year}&\multicolumn{2}{l}{World population}\\[2pt]
\hline\rule{0pt}{12pt}
8000 B.C.  &     5,000,000& \\
  50 A.D.  &   200,000,000& \\
1650 A.D.  &   500,000,000& \\
1945 A.D.  & 2,300,000,000& \\
1980 A.D.  & 4,400,000,000& \\[2pt]
\hline
\end{tabular}
\end{center}
\end{table}
\begin{theorem} [Ghoussoub-Preiss]\label{ghou:pre}
Assume $H(t,x)$ is
$(0,\varepsilon )$-subquadratic at
infinity for all $\varepsilon > 0$, and $T$-periodic in $t$
\begin{equation}
  H (t,\cdot )\ \ \ \ \ {\rm is\ convex}\ \ \forall t
\end{equation}
\begin{equation}
  H (\cdot ,x)\ \ \ \ \ {\rm is}\ \ T{\rm -periodic}\ \ \forall x
\end{equation}
\begin{equation}
  H (t,x)\ge n\left(\left\|x\right\|\right)\ \ \ \ \
  {\rm with}\ \ n (s)s^{-1}\to \infty\ \ {\rm as}\ \ s\to \infty
\end{equation}
\begin{equation}
  \forall \varepsilon > 0\ ,\ \ \ \exists c\ :\
  H(t,x) \le \frac{\varepsilon}{2}\left\|x\right\|^{2} + c\ .
\end{equation}

Assume also that $H$ is $C^{2}$, and $H'' (t,x)$ is positive definite
everywhere. Then there is a sequence $x_{k}$, $k\in \bbbn$, of
$kT$-periodic solutions of the system
\begin{equation}
  \dot{x} = JH' (t,x)
\end{equation}
such that, for every $k\in \bbbn$, there is some $p_{o}\in\bbbn$ with:
\begin{equation}
  p\ge p_{o}\Rightarrow x_{pk} \ne x_{k}\ .
\end{equation}
\qed
\end{theorem}
\begin{example} [{{\rm External forcing}}]
Consider the system:
\begin{equation}
  \dot{x} = JH' (x) + f(t)
\end{equation}
where the Hamiltonian $H$ is
$\left(0,b_{\infty}\right)$-subquadratic, and the
forcing term is a distribution on the circle:
\begin{equation}
  f = \frac{d}{dt} F + f_{o}\ \ \ \ \
  {\rm with}\ \ F\in L^{2} \left(\bbbr / T\bbbz; \bbbr^{2n}\right)\ ,
\end{equation}
where $f_{o} : = T^{-1}\int_{o}^{T} f (t) dt$. For instance,
\begin{equation}
  f (t) = \sum_{k\in \bbbn} \delta_{k} \xi\ ,
\end{equation}
where $\delta_{k}$ is the Dirac mass at $t= k$ and
$\xi \in \bbbr^{2n}$ is a
constant, fits the prescription. This means that the system
$\dot{x} = JH' (x)$ is being excited by a
series of identical shocks at interval $T$.
\end{example}
\begin{definition}
Let $A_{\infty} (t)$ and $B_{\infty} (t)$ be symmetric
operators in $\bbbr^{2n}$, depending continuously on
$t\in [0,T]$, such that
$A_{\infty} (t) \le B_{\infty} (t)$ for all $t$.

A Borelian function
$H: [0,T]\times \bbbr^{2n} \to \bbbr$
is called
$\left(A_{\infty} ,B_{\infty}\right)$-{\it subquadratic at infinity}
if there exists a function $N(t,x)$ such that:
\begin{equation}
  H (t,x) = \frac{1}{2} \left(A_{\infty} (t) x,x\right) + N(t,x)
\end{equation}
\begin{equation}
  \forall t\ ,\ \ \ N(t,x)\ \ \ \ \
  {\rm is\ convex\ with\  respect\  to}\ \ x
\end{equation}
\begin{equation}
  N(t,x) \ge n\left(\left\|x\right\|\right)\ \ \ \ \
  {\rm with}\ \ n(s)s^{-1}\to +\infty\ \ {\rm as}\ \ s\to +\infty
\end{equation}
\begin{equation}
  \exists c\in \bbbr\ :\ \ \ H (t,x) \le
  \frac{1}{2} \left(B_{\infty} (t) x,x\right) + c\ \ \ \forall x\ .
\end{equation}

If $A_{\infty} (t) = a_{\infty} I$ and
$B_{\infty} (t) = b_{\infty} I$, with
$a_{\infty} \le b_{\infty} \in \bbbr$,
we shall say that $H$ is
$\left(a_{\infty},b_{\infty}\right)$-subquadratic
at infinity. As an example, the function
$\left\|x\right\|^{\alpha}$, with
$1\le \alpha < 2$, is $(0,\varepsilon )$-subquadratic at infinity
for every $\varepsilon > 0$. Similarly, the Hamiltonian
\begin{equation}
H (t,x) = \frac{1}{2} k \left\|k\right\|^{2} +\left\|x\right\|^{\alpha}
\end{equation}
is $(k,k+\varepsilon )$-subquadratic for every $\varepsilon > 0$.
Note that, if $k<0$, it is not convex.
\end{definition}

\paragraph{Notes and Comments.}
The first results on subharmonics were
obtained by Rabinowitz in \cite{fo:kes:nic:tue}, who showed the existence of
infinitely many subharmonics both in the subquadratic and superquadratic
case, with suitable growth conditions on $H'$. Again the duality
approach enabled Clarke and Ekeland in \cite{may:ehr:stein} to treat the
same problem in the convex-subquadratic case, with growth conditions on
$H$ only.

Recently, Michalek and Tarantello (see \cite{fost:kes} and \cite{czaj:fitz})
have obtained lower bound on the number of subharmonics of period $kT$,
based on symmetry considerations and on pinching estimates, as in
Sect.~5.2 of this article.

\section{Introduction}

In order to understand biological phenomena, scientists take physical samples for analyses, often in concert with precision instruments, at specific locations to characterize the biological community and the contextual environmental conditions at the site.
For example, marine biologists may be interested in using the concentration of chlorophyll present in a body of water to guide physical sampling of algal blooms, or agricultural scientists may be interested in using crop health to guide physical sampling of plants.
Scientists later analyze these physical samples in a laboratory setting, which may be an expensive process.
Traditionally, expert heuristics underpin the selection of physical sampling locations.
In contrast, we propose performing an adaptive robotic survey to find locations of interest for physical sampling.
To specify these locations, we propose quantiling the distribution of interest so that the scientists can take physical samples at the quantiles they are interested in.
For instance, if a marine biologist is interested in taking 9 physical water samples that are spread over a range of chlorophyll concentrations, they may choose to sample the deciles of the concentration.
If only a small number of physical samples can be taken and the upper extrema values are of interest, they may choose to take samples at the $(0.90, 0.95, 0.99)$ quantiles.
Our goal is to guide physical sampling for scientists by using a robot to perform an adaptive survey and then finding locations to suggest based on the measurements it takes.
Specifically, we aim to find the desired quantile values of the measurement distribution by adaptively selecting robot measurement locations to maximize an objective function, and produce suggested locations for physical sampling that are likely to contain the estimated quantile values.
\begin{figure}[t]
    \centering
    \includegraphics[trim={.18cm .3cm .18cm .3cm},clip,width=\columnwidth]{figures/field_trial_sa2.png}
    \caption{\textbf{Visualization of a field trial modeling a crop health task.}
    Crosses are locations where a drone took images.
    The 9 stars show locations suggested by the drone to sample for the deciles.
    Darker stars correspond to higher quantiles.
    The measurement of interest is the amount of green in each pixel.
    The experiment was geofenced within the white border.}
    \label{fig:field-SA-20}
    \vspace{-0.25in}
\end{figure}
We develop our method using an adaptive sampling formulation\footnote{We use adaptive sampling to mean an algorithm by which a robot adaptively takes measurements of a value, and physical sampling to refer to a scientist gathering matter from the environment to analyze later.} and show that it outperforms an entropy- or Bayesian optimization-based objective baseline. Our contributions are:
\begin{itemize}
    \item A planner with custom objective functions for adaptively increasing the quality of estimated quantiles;
    \item A method to select spatial locations which have the values estimated for the quantiles;
    \item Quantitative evaluation of our method on point and camera sensors with previously collected aquatic datasets;
    \item A demonstration of our method on a robot in a real-world crop health estimation task.
\end{itemize}

\begin{figure*}[t]
    \centering
    \includegraphics[width=\textwidth, trim={0 2cm 1.75cm 0}, clip]{figures/hero-fig.png}
    \caption{\textbf{Full system.}
    The first phase is initialization.
    The middle phase is exploration where the robot plans motions, takes measurements, and updates its model of the distribution and quantile estimates.
    The final phase of selecting suggested locations (illustrated here by simulated annealing optimization) to represent estimated quantile values can be done offline.}
    \label{fig:hero}
    \vspace{-10pt}
\end{figure*}

\section{Related Work}
Adaptive sampling has a long history in use for studying biological phenomena~\cite{fossum_information-driven_nodate, denniston_icra_2020}.
Often, the objective in adaptive sampling is to generate good coverage of a distributed phenomenon using an information theoretic objective such as entropy~\cite{kemna_pilot_2018} or mutual information~\cite{guestrin_near-optimal_2005}.
Other common objectives include finding the highest concentration location~\cite{Marchanta} or sampling near hotspots~\cite{mccammon_topological_2018}.
Adaptive sampling has also been used in an objective for surgical robots with the goal of discovering tumors~\cite{salman2018tissueabnormalities}.
These specialized objective functions are typically tuned to locate a single specific point, often the extrema, by increasing the quality of the estimate of the underlying concentration.
Selecting physical sampling locations using adaptive surveys have typically focused on finding high-concentration areas from which to sample and perform the sampling onboard the robot~\cite{das_data-driven_2015}.

Planning for adaptive sampling as a partially observable Markov decision process (POMDP) has been explored~\cite{borenstein_bayesian_2014};
previous works have used this for finding maxima~\cite{Marchanta} and to adapt the parameters of a rollout-based POMDP solver online to improve its efficiency for adaptive sampling~\cite{denniston_icra_2020}.

Bayesian optimization objectives are used to locate extreme values or areas of high concentration and have shown success in doing so in simulation and in real field scenarios~\cite{Marchanta,blanchard_informative_2021,souza_bayesian_2014}.
Previous works have also investigated directly calculating the quantile values for distributions at points using specialized loss functions to extend the notion of uncertainty in Gaussian processes, but these do not directly transfer to our setting because they only estimate the quantiles of a specific location~\cite{boukouvalas_gaussian_2012,reich_spatiotemporal_2012}.

\section{Background}
\textbf{Gaussian Processes (GPs)} are non-parametric models with uncertainty quantification which are widely used for adaptive sampling.
They approximate an unknown function from its known outputs by computing the similarity between points from a kernel function~\cite{Rasmussen2006}.
GPs have been used to represent the belief distribution from observations in POMDP formulations of Bayesian optimization and informed path planning~\cite{borenstein_bayesian_2014,Marchanta,denniston_icra_2020}.
A GP can be used to estimate the value $\mu(x)$ and variance $\sigma^2(x)$ at a specific location $x$.

\textbf{Online Adaptive Sampling} consists of alternating between planning and taking an action, which usually corresponds to moving and measuring a value at the new location.
A plan described by a partial trajectory $p$ is created to maximize some objective function $f$ over the measured locations $\mathbold{X}$ and measured values $\mathbold{Y}$.
The combined plan $P$ is the concatenation of partial trajectories $p$.
The plan and act steps are iterated until the cost $c(P)$ exceeds some predefined budget.
Formally, this is is described by
$P^* = \argmax_{P \in \Phi} f(P) | c(P) \leq B$
where $\Phi$ is the space of full trajectories, and $P^*$ is the optimal trajectory~\cite{Hollinger2014,denniston_icra_2020}.

\textbf{Adaptive Sampling as a Partially Observable Markov Decision Process (POMDP)} provides a formulation for planning for taking measurements.
POMDPs are a framework that can determine optimal actions when the environment is not fully observable or there is uncertainty in the environment.
Using observations as measurements from the environment and a GP to represent the belief distribution, Bayesian optimization can be formulated as a Bayesian search game~\cite{borenstein_bayesian_2014}.
Measurements from the environment $GT(x)$ constitute observations which are partially observable components of the overall environment $GT$.
To adapt the Bayesian search game formulation to adaptive sampling, the belief state is augmented with the state of the robot $x$ and the actions the planner is allowed to take are restricted to local movements which are feasible for the robot~\cite{Marchanta}.
A complete description of the POMDP for adaptive sampling can be seen in \cref{tab:BayesianSearchAndPOMDPs}.

\begin{table}[]
\vspace{2pt}
\begin{tabular}{c|c}
\textbf{POMDP} & \textbf{Adaptive Sampling}        \\ \hline
States         & Robot position $g_t$, Underlying unknown function $GT$ \\ \hline
Actions        & Neighboring search points $g_{t+1}$                    \\ \hline
Observations   & Robot position $g_t$, Measured location(s) $x_t = o(g_t)$   \\
               & Measured value(s) $y_t = GT(x_t) $ \\\hline
Belief         & $GP(y_{1:t}| g_{1:t})$                                \\ \hline
Rewards        & $f(x_t)$
\end{tabular}
\caption{\textbf{Adaptive Sampling as a POMDP.} After~\cite{borenstein_bayesian_2014,denniston_icra_2020}. }
\label{tab:BayesianSearchAndPOMDPs}
\vspace{-0.25in}
\end{table}

\textbf{Estimation of Quantiles and Quantile Standard Error} has been proposed using statistical techniques.
We estimate the quantile value from measurements using $\tilde{v} = x_{\lfloor h \rfloor} + (h - \lfloor h \rfloor)(x_{\lceil h \rceil} -x_{\lfloor h \rfloor})$ where $h = (n - 1)q + 1$, $n$ is the number of measurements, and $q$ is the quantile (Equation 7 in~\cite{hyndman_sample_1996})\footnote{This is the default in the \texttt{numpy} Python package}.
Given a probability density function $p$, the standard error of the $q$th quantile is $\frac{\sqrt{q(1-q)}}{\sqrt{n}p(\tilde{v})}$.
This method requires $p$, which is typically not known.
To estimate $p$ from samples, a density estimate can be constructed~\cite{WILCOX2012103}.
Here we use a Gaussian Kernel density estimator.
Another method to estimate the confidence interval is the Maritz-Jarrett  method~\cite{maritz_note_1978}.
The standard error for quantile estimates may also be estimated through bootstrap or jackknife methods which involve calculating the quantiles over repeatedly sampled subsets of the data.
These methods can be slow for large datasets and require many iterations to converge.

\textbf{Continuous Non-Convex Gradient-Free Optimization} is used to solve general black-box optimization problems.
One common approach is the cross-entropy (CE) method \cite{de2005tutorial}.
CE works by maintaining an estimate about the distribution of good solutions, and iteratively updating the distribution parameters based on the quality of the solutions sampled at each step, where the quality is determined via some function of the solution configuration.
More precisely, a prior $Pr$ and a posterior $Po$ set of samples are maintained.
$Po$ contains $n$ configurations sampled from a Gaussian distribution defined by parameters $\vec{\mu}$ and $\vec{\sigma}$.
$\vec{\mu}$ and $\vec{\sigma}$ are computed from $Pr$, which is the best $\eta\%$ configurations from $Po$.
This continues iteratively for a fixed number of iterations or until a stopping criterion is met.
By taking these iterative steps, CE minimizes the cross-entropy between the maintained distribution and a target distribution~\cite{de2005tutorial}.

Another popular optimization method is simulated annealing (SA) \cite{kirkpatrick1987optimization}, an iterative improvement algorithm inspired by statistical mechanics. SA optimizes an energy function similar to a loss function in other optimization schemes, as configurations with lower energy are preferred. SA begins with a temperature $T = T_\t{max}$. At each iteration, $T$ is decreased exponentially, and the configuration is slightly perturbed randomly. The perturbed state is either accepted or rejected probabilistically based on its energy and $T$. The algorithm terminates when $T$ reaches a given threshold.

\section{Formulation}
We use a grid-based representation of the planning space, $\mathbold{G^*}$, which defines the set of locations that the robot could visit.
For a robot that moves in $\mathbb{R}^d$, $\mathbold{G^*} \subset \mathbb{R}^d$ and $|\mathbold{G^*}| < \infty$.
$\mathbold{X^*}$ is the set of locations the robot could measure.
If the robot sensor has finer resolution than $\mathbold{G^*}$, then $|\mathbold{X^*}| > |\mathbold{G^*}|$.
We define $\mathbold{X}$ as the locations the robot has already measured and $\mathbold{Y^*}$ and $\mathbold{Y}$ as the values at all possible measured locations, and the values the robot has measured, respectively.

We define the ground truth quantile values as $V =
quantiles(\mathbold{Y^*},Q)$, where $quantiles$ is a function which computes the quantiles $Q$ of a set of values.
To define the robot's estimated quantile values, we compute $\tilde{V} = quantiles(\mu(\mathbold{X^*}),Q)$, that is, the quantile values of the predicted values from the robot's current GP for all locations the robot could sense.
This is done  to prevent the number of measurements from which the quantile values are estimated from changing as the robot explores (instead of, e.g. using $\mu(\mathbold{X})$).
To assess estimation accuracy, we compute the error using $l_{p} (\tilde{V} , V)$ where $l_{p}$ is an accuracy estimate.
During planning, we aim to minimize this error by taking actions which maximize an objective function $f$.

To suggest locations for the quantile values, we aim to find a set of $|\quantiles|$ locations $\mathcal{Q}$ in the continuous space whose values at those locations are equal to the quantile ground-truth values.
A set of locations is defined as $\mathcal{Q} \in \mathcal{Q}^*$ where $\mathcal{Q}^* \subset \mathbb{R}^{d \times |Q|}$ and $\mathcal{Q}^*$ is continuous over the space of $\mathbold{G^*}$.
In practice, the robot only has knowledge of $\tilde{V}$ during the selection process, so the problem of finding $\tilde{\quantilespatiallocations}$ can be stated as shown in \cref{eq:point_selection} with some selection loss function $l_s$.

\begin{align}\label{eq:point_selection}
\begin{split}
    \mathcal{Q}[i] = x \in \mathbb{R}^d \quad
    &\t{s.t.} \quad GT(\mathcal{Q}[i]) = V[i] \quad \forall i \in [1, |\quantiles|] \\

    \tilde{\quantilespatiallocations} &= \argmin_{\mathcal{Q}' \subset \mathcal{Q}^*} \quad l_s (\tilde{V}, \mathcal{Q}')
\end{split}
\end{align}

\section{Approach}
Figure \ref{fig:hero} illustrates our method.
To plan which locations to sample, the robot uses the POMDP formulation of adaptive sampling.
In order to generate a policy, we use the partially observable Monte Carlo planner (POMCP)~\cite{silver2010pomcp}.
POMCP uses Monte Carlo tree search to create a policy tree.
To expand the tree and estimate rewards, the tree is traversed until a leaf node is reached.
Typically, from the leaf node, a random policy is executed until the discounted reward is smaller than some value $\epsilon$.
We modify the rollout reward to be fixed horizon which gives a reward of zero once a certain depth is reached.
We adopt the t-test heuristic for taking multiple steps from a POMCP plan for adaptive sampling to improve performance of the planner with fewer rollouts~\cite{denniston_icra_2020}.
Because the observations $GT(x)$ for unseen locations are not known during planning, the predicted value from the GP conditioned on the previous observations is used~\cite{Marchanta}.

\subsection{Planning Objective Functions}
Entropy is a common objective function for adaptive sampling when only good spatial coverage of the environment is desired~\cite{kemna_pilot_2018,guestrin_near-optimal_2005,denniston_comparison_2019}.
It provides a good baseline as it is often used when the specific values of the underlying concentration are unknown.
Entropy is defined by rescaling the variance in the GP at the location according to \cref{eq:entropy}:

\begin{equation}\label{eq:entropy}
   f_\t{en}(x_i) = \frac{1}{2} log(2 \pi e \sigma^2(x_i))
\end{equation}

Another objective function we compare against is expected improvement, which is widely used in Bayesian optimization for finding maxima~\cite{jones_efficient_1998, qin_improving_2017}.
Expected improvement favors actions that offer the best improvement over the current maximal value, with an added exploration term $\xi$ to encourage diverse exploration.
The expected improvement objective function is defined according to \cref{eq:ei}:

\begin{align}\label{eq:ei}
\begin{split}
    I = (\mu(x_i) - max(\mu(\mathbold{X^*})) - \xi) \qquad Z =\frac{I}{\sigma^2(x_i)}  \\
   f_\t{ei}(x_i)  =
     \begin{cases}
      0 & \sigma^2(x_i) = 0 \\
      I\Phi(Z) + \sigma(x)\phi(Z) & \sigma^2(x_i) > 0
   \end{cases} \\
\end{split}
\end{align}
where $\Phi$ and $\phi$ are the CDF and PDF of the normal distribution.

We develop two novel objective functions to improve the quality of planning for estimating quantile values.
Both functions compare a measure of the quality of the quantiles estimated by the GP before and after adding the measurement to the GP.
For both functions, we include an exploration term $c\sigma^2(x_i)$, inspired by the upper confidence bound acquisition function~\cite{Marchanta}, where $c$ is a chosen constant.
For both objective functions, $A = GP(\mathbold{X}_{0:i-1},\mathbold{Y}_{0:i-1}; \theta )$ is a GP conditioned on the points before measuring a proposed value, and $B = GP(\mathbold{X}_{0:i-1} \cup \{x_i\}, \mathbold{Y}_{0:i-1} \cup \{y_i\}; \theta )$ is a GP conditioned on the previous and proposed measurements, where $\theta$ are GP parameters.
For both proposed objective functions we use \cref{eq:general_objective}:
\begin{equation}\label{eq:general_objective}
    f(x_i) = \frac{\delta}{|\quantiles|} + c \sigma^2(x_i)
\end{equation}where $\delta$ is defined by the objective.

The first objective function, which we call \textit{quantile change}, is based on the idea of seeking out values which change the estimate of the quantile values by directly comparing the estimated quantiles before and after adding the measured values to the GP.
The idea behind this is that a measurement which changes the estimate of the quantiles indicates that the quantiles are over- or under-estimated.
This can be seen in in \cref{eq:quantile_change}:
\begin{equation}\label{eq:quantile_change}
  \delta_\t{qc} = ||quantile(\mu_{A}(\mathbold{X^*}),Q) - quantile(\mu_{B}(\mathbold{X^*}),Q) ||_{1} \\
\end{equation}

The second objective function we develop, which we call \textit{quantile standard error}, is based on the change in the estimate of the standard error for the estimated quantiles.
It draws from the same idea that if the uncertainty in the quantile estimate changes after observing a measured value, then it will change the estimate of the quantile values, shown in \cref{eq:standard_error}:

\begin{align}\label{eq:standard_error}
\begin{split}
   \delta_\t{se} &= ||se(\mu_{A}(\mathbold{X^*}),Q) - se(\mu_{B}(\mathbold{X^*}),Q) ||_{1} \\
\end{split}
\end{align}
$se$ is an estimate of the standard error of the quantile estimate for quantiles $Q$.
$se$ uses a Gaussian kernel density estimate (we found it faster and more stable than the Maritz-Jarrett  estimator, and considerably faster than sampling based estimators, such as bootstrap and jackknife).
To compute the objective function over a set of measured points, we average the objective function at each point.

\subsection{Finding Optimal Locations}
Our final goal is to produce a set of $|\quantiles|$ locations $\mathcal{Q}$, at which the concentration values will be equal to $V$, the values of the quantiles $Q$.
The problem of finding locations that represent $Q$ is difficult because the objective function over arbitrary phenomena in natural environments will likely be non-convex, and in a real-world deployment, the robot will only have an estimate $\tilde{V}$ of the $V$ it is searching for.

With the location selection problem formulation as in eq. \ref{eq:point_selection}, we use $l_s(\tilde{V}, \tilde{\quantilespatiallocations}) = ||(\tilde{V}, \mu(\tilde{\quantilespatiallocations}))||_{2}$.
The selection process can be done offline, since it does not affect planning.
The optimizer runs using $\tilde{V}$ and returns the suggested sampling locations $\tilde{\quantilespatiallocations}$.
We use both simulated annealing (SA) and cross-entropy (CE) optimization methods in our experiments.

\section{Experiments}
To evaluate our approach, we compare against baselines in two different adaptive sampling tasks in simulation using datasets collected in the real world.

In the first task, a drone is simulated with a virtual camera over orthomosaics collected of a lake using a hyperspectral sensor.
The drone collects many measurements from one location with each point being a pixel in a downsampled image.
As a proxy for chlorophyll concentration, we are interested in quantiling the pixel intensity.
The drone maintains a constant altitude and moves in a 2D plane with a north-fixed yaw and makes a move in either the $x$ or $y$ direction per step.
The two orthomosaics, A and B, are taken in the same location but on different days and times.

In the second task, an autonomous underwater vehicle (AUV) is tasked with exploring a 3D workspace interpolated from a 3D lawnmower survey collected previously.
The lawnmower survey is interpolated using a GP to the planning grid.
At each step the AUV may move in one $x$, $y$, or $z$ direction.
The AUV takes five evenly spaced samples when moving between locations.
The two AUV surveys, C and D, are taken in the same reservoir at different times and in different areas of the lake.

\subsection{Quantile Estimate Improvement}
To compare the ability of our proposed objective functions, quantile change (\cref{eq:quantile_change}) and quantile standard error (\cref{eq:standard_error}), we compare against a baseline entropy objective function (\cref{eq:entropy}).
For each task, we compare on two different datasets (A/B, C/D) and three different quantiles: deciles $(0.1,0.2, \dots 0.8,0.9)$, quartiles $(0.25,0.5,0.75)$ and upper extrema $(0.9,0.95,0.99)$.
For the upper extrema quantiles, we also compare against expected improvement (\cref{eq:ei}), as it is similar to a Bayesian optimization based adaptive sampling task.
In the planner, we use $\gamma = 0.9$, $\t{t-test}\_\t{value} = 0.1$, and each trial is run over 3 seeds.
The objective $c$ parameter is set to the approximate magnitude of the rewards seen for each environment, which we found experimentally to be an adequate value.
The parameters for the GPs were all found experimentally.

\subsubsection{Drone with Camera}
For this task, the drone is allowed to take 30 simulated pictures out of a grid with about 300 positions.
Each simulated picture is downsampled to 8 by 5 pixels with $37.1^{\circ}$ by $27.6^{\circ}$ field of view, similar to the drone used in the field trial reported in \cref{sec:field_trial}.
For each trial, the GP used by the robot is seeded with 100 evenly spaced points across the workspace.
In the planner, $300$ rollouts per step are used and the max planning depth is 7.

\Cref{fig:clearlake_planning_results} shows the results of planning with the proposed objective functions.
Quantile change and quantile standard error outperform the baseline entropy in estimating the deciles and upper extrema.
In quartiles in environment A, both proposed methods perform well, but in environment B entropy outperforms our methods.
We believe this because this specific configuration is the most difficult task as each method performs worse at the end than they do at 5 steps.
For the extrema, both methods perform better than expected improvement and entropy outperforms expected improvement in environment A.
We believe this is because expected improvement only looks to improve the maximal value and does not do a good job localizing high concentration areas instead of a single point.

\begin{figure}[t]
    \centering
        \begin{subfigure}{.32\columnwidth}
                \centering
                \includegraphics[width=\textwidth, trim=1cm .2cm 1.6cm .8cm, clip]{figures/EnvironmentADeciles.png}
        \end{subfigure}
        \begin{subfigure}{.32\columnwidth}
                \centering
                \includegraphics[width=\textwidth,  trim=1cm .2cm 1.6cm .8cm, clip]{figures/EnvironmentAQuartiles.png}
        \end{subfigure}
        \begin{subfigure}{.32\columnwidth}
                \centering
                \includegraphics[width=\textwidth,  trim=.8cm .2cm 1.6cm .8cm, clip]{figures/EnvironmentAExtrema.png}
        \end{subfigure}
        \begin{subfigure}{.32\columnwidth}
                \centering
                \includegraphics[width=\textwidth, trim=1cm .2cm 1.6cm .8cm, clip]{figures/EnvironmentBDeciles.png}
        \end{subfigure}
        \begin{subfigure}{.32\columnwidth}
                \centering
                \includegraphics[width=\textwidth,  trim=1cm .2cm 1.6cm .8cm, clip]{figures/EnvironmentBQuarties.png}
        \end{subfigure}
        \begin{subfigure}{.32\columnwidth}
                \centering
                \includegraphics[width=\textwidth, trim=.8cm .2cm 1.6cm .8cm, clip]{figures/EnvironmentBExtrema.png}
        \end{subfigure}
        \caption{\textbf{Simulated drone experiments with real data.} Error between ground truth quantile values and estimated quantile values in a task with a simulated drone with a camera using data collected in Clearlake, California.}\label{fig:clearlake_planning_results}
        \vspace{-0.25in}
\end{figure}
\subsubsection{AUV with Chlorophyll Sensor}
The AUV is simulated for 200 steps in a $12 \times 14 \times 2$ grid.
The planner uses $130$ rollouts per step and a max depth of $10$.
The GP is seeded with values from 50 locations.

\Cref{fig:ecomapper_planning_results} shows the results of this experiment.
Quantile standard error outperforms entropy in environment C when estimating deciles and quartiles, and performs equally well as entropy in all other tasks besides estimating the extrema in environment D.
Quantile change performs poorly in most tasks, and expected improvement performs poorly in estimating the extrema due to similar issues as the previous task.

\begin{figure}[t]
    \centering
        \begin{subfigure}{.32\columnwidth}
                \centering
                \includegraphics[width=\textwidth, trim=1cm .2cm 1.6cm .8cm, clip]{figures/EnivronmentCDeciles.png}
        \end{subfigure}
        \begin{subfigure}{.32\columnwidth}
                \centering
                \includegraphics[width=\textwidth, trim=1cm .2cm 1.6cm .8cm, clip]{figures/EnivronmentCQuartiles.png}
        \end{subfigure}
                \begin{subfigure}{.32\columnwidth}
                \centering
                \includegraphics[width=\textwidth, trim=.8cm .2cm 1.6cm .8cm, clip]{figures/EnivronmentCExtrema.png}
        \end{subfigure}
        \begin{subfigure}{.32\columnwidth}
                \centering
                \includegraphics[width=\textwidth, trim=1cm .2cm 1.6cm .8cm, clip]{figures/EnivornmentDDeciles.png}
        \end{subfigure}
        \begin{subfigure}{.32\columnwidth}
                \centering
                \includegraphics[width=\textwidth, trim=1cm .2cm 1.6cm .8cm, clip]{figures/EnivronmentDQuartiles.png}
        \end{subfigure}
        \begin{subfigure}{.32\columnwidth}
                \centering
                \includegraphics [width=\textwidth, trim=.8cm .2cm 1.6cm .8cm, clip]{figures/EnivronmentDExtrema.png}
        \end{subfigure}
        \caption{\textbf{Simulated AUV experiments with real data.} Error between ground truth quantile values and estimated quantile values. Dataset collected from a reservoir in California.}\label{fig:ecomapper_planning_results}
        \vspace{-0.07in}
\end{figure}

\subsection{Physical Location Selection}

To produce suggested physical sampling locations, we use the optimization algorithms simulated annealing (SA) and cross-entropy (CE) with the results from the quantile estimation task.

For SA, we use $T_\t{max} = 1000$, $T_\t{min} = 1$, and cooling rate $\t{cr} = 0.01$ which leads to approximately 690 optimization steps.
For CE, we use $\alpha = 0.9$, $\eta = 0.9$, $\t{n}\_\t{samples} = 50$, and $\t{n}\_\t{iterations} = 100$
where $\alpha$ is a weighting factor on new samples, $\t{n}\_\t{samples}$ is the number of different $\mathcal{Q}$s that are kept in the posterior, and $\t{n}\_\t{iterations}$ is the number of optimization steps.
We found experimentally that for higher $\t{n}\_\t{samples}$ or $\t{n}\_\t{iterations}$, CE becomes very computationally intensive without producing better output.
Overall, we found that SA tended to be faster and produce slightly better solutions, but in general both methods perform similarly for most experiments in terms of $l_s(\tilde{V}, \tilde{\quantilespatiallocations})$.

\subsubsection{Drone with Camera}
\begin{figure}[t]
    \centering

    \includegraphics[width=\columnwidth]{figures/contour-entropy.png}
    \includegraphics[width=\columnwidth]{figures/contour-se.png}

    \includegraphics[width=\columnwidth]{figures/raster-entropy.png}
    \includegraphics[width=\columnwidth]{figures/raster-se.png}
    \caption{
    \textbf{Physical locations (white stars) selected by the optimizers SA (left) and CE (right) for deciles.}
    Entropy and quantile standard error are the planning objective functions in the $1^\t{st}/3^\t{rd}$ and $2^\t{nd}/4^\t{th}$ rows, respectively.
    [Top] Black lines: model prediction contours.
    [Bottom] Red crosses: locations the robot visited, overlaid on the ground truth raster image.
    }
    \label{fig:contours}
    \vspace{-15pt}
\end{figure}

Figure \ref{fig:contours} shows results for one seed of the drone with a camera sensor when monitoring deciles.
Although the suggested locations, shown as white stars, differ spatially in all 4 versions, they generally align quite closely with the quantile value estimates $\tilde{V}$, shown by the contours.
This demonstrates the ability of the optimizers to produce good suggestions to guide physical sampling, given that the robot has had a chance to explore the environment sufficiently.

The bottom part of figure \ref{fig:contours} shows the same locations on top of the orthomosaic of what the drone measured during exploration.
This part of the figure highlights the difficulty of the problem of adaptive sampling for quantiles.
With only partial knowledge of the environment, the robot's model of the phenomenon will vary based on the particular points it visited, which in turn affects the estimates of the quantiles.
Given a set of estimated quantile values, the location selection optimizer consistently produces good suggested locations for those estimates.

\subsubsection{AUV with Chlorophyll Sensor}
\begin{figure}
    \centering
        \begin{subfigure}{0.45\columnwidth}
                \centering
                \includegraphics[width=\textwidth]{figures/entropy-3d-points.png}
        \end{subfigure}
        \begin{subfigure}{0.45\columnwidth}
                \centering
                \includegraphics[width=\textwidth]{figures/se-3d-points.png}
        \end{subfigure}
    \caption{\textbf{Physical locations (stars) selected by the CE optimizer for the quartiles with an AUV using a chlorophyll point sensor.}
    Entropy (left) and quantile standard error (right) are the planning objective functions. Blue/green points are the measured locations $\mathbold{X}$.}
    \label{fig:3d_points}
    \vspace{-0.15em}
\end{figure}

\begin{table}[]
\resizebox{\columnwidth}{!}{
\begin{tabular}{c|c|c|c|c}
                & \multicolumn{2}{c|}{Simulated Annealing (SA)}    & \multicolumn{2}{c}{Cross Entropy (CE)} \\
                & Estimated             & GT                          & Estimated             & GT \\ \hline \hline
 \textbf{Drone}               & & & & \\
deciles         & $0.06 \pm 0.05$   & $14.76 \pm 5.96 $           & $0.73 \pm 0.73$   & $14.34 \pm 2.88 $\\
quartiles       & $0.04 \pm 0.09$   & $10.51 \pm 3.42 $           & $0.04 \pm 0.03$   & $11.56 \pm 3.55 $\\
extrema         & $0.10 \pm 0.04$   & $64.15 \pm 18.30$           & $1.59 \pm 0.91$   & $59.00 \pm 14.22$ \\
\end{tabular}}

\resizebox{\columnwidth}{!}{
\begin{tabular}{c|c|c|c|c}
  \textbf{AUV}              &              &                         &              &  \\
deciles         & $0.02 \pm 0.02$   & $10.55 \pm 7.23 $         & $0.67 \pm 0.50$   & $12.25 \pm 9.00 $ \\
quartiles       & $0.01 \pm 0.01$   & $8.02 \pm 7.74  $         & $0.05 \pm 0.03$   & $8.75 \pm 7.26  $ \\
extrema         & $0.39 \pm 0.41$   & $23.23 \pm 15.67$         & $3.70 \pm 3.50$   & $22.97 \pm 16.04$ \\
\end{tabular}}

\caption{\textbf{Final optimizer loss for experiments in simulation.}
\textit{Estimated} columns: loss at selected locations $||(\tilde{V} - \mu(\tilde{\quantilespatiallocations}))||_2$; \textit{GT} columns $||(V - GT(\tilde{\quantilespatiallocations}))||_2$.
Results averaged over the 2 environments and 3 random seeds.
Units are pixel brightness for Drone and $\mu g/L$ chlorophyll for AUV.}
\label{tab:point_selection}
\vspace{-15pt}
\end{table}

For the AUV, figure \ref{fig:3d_points} shows the suggested locations for the quartiles for one seed.
Similar to the experiment with the drone, the suggested locations correspond well to $\tilde{V}$ produced by the planner.

Table \ref{tab:point_selection} shows final loss scores of the optimizers in both the Drone and the AUV experiments for the selected locations using the robot model loss
$||(\tilde{V} - \mu(\tilde{\quantilespatiallocations}))||_2$
and the ground truth model loss
$||(V - GT(\tilde{\quantilespatiallocations}))||_2$.
The robot model loss is consistently near $0$ with the exception of CE when estimating the extrema, which is slightly higher for both the Drone and AUV environments.
This shows that the optimizer consistently finds near-optimal locations to represent $\tilde{V}$.
In contrast, the ground truth model loss is higher, illustrating that the optimizer only has knowledge of the estimated quantile values.
Quartiles appear to be the most well-represented in terms of the ground truth loss, which corresponds to the lower error seen in \cref{fig:clearlake_planning_results} and \cref{fig:ecomapper_planning_results}.

\subsection{Field trial}\label{sec:field_trial}
In our final experiment we demonstrate our method on a crop health monitoring task, where the objective is to estimate the deciles of the green present in each pixel of the images (we use green as a proxy for plant health).
We use a commercial, off-the-the shelf drone with a standard camera to take measurements of the field at a constant height of 3m.
Similar to the simulated drone, the drone in this experiment moves in a 2D plane with a north-fixed yaw.
The drone can take 20 pictures (planning steps) in a $16\times16$ m square grid, where $|\mathbold{G^*}| = 10\times10 = 100$ points, and each picture is downsampled to 8 by 5 pixels.
For planning, we use the quantile change objective function because it performs well for camera sensors and is faster than quantile standard error.
Figure \ref{fig:field-SA-20} shows the resulting suggested locations using SA based on the 20 steps shown that the robot took.

\section{Conclusion}
Scientists traditionally take physical samples at locations selected using heuristics.
They later analyze these samples in a laboratory to characterize a phenomenon of interest (e.g., the distribution of algae in the water).
We propose to, instead, choose these physical sampling sites by first performing an adaptive sampling survey with a robot and then proposing locations which correspond to the quantiles of the distribution.
To accomplish this, we propose two novel objective functions, quantile change and quantile standard error, for improving the estimates of quantile values through adaptive sampling.
We test these in three settings: a drone with a camera sensor over lake imagery, an underwater vehicle taking chlorophyll measurements, and a field trial using a drone for a crop health monitoring task.
Our objective functions perform well on these tasks and specifically outperform information theoretic and Bayesian optimization baselines.
We also show that optimization methods like simulated annealing and cross-entropy can produce physical locations in the environment representative of a set of quantiles of interest when combined with an adaptive survey for those quantiles.
Our approach can be used to guide physical sampling in real field scenarios, as demonstrated by our field trial.
Experimentally finding parameters was difficult for both the baselines and our proposed methodology, particularly for the GP; this is a direction for future work. We also plan to incorporate our physical sampling suggestions into a larger field campaign involving multiple scientists.

\clearpage
\bibliographystyle{IEEEtran}


text:
Even when online voting doesn't look as ridiculous as this, it's still no panacea.
Online voting as the big fix for low turnout is not a brainwave, it's a brainfart
Julienne Molineaux | Guest writer
The commentary around local election turnout is littered with misunderstanding. Yes, there's a problem, but we should regard any suggestion of a single, simple solution with deep suspicion, writes local elections expert Julienne Molineaux
The Spinoff local election coverage is made possible thanks to The Spinoff Members. For more about becoming a member and supporting The Spinoff's journalism click here.
When you have an online voting hammer, every turnout issue looks like a nail.
There's a naive view that policy proceeds in a rational manner: a problem is detected (somehow) and then various potential solutions are investigated and the best one is selected. In reality, solutions and problems often exist independently of each other, and the best solution doesn't always get adopted. The push for online voting to solve local government election turnout problems exemplifies this.
For those who want online voting, any suggestion of turnout problems results in a call to introduce voting over the internet. They do not need to analyse the problem in detail because they have a ready answer.
Warwick Lampp, director of a private elections firm that makes its money from organising elections, including for some local councils, has been quoted as saying turnout in the 2019 local elections was likely to be at an "all-time low" and that "online voting was critical to halt that decline". While Lampp undoubtedly has expertise in the logistics of organising elections, he also has a commercial conflict of interest when pushing particular voting solutions. He is not a disinterested observer and his comments do not demonstrate awareness of the research on voter behaviour.
Auckland Council's Marguerite Delbet has led the charge for online voting. She, too, was quick last week to claim interim low turnout figures were an "obvious" sign that "postal voting has had its day" and, "I think this election has shown it's the end of postal voting."
Even the prime minister joined in.
Despite early returns being low, turnout didn't crash. Overall it was up slightly on 2016, despite the drag low turnout Auckland had on the average. Turnout in 2016, in turn, was slightly higher than 2013.
The average turnout figure masks much variation. Turnout can rise when there is an exciting contest, or pressing local issues at stake. Research on previous elections shows turnout tends to be higher for territorial authorities with smaller populations and where there are a greater number of elected representative per capita. This held true for 2019 where turnout was low in Auckland, Christchurch and Wellington, which have large populations and low representation levels.
Jean Drage has written about the turnout problem in Christchurch, saying, "many councils have become too big and too distant from our everyday lives and … local councils don't do enough to promote local elections."
Does Auckland's low turnout have something to do with the size, scale and operation of local government there?
The unitary Auckland Council has brought big and much-needed benefits to Auckland in the form of integrated planning and infrastructure development, and speaking with one voice when dealing with central government. But we need to ask if this has been at the expense of democracy.
In Auckland the highest turnouts were (once again) in the Aotea-Great Barrier and Waiheke Island local board areas, at 63.5% and 52.0% respectively. The Hauraki Gulf islands are obvious communities of interest, have small populations, and high levels of per capita local representation. People are more likely to know each other, the incumbents and challengers, and the issues. Unsurprisingly, they are more likely to vote.
Is local government in Auckland too big and too corporate to be really "local"? The further away voters live from the centre the lower they rate or trust the council. Voters on the periphery feel neglected and invisible.
Perhaps, too, Auckland Council could sort out its Get Out the Vote campaign. Why go for a Bunnings colour scheme when the Electoral Commission orange is instantly recognisable as the colour of elections? A bright colour that screams Look At Me! is the right colour to get people's attention, not a solid green. Better follow-through was needed across different parts of the council – libraries were designated as places with ballot boxes, but there was no or very little in the way of signs outside or even inside libraries about this opportunity to drop your papers off. Some librarians did not know what was happening, and in some cases, gave out incorrect information. The online "find your nearest post box" generator did not communicate its results in a user-friendly way – one of my results said "Massey/Te Manawa". It took me a while to realise this was a reference to a new library at Westgate. If communications can only be understood by those in the know, then they are missing their target. Auckland Council incorrectly told people they needed photo ID to cast a special vote. Oh, and one-stop shops ran out of ballot papers, too.
I'd like to see the expertise and resources of the Electoral Commission used to run local elections.
Online voting is a solution. Low turnout is a problem. Postal voting is not working for many people. But to assume online voting is the solution to these problems means ignoring the inequity of digital access that exists across New Zealand. It ignores the intractable security issues of online systems, which may serve to undermine confidence in election results, leading to greater public disengagement with institutional politics. It ignores the issues of engagement and information – if people don't care about local government or don't know enough about the candidates, it doesn't matter whether the ballot is on paper or a screen, they won't vote. Solving local government election problems will not be easy and that is why we need to question the claims of anyone suggesting there is a single, simple solution which we must urgently implement.
Read more of Julienne Molineaux's analysis of the problems and solutions of online voting here.
Why Nanaia Mahuta is right to repeal racist Māori wards legislation
Florence Dean
How local boards want to transform South Auckland over the next three years
Eight extremely topical and uniquely New Zealand Halloween costumes

redpajama_set_name: RedPajamaCommonCrawl


text:
Rolling Plan for ICT standardisation
Join this collection
Rolling Plan 2022
Annex I - List of Member States' Work Plans and Strategies
(A.) Policy and legislation
A.1) Policy objectives
Digital technologies are transforming the economy and society, and data is at the centre of this transformation. Data-driven innovation will be essential for the modernisation of Europe and the data economy which has the potential of bringingenormous benefits for citizens, for example in support to medicine, mobility, Green Deal.The key role of data is reflected in many chapters of the rolling plan outlining the respective sector specific aspects. On top of that, and addressed in this chapter, data is of foundational and horizontal relevance.
As stated in the Communication "A European strategy for data", policy initiatives aim to "create a single European data space – a genuine single market for data, open to data from across the world – where personal as well as non-personal data, including sensitive business data, are secure and businesses also have easy access to an almost infinite amount of high-quality industrial data, boosting growth and creating value, while minimising the human carbon and environmental footprint ... [and]where EU law can be enforced effectively, and where all data-driven products and services comply with the relevant norms of the EU's single market".
The right to the protection of personal data is guaranteed by the EU Charter of fundamental rights and, together with the single market, is one of the EU founding principles. The European Commission is committed to ensuring fairness in how the value from using data is shared among businesses, consumers and accountable public bodies.
The GDPR and the new ePrivacy Regulation, expected to replace the ePrivacy Directive, provide the basic legal framework for respecting the European Charter in terms of data protection. The collection and use of personal data in compliance with the rules on the one hand, and the availability of non-personal data on the other hand, are necessary conditions to maximise the benefits from innovation and competition.
The European strategy for data is essential to govern new technologies and create business opportunities, while respecting fairness and the EU fundamental rights. Standards are one of the key elements of the data strategy instruments to support its implementation enabling international competition in a geopolitical context and on the basis of European values and rights.
The following tasks are especially in the focus of policy initiatives and of needs for a thriving data economy:
Availability of data
Imbalances in market power
Data interoperability and quality
Data infrastructures and technologies
Data lifecycle: collection, record keeping, archival and long-term preservation of information
(A.2) EC perspectiveand progress report
The main initiatives already adopted to date are:
Regulation (EU) 2016/679 (GDPR) andePrivacy Directive 2002/58/EC (to be replaced with ePrivacy Regulation), with regard to the processing of personal data - dealt with in chapter 3.0.3 on e-Privacy
Regulation (EU) 2018/1807 on the free flow of non-personal data- dealt with in chapter 3.1.3 on Big Data, Open Data and Public sector information that covers data other than personal data as defined in the GDPR and introduces requirements on Member States not to introduce restrictions on their territory on the processing of non-personal data, with few exceptions;
Regulation (EU) 2019/881 on the Cybersecurity Act (CSA)- dealt with in chapter 3.0.2 on Cybersecurity;
Directive (EU) 2019/1024 on open data and re-use of public sector information -dealt with in chapter3.1.3 on Big Data, Open Data and Public sector information and in chapter 3.2.4 on eGovernment;
Building on what has already been achieved in recent years, the European Strategy forData aims to achieve a genuine single market for data by providing for the introduction of policy measures and funding.
The four key instruments of the European Strategy for Data
The European Strategy for Data aims to identify rules to balance rights and obligations for online and offline services to respect the rights of the European Charter.
In particular, the European Strategy for Data has four key instruments at its core aiming at creating a fair and trusted environment, regulate market power and drive innovation with data as raw material:
The Data Governance Actaims to foster the availability of data for use by increasing trust in data intermediaries and by strengthening data-sharing mechanisms across the EU;
the Digital Market Act (DMA)aims to regulate large online platforms that qualify as gatekeepers, i.e. operators who control access to a certain market or platform;
The Open Data Directive - this is dealt with in detail in chapter 3.1.3 on Big Data, Open Data and Public sector information
The Data Act which is under development and intended to ensure fairness in the allocation of data value among the actors.
These four key instruments are complemented by other legal acts and policies. These include the Digital Services Act which addresses the context of the provision of digital services to citizens and businesses; the proposal aims to balance the responsibilities of users, platforms and public authorities by defining a common European framework that gives greater legal certainty to digital service providers while ensuring respect for European values.
The European Interoperability Framework (EIF) recommends that a long-term preservation policy is formulated for records and information in electronic form held by public administrations for the purpose of documenting procedures and decisions, to keep their legibility, reliability and integrity for as long as need be accessed.
Data lifecycle, including data collection, record keeping, archival and - when necessary - long term preservation of information, supports society's demand for trustworthy records and legal certainty associated with Data Strategy key instruments and application of AI algorithms.
The following section A.3 provides all relevant references.
(A.3) References
New European interoperability framework - Promoting seamless services and data flows for European public administrations
COM(2020) 66 final Communication from the Commission "A European strategy for data"
Proposal for a Regulation concerning the respect for private life and the protection of personal data in electronic communications and repealing Directive 2002/58/EC (Regulation on Privacy and Electronic Communications)
Regulation (EU) 2016/679 on the protection of natural persons with regard to the processing of personal data and on the free movement of such data, and repealing Directive 95/46/EC (General Data Protection Regulation)
Regulation (EU) 2018/1807 on a framework for the free flow of non-personal data in the European Union
Regulation (EU) 2019/881 on ENISA (the European Union Agency for Cybersecurity) and on information and communications technology cybersecurity certification and repealing Regulation (EU) No 526/2013 (Cybersecurity Act)
Directive (EU) 2019/1024 on open data and the re-use of public sector information
Proposal for a Regulation on European data governance (Data Governance Act)
Proposal for a regulation on a Single Market For Digital Services (Digital Services Act) and amending Directive 2000/31/EC
Proposal for a Regulation on contestable and fair markets in the digital sector (Digital Markets Act)
Decision (EU) 2015/2240 on interoperability solutions and common frameworks for European public administrations, businesses and citizens (ISA2 programme) as a means for modernising the public sector (ISA2)
Council recommendation of 14 November 2005 on priority actions to increase cooperation in the field of archives in Europe
(B) Requested actions
Action 1 SDOs to identify and inform about standards that are available or under way and that are of relevance in supporting the digital transformation at the level of data-innovation and of the data economy.
Action 2 SDOs to collaborate on developing a programme for addressing standardisation needs around all the data lifecycle, from data collection to record keeping, archiving and long term preservation of information and start the respective standardisation activities.
Action 3 In the context of the MSP, start an analysis on the role of open source software complementing standardisation for the data economy, e.g. with APIs, protocols, service delivery and other platforms.
Action 4 SDOs to identify and inform about standards that are available or under way and that are of relevance in supporting the interoperability of data as well as data sharing services between different sectors and domains.
Action 5 SDOs to develop standards in support of the Data Governance Act, the Digital Services Act and the Digital Markets Act, taking into account the results of ISA2 program.
(C) Activities and additional information
(C.1) Related standardisation activities
CEN and CENELEC
CEN/TC 468 'Preservation of digital information'
CEN/TC 468 works on standardisation of the functional and technical aspects of the preservation of digital information. It will develop standards aiming at achieving a European harmonization on best digital preservation practices: interoperability, integrity, portability of information during its lifecycle, etc. The development of these standards will follow the principles of Security by Design and Privacy by Design, in order to ensure highest security requirements and privacy protection for European citizens. One of the main objectives for the TC will be to coordinate and share national approaches and knowledge, in order to identify similarities and common views that will help to elaborate, through consensus, a European approach to the subject matter. As such, digital preservation can be part of the eIDAS-ecosystem, relying on a framework for eIDAS-based trust services and for European Digital Identities and preserving evidence.
CEN-CLC/WS DS 'Digital sovereignty'
This workshop, proposed by AFNOR, VDE/DKE and IEEE, aims at defining the concept of digital sovereignty with its associated terminology and framework. It will allow to identify and anticipate future associated standardisation requirements supporting the implementation of a European approach on Sovereignty, including promoting an open market through the development of interoperability standards.
ETSI TS 119 511 Electronic Signatures and Infrastructures (ESI); Policy and security requirements for trust service providers providing long-term preservation of digital signatures or general data using digital signature techniques
ETSI TS 119 512 Electronic Signatures and Infrastructures (ESI); Protocols for trust service providers providing long-term data preservation services
ISO 14721:2012 Space data and information transfer systems — Open archival information system (OAIS) — Reference model
ISO 20614:2017 Information and documentation — Data exchange protocol for interoperability and preservation
ISO 15489 Information and documentation — Records management (multipart)
ISO 20104:2015 Space data and information transfer systems — Producer-Archive Interface Specification (PAIS)
ISO 20652:2006 Space data and information transfer systems — Producer-archive interface — Methodology abstract standard
ISO/IEC JTC 1/SC 32 Data management and interchange
Standards for data management within and among local and distributed information systems environments
ISO/IEC JTC 1/SC 7 Software and systems engineering
ISO/IEC 25012 "Data quality model" defines a quality model for data in structured format, which can be used to establish requirements, to define measures or to plan and perform data quality assessments.The concept of "data quality" refers to the usefulness of the information derived from data.
ISO/IEC JTC 1/SC 40 IT Service Management and IT Governance
Published standards:
ISO/IEC 38500:2015 Information technology - Governance of IT for the Organization
ISO/IEC TS 38501:2015 Information technology - Governance of IT - Implementation Guide
ISO/IEC TR 38502:2017 Information technology - Governance of IT - Framework and Model
ISO/IEC TR 38504:2016Governance of information technology — Guidance for principles-based standards in the governance of information technology
ISO/IEC 38505-1:2017 Information technology — Governance of data — Part 1: Application of ISO/IEC 38500 to the governance of data
ISO/IEC 38505-2:2018 Information technology — Governance of data — Part 2: Implications of ISO/IEC 38505-1 for data management
Standards under development:
ISO/IEC FDIS 38503 Information technology — Governance of IT — Assessment of the governance of IT
ISO/IEC PRF TS 38505-3 Information technology — Governance of data — Part 3: Guidelines for data classification
ISO/IEC WD TS 38508 Information technology— Governance of IT— Governance implications of the Use of Shared Digital Service Platform among Ecosystem Organizations
ISO/IEC JTC 1 SC 27 WG 5 Identity management and privacy technologies: Please see the chapter on cybersecurity
Relevant standards for data security and privacy are developed. Please see the respective chapters on "Cybersecurityand on "Privacy" in this Foundational Drivers section.
The OASIS Open Data Protocol (Odata) standards support querying and sharing and re-use of data across disparate applications and multiple stakeholders. OASIS OData standards have been approved as ISO/IEC 20802-1:2016 and ISO/IEC 20802-2:2016.
The OASIS ebXML RegRep standards define service interfaces, protocols and information model for an integrated registry and repository. The repository stores digital content while the registry stores metadata that describes the content in the repository.
Selected List:
The Web of Things (WoT)
Data Catalog Vocabulary (DCAT) - Version 2 (2020-02-04) Recommendation and Working Draft on DCAT Version 3
JSON-LD 1.1 (2020-07-16)
Open Digital Rights Language (ODRL) Version 2.2.(2018-02-15)
Shapes Constraint Language (SHACL)(2017-07-20)
Web Annotation Data Model (2017-02-23)
Data on the Web Best Practices (2017-01-31)
Provenance (Overview with links to standards of the provenance familiy 2013-04-30)
Data Privacy Vocabularies and Controls CG
RDF-DEV CG developing RDFstarextends RDF with a compact way of annotating triples (and creates interoperability with property graphs)
See Data Activity Page for an overview.
(C.2) Other activities related to standardisation
The European Interoperability Framework (EIF)
The European Interoperability Framework (EIF) adopted on 23 March 2017 provides specific guidance on how to set up interoperable digital public services. EIF is undertaken in the context of the Commission priority to create a Digital Single Market in Europe. It offers public administrations 47 concrete recommendations on how to improve governance of their interoperability activities, establish cross-organisational relationships, streamline processes supporting end-to-end digital services, and ensure that both existing and new legislation do not compromise interoperability efforts.
A related on going framework is under development i.e. the Smart Cities and Communities European Interoperability Framework (EIF4SCC). EIF4SCC aims to support local administrations and other actors with challenges that relate to providing interoperability services to citizens and businesses. The Framework intends to support primarily local administrations and, in particular, local policy makers. This work in progress is jointly managed by DG DIGIT as part of the ISA² Programme (2016-2020), and by DG CONNECT in the framework of the Living-in.eu movement.
CEF e-Archiving
Important information should be kept accessible and reusable for years to come, regardless of the system used to store it. eArchiving provides core specifications, software, training and knowledge to help people preserve and reuse information over the long-term.
DILCIS Board
The Digital Information LifeCycle Interoperability Standards Board (DILCIS Board) develops, publishes and supports standards which provide practicalinteroperability in digital archiving. SIARD (Software Independent Archiving of Relational Databases) v2.2, August 31, 2021) https://dilcis.eu/content-types/siard
E-ARK Project (European Archival Records and Knowledge Preservation)
E-ARK was a multinational big data research project that improved the methods and technologies of digital archiving, in order to achieve consistency on a Europe-wide scale. https://www.eark-project.com/
SWIPO
SWIPO (Switching Cloud Providers and Porting Data), is a multi-stakeholder association facilitated by the European Commission, in order to develop voluntary Codes of Conduct for the proper application of the EU Free Flow of Non-Personal Data Regulation / Article 6 "Porting of Data". See https://swipo.eu
Gaia-X is the European Association for Data and Cloud AISBL founded with the goal to develop technical solutions and regulatory frameworks and ensure that necessary central facilities as well key federation services to guarantee the envisaged data infrastructure are made available. Seehttps://www.gaia-x.eu/
The official portal for European data https://data.europa.eu/en
https://dataspaces4.eu/
https://i4trust.org/about/


text:
Q: Filter where value is in column of another DataFrame I am trying to create a new column in a DataFrame which will be 'true' if the value of another column is in a column of another DataFrame. I have tried the following, but the syntax for isin() is wrong I believe because I am passing a DataFrame with a single column.
customers:
customer_id     name
          1     John
          2     Mary
          3     Jane
          4     Jack
          5     Emma

customer_referred_customer:
from    to
   1     3
   2     4

Result:
customer_id     name    is_referral
          1     John          false
          2     Mary          false
          3     Jane           true
          4     Jack           true
          5     Emma          false

Attempt:
customers.withColumn(
    "is_referral",
    F.when(
        F.col("customer_id").isin(
            customer_referred_customer.select("to")
        ),
        F.lit("true"),
    ).otherwise(F.lit("false")),
)

How can I fix this?

A: I would do it like this:
customers.join(
customer_referred_customer,
customers.customer_id ==customer_referred_customer.to,
 "left")
.withColumn("is_referral",
 f.when(customer_referred_customer["to"].isNull(),f.lit("false"))
.otherwise(f.lit("true"))
.select(customers["customer_id"],customers["name"], "is_referral")

A: Use semi join and anti join. You didn't provide the data so I can't test, but the idea of the code is:
customers = customers.join(
    customer_referred_customer,
    customers.customer_id == customer_referred_customer.to,
    'left_semi'
).withColumn(
    'is_referral',
    F.lit('true')
).unionAll(
    customers.join(
        customer_referred_customer,
        customers.customer_id == customer_referred_customer.to,
       'left_anti'
    ).withColumn(
        'is_referral',
        F.lit('false')
    )
)

A: Create list of the check column and use .isin()
df.withColumn('is_referral', df.customer_id.isin(df1.select("to").rdd.flatMap(list).collect())).show()

+-----------+----+-----------+
|customer_id|name|is_referral|
+-----------+----+-----------+
|          1|John|      false|
|          2|Mary|      false|
|          3|Jane|       true|
|          4|Jack|       true|
|          5|Emma|      false|
+-----------+----+-----------+

A: Use full outer join & then derive new column is_referral using withColumn("is_referral",col("to").isNotNull())
Check below code.
customers
.join(customer_referred_customer,customers.customer_id == customer_referred_customer.to,"full")
.withColumn("is_referral",col("to").isNotNull())
.select("customer_id","name","is_referral")
.orderBy(col("customer_id").asc())
.show(false)

+-----------+----+-----------+
|customer_id|name|is_referral|
+-----------+----+-----------+
|1          |John|false      |
|2          |Mary|false      |
|3          |Jane|true       |
|4          |Jack|true       |
|5          |Emma|false      |
+-----------+----+-----------+

redpajama_set_name: RedPajamaStackExchange


text:
Inland Pacific Ballet brings back 'The Nutcracker' in person – Press-Enterprise
December 5, 2021Enterprise
Inland Pacific Ballet's annual production of "The Nutcracker" is returning this holiday season with in-person performances at the Fox Performing Arts Center, 3801 Mission Inn Avenue, Riverside.
Performances are 2 and 7:30 p.m. Dec. 11 and 18 and 2 p.m. Dec. 12 and 19. Tickets are $20-$79, available at ticketmaster.com/inland-pacific-ballet-tickets/artist/887616 and ipballet.org or by calling the Fox Performing Arts Center box office at 951-779-9800.
Inland Pacific Ballet, based in Montclair, has presented "The Nutcracker" during the holiday season for more than 25 years, though the 2020 version was a digital release rather than in-person performances.
"The entire IPB team and the cast are so excited to return to the theater. The energy exchange between the audience and the performers is really what creates the magic," Zaylin Cano, Inland Pacific Ballet's executive director, said in a news release. "We hope our audiences will come out to see 'The Nutcracker' this year to support keeping live performances possible in the Inland Empire region."
The ballet, based on a story by E.T.A. Hoffmann and set to music by Pyotr Ilyich Tchaikovsky, tells the story of a young girl named Clara who receives a magical nutcracker doll on Christmas Eve and sets out on a journey to the Land of the Snow and the Kingdom of Sweets. Toy soldiers, life-sized dancing dolls, battling mice, dancing snowflakes, waltzing flowers, gingerbread characters and the Sugar Plum Fairy are all part of the ballet.
Proof of vaccination or negative COVID-19 test is required for everyone in the audience, and face masks must be worn.
Inland Pacific Ballet was founded in 1994 by Southern California natives Victoria Koenig and Kevin Myers. The company's repertoire includes such classics as "A Midsummer Night's Dream" and "Les Sylphides" and a growing body of original works.
Inland Pacific Ballet's educational outreach program, "A Young Person's Guide to the Ballet," is back this season with two abbreviated performances of "The Nutcracker" for pre-kindergarten through 12th-grade students from area schools, at 10 a.m. Dec. 10 and 16. Students are encouraged to participate in movement activities in their seats and then view the professional ballet performance, followed by a question-and-answer session.
For information about Inland Pacific Ballet, its performances and educational programs, go to ipballet.org
Southern California still 295,700 jobs short of pre-pandemic employment – Press-Enterprise
No. 16 USC seeing Reese Dixon-Waters becoming a contributor – Press-Enterprise
Man who hacked Chico State computers gets probation – Chico Enterprise-Record
Magdalena's Daughters works to prevent human trafficking in Inland Empire – Press-Enterprise
Amid Volcanic Crisis in Tonga, Arts Enterprise TBA21-Academy Calls for Support – ARTnews
How To Unsend The Gmail Email That You Really Shouldn't Have Sent
Coca-Cola Sidelines Super Bowl Ads for the Second Year in a Row
Rainbow Six Extraction: 9 tips and tricks for beginners
The Future of Food, EVs in the Spotlight, and 3 Trends to Watch in 2022 – Motley Fool
TikTok is letting creators test paid subscriptions


Whether your trip is for business or leisure, you will find our location one block south off Interstate 70 at Exit 31 a convenient gateway to Grand Junction and surrounding attractions.
Turn left at end of ramp onto Horizon Dr.
Hotel in view on right side of street.
Turn right at end of ramp onto Horizon Dr.
Hotel in view on right.
Highway 50 ends in Grand Junction and becomes 5th Street.
Turn Right on Main St. and follow it to 12th.
Turn left onto 12th and follow to traffic circle.
First right turn becomes Horizon Dr.
Follow Horizon Dr. north to property, which will be on left approximately 1 block south of I-70.


Horti-Cote Topdress is a partial resin coated total fertilizer specially developed for topdressing. Horti-Cote Topdress contains an uncoated starter freaction that provides a good start at the beginning of the growing season. This uncoated part also gives a better solidity on the pot. Horti-Cote Topdress is a resin coated N+P+K+MgO+Fe+TE fertilizer, with a temperature determined release. Every standard analysis is available in various longevities for an optimum base fertilisation for the whole growing season. By using resin coating the leaching of the nutrients is minimal, the uptake of the nutrients optimum and the effect on the environment minimal.


We are almost 1 month away from (hopefully) moving into our tiny house!
Before that, there are some important things that need to be addressed. One BIG thing is where we are going to put (park) the house.
This entry was posted in Tiny House and tagged Bay Area, california, craigslist, land, Park, rent, rent land, san francisco, San Francisco Bay Area, simple life, tiny house, Tiny House Movement, tiny life, trainertinyhouse.com.


text:
Home » BSU News » School of Technology, Art & Design Signs Transfer Agreement With Pine Technical College
School of Technology, Art & Design Signs Transfer Agreement With Pine Technical College
BSU and Pine Tech celebrate after signing the transfer agreement
L to R: Lyle Meulebroeck, Mike Lund, Dave Towley and Jim Barta from BSU
Jim Barta (center) signs the transfer agreement with Joe Mulford (left), Pine Tech president, and Denine Rood, Pine Tech vice president for academic & student affairs.
The signing table
On October 2, officials from Bemidji State University and Pine Technical College signed a transfer agreement making it easier for Pine Tech manufacturing students to complete bachelor's degrees at Bemidji State.
Under the agreement, students in Pine Tech's advanced manufacturing programs — which include applied engineering technology, automated systems technology and its industrial equipment emphasis area, precision machining technology, welding and 360 online manufacturing — can more easily transfer into Bemidji State programs to complete their four-year degrees.
BSU's programs participating in this transfer agreement, all in its School of Technology, Art & Design, include applied engineering, applied management, engineering technology, project management, operations management, construction and facility management, and product development.
Dave Towley, assistant professor of technology, art & design at Bemidji State, participated in the signing and said he appreciated the opportunity to meet in person with Pine Tech faculty as the two institutions launch this transfer relationship.
"We were able to see first-hand the great work that they are doing at Pine Technical College," Towley said. "We should expect to see very positive effects with students coming here as a result of this agreement."
Joining Towley on the trip were Jim Barta, dean of the College of Art, Education & Humanities; Mike Lund and Lyle Meulebroeck, associate professors of technology, art & design; and Dan Voss, university articulation coordinator.
Voss said he was encouraged by the event and believes it will create new opportunities for Pine Technical College students to complete their bachelor's degrees.
"This will be a strong transfer partnership, now and in the future," he said.
BSU Magazine – Fall/Winter 2019
Fall/Winter 2019 BSU Magazine Commemorative Issue
BSU Magazine Spring 2019
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Has 'Grand Theft Auto Online' become too much of a grind?
GTA Online Best Updates +images+ | (Red Bull Games/Youtube)
Rockstar has constantly increased the amount of in-game currency required to purchase items in the online mode, but how much is too much?
by Wyatt Coplin (article) and Maid Milinkic (video)
February 25, 2018 at 8:37 AM February 25, 2018 at 8:37 AM
Rockstar Games becoming more greedy - Video
We've all been there, you're grinding with your friends and just finished that super challenging heist. Now it's time for payday. You go to deposit your cash into your bank account and bam, 200k in the bank. Eventually, you make your way over to one of the various sites where you can spend your hard-earned money.
Much to your surprise, you can barely afford an average NPC car, let alone a laser tank or flying Delorean. How can this be? Were all those hours of elaborate planning and execution really worth it?
In my opinion (a player with over 500 hours of "GTA Online" experience) it, quite simply, isn't.
Is it worth it to grind in 'GTA Online'?
Since the release of their lucrative online mode, Rockstar has been steadily increasing their prices of in-game items, resulting in ungodly prices that almost force you to buy their ridiculously priced microtransaction "Shark Cards." To put it into perspective, you would have to fork over a hefty 100 American dollars just to get a yacht. Want a few cars? That'll be another hundred dollars.
By the time you're a certified crime lord, your wallet will be all but empty. It eventually gets to a point where it feels more like a pay to win MMO rather than a GTA game.
Three years ago, I could have easily bought whatever I desired with a little bit of grinding. With the release of the heists update, it was easier than ever to earn money to fund your criminal habits. Races and Adversary modes also gave sufficient rewards to provide an incentive to play them.
Rockstar's new Online mode seemed to be a fantastic MMO with nearly limitless opportunities for future content. Little did we know, that was no longer going to be possible in the near future.
The downhill spiral
The release of the Finance & Felony and Bikers updates marked the start of the downhill spiral that "GTA online" has fallen into. It introduced such items as the Vapid FMJ sports car, the Volatus helicopter, and the infamous X80 Proto, which remains to this day the most expensive mainstream car in the entire game.
These updates, however, had a redeeming quality.
They also sold CEO offices and Motorcycle Clubhouses, which in turn allowed the player to earn money at an unprecedented speed through the use of multiple new mission types. These mission types included importing and exporting expensive cars to make a sizeable profit, as well as the "businesses" which allowed for Motorcycle Club owners to earn money while idling or taking part in other activities, effectively doubling the rate at which players earn money.
More recently, they have released the "Gun Running," "Smugglers Run," and "Doomsday" updates. Because of the increase in speed at which players were earning in-game money, Rockstar took the liberty to increase the price of many items in the game drastically.
All of the sudden every new car that was even slightly decent was priced north of a million dollars. Tanks and Jets increased in price tenfold.
Even the clothing costs hundreds of thousands of dollars for certain outfits. It became clear that Rockstar was more interested in making revenue off of microtransactions than providing their players with an entertaining experience.
Don't get me wrong, "Grand Theft Auto Five" is a fantastic game. The single-player story mode alone is more than enough to warrant a full 60$ price tag for this masterfully crafted experience.
The online mode, however, has devolved into too much of a Grind to be enjoyable without hundreds, if not thousands of dollars available to spend on the game's microtransactions.
"Grand Theft Auto Online" serves as a prime example of how corporate greed can all but ruin some of the most interesting and entertaining experiences available.
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Wyatt Coplin
Hi, I'm a part-time writer and professional dumbass in the Northwest Area .
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Home Conventions CON NEWS: Price sells Mid-Ohio Con
CON NEWS: Price sells Mid-Ohio Con
Heidi MacDonald
Roger Price, who has been running the Mid-Ohio con for 27 years, sent out an open letter over the weekend:
After 27 years, I must regrettably announce that the time has come for me to retire as the promoter of Mid-Ohio-Con.
The difficult decision to take this action is based solely on personal reasons, including a desire to pursue several new professional opportunities.
The show itself remains viable, and it is my sincere desire that Mid-Ohio-Con will continue under new ownership. To that end, R.A.P. Promotions will entertain offers from seriously interested parties starting immediately. Those wishing to obtain additional information and submit an offer are asked to first contact me in writing either via e-mail at < href = "mailto:[email protected]">[email protected], or at PO Box 3831, Mansfield, Ohio 44907.
Since creating Mid-Ohio-Con in 1980, I have had the unique opportunity to watch a small, local gathering of comic book fans and collectors grow into one of the most popular events of its kind in America. During that time I have been blessed with more wonderful life experiences and treasured friendships than I could have ever imagined.
Special thanks must go to my inner circle of family and friends who have given so much to support me and Mid-Ohio-Con. The success and popularity of Mid-Ohio-Con is a testament to all of you.
My sincere thanks to all of the retailers, exhibitors, industry professionals and media personalities who have participated in and supported Mid-Ohio-Con over the years. It has been an honor to work with every one of you.
Finally, to all the thousands of fans and collectors who have become such an important part of the Mid-Ohio-Con family, thank you for allowing me the privilege of entertaining you over the years. I hope we will see each other again in the very near future.
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Heidi MacDonald is the editor-in-chief of The Beat and an award winning author and editor. She is the co-author of The Secret Teachings of a Comic Book Master.
Tom S. 01/22/2008 8:34 am At 8:34 am
Maybe, we will see the show go Non-Profit. The strongest organization in Ohio is the group running Ohayocon and that is going Non-Profit. I think the most like scenario is that Mid Ohio Con dies permanently (not finding a buyer) or is at least canceled for 2008 and possible 2009.
Al 01/22/2008 8:44 am At 8:44 am
Excuse, me, but someone is SELLING a convention? oh, the name of it, oh, I get it.
stan sakai 01/22/2008 9:38 am At 9:38 am
I've been to a few Mid Ohio Cons, and Roger did put together a terrific convention. I'm sorry to hear he's stepping down, and hope someone takes it over.
Chuck Moore 01/22/2008 10:15 am At 10:15 am
Roger has always been a great person to work with and his dedication to tying Mid-Ohio-Con to charities throughout the years has been admirable. I will miss hearing him on the PA during future shows (if/when a buyer might be found).
As an attendee and someone who covered the '07 show, I found it to be an exceedingly fun event. Mid-Ohio-Con has always had that rare distinction of drawing an interesting group of celebrity guests yet maintaining a laid back feel. Crowds seemed solid in '07, yet you didn't feel as rushed when you wanted to talk to a creator or company rep. This last show also featured a solid group of indie creators sharing some of the better work I took in all year.
If this show fades, it will be a real loss in my opinion.
Tommy Raiko 01/22/2008 10:32 am At 10:32 am
"Excuse, me, but someone is SELLING a convention? oh, the name of it, oh, I get it. "
Well, a convention is, after all, a business, with assets and liabilities and value and all that stuff. Although it may be harder to visualize (or evaluate) the sale of a business that doesn't seem to trade in tangible goods, trade shows and gatherings and shows and conventions do get bought and sold all the time. Heck, when Wizard moved into organizing conventions, they did so by buying the Chicago Comic-Con…
Chris 01/22/2008 11:58 am At 11:58 am
Please don't let it be Wizard. Please don't let it be Wizard.
W3r3 02/26/2008 1:47 pm At 1:47 pm
Who do you think is in a position to buy it?
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