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Home/Business/Understanding the Plagiarism Risk Detector of Spotify
Understanding the Plagiarism Risk Detector of Spotify
Cheryl Henson Send an email January 9, 2021
The music streaming platform Spotify is putting forward an interface by which any artist or composer can input their music in to root out the similitude to other songs in order to circumvent any potential lawsuits that can be filed against them. Here, it becomes pertinent to carry out a patent search online in India before applying for any trademark or patent as non-recognition of such an act could lead to detrimental circumstances.
As patents provide the owners with the prerogative to restrict others from making, getting, using or importing, or selling their invention without prior approval. Hence, it is crucial to conduct a patent search online before initiating the patent process.
Recently, music streaming platform Spotify has applied for a patent named, 'Plagiarism risk detector and interface' that would scan inserted music for plagiarism, as per the submissions acquired by the Music Business Worldwide. Such an interface is developed to assist artists in circumventing potential lawsuits against them by identifying similitude in already published songs and music.
This technology needs every song to be scanned with the help of a 'lead sheet' which can be described as a form of musical hieroglyphic usual in the music industry. The plagiarism detection of the interface utilizes AI (artificial intelligence) which is 'instructed on a plurality of pre-existing encoded lead sheets' as per the patent fillings.
Such a form of the database enables the program to potentially examine a 'level' of plagiarism in the song or music in close to real-time. It offers the users a 'resembling value' compared to the theme of other lead sheets in the Spotify database. Spotify reckons that such information can enable artists to alter the song's offending components to circumvent a lawsuit. The program also tells the users if the composition is wholly new and unique such as not detected in any lead sheets logged with Spotify.
To support artists creating music, services such as IBM Watson Beat, Google Magenta's NSynth Mega, Jukedeck, and Spotify's own Creator Technology Testing Lab are already creating services. Theoretically, there are fears that artificial intelligence, using algorithms to "cram simplistic earworms down our auditory cavities from now until the end of time," might eliminate music's individuality. Artists have pushed back on that definition, though, not since it does not exist, but because it already exists.
Spotify told the publication that not every patent becomes part of its offering but would not say whether it was enforced.
As artificial intelligence is often used to create songs, artificial intelligence to detect copyright infringement in songs could run into a technological arms race.
Others opposed the patent of Spotify as a possible method for the corporation to cover itself rather than musicians, implying that in the case of a lawsuit, the company might use the instrument as a proactive measure to avoid plagiarism, but that artists would possibly find that using the same patented and untested tool would not shield themselves from copyright infringement claims.
The patent filings emphasize a push for an attainable program that any artist or composer could utilize. Plagiarism detection methods that are already in use, 'needs remarkable expertise and are not befitted for operation by generic artists and composers', the filling utters, and 'manual detection of music plagiarism needs substantial efforts, excellent memory, and skill that usually seem impractical'.
On the other hand, this new technology by Spotify 'is a GUI (graphical user interface) that is far more precise, intuitive as to the portion of work that might be regarded as plagiarized and that offers dynamic visual feedback in considerable real-time'.
A spokesperson of the music streaming platform Spotify has not confirmed or gained the integrity of the patent filing in a statement he has given to The Fader, 'Spotify has submitted a patent application for several inventions, and we frequently submit new applications. Some of them become part of future products, while others do not. Our goal is to make the best audio experience for all listeners out there, but we do not possess any news to share at this time publicly'.
Retardation in USA Economy is not going to Hamper Indian IT
Why Is Reading Important for Children?
Incredible Benefits of Using Online Classified Ads

redpajama_set_name: RedPajamaCommonCrawl


Those of you who have coughed up for a Punchline jigsaw and been waiting patiently to pick up their goods can now come and collect their puzzle.
Boxes arrived last week containing the 500-piece Moose Marketing and PR-designed jigsaw, which features 247 faces of business and civic leaders from across Gloucestershire - as featured in this month's edition of our bi-monthly magazine.
Not only does it champion many of the movers and shakers who make the county such a great place to do business, all of the money raised from sales will go to three county charities.
Mark Owen, editor of Punchline-Gloucester.com said: "There has been an unbelievable response to the release of our jigsaw.
"The Punchline team has been out and about delivering magazines across the county and has been bombarded with questions about how and where to get hold of one.
"Each sale guarantees more money being donated to three wonderful charities and I would urge anyone who wants to guarantee themselves a copy to get in touch now, before they're all gone.
"All people have to do to pick them up is drop into our office at The Old Fire Station, Barbican Road, Gloucester (GL1 2JF)."
The jigsaw, that costs just £20, is raising money for three Gloucestershire charities: Sue Ryder, Nelson Trust and Pied Piper Appeal.


"PO PYU KALAY" IS AN UNIQUE ASIAN MANGO FROM THE EXOTIC NATION OF MYANMAR (FORMERLY BURMA). THE LARGE, VIGOROUS TREE PRODUCES SMALL, YELLOW, ELONGATED AND SOMEWHAT POINTED FRUIT WITH A BRIGHT LEMON-YELLOW, MOIST, SPICY FLESH. COMMERCIALLY IT HAS BEEN DUBBED THE "LEMON MERINGUE" MANGO FOR ITS AROMA.


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Lexpert's Top Deals of 2007
Four Bennett Jones deals were recognized in Lexpert's Top 10 Corporate Deals of 2007: The $2.3-billion sale of Alliance Atlantis Communications Inc.'s outstanding shares, Marathon Oil Corp.'s $6.66-billion acquisition of Western Oil Sands Inc., Russian Machines' $1.5-billion investment in Magna International Inc., and Ontario Teachers' Pension Plan in connection with its proposed $266-million investment in the offer made in February 2007 by James Richardson International Limited for Agricore United. The firm also received recognition for its involvement in Royal Dutch Shell plc's $8.7-billion acquisition of the outstanding shares of Shell Canada (the largest going-private transaction in Canada to-date) and SSAB Svenskt Stal AB's US$7.7-billion acquisition of Ipsco Inc.
For more information about the top deals of 2007, please visit www.lexpert.ca.
Harinder S. Basra, Partner
Thomas A. Bauer, Partner
Adam Kalbfleisch, Partner
Jeffrey Kerbel, Partner
Darcy D. Moch KC, Partner
Anu Nijhawan, Partner
William S. Osler KC, Partner
Arthur J. Peltomaa, Partner
John E. Piasta, Partner
Barry J. Reiter, Partner
Gary S.A. Solway, Partner
Robert W. Staley, Vice Chair and Partner
Celebrating our Centennial Chronicle


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To Venus and Back è il quinto album in studio della cantante e compositrice statunitense Tori Amos. L'album è composto da due dischi, l'album in studio (Venus: Orbiting) e un album live (Venus Live: Still Orbiting), il primo pubblicato dall'artista, contenente le esibizioni del Plugged '98 Tour.

Dall'album sono stati tratti quattro singoli: Bliss, Glory of the 80s, 1000 Oceans e Concertina.

Stile
Nell'album è presente un nuovo sound trip hop e il contenuto di canzoni come "Dātura", che usa i rituali sciamanici come metafora per sesso e divinità, lo rendono un album molto originale.
Ma anche in quest'album ci sono molte caratteristiche tipiche degli album della Amos: armonie complesse, testi criptici, le immagini religiose e mitologiche, le canzoni intense e crudi come "Juarez", ispirata dai massacri, stupri e rapimenti delle donne sul confine tra USA e Messico.

Tracce
Disco 1 - Venus: Orbiting

Disco 2 - Venus Live: Still Orbiting

Classifiche

Note

Collegamenti esterni

redpajama_set_name: RedPajamaWikipedia


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IMF Announces New "Precautionary and Liquidity Line"; Fed Discusses More Stimulus; Both Much Ado Over Nothing; Expect Continued Bull Market in Meaningless Headlines
The market spurted higher mid-morning over new and improved credit lines by the IMF, and another never-ending discussion by the Fed about increasing liquidity.
Bloomberg reports IMF Revamps Credit Lines to Lure Nations
The Washington-based IMF today said the new instrument, the Precautionary and Liquidity Line, can be tapped by countries with strong economies currently facing short-term liquidity needs. Countries with potential needs can also apply, as they did in the past under the Precautionary Credit Line that the new instrument replaces.
"The reform enhances the Fund's ability to provide financing for crisis prevention and resolution," IMF Managing Director Christine Lagarde said in an e-mailed statement. "This is another step toward creating an effective global financial safety net to deal with increased global interconnectedness."
The changes, which enable countries that pre-qualify to request IMF funds without having to make as many policy changes as with traditional loans, come as Europe's crisis threatens to spread to Spain and France. The IMF is co-financing bailouts in Greece, Portugal and Ireland and is preparing to send a team to Italy for an unprecedented audit of the country's efforts to cut its debt.
The Standard and Poor's 500 Index pared losses after the report.
Not Big News
Via email, Bank of America / Merrill Lynch says "This is Not Big News"
The IMF has announced some easier access to their limited supply of funds (as below). Despite the eye catching headlines, BofAML do not think that this is particularly new news, nor that financially impactful, unfortunately except possibly for smaller countries and even that is unclear.
Thanos (ex-IMF): Thinks the IMF's PLL is in no way a game changer by itself. The PLL could be used in east Europe. It could also be used in Italy and Spain, but more for its conditionality than for its limited firepower compared to funding needs. And in any case, an SBA or even an EFF would be better for Italy and Spain, as such arrangements have more conditions linked to reforms.
Laurence Boone (Head of Euro Econ): Thinks this does not necessarily mean more money. It means easier access to IMF money. In 2008/09 euro national central banks lent about $75bn to the IMF, a repeat of this lending is something they may or may not be able to repeat this time.
Ardash (BofAML APAC): Points out the PLL was flagged during the G20 summit and mentioned in its communique – officials have already suggested it would be more appropriate for financing needs of smaller countries, rather than the big fish (Italy and Spain).. even 10x quota is simply not enough, let alone judging whether they are committed to "sound policies".
Expect Continued Bull Market in Meaningless Headlines
Note the market continues to move on meaningless headlines. Also note the duration of each move higher keeps getting shorter. That means we can expect a huge bull market in meaningless headlines as EU officials, Eurozone officials, and the IMF keep searching for things to say to placate the markets.
"Lure" the Perfect Word
By the way, Bloomberg's headline title is near-perfect. The phrase "lure nations" is appropriate. "To their economic death" needs to be added.
This is what I think of the IMF as noted in To Ireland With Love.
IMF's Trojan Horse Gift to Ireland
I believe we have all heard the story and know how it ends.
Click Here To Scroll Thru My Recent Post List
Mind The Rent!
Rising Yields Push Investors Toward Bank Loan and Inflation Protected Bond Funds for the Week
Consumers, Producers, and the Unsettled End of 2020
"All Hands On Deck" - Up To 25,000 National Guard Now Authorized In DC For Biden Inauguration


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\section{Introduction}

Submesoscale processes, i.e., with length scales of 0.1--10 km
\citep{Thomas-etal-08}, are believed to be important in the upper
ocean \citep[][]{McWilliams-08a, Klein-09}.  These are the transition
scales between the largely balanced quasi-2D flows at the mesoscales
and 3D (unbalanced) flows at smaller scales.  While observational
evidence of submesoscale activity in the ocean is accumulating,
important questions about their dynamics and the consequences for
transport remain.

In the atmosphere, the balanced scales are characterized by a kinetic
energy spectrum proportional to $k^{-3}$, where $k$ is the horizontal
wavenumber \citep{Nastrom-Gage-85}.  The consensus is that this
reflects a quasi-2D enstrophy cascade toward smaller scales
\citep{Kraichnan-67, Charney-71}. At scales of several hundred
kilometers, the spectrum transitions to a $k^{-5/3}$ dependence.
This primarily reflects divergent motions (inertia--gravity waves),
at scales where the Rossby number exceeds one \citep{Callies-etal-14}.
\citet{Callies-Ferrari-13} suggest a similar situation exists in
the ocean.

The slope of the energy spectrum is important for Lagrangian transport
\citep[e.g.,][]{Bennett-06, LaCasce-08}. With a $-5/3$ slope the
dispersion of pairs of particles (or ``relative dispersion'') is
\emph{local}, meaning separations between pairs of particles are
dominated by eddies of comparable scales. With a $-3$ or steeper
slope the dispersion is \emph{nonlocal} and governed by the largest
eddies in the $k^{-3}$ range.  Local dispersion results in small
scale ``billowing,'' as with smoke from a stack, while nonlocal
dispersion produces filaments.  Particle dispersion can thus be
used to infer aspects of the energy spectrum, which can be useful
in the ocean at scales below those resolved by satellite altimetry.

Hereafter we examine relative dispersion at the surface of the Gulf
of Mexico (GoM).  The study was motivated by the Grand LAgrangian
Deployment (GLAD), which was conducted in the vicinity of the
\emph{Deepwater Horizon} (DwH) site in July 2012 and in which a
large number of surface drifters were deployed \citep{Olascoaga-etal-13,
Poje-etal-14, Jacobs-etal-14, Coelho-etal-15}.  A primary goal of
GLAD was to study dispersion at the submesoscales in the GoM.

Relative dispersion in the GoM has been studied previously.
\citet{LaCasce-Ohlmann-03} examined ``chance pairs'' of drifters
(i.e., drifters not deployed together) from the Surface-CUrrent and
Lagrangian drifter Program (SCULP) \citep{Ohlmann-Niiler-05} and
found nonlocal dispersion below the deformation radius, $L_\mathrm{D}$,
which is approximately 45 km in the GoM \citep{Chelton-etal-98}.
Supporting evidence, using pair separation probability distribution
functions (PDFs), was obtained by \citet{LaCasce-10}.  However,
using different measures (the second order longitudinal velocity
structure function and the separation-averaged relative diffusivity)
with the GLAD drifters, \citet{Poje-etal-14} concluded the dispersion
was local, from few hundred meters to several hundred kilometers,
implying a shallower kinetic energy spectrum.

Relative dispersion is often studied using two types of measures
\citep{LaCasce-08}. The first treats \emph{time} as the independent
variable. This includes the relative dispersion (the mean square
pair separation), the kurtosis (the normalized fourth moment) and
the separation PDF. The second type uses \emph{distance} as the
independent variable. This includes the structure functions, the
separation-averaged relative diffusivity and the finite-scale
Lyapunov exponent (FSLE) \citep{Artale-etal-97, Aurell-etal-97}.
The two types often produce different results, but the reasons for
this are rarely examined.

In the present paper, we examine both types of statistics, using
synthetic particles and drifters in the GoM.  The former were
obtained by integrating surface velocities produced by a data-assimilative
simulation with the 1-km-resolution Navy Coastal Ocean Model (NCOM)
\citep{Jacobs-etal-14}, and the latter are the drifters in the GLAD
experiment. The model allows for large numbers of particles,
increasing statistical reliability, whereas the drifters more
accurately reflect the actual situation in the GoM.

The paper is organized as follows.  In Section 2 and Appendix A we
present relevant theory for pair-separation statistics.  In Section
3 we examine the NCOM pair separations, and the GLAD pairs in Section
4.  A summary and concluding remarks are offered in Section 5.
Details of the numerical simulation and the GLAD experiment are
given in Appendices B and C, respectively.

\section{Theory}\label{sec:theory}

Let $r_0$ be the distance between two fluid parcels at time $t =
0$ and $r$ be the separation at time $t$.  In homogeneous, stationary,
and isotropic 2D turbulence, the PDF of pair separations, $p(r,t)$,
obeys a Fokker--Planck equation:
\begin{equation}
  \partial_t p = r^{-1} \partial_r(r\kappa_2 \partial_r p),
  \label{eq:fp}
\end{equation}
where $\kappa_2(r)$ is the scale ($r$) dependent relative diffusivity.
The 3D version of \eqref{eq:fp} was proposed by \citet{Richardson-26}
to describe smoke dispersion in the atmospheric boundary layer.
Richardson obtained a self-similar solution, based on an empirical
diffusivity derived from observations.  The equation was later
derived by \citet{Kraichnan-66} using his ``abridged Lagrangian
history direct interaction approximation'' and by \citet{Lundgren-81},
assuming an advecting velocity with a short correlation time. For
an overview, see \citet[Chapter 11]{Bennett-06}.

Pair dispersion depends on whether the pair velocities are correlated
or not, specifically whether the normalized Lagrangian velocity
correlation
\begin{equation}
  \frac{2\langle v_i \cdot v_j \rangle}{\langle v_i^2 \rangle +
  \langle v_j^2 \rangle} = 1 - \frac{\langle (v_i - v_j)^2
  \rangle}{\langle v_i^2 \rangle + \langle v_j^2 \rangle}
  \label{eq:corr}
\end{equation}
(where the angle bracket indicates statistical average) equals 1
or 0, respectively \cite[e.g.,][]{Koszalka-etal-09}.
The second term on
the right side is proportional to the
second-order velocity structure function,
\begin{equation}
  S_2(r) := \langle v^2 \rangle \equiv \langle (v_i - v_j)^2
  \rangle,
  \label{eq:s2}
\end{equation}
where $v$ is the difference in the Eulerian velocity between points
separated by a distance $r$.  The Eulerian--Lagrangian equivalence
in \eqref{eq:s2} is a distinguishing aspect of homogeneous, isotropic
turbulence \citep{Bennett-84}.

At large separations, when the pair velocities are uncorrelated,
the relative diffusivity $\kappa_2$ is constant and equal to twice
the single particle diffusivity. At smaller scales, $\kappa_2$ can
be inferred if the energy spectrum has a power law dependence, i.e.,
$E(k) \propto k^{-\alpha}$ \citep{Bennett-84}.  In either case
equation (\ref{eq:fp}) can then be solved \citep{Bennett-06}.
Relevant 2D solutions are given in \citet{LaCasce-10} and
\citet{Graff-etal-15}, and are reproduced in Appendix A. From these,
the (raw) statistical moments, given by
\begin{equation}
  \langle r^n \rangle := 2\pi \int_0^\infty
  r^{n+1}p(r,t)\,\mathrm{d}r,
  \label{eq:mom}
\end{equation}
can be calculated.  Table \ref{tab:sum} shows the time dependences
for $\langle r^2 \rangle$ (the relative dispersion) and the $\langle
r^4 \rangle/\langle r^2 \rangle^2$ (kurtosis) in the three specific
2D dispersion regimes considered here.

\begin{table}
  \caption{The pair-separation measures in the three regimes
  considered here.  The measures are the kinetic energy spectrum,
  $E(k)$, where $k$ is wavenumber; the two particle diffusivity,
  $\kappa_2(r)$, where $r$ denotes separation; the second-order
  longitudinal structure function, $S_2(r)$; the relative dispersion,
  $\langle r^2 \rangle$; and the separation kurtosis, $\langle r^4
  \rangle/\langle r^2 \rangle^2$. The latter two are based on the
  (raw) statistical moments of the time-dependent probability
  distribution function (PDF) of pair separations, obeying \eqref{eq:fp}.
  The results shown for the Richardson and Rayleigh cases are the
  asymptotic (long time) limits.} \label{tab:sum}
  \begin{center}
  \begin{tabular}{lcccc}
  \topline & Lundgren & Richardson & Rayleigh \\ \midline $E(k)$ &
  $\propto k^{-3}$ & $\propto k^{-5/3}$  & --   \\ $\kappa_2(r)$ &
  $=r^2/T$ & $=\beta r^{4/3}$ & $= \mathop{\rm const}$ \\ $S_2(r)$      &
  $\propto r^2$ & $\propto r^{2/3}$  & $= \mathop{\rm const}$ \\ $\langle r^2
  \rangle$ & $= r_0^2 \mathrm{e}^{8t/T}$ & $\sim 5.2675 \beta^3
  t^3$  & $\sim 4 \kappa_2 t$ \\ $\langle r^4 \rangle/\langle r^2
  \rangle^2$ & $= \mathrm{e}^{8t/T}$ & $\sim 5.6$ & $\sim 2$ \\
  \botline
  \end{tabular}
  \end{center}
\end{table}

The nonlocal regime [which we refer to as the ``Lundgren regime,''
after \citet{Lundgren-81}] corresponds to an energy spectrum at
least as steep as $k^{-3}$, with a structure function $S_2 \propto
r^2$.  The PDF is not self-similar, but rather becomes more and
more peaked. Both the dispersion and kurtosis increase exponentially
in time.  The local regime we will consider has a Kolmorogorov
energy spectrum, $E \propto k^{-5/3}$, or equivalently $S_2 \propto
r^{2/3}$, and referred as the ``Richardson regime'' after
\citet{Richardson-26}.  In this case the separation PDF asymptotes
to a self-similar form, with a kurtosis of 5.6, and the dispersion
increases as time cubed.  With uncorrelated pair velocities, the
second-order structure function is constant with separation (and
equal to twice the mean square single particle velocity). The PDF
also asymptotes to a self-similar form, with kurtosis of 2 and the
dispersion increasing linearly in time. This self-similar PDF is a
Rayleigh distribution, so we refer to this as the ``Rayleigh regime.''

\section{Simulated pair-separation statistics}

The simulated trajectories were constructed by integrating surface
velocities produced by an NCOM simulation (cf.\ Appendix B).  The
integrations were carried out using a stepsize-adapting fourth/fifth-order
Runge--Kutta method with interpolations obtained using a cubic
scheme.  One-month-long records, with 10 positions per day, were
produced with a range of initial separations, from the smallest
scale resolved by the model simulation up to 30 km ($r_0 =$ 1, 5,
10 and 30 km).  The trajectories were initiated every other day in
the northern GoM near the DwH site, in two $5 \times 5$ 100-km-width
grids displaced by the chosen separation.  The reference and auxiliary
grids with $r_0 = 1$ km are shown in \figref{fig:ics}.  The
trajectories were started 1 July 2013 and 1 February 2014 to survey
summer and winter conditions.  The two were expected to exhibit
different pair-separation statistics, as the mixed layer is deeper
in winter.

\begin{figure}
  \centerline{%
  \includegraphics[width=.475\textwidth]{sepgom-ics}
  \caption{The rectangles indicate the boundaries of the grids of
  initial positions for the integration of trajectory pairs (with
  $r_0 = 1$ km initial separation) using surface velocities produced
  by the 1-km-resolution Navy Coastal Ocean Model (NCOM) simulation
  of the Gulf of Mexico (GoM).  Dots indicate deployment locations
  of drifters from the Grand LAgrangian Deployment (GLAD).}
  \label{fig:ics}%
\end{figure}

However, snapshots of the instantaneous surface vorticity
(\figref{fig:vor}) reveal roughly the same range of eddy scales in
the two seasons. The results seen hereafter similarly show only
small changes with season.  These figures also reveal that the West
Florida Shelf and the Bay of Campeche are relatively eddy inactive
regions, and that an anticyclonic ring has pinched off from the
Loop Current. Apart from these regions however the eddy field does
not exhibit significant spatial variability.  Thus we assume
homogeneity holds fairly well, as assumed in Section
\ref{sec:theory}.

\begin{figure}
  \centerline
  \includegraphics[width=.475\textwidth]{sepgom-vor}}%
  \caption{Snapshots of surface vorticity (normalized by
  the mean Coriolis parameter in the GoM) from the NCOM simulation
  in summer (top) and winter (bottom).}
  \label{fig:vor}%
\end{figure}

An additional theoretical prerequisite is stationarity.  While
temporal variability of the simulated background eddy field is
evident, this mainly manifests on seasonal timescales.  Therefore,
considering motion over a period of 1 month, as we do here, is not
restrictive but rather necessary for stationarity to be fairly well
guaranteed.

Isotropy, the remaining prerequisite, is also realized. This can
be seen by plotting the ratio of the zonal to the meridional relative
dispersion ratio as a function of scale \citep{Morel-Larcheveque-74},
as shown in \figref{fig:iso}.  Isotropy holds in both summer (solid)
and winter (dashed), irrespective of the initial pair separation.
At separations exceeding 100 km, the dispersion becomes zonally
anisotropic, as it does in the atmosphere \citep{Graff-etal-15}.
But below that, the dispersion is isotropic.

\begin{figure}
  \centerline{%
  \includegraphics[width=.475\textwidth]{sepgom-iso}}%
  \caption{Zonal-to-meridional relative dispersion ratio as a
  function of pair separation in summer (solid) and winter (dashed)
  based on simulated trajectory pairs with various initial separations.
  The vertical line indicates the gravest baroclinic Rossby deformation
  radius.}
  \label{fig:iso}%
\end{figure}

We then determine over which scales the pair motion is correlated.
Inspection of \figref{fig:cor} reveals that, fairly insensitive to
the initial pair separation, the motion is correlated below the
deformation radius, in both seasons. At $L_\mathrm{D}$, the correlation
is roughly 0.5. The motion is strongly correlated below 20 km and
decorrelated above 100 km. Thus the proper framework for interpretation
above 100 km is absolute dispersion, possibly with the inclusion
of a mean zonal shear.

\begin{figure}
  \centerline{%
  \includegraphics[width=.475\textwidth]{sepgom-cor}}%
  \caption{The normalized Lagrangian velocity correlation as function
  of scale in summer (solid) and winter (dashed) for various initial
  separations in the NCOM simulation.  The vertical line indicates
  the Rossby deformation radius.}
  \label{fig:cor}%
\end{figure}

We now inspect the pair separation PDFs and compare them to the
theoretical predictions (\figref{fig:pdf}). We calculated the PDFs
using kernel density estimation as implemented in Matlab's function
\texttt{ksdensity} with positive support.  Each theoretical PDF has
two parameters: the initial separation, $r_0$, and a growth parameter.
Since all pairs have the same initial separation, we assume $r_0$
is the same as in the simulation.  The growth parameters for the
Lundgren and Richardson distributions ($T$ and $\beta$, respectively)
were determined by fitting the dispersion using least squares during
the initial period, up to the point when the root-mean-squared (rms)
separation was a factor $a$ greater than the initial value.  We
chose $a = 5$, but the results are fairly insensitive to the choice.
The parameter for the Rayleigh PDF ($\kappa_2$) was calculated from
the relative dispersion at late times, after the pair motion was
decorrelated, as described in Appendix A.

\begin{figure}
  \centerline{%
  \includegraphics[width=.475\textwidth]{sepgom-pdfks-ksdens}}%
  \caption{(top) Pair separation probability distribution
  functions (PDFs) in summer (red) and winter (blue) for various
  initial separations.  The PDFs are shown at time $t = 3.5$ d.
  Solid and dashed, and dot-dashed curves are theoretical PDFs
  in the Lundgren, Richardson, and Rayleigh regimes,
  respectively. Parameters $T$ (with units d$^{-1}$) and $\beta$
  (with units km$^{2/3}$d$^{-1}$) for the Lundgren and
  Richardson PDFs, respectively, were obtained by comparing the
  theoretical and observed dispersion curves via least squares
  out to the time by which $\sqrt{\langle r^2\rangle} = 5r_0$.
  The relative diffusivity $\kappa_2$ (with units
  km$^2$d$^{-1}$) for the Rayleigh distribution was calculated
  as the mean of the relative dispersion divided by $4t$ after
  $t = 10$ d (Appendix A).  When a theoretical curve is
  statistically similar to the observed PDF in summer at the
  95\%{ } confidence level, it is drawn in bold.  (bottom) The
  Kolmogorov-Smirnov probability for the theoretical curves vs
  the summer PDF as a function of time.}
  \label{fig:pdf}%
\end{figure}

The PDFs are plotted with the theoretical curves at $t = 3.5$ d.
Several initial separations are used, for particles deployed in summer
(in red) and winter (in blue), and the parameters obtained for the
theoretical curves are indicated in the inserts.  The observed and
theoretical PDFs were compared using the Kolmogorov--Smirnov (KS)
statistic \cite[cf., e.g.,][]{Press-etal-07}; since the winter and
summer distributions are so similar, we used the summer PDF for
this. The degrees of freedom for the KS test are determined by the
number of independent pairs. The pairs were deployed every 2 d and
100-km apart in the present simulation, so we can safely treat all
pairs as independent.  In the figure, the bold curve is statistically
similar to the observed summer PDF, with 95\%{ } confidence. The lower
panels show how the KS probability evolves with time, over the first
15 days. When a curve exceeds 0.05, it is plotted in bold.

Consider the case with $r_0 = 1$ km initial separation. The summer
and winter PDFs are very similar and are highly kurtosed, with most
pairs having small separations but some having much larger ones.
The Lundgren distribution (solid) has a similar shape, and indeed
is statistically the same at the 95\%{ } confidence level.  In
contrast, the Richardson (long-dashed) and Rayleigh (short-dashed)
distributions have a shorter tail and much larger mode, respectively.
The KS probability (lower panel) though suggests the Lundgren PDF
is significantly similar only during a brief period, near $t = 3$
d.

The results with $r_0 = 5$ and $10$ km are similar, in that observed
PDFs resemble the Lundgren distribution. The similarity moreover is
significant at the 95 \%{ } level for much of the first 10 d. The
Richardson PDF on the other hand is not similar over the same period.
With $r_0 = 30$ km, the PDF is statistically similar to the Lundgren
only briefly, but then resembles the Richardson. However, recall
that 30 km is only slightly less than the deformation radius, when
the pair velocities are significantly decorrelated. We do not find
similarity with the Rayleigh distribution in any case, during these
initial 15 d.

The relative dispersion curves are shown in \figref{fig:r2}. The
winter (red) and summer (blue) curves are nearly identical, again
supporting similar behavior in the two seasons. The initial growth is
close to exponential initially, with an e-folding time on the order of
1 d. The exception is the $r_0 = 30$ km case, where the separations
are only briefly below the deformation radius (indicated by the
horizontal line). With the two larger initial separations, the late
dispersion increases linearly, in line with diffusive growth, but this
is not apparent in the 1 and 5 km cases. There is a clear suggestion
of Richardson-like growth with $r_0 = 10$ km, but in the other cases
the dispersion is either greater or less than this.

\begin{figure}
  \centerline{%
  \includegraphics[width=.475\textwidth]{sepgom-r2}}%
  \caption{Relative dispersion (second moment of the pair-separation
  PDF) in summer (red) and winter (blue) for the NCOM pairs with
  various initial separations.  The Lundgren and Richardson predictions
  are indicated in solid and long-dashed curves, respectively.  The
  short-dashed line is the long-time asymptotic Rayleigh relative
  dispersion.  The horizontal dashed line indicates the deformation
  radius. Note that the $t$-axis is logarithmic until $t = 10$ d
  and linear thereafter.}
  \label{fig:r2}%
\end{figure}

Being the fourth moment of the PDF, the kurtosis (\figref{fig:r4}) is
more sensitive to the tails of the distribution. With the smallest
initial separation ($r_0 = 1$ km), the kurtosis grows rapidly,
reaching values greater than 20, in both seasons.  Under nonlocal
dispersion the kurtosis grows exponentially and at the same rate as
the dispersion (Table \ref{tab:sum}). The observed growth is roughly
consistent with this, with an e-folding time of roughly 1 d.  With
$r_0 = 5$ km, the initial growth is curtailed and the maximum values
obtained are less. With $r_0 = 10$ and 30 km, the kurtosis quickly
relaxes toward 2, the asymptotic limit for the Rayleigh
distribution. There is little support for a Richardson regime here;
the kurtosis exceeds the asymptotic limit of 5.6 at the smallest
separations and falls below that at the larger separations.

\begin{figure}
  \centerline{%
  \includegraphics[width=.475\textwidth]{sepgom-r4}}%
  \caption{Kurtosis (normalized fourth moment of the pair-separation
  PDF) in summer (red) and winter (blue) for the NCOM pairs with
  various initial separations.  The Lundgren and Richardson curves
  are indicated by the solid and long dashed curves, respectively.
  Parameter-independent long-time asymptotic limits in the Rayleigh
  and Richardson regimes are indicated by the short- and long-dashed
  horizontal lines. As in the previous figure, the $t$-axis is
  logarithmic until $t = 10$ d and linear thereafter.}
  \label{fig:r4}%
\end{figure}

The velocity structure functions ($S_2$) are shown in \figref{fig:s2}
for summer (solid) and winter (dashed) pairs.  These are very
similar, flattening out at scales exceeding 100 km, as expected for
uncorrelated motion.  With $r_0 = 1$ km, $S_2$ exhibits the $r^2$
dependence expected in a nonlocal regime at the smallest separations.
With larger $r_0$ the curves do not have a unique power-law-dependence
but suggest instead a transition between the $r^2$ and $r^0$
asymptotic limits. We also calculated the Eulerian $S_2$ using
velocity time series at fixed positions (curves with circles), and
this mirrors the Lagrangian $S_2$ well, supporting the assumptions
of homogeneity and isotropy.

\begin{figure}
  \centerline{%
  \includegraphics[width=.475\textwidth]{sepgom-s2}}%
  \caption{Second order structure functions in summer (solid) and
  winter (dashed). Colored curves are Lagrangian estimates for
  different initial separations.  The curves with circles are
  Eulerian estimates.  Solid and dashed straight lines have structure
  function slopes (indicated) in the theoretical Lundgren and
  Richardson regimes, respectively. The vertical line indicates the
  Rossby deformation radius.}
  \label{fig:s2}%
\end{figure}

Thus both the time- and distance-averaged measures indicate nonlocal
dispersion at the smallest separations and uncorrelated motion above
100 km. There was some suggestion of an intermediate Richardson regime
(primarily in the dispersion), but the kurtoses and structure
functions imply these scales are rather a transition between the small
and large scale limits.

One wonders of course to what extent numerical dissipation in the
model is responsible for the nonlocal dispersion at the smallest
scales.  So we turn to the GLAD drifters, which are not so affected.

\section{Observed pair-separation statistics}

The GLAD pairs were obtained from quarter-hourly drifter positions
from the GLAD experiment (cf.\ Appendix C).  The drifters were
deployed near the DwH site, as indicated by the black dots in
\figref{fig:ics}.  Various initial separation classes were identified:
$r_0 \approx$ 0.15, 1, and 10 km. A total of 132, 127, and 276
original pairs were obtained in each class. \footnote{The specific
initial separation ranges are: $0.12\text{ km} < r_0 < 0.19\text{
km}$, $0.84\text{ km} < r_0 < 1.19\text{ km}$, and $9.85\text{ km}
< r_0 < 10.19\text{ km}$.}  As in \citet{Poje-etal-14}, we consider
trajectory records spanning the initial 25 d after deployment, to
avoid enhanced windage effects on the drifters during the passage
of hurricane \emph{Issac}.

As the trajectories span no more than one month, we assume stationarity
holds. Homogeneity cannot be determined with the available data,
but the NCOM results suggest this is not an unreasonable assumption.
Isotropy is found for separations less than about 100 km or so
(\figref{fig:isocor-glad}, top panel). Furthermore, the pair
velocities are correlated over the isotropic scales, with correlations
falling below 0.5 above 100 km (\figref{fig:isocor-glad}, bottom
panel).

\begin{figure}
  \centerline
  \includegraphics[width=.475\textwidth]{sepgom-isocor-glad}}%
  \caption{As in Figs.\ \ref{fig:iso} (top) and \ref{fig:cor}
  (bottom) but based on GLAD trajectory pairs in three
  initial separation classes.}
  \label{fig:isocor-glad}%
\end{figure}

The time-based statistics are shown in \figref{fig:pdfr2r4-glad}.
The parameters for the theoretical curves were obtained as before,
by matching the observed dispersion from the initial separation up
to the scale at which the rms separation $\sqrt{\langle r^2 \rangle}
= 5 r_0$. In principle one could also treat the initial separation
as a free parameter, since a range of initial values is present,
but we chose to set $r_0$ equal to the mean value for the drifters
in each chosen range.

\begin{figure}
  \centerline{%
  \includegraphics[width=.475\textwidth]{sepgom-pdfksr2r4-glad-ksdens}}%
  \caption{As in Figs.\ \ref{fig:pdf} (first and second rows),
  \ref{fig:r4} (third row), and \ref{fig:r2} (fourth row) but for
  separations experienced by the raw (red) and lowpass-filtered (blue)
  GLAD trajectory pairs.  The cut-off period for the filter is 2.5 d.}
  \label{fig:pdfr2r4-glad}%
\end{figure}

The GLAD PDFs 3-d after deployment are shown in red in the top panels
of \figref{fig:pdfr2r4-glad} for the 3 initial separations above.  The
PDFs are somewhat coarser than for the synthetic particles as there
are fewer pairs, but they too are peaked at the smallest separations
and exhibit extended wings.

Again, assessing the differences with the theoretical PDFs requires
knowing the number of degrees of freedom, i.e., the number of
independent realizations.  However this number was fairly small for
the GLAD experiment, as the deployment was made over a limited
geographical area.  Drifter clusters were deployed very near one
another, so that the distance between different clusters was often
much less than the putative energy-containing eddy scale of 100 km.
As such, many of the pair trajectories are similar.

In fact the trajectories can be grouped into 6 classes, as shown in
\figref{fig:pairs}. The numbers of pairs ($N$) in each group are
indicated in the inserts, and these range from 13 to 29. As most of
the drifters in each group were deployed on a single day, these
obviously should not be considered as independent realizations.  The
exception was the $N = 17$ group, which were launched on two different
days. Thus the number of independent realizations here is only 7, 1
for each class and 2 for the $N = 17$ group. However, allowing for
some variation in each group, we estimated the degrees of freedom as 3
times this, or 21. As such, we effectively treat each group as a
triplet of drifters.

\begin{figure}
  \centerline{%
  \includegraphics[width=.475\textwidth]{sepgom-pairs}}%
  \caption{GLAD trajectory pairs with initial separation $r_0 \approx
  1$ km arranged into groups exhibiting similar behavior.  The
  number ($N$) of pairs in each group is indicated.}
  \label{fig:pairs}%
\end{figure}

With so few degrees of freedom, one cannot distinguish the theoretical
curves at the 95\%{ } confidence level. Thus both the Lundgren and
Richardson PDFs are statistically similar over the initial 10 d, with
all three separations. Only the Rayleigh distribution can be excluded
during this period.

The relative dispersion is indicated by the red curves in the third
row of panels in \figref{fig:pdfr2r4-glad} (the curves are often
obscured by blue curves indicating the dispersion for a lowpass
filtered data set, discussed hereafter).  The dispersion with the
smallest initial separation is close to exponential initially but
increases more slowly after $t = 2$ d. With $r_0 = 1$ km however the
dispersion follows the Richardson prediction over much of the first 20
d. With this separation and $r_0 = 10$ km, the dispersion asymptotes
to linear growth at late times.

The kurtoses are plotted in red in the bottom panels of
\figref{fig:pdfr2r4-glad}.  With $r_0 = 0.15$ km the kurtosis grows
and then oscillates around the Richardson asymptotic limit of 5.6.
With $r_0 = 1$ km, the kurtosis increases more slowly, lying between
the asymptotic limits for the Richardson and Rayleigh regimes, while
the kurtosis is close to the latter limit for most of the period
with $r_0 = 10$ km.

The second-order structure functions (\figref{fig:s2-glad}, solid
curves) on the other hand are clearly suggestive of a Richardson
regime.  With the $r_0 = 0.15$ km pairs, the curve exhibits a
power-law-dependence near $r^{2/3}$ from the smallest scales to
roughly 200 km, consistent with the results of \citet{Poje-etal-14}.
However, with $r_0 = 10$ km a plateau is observed above 100 km, in
agreement with the motion being largely uncorrelated at those scales.

\begin{figure}
  \centerline{%
  \includegraphics[width=.475\textwidth]{sepgom-s2-glad}}%
  \caption{As in \figref{fig:s2} but using raw (solid) and lowpassed
  (dashed) GLAD trajectory pairs.}
  \label{fig:s2-glad}%
\end{figure}

Thus the GLAD results are ambiguous. The PDFs are inconclusive, due to
having too few degrees of freedom. The dispersion curves suggest
nonlocal dispersion at small scales while the kurtosis and the
structure functions are more consistent with a Richardson regime. What
causes these differences among the measures, and are the results
actually different than those from the synthetic pairs?

\subsection{Inertial oscillations}

One important difference can be seen in the trajectories themselves
(\figref{fig:pairs}). Many of the GLAD drifters experience inertial
oscillations: anticyclonic loops with a period near 1 d (the local
inertial period) \cite[cf., e.g.,][]{Gill-82}.  Frequency spectra
of the individual velocities, as in the example in \figref{fig:Puu},
exhibit a significant peak at the inertial period (right).  Except
for this, the energy resides primarily at the lowest frequencies.
Consistently, the trajectory (left) exhibits anticyclonic loops
superimposed on a larger scale structure.

\begin{figure}
  \centerline{%
  \includegraphics[width=.475\textwidth]{sepgom-Puu}
  \caption{(left) Raw (red) and lowpassed (blue) GLAD drifter
  trajectory.  (right) Corresponding zonal velocity power
  spectra.}
  \label{fig:Puu}%
\end{figure}

While inertial oscillations have a narrow frequency spectrum [unless
modified by background rotation \citep[e.g.,][]{Kunze-85}], the
Lagrangian motion possesses a range of spatial scales. These are
determined by the particle velocity, with faster-moving particles
executing larger loops. So the spectral profile in wavenumber space
is broader; as such, the oscillations could potentially influence the
separation statistics.

To test this, we applied a lowpass filter to remove the inertial
oscillations.\footnote{The filter was a sixth-order lowpass Butterworth
filter with 2.5 d$^{-1}$ cut-off frequency.} The resulting spectrum
and the corresponding trajectory are shown in blue in \figref{fig:Puu}.
The filter eliminates the peak near the inertial frequency while
preserving the larger meandering motion.

Lowpass filtering has relatively little effect on the time-based
dispersion measures. The blue curves in \figref{fig:pdfr2r4-glad}
correspond to the filtered GLAD trajectories, and in all cases these
mirror the results for the unfiltered trajectories. This is because
the inertial oscillations on nearby drifters are very similar (see
below) and thus do not greatly alter their separation. Moreover, as
the drifters return approximately to their previous positions every
inertial period, the net effect is small.

The impact on the velocity structure function however is greater
(\figref{fig:s2-glad}). With the lowpass filter (dashed curves),
the energy at small scales is reduced and the structure function
increases faster than $r^{2/3}$.

Inertial oscillations are only weakly captured in the NCOM simulation,
so this effect is missed in the synthetic trajectories, which are
furthermore computed from daily velocities.  To test how they would
have altered the statistics, we \emph{added} inertial oscillations
to the NCOM trajectories. This was done by modifying the $i \neq
j$ positions as
\begin{align}
  x_i(t) &\mapsto x_i(t) + A (\sin\omega t, \cos\omega t - 1)\\
  x_j(t) &\mapsto x_j(t) + \left(A + B(r_{ij})\right) (\sin\omega t, \cos\omega t - 1).
  \label{eq:nio}
\end{align}
Here $2\pi/\omega = 1$ d, roughly equal to the local inertial period.
The amplitude, $A$, was taken to be a random number varying over
the range of observed loop amplitudes. The amplitude $B(r_{ij}(t))$
represents the growing difference between amplitudes on nearby
drifters.

The latter was chosen to mimic the behavior of the GLAD pairs.  The
inertial wave scale is generally much larger than the smallest pair
separations here \citep[e.g.,][]{Webster-68, Pollard-80, Young-Jelloul-97,
Chant-01}.  Consistently, the high-passed pair velocities decorrelate
on scales comparable to those of the full velocities (not shown),
indicating scales of at least 100 km. As the pair velocities are
similar for nearby drifters, the loops are correlated and similarly
large.  But as the drifters separate, the difference in loop amplitude
grows as the velocity difference grows.  To gauge this, we calculated
the rms difference in the highpass filtered pair separation and
plotted it against the rms pair separation, determined from the
lowpass filtered trajectories.  This is shown in black in the left
panel of \figref{fig:nio-r2pair}.  The rms difference is roughly
0.5 km initially and increases to a value near 2 km at separations
greater than 20 km.

\begin{figure}
  \centerline{%
  \includegraphics[width=.475\textwidth]{sepgom-nio-r2pair}}%
  \caption{(left) The root-mean-squared (rms) separation for
  highpass-filtered GLAD trajectory pairs (black) plotted against
  the rms separation of the lowpass-filtered trajectories.  The red
  curve is an empirical fit used to determine the difference in
  amplitude of the artificial near-inertial oscillations imposed
  on the NCOM trajectories.  The GLAD trajectories belong to the
  $r_0 \approx 1$ km initial separation class and the NCOM trajectories
  start at GLAD positions.  (right) An example of an NCOM pair,
  without (blue) and with (red) the near-inertial oscillations
  superimposed.}
  \label{fig:nio-r2pair}%
\end{figure}

Choosing $B(r_{ij}(t)) = B_0\sqrt[4]{r_{ij}(t)/r_0}$ with $B_0 =
3/4$ yields the separation curve shown in red. This mimics the
observed growth fairly well. The effect of the addition on a single
pair is shown in the right panel, with the modified trajectories
exhibiting anticyclonic loops.

The effect on the synthetic particle statistics is seen in the
middle panels of \figref{fig:nio-pdfr2r4s2}. These are for a set
of NCOM trajectories initiated at the GLAD launch positions, with
$r_0 = 1$ km.  The blue curves are for the unmodified trajectories
and the red have the inertial oscillations superimposed.  The PDFs,
relative dispersion, and kurtosis are almost unaffected by the
addition of the oscillations. But the structure function is
significantly altered, with that for the modified trajectories
exhibiting more energy at subdeformation scales. While $S_2$ increases
as $r^2$ for the original trajectories, the dependence for the
modified set is nearer $r^{2/3}$.

\begin{figure}
  \centerline{%
  \includegraphics[width=.475\textwidth]{sepgom-nio-pdfr2r4s2-ksdens}
  \caption{Separation PDFs (top), relative dispersion (second row),
  kurtosis (third row), and velocity structure function (bottom)
  for: NCOM pairs at $r_0 = 1$ km separation, as shown in Figs.\
  \ref{fig:pdf}--\ref{fig:s2}, for comparison (left);  NCOM
  trajectories started from the GLAD positions with $r_0 \approx
  1$ km (middle);  and actual GLAD trajectories with $r_0 \approx
  1$ km  (right).  In blue are results based on NCOM trajectories
  or lowpassed GLAD trajectories.  In red are results based on NCOM
  trajectories with near-inertial oscillations superimposed or raw
  GLAD trajectories.  In green are results based on highpassed
  trajectories.}
  \label{fig:nio-pdfr2r4s2}%
\end{figure}

Shown in green are the statistics for the inertial oscillations
alone, obtained from the trajectories following highpass filtering
(with a cut-off of 2.5 d). These show that the contributions to the
dispersion and kurtosis from the inertial oscillations are much
less than from the low frequency components. But below separations
of roughly 20 km, the inertial component dominates the second order
structure function.

We find that adding the oscillations affects other distance-based
measures as well, such as the relative diffusivity and the FSLE
(not shown).  But as they do not significantly alter the time-based
metrics, they cannot explain the other differences between the GLAD
and NCOM statistics.

\subsection{Sampling}

The second factor influencing the GLAD results is the sampling
strategy alluded to earlier. Most of the GLAD pairs were deployed
very near one another and behaved similarly. This reduced the
effective degrees of freedom, and the mesoscale dispersion was
not captured well.

The effect can be assessed by comparing in \figref{fig:nio-pdfr2r4s2}
the statistics for the $r_0 = 1$ km NCOM pairs deployed at the GLAD
locations (middle) with those from the full NCOM deployment (left)
and the GLAD set (right).  The statistics for the reduced NCOM set
are strikingly similar to those from GLAD, both the time- and the
distance-based measures.  The kurtoses are somewhat lower with the
GLAD drifters, and the transition scale below which the structure
function from the highpassed velocities crosses that from the
lowpassed velocities is smaller (10 vs 20 km). But the addition or
removal of inertial oscillations otherwise affects the trajectories
in the same ways.  And the results from both sets differ markedly
from those for the full NCOM set.

This implies the differences between the GLAD statistics and those
of the full NCOM set may be due to sampling rather than to dynamics.
With identical sampling, the NCOM model gives an accurate representation
of the dispersion and the structure function. This is remarkable,
given that the model resolution is only 1 km.  The reason however
can be inferred from the frequency spectrum in \figref{fig:Puu}:
except for the peak at the inertial frequency, the spectrum is
dominated by low frequency motions. It is these motions, due to
mesoscale features, which dominate the pair dispersion, and these
are captured by the model. This is the essence of nonlocal
dispersion---it is controlled by structures with larger scales and
lower frequencies.

\section{Summary and concluding remarks}

We have investigated the dispersion experienced by simulated and
observed pairs initiated near the \emph{Deepwater Horizon} (DwH)
site in the northern Gulf of Mexico (GoM).  The simulated separations
were produced using synthetic pairs advected by surface velocities
from a data-assimilative Navy Coastal Ocean Model (NCOM) simulation,
with an effective horizontal resolution of 1 km, during July 2013
and February 2014.  The observed separations come from drifter pairs
from the Grand LAgrangian Deployment (GLAD), conducted in July 2012.
The investigation involved various statistical descriptors, namely,
the probability distribution function (PDF) of pair separations,
its second moment (relative dispersion), its fourth moment (kurtosis),
and the (second-order) velocity structure function.

The measures are consistent for the NCOM pairs, suggesting nonlocal
dispersion at the smallest separations and diffusive dispersion at
separations greater than 100 km, where the pair velocities are
decorrelated. Similar results were obtained in both winter and summer
seasons. The results were more ambiguous with the GLAD pairs.  While
the pair motion is also uncorrelated at scales exceeding 100 km, the
dispersion regime cannot be distinguished from the PDFs, dispersion or
kurtosis. The structure functions on the other hand indicate
Richardson dispersion from the smallest scales to beyond the
decorrelation scale.

Two effects impact the GLAD results. With such high temporal
resolution (10-min sampling), the drifters resolve inertial
oscillations. These energetic motions however only weakly affect pair
dispersion.  The size of the loops depend on the drifter velocity
\cite[e.g.,][]{Gill-82}, and since nearby drifters have nearly the
same velocity, the size of the loops is nearly the same initially.  As
the pair separates however, the velocity difference grows and the
amplitude difference increases. However, as the drifters return
approximately to their starting position after an inertial period, the
net effect on the separation during that time is small. As such, the
effect is greatly overwhelmed by mesoscale stirring.

The oscillations do however alter distance-averaged measures. The
velocity structure function is one such measure, and this is dominated
by inertial oscillations below roughly 10 km.  Filtering the
trajectories to remove the inertial oscillations steepens the
structure functions without affecting the time-based measures.
Likewise, adding inertial oscillations to the trajectories from the
model, which has weak inertial variability, causes the structure
function to shallow, lending the appearance of local dispersion.

The second effect concerns the sampling in GLAD. As the goal was
to resolve submesoscale dispersion in the region, the drifters were
deployed in several tight clusters. As these spanned scales much
less than the correlation length scale (100 km), the pairs behaved
similarly. We found the drifters could be separated into 6 distinct
classes, each displaying a characteristic path. This reduced the
degrees of freedom and led effectively to an undersampling of the
mesoscale stirring.  Using synthetic particles deployed at the same
locations yielded nearly identical, and equally ambiguous, dispersion
statistics.

The conclusion is that the 1-km model likely captures the dispersion
in the GLAD experiment over the sampled scales. This argues in favor
of nonlocal dispersion, because the stirring is dominated by large
scale, low frequency motions which are well-resolved by the model.
It also supports using altimeter-derived geostrophic velocities to
study dispersion here, as the dominant eddies are marginally resolved
by altimetry. \citet{Olascoaga-etal-13} suggested the mesoscale
circulation dominates in shaping the patterns formed by drifters
in the GLAD experiment, and the present results are consistent with
this.

Previously, \citet{LaCasce-Ohlmann-03} observed exponential dispersion
among ``chance pairs'' from the Surface-CUrrent and Lagrangian
drifter Program (SCULP), from separations of 1 km up to $L_\mathrm{D}$
($\approx 50$ km).  The SCULP pairs exhibited an e-folding time on
the order of 1 d, similar to the time scales inferred here, and
exhibited large kurtoses. \cite{LaCasce-10} found moreover that the
SCULP PDFs resemble the Lundgren distribution.  Note the SCULP
drifters had daily positions and so were essentially devoid of
inertial oscillations.  \citet{LaCasce-Ohlmann-03} did not observe
diffusive dispersion at super-deformation scales but something
closer to ballistic growth, with the dispersion increasing as
$t^{2.2}$. Given that the pair motion is uncorrelated above
$L_\mathrm{D}$, such growth most likely reflects shear dispersion,
due to a large scale flow. Indeed, many of the SCULP drifters were
advected by boundary currents.

\citet{Poje-etal-14} presented the first analysis of the GLAD pair
trajectories and concluded the dispersion was consistent with the
Richardson regime, from the smallest sampled scale (0.1 km) to
several hundred kilometers.  However, their conclusions were based
solely on distance-based measures (the second order structure
function and the relative diffusivity) which are affected by inertial
oscillations.  It should be emphasized too that a turbulence framework
cannot be applied to interpret results at separations of hundreds
of kilometers, as the pair velocities are uncorrelated.

\citet{Jullien-etal-99} and \citet{Jullien-03} calculated separation
PDFs from pairs of particles deployed in 2D turbulent flows in the
laboratory. They suggested that the separation PDF could be fit
with an empirical function of the form:
\begin{equation}
  p(r,t) = \frac{a}{2\pi\sigma r} \exp\left(-b
  \sqrt{\frac{r}{\sigma}}\right),
  \label{eq:jull}
\end{equation}
where $\sigma = \langle r^2 \rangle^{1/2}$, and $a$ and $b$ are
constants. They claimed that the same PDF applied for
\emph{both} the energy and enstrophy cascade ranges, with slightly
different values of $a$ and $b$.\footnote{The PDF they proposed was not
properly normalized.  Doing so yields $a = b^{2}/2$.}
It is straightforward to show that the kurtosis for this empirical
PDF \eqref{eq:jull} is:
\begin{equation}
  \frac{\langle r^{4}\rangle }{\langle r^{2}\rangle ^{2}} =
  \frac{9!}{5!^2} = 25.2.
  \label{eq:jullku}
\end{equation}
There is no indication of such a large asymptotic limit in either the
simulated trajectories or the GLAD data.  So we can most likely rule
out this type of dispersion.

The present results serve as a cautionary note on using relative
dispersion to deduce kinetic energy spectra. The inertial oscillations
contribute to the spectra but do not greatly impact dispersion.  So
finding exponential relative dispersion does not necessarily imply
steep spectra. Conversely, having shallower spectra at small scales,
as in the atmosphere \citep{Nastrom-Gage-85} and ocean
\citep{Callies-Ferrari-13}, does not rule out nonlocal pair dispersion.

It is also worth noting that the submesoscale spectrum here exhibits a
scale separation. The Lagrangian frequency spectra has peaks at low
frequencies and at the inertial frequency, with little energy in
between. So it is possible to partition the flow into mesoscale
turbulence and inertial oscillations. If instead an inverse energy
cascade were occurring from the submesoscales, the intermediate scales
and frequencies would be energetic.

The results also have implications for the design of dispersion
experiments. Care should be taken to ensure sufficient sampling at
scales exceeding those of the energy-containing eddies. Otherwise one
might obtain many similar pair trajectories, with a corresponding loss
of statistical confidence.

\acknowledgments

We thank Angelique Haza, Tamay \"Ozg\"okmen, and Andrew Poje for
discussions on pair-separation statistics and Jonathan Lilly on
inertial oscillations. We are also grateful to three anonymous
reviewers, whose comments led to significant improvements in the
manuscript. The GLAD trajectory pairs were kindly identified by
Angelique, who independently computed kurtosis in the several initial
separation classes considered here.  The GLAD drifter trajectory
dataset is publicly available through the Gulf of Mexico Research
Initiative Information \& Data Cooperative (GRIIDC) at
https://data.gulfresearchinitiative.org  (DOI:10.7266, N7VD6WC8).
The NCOM simulation was produced at the Naval Research Laboratory
and can be obtained from http://\allowbreak dx.doi.org/\allowbreak
10.7266/\allowbreak N7FQ9TJ6, N76Q1V5G, and N72Z13F4.  The work was
supported by the Gulf of Mexico Research Initiative (FJBV) and under
grant 221780 from the Norwegian Research Council (JHL).

redpajama_set_name: RedPajamaArXiv


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text:
New laws to power insurance industry
By Sonia K.
Brunei Darussalam is endeavouring to make the insurance industry, along with other financial sectors, a key component of the country's national economic diversification efforts. With this in mind, His Majesty the Sultan and Yang Di-Pertuan of Brunei Darussalam has consented to approve several new laws, relating to the supervision of insurance activities in this country.
The Minister of Finance II, Pehin Dato Haji Abd Rahman bin Haji Ibrahim, said this at the opening ceremony of the 23rd East Asian Insurance Congress 2006, at the International Convention Centre, yesterday.
The minister said the introduction of this new legislation is part of the Ministry of Finance's ongoing efforts in enhancing supervision of this sector, in line with international best practices.
"Another key objective of this legislation is to ensure that our insurance companies remain financially strong so that the interest of the public as policyholders are properly protected. In turn, it is hoped that this would encourage the general public to also embrace insurance as a key component of their long term financial plans, be it for protection or investment," he said.
The minister said this conference has a strong significance for Brunei. For the insurance industry, this is a congregation of some more than 900 delegates, consisting of distinguished speakers, experts and consultants, regulators and key players from around the world.
"In terms of the fundamental landscape of the industry, since the turn of the new millennium, this region has borne witness to the impact of both natural and man-made catastrophes such as tsunamis, earthquakes, accidents attributable to negligent or sub-standard construction and developments and as well as the accelerating rise in geopolitical risks.
"These events, undoubtedly, cause both destruction to lives and properties and untold human sufferings, and at times, bring significant business disruptions to whole industries as witnessed post 9/11, SARS and South Asian tsunami.
"Faced with such new realities, both regional and global players will need to boost their existing structural and financial capabilities, to properly serve their intended 'insurers' functions, and withstand the potentially deleterious effect of such calamity," the minister said.
"Going forward, the industry continues to face an extremely challenging outlook for the world economy, with on-going volatile energy and commodity prices, structural imbalances in various economies, the real risk of pandemics, such as SARS and now avian influenza, and potential escalation of regional conflicts.
This will obviously change the landscape of the entire insurance industry. "Markets will have to take on board these uncertainties with regulatory authorities and market players continuing to work in the spirit of cooperation with one another in order for the industry to serve its purpose effectively," the minister added.
"Insurance is an integral part of the financial services industry. The traditional role of the industry to provide insurance coverage, critical for foundations for businesses and industry survival and continuity remains vital. In addition to providing such traditional function of protection, we have witnessed numerous innovations in terms of novel product offerings (not least in saving and investments), and also new types of distribution channels.
"These advancement are both as a result of the progression of technology as well as the creativeness of the players in response to dynamic and ever evolving market. With this in view, we expect to see further innovations from this industry in the future," said the minister.
The minister hoped the conference would create new networking opportunities between delegates and strengthen the existing regional and international ties and cooperation. He also hoped that the conference would be able to identify do-able measures and responses, which can address various pertinent issues within this industry.
The Chairperson of the 23rd East Asian Insurance Congress, Ms Dorothy Newn, in her speech said that with the region booming, the theme, "East Asian Insurance at the Crossroads of Growth and Profitability", takes on an added meaning.
A total of 45 speakers will be deliberating on a wide range of topics ranging from economic and market trends, to current burning issues as cover for natural disasters and the impact of the avian flu on society.
EAIC President, Mr Chai Sophonpanich, also spoke.
The keynote address was delivered by Mr Nicholas C. Walsh, Executive Vice President, Foreign General Insurance of American International Group, Inc. (AIG), President and Chief Executive Officer of American International Underwriters (AIU).
He spoke on "Change and the Economic and Geopolitical Impact on Our Markets". His keynote address was moderated by veteran business journalist, Lorraine Hahn, host of Talk Asia on CNN.
The second keynote address delivered yesterday morning was on "The Challenges of regulating the Insurance Industry in a market with Takaful and Convention Insurance".
This was delivered by Haji Mohd Roselan bin Haji Mohd Daud, Acting Director of Financial Institutions Division, Ministry of Finance.
The insurance congress held for the first time in Brunei will include three plenary sessions and two panel discussions featuring distinguished speakers from across the region. - Borneo Bulletin (1st August 2006)


text:
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British rolled equip couches are extra comfortable because of the large, soft cushions at the back as well as for the seats. Low arms are comfy for lying down and the uncovered thighs keep this sofa style from sensation too heavy or imposing. It actually came from at the turn of the hundred years and can be related to some thing usual for the English countryside. Distinguishing qualities generally consist of reduced uncovered legs, soft, large cushions, a tight back again and recessed arms. Even though it is considered a classic style, it's also a perfect accessory for a modern day room thanks to its comfortable and flexible appear.
If you are looking for some serious rest, this loveseats solid pillow back and rolled hands will deliverbut at a higher cost. Every chair cushioning consists of 30 person pocketed circles for springtime and support, and high strength chair froth for an extra layer of plushness and sturdiness. Plus, the foam soft cushions are topped with super gentle, blended lower down. For your additional comfort and ease, you will find 3 regular jobs: sitting, a slight lie down by having an raised foot rest, and a full lie down by having an elevated footrest. It doesnt hurt this reclining loveseat looks lux, either. Its all-leather-based upholstery and decorative nail head cut give it a vintage look that can function with lots of home decorations designs, from conventional to country to crafts and arts. In addition, leather-based stands up nicely against daily use, children and pet hair and fingernails. Just be sure you situation the leather-based every six to 12 months.
British folded arm couches are extra comfy thanks to the large, pillows at the back and for the chairs. Reduced arms are comfy for laying and the exposed thighs keep this couch style from feeling overweight or impacting. It really came from at the change of the century and could be associated with something usual for the English country side. Differentiating qualities generally include reduced exposed legs, gentle, generous cushions, a tight back again and recessed hands. Though it may be considered a vintage style, it's also a perfect accessory for a contemporary room thanks to its comfy and versatile appear.
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Finally event organisers realised we wanna see cooking barrels instead of choppy pap walls being ridden by the world's best surfers....and moved the event down to the road to the infamous Box. Think Kalk Bay reef on steroids. Super shallow gnarly reef that will hand out beatings to all comers.
Quite a tricky one for Jordy Smith - first time he'd ever surfed there and it was in a heat he had to win! Luckily he made it through his Rd 5 clash and now meets Bede again. He lost to Bede in the 3 man Rd 4 no-loser heat. Gonna be a tough quarterfinal for our man, cos Bede knows the Box pretty well, and Jordy only just popped his cherry there.
Kerrsy took out fellow Aussie Yadin Nicol in a heat blessed with some smokers. Josh meets brazzo high-flyer Medina in his QF. Parko rides a barrel better than most and took out Filipe Toledo....only to end up with a heat against Kelly. Might be a big heat in the greater scheme of things if you're looking at 2 guys who hope to be in the world title race at the end of the year.
If you pick the winner you go into the draw to win this awesome prize from Billabong, valued at R1600. Kiff boardies, TShirt, cap, deckgrip and leash.


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Just by that header, you can imagine it was not a great night for our dressage squad….we finished in fourth just out of the medals. Courtney from yesterday with a 70.4 and Steffen with his 70.00 could not bring up the total enough to beat the Danish squad. Poor Debbie and our wonderful mare Brentina, had a rough day and only scored, I hate to say, 63.00….something was truly wrong with her tonight. Again, I did not get to talk to any of our team or staff, but I know they are really disappointed. It is so tough in this format when you have no drop score (all three scores count now)…so that when one of the team has a bad day, you cannot make up with another 3rd score. Too bad, because this is Brentina's last go round…she is going to be retired. I know Debbie feels really down and sad, so let it pass before you ask any questions on her blog, etc. Steffen (last to go) had a splendid test and he and Ravel are going to be our new shining stars of the world, along with (the NEWLY crowned) VETERAN Olympic rider, Courtney King Dye!! How about that title…she has elevated herself to the ranks of the "top in the world" this week…no doubt that she is here , and here to stay. Lovely lady, lovely rider, lovely experience…She is a real player now….watch out!
Worth , who blew the crowd and competition away. This horse is beyond wonderful..they were almost flawless…only a few mistakes cost her a higher score..but she beat out Salinero and Anky ( 76.417 to 74.75)…the battle at the Bighorn is coming up starting on Sat night…Gp special (50%) and then on Tuesday the Freestyle (50%)..these two are on a path to destiny…..25 riders move on, but the battle will be between these two juggernauts. Great dressage and competition. The Netherlands won the silver on the back of Anky and Salinero. This pair had a good solid test, but having seen him in better form, it was not the best outing. A little tight in the beginning, a loss of straightness in the half pass tour, and some, inconsistent, piaffe, I think, cost them better marks. He was very strong in the bridle and of course, Anky rode beautifully. Satchmo was better tho…he came out with some kind of trot work, whew!!, and started out in the mid 80's after the first 4 movements. We were so blown away with the power and control and collection. It is some kind of wonderful to be this close to these horses and riders……they are truly in a class by themselves. The Danish team with Andreas Helgstrand with Don Schufro (68.8) , Nathalie Wittgenstein on Digby (70.4) and Anne Von Olst on Clearwater 67.35, earned the bronze outright and were very elated with the medals..They deserved it, for their strong and solid tests,,,all three.
Another weird result too… the Portugese rider, Miguel Duarte, riding the Luisitana mare, Oxalis, had to retire in the middle of the test, as she resisted, reared up and said "I;m done here!" I don't know whether it is an Olympic first, but it was really strange, and sad, to see a rider have to leave, because his horse shut down on him. It didn't look like any sort of medical or injury problem…horses I guess…….
And finally, another US Olympic participant stumbled at his first Olympic Games….ME! After a week of announcing and crazy schedules, etc. I made an Olympic mistake on the mic..I introduced the wrong rider!! Yep….dumb play offense…20 yrs….I got caught up in a scoring problem with my computer, looked up to see the French rider about to enter (instead of taking a tour around the arena before starting –which really threw me – I looked down on my start list and introduced her as the next German rider ( Nadine Cappellmann)….she, Julia Chevanne, for France was already into her test when the announcing team told me what I had done. Our Chinese announce had done her correctly (thank God) and I decided not to correct the error while Julia was riding. She did not have a very good test either, and that made it (for me) worse. I apologized over the PA to her and the French team when she was done, as I correctly introduced her when she was finished, but the damage was done! Needless to say, I was stunned, upset, and felt really bad. I was hoping for a mistake free Games…..I asked the TD whether or not I should write an apology to the rider, but Mariette told me to find the coach sometime and apologize that way.. I will be on that tomorrow. I started great, had the blunder in the middle, and finished strong again. Let's hope it goes away….however, all of the other top announcers (mostly Brits) started ribbing me (and rightly so….) but I know this won't be the end of it! Goes with the turf, I guess……I certainly will feel better about the whole thing….later. I had to tell you guys……we all stumble sometimes…even at the Olympics. I will have my "A" game on , from here on out, I promise you.
Thanks for the great commentary, you've been by far the fastest & best at getting results back to us, but having worked with you for many years at Devon & Gladstone (tall redhead, always ring/warm-up stewarding), I would have expected nothing less.
Please tell Debbie, Courtney, & Steffen we're so proud of all three,we've been riding every stride with them & our hearts are breaking for Debbie, what a great job she did just to get through that, she needs to know she & "Mamma" will still forever be American dressage icons.
Great reading your commentary. It really brings it home.
As you are ever the professional, of course you are going to beat yourself up about a mistake. Those that admire you and love you know how great you are but no-one is perfect and none of us are going to love you less for it. The rider got her her ride at the olympics and is in the programme (if there is one)and doubtless the video, she will be fine.
I remember you coming to Pebble Beach in 1987 and making my show a huge success, and you are still doing it in 2008, you are the best, don't forget that.
I look forward to 2009 when you will make our show wonderful again. Don't lose any sleep you are human and no baby died.!!!
Thanks for the photos of the sidelines. Always just out of view. Nice to see a little of the atmosphere that never makes it on camera.
Hey Brian, you didn't think cuz you were good enough to go to the Olympics meant you were perfect. It's the place for the best in their field to do their best on any day, you are seeing & reporting to us those efforts... none of them perfect.
Think perhaps you are dehydrated & need electrolyte replacement therapy (read beer & citrus). Take Dr.Pats advice & hydrate.
Responding to someone's question earlier, the Live Commentary on the stream is Imtaz Aneese - an event rider(riding for India) who's been living & competing from the Atlanta for the past 10 yrs.
I didn't get to see Debbie's ride. What happened? Is there a video available anywhere? I just love Debbie and Brentina and I'll always be proud of them no matter what happened. I'm just curious to see what everyone is talking about.
i've been at many shows where you were the announcer and i think you're great. i've always enjoyed your "mounted" dressage demonstration. i know for you the mistake you made must be a hard pill to swallow, being the professional you are, but don't sweat it. it happens to the best of us.


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