Hi,
my
name
is
Ryan
Parker,
and
I'm
excited
to
be
here
today
with
Clay
Barker
to
share
with
you
some
new
tools
that
we've
added
to
help
you
analyze
spectral
data
with
the
Functional
Data
Explorer
in
JMP Pro
17.
So
what
do
we
mean
by
spectral
data?
We
have
a
lot
of
applications
from
chemometrics
that
have
motivated
a
lot
of
this
work.
But
I
would
just
start
off
by
saying
we're
really
worried
about
data
that
have
sharp
peaks.
This
may
not
necessarily
be
spectral
data,
but
these
are
the
type
of
data
that we've had
a
hard
time
modeling
in
FE
up
to
this
point.
And
so
we
really
wanted
to
focus
on
trying
to
open
up
these
applications
and
make
it
a
lot
easier
to
handle
these
sharp
peaks.
Maybe
potential
discontinuities.
Just
these
large,
wavy
features
of
data.
Where
in
this
specific
example,
with
spectroscopy
data,
we're
thinking
about
composition
of
materials,
and
these
peaks
can
represent
these
compositions,
and
we
want
to
be
able
to
try
to
quantify
those.
So
another
application
is
from mass spectrometry,
and
here
you
can
see
these
very
sharp
peaks.
They're
all
over
the
place
in
these
different
functions.
But
these
peaks
are
representing
proteins
from
these
spectrums,
and
they
can
help
you,
for
example,
compare
differences
between
things
from
a
patient
with
cancer
and
patients
without
cancer
to
understand
differences.
I mean, again,
it's
really
important
that
we
try
to
model
these
peaks
well
so
that
we
can
quantify
these
differences.
An
example
that
Clay
is
going
to
show
comes
from
chromatography.
This
is
where
we're
trying
to
...
In
this
case,
we
want
to
look
at
quantifying
the
difference
between
an
olive
oil
versus
other
vegetable
oils.
And
so
the
components
of
these
things
represented
by
all
of
these
peaks,
we
need
to,
again,
try
to
model
these
well.
The
first
thing
I
want
to
cover
are
four
new
tools
to
preprocess
your
data,
spectral
data
before
you
get
to
the
modeling
stage.
The
first
one
is
the
Standard
Normal
Variate.
So
with
the
Standard
Normal
Variate,
we're
thinking
about
standardizing
each
function
by
their
individual
mean
and
variance.
So
we're
going
to
take
every
function
one
at
a
time,
subtract
off
the
mean,
divide
by
the
variance,
so
that
they
all
have
mean
zero
and
variance
one.
This
is
an
alternative
to
the
existing
tool
we
have
standardized,
which
is
just
looking
at
a
global
mean
in
variance
so
that
the
data
themselves
have
been
scaled,
but
certain
aspects,
like
means,
are
still
there,
whereas
with
the
Standard
Normal
Variate,
we
want
to
remove
that
for
every
function.
The
next
tool's
Multiplicative S
catter
Correction.
It
is
similar
to
Standard
Normal
Variate,
the
results
end
up
being
the
same,
similar.
But
in
this
case,
we're
thinking
about
data
where
we
have
light
scatter.
So
some
of
these
spectral
data
come
where
we
have
to
worry
about
our
light
scatter
from
all
the
individual
functions
being
different
from
a
reference
function
that
we're
interested
in.
Usually
this
is
the
mean.
So
what
we'll
do
is
we
will
set
a
simple
model
between
the
individual
functions
to
this
mean
function.
You know,
we will get coefficients
that
we
can
subtract
off
this
mean
feature,
divide
by
the
slope
feature,
get
us
to
that
similar
standardizing
the
data,
and
in
this
case,
focused
on
this
light
scatter.
Okay,
so
at
this
point,
we're
thinking
about
what
if
we
have
noise
in
our
data?
What
if
we
need
to
smooth
it?
So
the
models
that
we
want
to
fit,
for
spectral
data,
these
wavelets,
they
don't
smooth
the
data
for
you.
So
if
you
have
noisy
data,
you
really
want
to
try
to
handle
that
first,
and
that's
where
the
Savitzky-Golay
Filter
comes
in.
What
this
is
going
to
do
is
fit
n-
degree
polynomials
over
a specified
bandwidth
to
try
to
find
the
best
model
that
will
smooth
your
data.
So
we
search
over
a
grid
for
you,
pick
the
best
one,
and
then
present
the
results
to
you.
And
I
do
want
to
note
that
the
data
are
required
to
be
on
a
regular
grid,
but
if
you
don't
have
one,
FDE
will
create
one
for
you.
We
have
a
reduce
option
that
you
can
use
if
you
want
some
finer
control
over
this,
but
by
default,
we
are
going
to
look
at
the
longest
function,
choose
that
as
our
number
of
grid
points,
and
create
a
regular
grid
from
that
for
you.
But
the
nice
thing
about
the
S
avitzky-Golay Filter
is
because
of
the
construction
with
these
polynomials,
we
have
easy
access
to
the
first
or
second
derivative.
Even
if
you
don't
have
spectral
data
and
you
want
to
access derivative functions
this
will
be
your
pathway
to
do
that.
And
if
you
do
request,
say,
the
second
derivative,
our
search
gets
constrained
to
only
polynomials
that will allow us to
give
you
a
second
derivative,
for
example.
But
this
would
be
the
way
to
access that,
even
if
you
weren't
even
worried
about
smoothing.
You
can
now
get
to
derivatives.
The
last
preprocessing
tool
I'll
cover
is
Baseline
Correction.
So
in
Baseline
Correction,
you
are
worried
about
having
some
feature
of
your
data
that
you
would
just
consider
a
baseline
that
you
want
to
remove
before
you
model
your
data.
So
the
idea
here
is
we
want
to
fit
a
baseline
model.
We
have
linear,
quadratic,
exponential
options for you,
so
we
want
to
fit
this
to
our
data
and
then
subtract
it
off.
But
we
know
there
are
important
features,
typically
these
peaks,
so
we
want
to
not
use
those
parts
of
the
data
when
we
actually
fit
these
baseline
models.
So
we
have
the
option
here
for
correction
region.
I
think
for
the
most
part
you
would
likely
use
entire
function.
So
what
this
just
means
is,
what
part
are
we
going
to
subtract
off?
So
if
you
select
within
regions
only things
within
these
blue
lines
are
going
to
be
subtracted.
But
I've
already
added
four
here.
Every
time
you
click
add
on
baseline regions,
you're
going
to
get
a
pair
of
these
blue
lines
and
you
can
drag
them around
to
the
important
parts
of
your
data,
and
what
this
will
do
is,
when
you
try
to
fit,
say,
a
linear
baseline
model,
it's
going
to
ignore
the
data
points
that
are
within
these
two
blue
lines.
So,
function
one,
we
set
a
linear
model,
but
we
exclude
all
these
sharp
peaks
that
we
really
want,
that
we're
interested
in.
And
so
then
we
take
the
result
from
this linear model
and
subtract
it
off
from
the
whole
function.
The
alternative
to
that
is
an
Anchor
Point,
and
that's
if
you
say,
I
really
would
like
for this specific point
to
be
included
in
the
baseline
model.
Usually
this
is
if
you
have
smaller
data
and
you
know,
okay,
I
want
these
few
points.
These
are
key.
These
represent
the
baseline.
If
I
were
able
to
fit, you know,
say a
quadratic model to these points,
that's
what
I
want
to
subtract
off.
So
it's
an
alternative.
When
you
click
those,
they'll
show
up
as
red
as
an
alternative
to
this
blue.
But
this
will
allow
you
to
correct
your data
remove
the
baseline
before
proceeding.
So
that
gets
us
to
how
we
model
spectral
data
now
in
JMP Pro
17,
and
we're
using
wavelets.
The
nice
thing
about
wavelets
is
we
have
a
variety
of
options
to
choose
from.
So
these
graphs
represent
what
are
called
mother
wavelets
and
they
are
used
to
construct
the
basis
that
we
use,
that
models
the
data.
So
the
simplest
is
this Haar
wavelet,
which
is
really
just
step
functions,
maybe
hard
to
see
that
here,
but
these
are
just
step
functions.
But
this
biorthogonal,
it
has
a
lot
of
little
jumps
and
you
can
start
to
imagine,
okay,
I
can
see
why
these
make
it
a
lot
easier
to
capture
peaks
in
my
data
other
than
the
Haar
wavelet.
All
these
have
parameters
that
are
changing
the
shape
and
the
size
of
these,
so
I've
just
selected
a
couple
here
to
just
show
you
the
differences.
But
you
can
really
see
where,
okay,
if
I
put
a
lot
of
these
together,
I
can
understand
why
this
is
probably
a
lot
better
to
model
all
these
peaks
of
my
data.
And so here's
an
example
to
illustrate
that
with
one
of
our
new
sample
data,
a NMR
design
of
experiments.
So
this
is
just
from
one
function
where
let's
start
with
B-Splines.
This
is
sort
of
the
go
to
for
most
data
place
to
start
in
FDE.
But
we
can
see
that
it's
really
having
a
hard
time
picking
up
on
these
peaks.
Now, there are,
we
have
provided
you
tools
to
change
where
knots are at
in
these
beastline
models.
So
you
could
do
some
customization.
Probably
fit
this
a
lot
better
than
the
default.
But
the
idea
is
that
now
you've
had
to
go
and
move
things around
and
maybe
it
works
for
some
functions,
but
not
others,
and
you
need
a
more
automated
way.
So
that's
one
alternative
to
that
is
P-Sp
lines.
That
is
doing
that
a
little
bit
for
you,
but
it's
still
not
quite
capturing
the
peaks
maybe
as
well
as
wavelets.
It's
probably
doing
the
best
for
these data.
relative
to
wavelets
and
almost
a
model
-free
approach
where
we
model
the
data
just
directly
on
our
shape
components,
this
direct
functional
PCA.
It's
maybe
a
bridge
between
P-Splines
and
B-Splines
where
it's
not
quite
as
good
as
P
-Splines
but
it's
better
than
B
-Splines
but
this
is
just
a
quick
example
to
highlight
how
wavelets
can
really
be
a
lot
quicker
and
powerful.
What
are
we
doing
in
FDE?
We
construct
a
variety
of
wavelet types
and
their
associated
parameters
and
fit
them
for
you.
So
similar
to
the
S
avitzky-Golay Filter,
we
do
require
that
the
data
are
on
a
regular
grid.
And
good
news,
we'll
create
one
for
you.
But
of
course
you
can
go
to
reduce
the
control
that
if
you
would
like.
But
now
the
nice
thing
about
once
data are
on
the
grid,
we
can
use
a
transformation
that's
super
fast.
So
P
-Splines
would
also,
for
these
data,
be
what
you
would
really
want
to
have
to
use,
but they can take a longtime to fit,
especially
if
you
have
a
lot
of
functions
and
you
have
a
lot
of
data
points
per
function.
But
our
wavelet
models
are
going
to
essentially
last
so
all
of
the
different
basis
functions
that
construct
this
particular
wavelet
type
with
parameter
and
what
that's
going
to
allow
us
to
do
is
just
really
force
a
lot
of
those
coefficients
that
don't
really
mean
anything
to
zero
to
help
create
a
sparse
representation
for
the
model.
So
those
five
different
wavelet
types
that
I
showed
before,
those
are
available,
and
once
we
fit
them
all,
we're
going
to
construct
model
selection
criteria
and
choose
the
best
for
you
by
default.
You
can
click
through
these
as
options
to
see
other
fits.
And
a
lot
of
times
these
first
few
are
going
to
look
very
similar
and
it's
really
just
a
matter
of,
there
are
certain
applications
where
they
know,
"Okay, I
really
want
this
wavelet type,"
so
they'll
pick
the
best
one
of
that
type
in
the
end to use.
So
the
nice
thing
about
these
models
is
they
happen
on
a
resolution.
They're
modeling
different
resolutions
of
the
data.
So
we
have
these
coefficient
plots
where
at
the
top
they're
showing
low-frequency,
larger
scale
trends,
like
an
overall
mean,
and
as
you
go
down
in
the...
Or
I
guess
you
go
up
in
the
resolutions,
but
down
in
the
plot,
you're
going
to
look
at
high
-frequency
items,
and
these
are
going
to
be
things
that
are
happening
on
very
short
scales,
so
you
can
see
where
it's
picking
up
a
lot
of
different
features.
In
this
case,
it's taking...
A
lot
of
these
are
zero
for
the
highest
resolutions.
So
it's
picking
up
some
scales
that
are
at
the
very
end
of
this
function.
It's
picking
up
some
of
these
differences
here.
But
this
gives
you
a
sense
of
kind
of
where
things
are
happening at
both
location
and
then
is
that
high-frequency
or
low-frequency
parts
of
the
data.
So
the
last
thing
we've
added
to
complete
the
wavelet
models
that's
a
little
bit
different
from
what
we
have
now
is
called
Wavelets
DOE.
So
if
you've
used
FDE
before,
you've
likely
tried
functional
design
of
experiments
and
that
is
going
to
allow
you
to
take
functional
principle
component scores,
connect
design
of
experience
factors
to
the
shape
of
your
functions.
But
now,
wavelet
models
in
particular,
they're
coefficients,
because
they
do
represent
resolutions
and
locations,
these
can
be
more
interpretable
and
they
have
more
direct
impact
to
understanding
what's
happening
in
the
data,
that
may
be
a
functional
principle
component
isn't
as
easy
to
connect
with.
We
have
this
energy
function
and
it's
standardized
to
show
you,
"Okay,
this
resolution
at
3.5,"
just
representing
more
on
this
end
point.
That's going to have...
That's
where
the
most
differences
are
in
all
of
our
functions,
and
it's
representing
about
12%.
So
you
can
scroll
down.
We
go
up
to
where
we
get
90%
of
this
energy,
which
is
just
the
squared
coefficient
values
that
we
just
standardized
here.
But
energy
is
just
how
big
are these coefficients
relative
to
everything
else?
But
this,
similar
to
Functional
DOE,
you
can
change
the
factors,
see
how
the
shape
changes,
and
we
have
cases
where
both
Wavelets
DOE
and
Functional
DOE
work well.
Sometimes
Wavelets DOE
just
get
the
structure
better.
Doesn't
allow
for
some
maybe
negative
points
that
Functional
DOE
might
allow
in
this
example.
So
it's
just
they're
both
there,
they're
both
fast.
I mean, you
can
use
both
of
them
to
try
to
analyze
the
results
of
wavelet
models.
But
that's
my
quick
overview.
So
now
I
just
want
to
turn
it
over
to
Clay
to
show
you
some
examples
of using wavelet
models
with
some
example
data
sets.
Thanks,
Ryan.
So,
as
Ryan
showed
earlier,
we
found
an
example
where
folks
were
trying
to
use
chemometrics
methods
to
classify
different
vegetable
oils.
So
I've
got
the
data
set
opened
up
here.
Here
we
have
our
each
row
of
the
data
set
is
a
function,
so
each
row
in
the
data
set
represents
a
particular
oil,
and
as
we
go
across
the
table,
that's
the
chromatogram.
So
I've
opened
this
up
in
FDE
just
to
save
a
few
minutes.
The
wavelet
fitting
is
really
fast,
but
I
figured
we'd
just
go
ahead
and
start
with
the
fit
open.
So
here's
what
our
data
set
looks
like.
You
can
see
those
red
curves
are
olive
oils.
The
green
curves
are
not
olive
oils.
So
we
can
see
there's
definitely
some
differences
between
the
two
different
kinds
of
oils
and
their
chromatograms.
So,
as
Ryan
said,
we
just
go
to
the
red triangle menu
and
we
ask
for
wavelets
and
it
will
pick
the
best
wavelet
for
you.
But
like
I
said,
I've
already
done
that,
so
we
can
scroll
down
and
look
at
the
fit.
Here
we
see
the
best
wavelet
that
we
found
was
called
the
Symlet 20,
and
we've
got
graphs
of
each
fit
here
summarized
for
you.
As
you
can
see,
the
wavelets
have
fit
these
data
really
well.
But
in
this
case,
we're
not
terribly
interested
in
fitting
the
individual
fits.
We
want
to
see
if
we
can
use
these
individual
chromatograms
to
predict
whether
or
not
an
oil
is
an
olive
oil
or
not
an
olive
oil.
So
what
we
can
do
is,
we
can
save
out
these
wavelet
coefficients,
which
we've
gotten
a
big
table
here,
and
there's
thousands
of
them.
In
fact,
there's
one
for
every
point
in
our
function.
so
here
we've
got
4,000
points
in
each
function.
This
table
is
pretty
huge.
There's
4,000
wavelet
coefficients.
But
as
Ryan
was
saying,
you
can
see
that
we've
zeroed
some
of
them
out.
So
these
wavelet
coefficients
drop
out
of
the
function.
So
that's
how
we
get
smoothing.
We
fit
our
data
really
well,
but
zeroing
out
some
of
those
coefficients
is
what
smooths
the
function out.
So
how
can
we
use
these
values
to
predict
whether
or
not
we
have
an
olive
oil?
Well,
you
can
come
here
to
the
function
summaries
and
ask
for
save
summaries.
So
what
it's
done
is
it
saves
out
the
functional
principal
components.
But
here
at
the
end
of
the
table,
it
also
saves
out
these
wavelet
coefficients.
So
these
are
the
exact
same
values
that we saw
in
that
wavelet
coefficient
table
in
the
platform.
So
let
me
close
this
one.
I've
got
my
own
queued
up
just
so
that
I
don't
have
anything
unexpected
happen.
So
here's
my
version
of
that
table.
And
what
we
want
to
do
is
we
want
to
use
all
of
these
wavelet
coefficients
to
predict
whether
the
curve
is
from
an
olive
oil
or
from
a
different
type
of
oil.
So
what
I'm
going
to
do
is,
I'm
going
to
launch
the
generalized
regression
platform,
and
if
you've
ever
used
that
before,
it's
the
place
we
go
to
build
linear
models
and
generalize
linear
models
using a
variety
of
different
variable
selection
techniques.
So
here
my
response
is
type.
I
want
to
predict
what
type
of
oil
we're looking at
and
I
want
to
predict
it
using
all
of
those
wavelet
coefficients.
So
I
press
run.
In
this
case,
I'm
going
to
use
the
Elastic Net
because
that
happens
to
be
my
favorite
variable
selection
method.
And
I'm
going
to
press
go.
So
really
quickly,
we
took
all
those
wavelet
coefficients
and
we
have
found
the
ones
that
really
do
a
good
job
of
differentiating
between
olive
oils
and
non
-olive
oils.
So
in
fact,
if
we
look
at
the
confusion
matrix,
which
is,
this
is
a
way
to
look
at
how
often
we
predict
properly,
right?
So
for
all
49
other
olive
oils,
we
correctly
identified
those
as
not
olive
oils.
And
for
all
71
olive
oils,
we
correctly
identified
those
as
olive
oils.
So
we
actually
predicted
these
perfectly
and
we
only
needed
a
pretty
small
subset
of
those
wavelet
coefficients.
So
I
didn't
count,
but
that
looks
like
about
a
dozen.
So
we
started
with
thousands
of
wavelet
coefficients
and
we
boiled
it
down
to just the
12
or
so
that
were
useful
for
predicting
our
response.
So
what
I
think
is
really
cool
is,
we
can
interpret
these
wavelet
coefficients
to
an
extent,
right?
So
this
coefficient
here
is
resolution
two
at
location
3001.
So
that
tells
us
there's
something
going
on
in
that
part
of
the
curve
that helps us differentiate
between
olive
oils
and
not
olive
oils.
So
what
I've
done
is,
I've
also
created
a
graph
of
our
data
using...
Well,
you'll
see.
So
what
I've
done
is
here
the
blue
curve
is
the
olive
oils.
The
red
curve
is
the
non
-olive
oils,
and
this
is
the
mean
chromatogram.
So
averaging
over
all
of
our
samples.
And
these
dashed
lines
are
the
locations
where
the
wavelet
coefficients
are
nonzero.
So
these
are
the
ones
that
are
useful
for
discriminating
between
oils.
And
as
you
can
see,
some
of
these
non-zero
coefficients
line
up
with
peaks
and
the
data
that
really
tend
to
make
sense,
right?
So, here is,
here's
one
of
the
non
-zero
coefficients,
and
you
can
tell
it's
right
at
a
peak
where
olive
oil
is
peaking,
but
non-olive
oils
are
not,
right?
So
that
may
be
meaningful
to
someone
that
studies
chromatography
and
olive
oils
in
particular.
But
so
we
like
this
example
because
it's
a
really
good
example
of
how
wavelets
fit
these
chromatograms
really
well.
And
then
we
can
use
the
wavelet
coefficients
to
do
something
else,
right?
So
not
only
have
we
fit
the
curves
really well,
but
then
we've
taken
the
information
from
those
curves
and
we've
done
a
really
good
job
of
discriminating
between
different
oils.
And
so
I've
got
one
more
example.
Ryan
and
I
are
both
big
fans
of
Disney
World,
so
this
is
not
a
chromatogram.
This
is
not
spectroscopy.
But
instead
we
found
a
data
set
that
looks
at
wait
times
at
Disney
World,
so
we
downloaded
a
subset
of
wait
times
for
a
ride
called
Disney's
the
Seven
Dwarfs,
Mind
Train.
And
if
you've
ever
been
to
Disney
World,
you
know
it's
a
really
cool
roller
coaster
right
there
in
fantasyland.
But
it
also
tends
to
have
really
long
wait
times, right?
You
spend
a
lot
of
time
waiting
your
turn.
So
we
wanted
to
see
if
we
could
use
wavelets
to
analyze
these
data
and then use
the
Wavelet
DOE
function
to
see
if
we
can
figure
out
if
there's
days
of
the
weeks
or
months
or
years
where
wait
times
are
particularly
high
or
low.
So
we
can
launch
FDE.
Here you
can
see, we've got
each
day
in
our
data
set,
we
have
the
wait
times
from the time that
the
park
opens,
here,
to
the
time
that
the
park
closes
over
here.
And
to
make
this
demo
a
little
bit
easier,
we've
finessed
the
data
set
to
clean
it
up
some.
So
this
is
not
exactly
the
data,
but
I
think
some
of
the
trends
that
we're
going
to
see
are
still
true.
So
what
I'm
going
to
do
is
I'm
going
to
ask
for
wavelets,
and
it'll
take
a
second
to
run,
but
not
too
long.
So
now
we've
found
that
a
different
basis
function
is
the
best.
It's
the Daubechies 20
and
I
apologize
if
I
didn't
pronounce
that
right.
I've
been
avoiding
pronouncing
that
word
in
public,
but
now
that's
not
the
case
anymore.
So
we've
found
that's
our
favorite
wavelet
and
what
we're
going
to
do
is
we're
going
to
go
to
the
Wavelet
DOE
analysis,
and
it's
going
to
use
these
supplementary
variables
that
we've
specified
day
of
the
week,
year
and
month
to see if we can
find
trends
in
our
curves
using
those
variables.
So
we'll
ask
for
Wavelets
DOE,
and what's
happening
in
the
background
is
we're
modeling
those
wavelet
coefficients
using
the
generalized
regression
platform,
so
that's
happening
behind
the
scenes,
and
then
it
will
put
it
all
together
in
a
Profiler
for
us.
So
here
we've
got, you know,
this
is
our
time
of
day
variable.
We
can
see
that
in
the
morning.
The
wait
times
sort
of
start,
you know, around
an
hour.
It
gets
longer
throughout
the
day,
you know,
peaking
at
about
80
minutes,
almost
an
hour
and
a
half
wait.
And
then,
as
you
would
expect,
as
the
day
goes
on
and
kids
get
tired
and
go
to
bed,
wait
times
get
a
little
bit
shorter
until
the
end
of
the
day.
Now,
what
we
thought
was
interesting
is looking
at
some
of
these
effects,
like
year
and
month.
So
we
can
see
in
2015,
the
wait
times
sort
of
gradually
went
up,
right,
until
2020.
And
then
what
happened
in
2020?
They
increased
in
February,
and then, shockingly,
they
dropped
quite
a
bit
in
March
and
April.
And
I
think
we
all
know
why
that
might
have
happened
in
2020.
Because
of
COVID,
fewer
people
were
going
to
Disney
World.
In
fact,
it
was
shut
down
for
a
while.
So
you
can
very
clearly
see
a
COVID
effect
on
Disney
World
wait
times
really
quickly
using
Wavelet
DOE.
One
of
the
other
things
that's
interesting
is
we
can
look
at
what
time
of
year
is
best
to
go.
It
looks
like
wait
times
tend
to
be
lower
in
September,
and
since
Disney
World
is
in
Florida, you know,
that's
peak
hurricane
season,
and
kids
don't
tend
to
be
out
of
school.
So
it's
really
cool
to
see
that
our
model
picked
that
up
pretty
easily, right?
So, but
don't
start
going
to
Disney
World
in
September.
That's
our
time.
We
don't
want
it
getting
crowded.
But
yeah,
so
with
just
a
few
clicks,
we
were
able
to
learn
quite
a
few
things
about
wait
times,
Seven
Dwarfs
Mine
Train
at
Disney.
But
we
really
wanted
to
highlight
that these methods were
focused
on
chromatography
and
spectrometry,
but
there's
a
lot
of
applications
where
you
can
use
Wavelets,
and
I
think
that's
all
we
have.
So
thank
you.
And thank
you,
Ryan.
