►
Description
Attendees: Bradly Alicea, Mayukh Deb, Jesse Parent, Ujjwal Singh, and Vinay Varma. GSoC Updates, project board, and paper on Topological Data Analysis (TDA).
B
A
B
C
C
A
B
A
E
D
E
C
D
C
C
C
C
C
A
E
Me
yeah,
so
I've
been
working
decision
that
is,
I
went
back
to
the
epicly.
The
city
like
I,
did
some
stuff
on
it
on
leaving
my
phase
1.
So
this
time
it
was
more
about
them
indicating
the
video
data
with
the
annotations.
So
the
first
problem
that
I
was
facing
was
that,
like,
as
you
can
see,
wait
I'll
show
you
can
you
see
like
this?
Is
enough.
A
E
And
in
the
number
of
edited
time,
points
was
one
satellite
that
is
fine,
but
then
a
number
of
frames
in
the
video
was
237
only
so
the
first
problem
was
a
relatively
dispute.
Those
two
37
frames
into
those
135
time
points
do
something
with
it
to
do
anything
to
at
least
like
get
the
ready,
smash
things
with
the
data
points
within
the
metadata
and
to
CSV
files.
Okay,
so
that
was
big
and
smooth
I
think
it
was
this
one
here,
so
any
she
I
just
have
to
do
that.
One
and
then
I.
E
E
So
then
I
I
just
look
at
the
frames,
do
what
I
saw
was
that
they
were
very
noisy
and
they
were
too
lazy
to
actually
do
something
with
them.
So
I
had
to
first
remove
the
noise
and
like
after
doing
something
like
some
basic
stuff
with
open
CV
I
could
just
smooth
around
the
edges
a
little
bit
so
that
there's
no
noise
but
the
day
since
you
came,
you
can
see
the
Senators
right
here.
Can
you
see
yeah
yeah?
These
are
like
the
Dino
sentence,
so
everything
almost
all
the
data
by
Dino
any
minute.
E
So
after
that,
I
didn't
come
to
like
I
just
saw
I
just
failed
at
the
quality
planning
model
on
it
and
what
he
does.
Is
it
I'll
just
keep
these
first.
Like
you
can
see,
the
data
is
neck,
as
always
like
this
picture,
and
the
label
is
like
1304
and
all
of
these
values.
There
are
the
populations
of
each
cell
any
needs
at
that.
E
Very
little
data
this
is
a
tell
I'll
show
like
there
are
too
many
cells,
and
there
are
so
many
umpires
I
know.
I
only
have
the
time
to
like
do
it
for
you,
but
now
my
next
objective
would
be
to
automate
the
process
to
download
all
of
this
data
by
you
just
web
scraping
and
then
like
I,
will
make
it
efficient
enough,
so
it
will
automatically.
E
E
A
E
This
is
from
the
validation
loader,
so
the
model
never
saw
these
images.
This
is
the
question
you've
seen
with
images.
I
paint
it
on
the
paint
roller
and
this.
This
is
a
small
slice
of
the
payload
which
I
kept
separately,
which
the
model
would
never
see
that
would
only
release
from
st,
but
this
is
from
that
slice.
So
this
is
the
completely
unknown
images
to
the
model,
and
these
are
like
I
dunno.
How
many
time
we
get
it
because
I
didn't
find
the
nito,
maybe
they
might
have.
D
E
So
I
had
a
question
actually
that
other
question
was
that
all
of
the
images
that
you
see
in
this
case,
like
these
images
they're
only
from
one
string,
that
was
the
C
eh-
Straley
yeah.
So
is
it
a
problem
if
I
use
all
the
like?
Are
there
certain
differences
if
I
use
all
the
different
strains,
because
there
are
a
lot
of
strings
here
so
would
it
be
a
problem
if
I
use
all
of
the
strings,
because
is
it
different
for
different
strings.
A
D
E
D
E
A
So
the
only
difference
you
have
in
the
embryo
terms
of
cells
would
be
just
like
there's
some
mutants
that
have
like
don't
have
certain
cells,
but
those
are
I,
don't
I
think
they're
all
dealing
with
wild-type
genotypes,
so
the
strains
are
just
like
basically
a
line
that
they
raise
and
so
the
strain
is
you
know
it's.
It's
not
really
that
much
different
in
terms
of
the
cells
that
are
that
are
born
and
that
survived
so
you're
gonna
get
the
same
cells
and
roughly
the
same
position.
A
E
F
E
E
Is
when
I
actually
load
the
data?
This
is
a
custom
class
which
I
have
to
build
like
first,
what
like
there
is
a
very
unique
form
which
is
in
the
face,
which
was
that,
like
the
population
for
I'll
just
show
you
the
chart
like
come
see
this
right,
yeah
yeah.
What
was
happening
is
that
the
population
of
a
is
vaguely
larger
than
all
the
others.
E
So
what
do
modern
was
meaning
was
that
the
model
was
only
approximating
the
population
of
a
very
well
and
it
was
doing
very
bad
with
the
other
populations,
because
a
model
is
being
that
it
can
go
to
a
very
good
minimal
display,
identify
gain,
not
the
others,
yeah
okay,
so
that
was
kind
of
what
I
was
seeing,
that
it
was
doing
a
almost
perfectly,
but
not
the
others,
but
then
to
fix
that.
What
I
had
to
do
was
that
I
had
to
clamp
all
of
those
values
down
to
0
to
1.
E
Like
I
see
you
can
see
already
on
the
even
on
the
five
columns
of
the
dataset,
like
a
you
already
in,
for,
while
all
of
the
most
Alexi
go.
So
he
has
a
pretty
large
value
and
it
affects
the
loss
much
more
than
all
the
other
values,
but
the
fencing
a
is
a
lot
costlier
to
the
model
than
a
difference
in
Zod.
So
then
I
had
to
plant
all
of
them
to
between
zero
and
one
so
that
all
of
them
met
equally
to
the
model.
So
then,
now
it's
performing
better,
but
not
the
best.
A
Yeah
that
we're
yeah,
okay,
so
yeah.
So
you
showed
me
this
on
slack
and
so
comments.
So
these
these
letters
are
for
sub
lineages
and
a
is,
is
the
most
abundant
in
the
embryo.
So
that's,
roughly
half
of
the
embryo
is
a
a
B,
the
aviation
and
then
the
rest
of
these
are
kind
of
like
in
the
second
half
of
the
of
the
worm.
But
since
there's
so
many
of
them,
you
get
like
a
very
small
number
of
them.
Total
to
work
with
Z
is
by
far
the
smallest,
because
it's
part
of
the
germline.
A
Now
that's
that's
a
good
thing.
You
were
able
to
normalize
that,
because
it's
there,
probably
some
they're,
probably
gonna-
be
some
irregular
trends
in
these
other
sub
lineages.
Because
of
this,
the
way
they
divide
and
what
they
do,
but
I
think
a
is
probably
good
to
see
that
it
actually
works
to
predict
the
sort
of
doubling
rate,
yeah
I.
Think
that's
a
good.
That's
a
good
graph
and
I
think
he
did
a
pretty
good
job
on
her
Moi's
in
the
data
and.
E
C
Yes,
Oh
father
thing
is
like:
oh,
we
can
definitely
start
on
the
models
that
we
have
completed,
so
we
have
to
case
trouble
with
the
models.
First,
we
have
to
entail
on
the
website
and
second,
we
will
also
have
to
exported
as
a
Python
library
so
that
any
researcher
can
use
it
just
by
importing
a
dinner
or
nanotube
in
a
notebook.
So
we
can,
let's
maybe
start
from
the
lake
street
I
guess
yeah.
E
E
E
E
A
Yes,
I
mean
I.
Would
probably
you
know,
keep
me
in
the
loop
on
this,
but
I
would
coordinate
between
the
two
you
on
how
to
integrate
it,
because
what
well
of
course,
is
going
to
be
doing
the
integrating
some
of
the
integrating
and
Mike's
has
to
refine
the
models
and
then
Oswald
course
has
some
models
that
he
wants
to
integrate
as
well.
I
mean
I,
don't
know
how
you
you're
doing
it
as
well,
but
yeah.
That's
something
we
should
probably.
C
A
E
E
C
E
E
Well,
just
now,
with
the
CLC
as
offense
in
this,
but
I,
actually,
love
movies,
like
I
got
this
one
EP
and
already
an
LED
compromise,
so
yeah
I'll,
just
download
his
heels,
be
Sonia
what
will
be
downloaded
and
he
this
bulk
Texas
filed
before
in
some
other,
like
in
axis
in
my
Depot
days,
another
small
rectangle,
which
just
something
else.
It
classifies
the
lineage
from
the
positions
and
size
and
the
time
value,
but
that's
a
different
story
in
a
different
model
and
in
our
case
we
need
filling.
A
E
A
A
A
D
A
A
A
E
E
A
E
E
A
Let
me
use
to
think,
or
do
you
want
his
ingredients?
I
think
it
would
be
I
think
it
would,
because
we,
you
know
we're
kind
of
interested
in
sort
of
maybe
like
behavior,
that
it's
happening
in
the
embryo,
the
movement
and
all
that
so
I
think
that
would
be
a
good
way
to
sort
of
summarize
a
lot
of
those
that.
E
E
E
E
A
A
A
So
actually,
there's
a
in
the
code
section
here
there
are:
some
directories
bring
people's
attention
to
them.
We
have
definitions
and
concepts,
and
we
have
our
movement
I.
Think
definitions
and
concepts
have
what
I'm
looking
for
I
have
a
document
meta
features
which
define
some
things
in
general
like
things
about
these
meta
features
that
we
were
talking
about,
but
I
think
maybe
in
this
area
we
can
or
maybe
another
directory
here
at
the
root
of
G
soft
2020.
A
We
can
create
a
document
where
we
can,
like
you
know,
request
like
different
models
or
discuss
like
different
things
that
maybe
we
should
incorporate
into
this
I
mean
now
that
we
have,
you
know
good
start
on
it.
The
good
running
start
me
and
see
kind
of
what
is
going
on
so
I
I.
Don't
know
it
could
be
machine
learning
models.
I
could
be
maybe
other
types
of
predictive
models
and
just
keep
in
mind
that
they
don't
necessarily
implement
it.
But
it's
just
something
to
think
about.
If
it's
something.
A
A
C
A
A
C
C
C
A
C
A
Alright,
that's
done
and
then
I
think
the
weekly
blog
posts
are
something
that
you
guys
are
doing.
It's
not
required,
but
you
can
keep
doing
those
if
you're
doing
them
and
give
updates
the
optimized
color
palette
is
something
another
which
wall
said.
He
was
working
on
and
slack
where
he
said
in
slack
that
he
was
working
right
and.
D
A
A
A
I
can't,
remember,
I
mean
it
another
comment,
but
those
are
just
meant
for
you
to
kinda
draw
your
attention
to
things
if
you're
already
doing
them,
that's
good,
but
I
wanted
to
make
sure
that
I
had
you
know
there,
there's
the
room
for
improvement
and
to
make
sure
that
you're
getting
the
most
out
of
the
program
and
that
we
can,
you
know
the
a
lot
of
the
open
source
software.
No,
it
relies
upon
not
just
people
contributing
to
projects
but
the
documentation.
A
So
that
when
someone
else
wants
to
do
something
or
use
it,
it's
transparent,
so
I
was
gonna,
actually
do
two
more
things.
As
this
meeting
I'm
gonna
go
over
some
papers
in
a
minute,
but
I'm
gonna
briefly,
first
talked
about
the
knurl
match
Academy,
which
is
something
that
is
going
to
happen
soon,
and
my
other
group
actually
is
pretty
deep
into
this
Academy.
So
it's
a
summer
school
for
people
want
to
learn
about
neuroscience
and
I've
created
a
study
group
for
this
and
I've.
Actually
I've
done
this
in
consultation
with
the
large
summer
schools.
A
So
basically,
what
this
is
is
this
is
a
summer
school
for
people
who
want
to
learn
about
basically
computational
neuroscience,
so
it's
it's
neuroscience,
but
it's
computationally
oriented,
and
so
this
is
an
open
school.
There
is
an
enrollment,
a
formal
one
woman,
but
a
lot
of
people.
You
know
don't
really
have
time
to
enroll
for
a
full
summer
school,
so
they're
actually
making
some
of
their
materials
available
online
and
they
have
them
on
github.
So
there's
a
github
go
match.
A
A
There's
there's
some
resources
for
you
know
and
prepping
yourself
for
they're
there.
So
you
know
you
have
to
come
in.
You
have
to
know
a
little
bit
about
programming.
What
a
bit
about
Matt,
linear,
algebra
things
like
that
and
a
little
bit
about
neuroscience,
and
so
the
the
prep
is
mostly,
you
know,
sort
of
discussing
things.
You
know
concepts
that
you'll
need
to
to
know
to
do
successfully
in
the
school,
but
the
school
is
actually
meant
to
be
pretty
pretty
blank
slate.
A
You
don't
need
to
know
a
lot
about
any
of
those
topics
to
participate,
and
so
you
know
for
a
lot
of
you
in
this
group.
You
might
not
have
time
to
do
the
summer
school
and
it's
you
know,
but
there
are
actually
some
things
in
these
in
these
repos.
That
are,
you
know
something
you
can
take
something
away
from.
So
there
are
lessons
on.
You
know
different
topics
and
neuroscience
different
topics.
So
this
is
the
course
outline
people.
They
have
a
series
of
lectures
on
models
and
model
fitting.
A
There
are
some
machine
learning
and
then
you
get
into
statistics.
So
you
get
into
linear
systems,
Bayesian
statistics
a
little
bit
of
optimal
control,
which
is
like
control
theory,
a
little
bit
about
reinforcement,
learning
and
then
getting
into
like
neurons
and
neural
networks
or
neuronal
networks,
which
are
role,
neurons,
doing
making
networks,
and
so
you
know
it
it's
it's
a
little
taste
of
everything.
So
if
you're
interested
in
you
know
learning
a
little
bit
about
neuroscience,
you
might
get
involved
in
this.
A
Some
of
these
are
actually
from
Ybor
memo
every
cycle,
the
some
of
them
are
from
other
groups,
and
so
you
know
check
it
out.
If
you
have
time
if
you're
interested
in
learning
about
neuroscience
or
about
data
geek
for
this
computation,
you
know
maybe
you're
wanting
to
get
something
out
of
the
computation
part,
but
that's
that
I
just
wanted
to
bring
your
mom's
attention
to
that.
A
So
that's
it.
If
you're
interested
contact
me
I,
know,
Krishna
asked
me
about
learning
about
neuroscience
and
I
didn't
have
a
good
answer
for
him
at
the
time.
So
it's
you
know,
it's
not
one
of
the
things
I
can
give
you
a
15
minute
tutorial
on,
but
this
is
actually
a
good
substitute
if
you
go
through
some
of
these
materials,
and
we
can
talk
more
about
like
how
to
you
know,
learn
more
about
neuroscience
in
a
way.
F
A
F
Will
just
add
there
there's
still
opportunity
to
join
or
let's
do
the
observer
track
for
I
believe,
and
so
you
can
check
out
the
lectures
and
also
there's
a
there's.
A
discussion
forum
on
neuro
stars
or
which
is
sort
of
a
general
will
be
more
for
the
course
specifically
and
then
definitely
if
you
artist
said,
like
I'm
gonna,
be
fairly
involved
with
it.
Another
lab
group
as
well
so
I
mean
there's
actually
ways
where
you
can
participate
through
through
that
and
the
links
that
Bradley
Suns.
F
Even
you
can
you
can
interact
with
some
things
on
github
or
if
it
is
a
slack
in
a
key
base.
So
there's
a
lot
of
ways
to
be
involved
so,
and
you
know,
I
encourage
people
to
do
that
if
you're,
just
looking
at
the
narrow,
manage
stuff
itself
or
linking
up
with
what
what
no
Bradley
is,
is
kind
of
helping
to
facilitate
elsewhere,
and
it
was
really
cool,
I'm,
really
impressed
by
the
community
behind
no
match
I
have
a
tattoo.
F
They
did
two
impromptu
conferences
earlier,
like
no
match
one
and
two
unconferences
virtually
and
led
to
the
summer
school
and
it's
a
very
new
thing.
It's
kind
of
only
been
existence
for
a
couple
months
tells
some
hiccups,
but
but
it's
a
really
great
endeavor,
so
check
it
out.
That's
my
plug
for
it.
Yeah.
A
Thank
You
Jessie
yeah,
so
we
can
talk
more
about
that
offline
on
slack
so
first,
so
the
paper
I
wanted
to
talk
about
today
was
this
is
a
new
paper
and
something
I've
talked
about
in
the
group,
maybe
a
little
bit,
but
it
we
haven't
really
discussed.
We
haven't
really
done
anything
with
it.
It's
called
topological
data
analysis,
and
so
the
reason
I
bring
this
paper
up
in
this
group
is
because
it
is
actually
something
on
order
morphometrics,
and
so
this
is
really
nice.
A
A
So
the
abstract
I,
like
this
first
sentence
shape
is
data
and
data
is
shape,
and
so
we
we've
been
looking.
Actually
the
paper
you
all
talked
about.
The
3d
MMS
is
a
good
kind,
of
example,
of
that
where
you
can
take
data
and
you
can
build
a
model
of
shape
and
we've
had
a
couple
of
papers
like
that,
where
you
know
you
can
you
want
to
build
a
model?
That's
a
geometric.
A
It
has
a
shape,
a
volumetric
model
where
it
has
a
shape
and
extruding
that
from
some
data
that
we're
collecting,
so
we
have
this
organism.
That's
like
this
complex
shape
or
this
embryo.
You
know
that
has
a
certain
shape
cells
and
the
actual
embryo.
We
extract
data
from
that,
so
we
can
measure
it,
but
then
we
have
to
reconstruct
the
shape
on
the
other
end,
and
so
that's
kind
of
what
they're
doing
here,
but
they're
looking
going
to
step
further
and
then
say
how
can
we
produce
meaningful
parameters
to
describe
those
shapes?
A
And
so
biologists
are
accustomed
to
thinking
about
how
the
shape
of
biomolecules
cells,
tissues
and
organize
um's
arise
from
the
effects
of
genetics,
development
in
the
environment?
Less
often
do
we
consider
the
data
itself
has
shape
and
structure
or
that
it
is
possible
to
measure
the
shape
of
data
and
analyzed
it.
So
they
want
to
know
like
how
do
you
measure
that
shape
and
analyze
it
and
say
something
statistically
meaningful
about
it?
A
Here
we
review
applications
of
topological
data
analysis
to
biology
in
a
way
accessible
to
biologists
and
applied
mathematicians
alike.
Tda's
principle
uses
principles
from
algebraic,
topology
to
comprehensively
measure,
shape
and
datasets
and
say
they
use
a
function
that
relates
the
similarity
of
data
points
to
each
other.
A
We
can
monitor
the
evolution
of
a
topological
feature,
so
these
are
things
like
connected
components,
loops
and
voids,
and
so
topological
features
are
those
things
in
the
shape
that
you
know
it's
they're
interesting
features
of
that
you
can
think
of
them
as
features
or
a
feature
space,
but
they're
mathematical
objects.
Basically,
so
the
of
loops
connected
components-
I
didn't
bring
this.
A
If
there's
a
gift
that
shows,
it's
I,
think
it's
on
the
Wikipedia
page
for
like
topology
or
one
of
those
topics
where
it's
like
they
have
a
donut
that
morphs
into
a
a
mug
with
a
handle
on
it.
That's
kind
of
the
idea
behind
topological
analysis
where
you
have
like
this
shape,
that's
like
a
doughnut
and
then
you
transform
it
into
another
shape
that
might
share
some
of
the
features
it
might
not
share
some
of
the
features,
but
the
description
there
mathematically
is
to
characterize
a
transformation.
A
So
there's
a
lot
of
math
being
done
in
this
area.
So,
like
a
lot
of
the
machine
learning
stuff,
you
know
we're
interested
in,
like
you
know,
segmenting
images
or
building-
maybe
a
volumetric
model,
but
there
is
a
second
part
of
that,
which
is
the
analysis
of
the
shape
itself,
and
so
they
so
that's
the
evolution
on
top
of
topological
features.
A
A
A
If
we
know
you
know,
their
shape
is
very
important,
saying
leaves
or
in
embryos
or
mature
organisms,
and
we
talked
I
think
we've
talked
a
little
bit
in
a
couple
weeks
ago
about
Darcy
Thompson,
who
did
a
lot
of
work
about
a
hundred
years
ago
on
analyzing
different
transformations
in
shape
and
they're
kind
of
taking
off
from
that
point.
Actually,
they
do
mention
Darcy
Thompson
here
beyond
an
observation
and
documentation,
we
can
measure
shapes
just
as
we
analyze
data
Darcy
Thompson
in
his
on
earth.
A
A
These
are
sort
of
linear
scalings
of
like
so,
if
you
have
an
organism-
and
it
has
say
a
beak
and
the
beak
changes
shape.
Okay
with
growth
or
with
late
evolution,
you
can
put
landmarks
on
different
parts
of
the
beak
and
look
at
different
beaks
from
across
nature,
so
from
across
species
or
across
development,
and
you
can
figure
out
like
there's
a
growth
trend
that
happens
between
those
two
landmarks,
and
so
those
the
growth
trend
is
characterized
as
a
llama
tree.
It's
just
a
mathematical
function
that
describes
sort
of
the
transformation
of
that
that
metric.
A
So
you
know
like
sometimes
single
scale
head
size
versus
body,
size
and
they'll,
get
a
ratio
and
that
ratio
then
scales
with
as
the
organism
grows
in
size.
It
will
scale
you
know,
maybe
linearly
or
nonlinearly,
with
growth
in
the
organism.
So
this
is
something
that
we
can
do
as
well
and
understand
what's
going
on
with
with
phenotypes,
but
this
is
an
example
on
the
left
of
what
they've
done
with
a
leaf
here.
A
So
they've
looked
at
this
leaf
and
they're
kind
of
decomposing,
it
mathematically
they're,
building
this
this
network,
I
guess
of
things
along
the
surface
of
the
leaf
and
of
course
the
leaf
is
basically
a
vascular
network
but
they're
decomposing
it
in
this
way
and
they're.
Looking
at
the
variation
across
different
leaf
types,
fancy
there's
variation
in
the
leaf
type,
but
they're
basically
decomposing
it
into
maybe
common
features,
so
they're
using
this
network
to
find
common
features
across
these
leaves
in
there.
They
look
to
the
eye
very
different.
A
You
can
use
different
types
of
analysis
to
get
information
out
of
this
and,
if
you're
interesting,
you
can
go
through
this
article
and
they
mention
a
bunch
of
different
analyses.
They
throw
up
like
pro
Kristy's
analysis
and
geometric
morphometrics,
all
those
sorts
of
things.
So
does
you
know
that's
something
you
can
look
up
later
than
three
them.
You
know
the
way
people
write
an
article
like
this.
Is
they
could?
A
Oh,
they
pack
it
with
a
lot
of
references,
and
you
know
mentions
of
things
and
then
your
job
is
to
look
up
those
things
later,
but
they
actually
do
then
take
these
networks
and
find
the
principal
components.
So
we've
talked
about
principal
component
analysis
where
you
plot
the
one
principal
component
versus
the
second
principal
component,
and
that
describes
a
lot
of
the
variation
in
the
data
set.
So
in
with
these
regard,
to
these
sets
of
leaves,
you
get
distinct
groups
on
your
in
your
principal
component
analysis.
A
Another
way
so
then
they
talk
about
that
and
they
talk
about
different
methods.
Now
they
get
into
the
get
into
what
they
call
PDA
or
topological
data,
and
this
is
what
they
call
middle
ground
between
mathematics
and
biology.
So
TDA
is
they
kind
of
go
through
te?
A
here
and
I've,
never
really
understood
what
it
is
or
how
to
do
it,
but
I've
always
wanted
to
get
into
it.
It's
you
know
the
tools
are
coming
online.
It's
a
relatively
new
technique,
it's
something
that
you
know
the
mathematics.
A
So
they
talk
about
in
a
mathematical
context.
Networks
are
referred
to
as
graphs
nodes
are
points
are
referred
to
as
vertices
while
links
between
nodes
and
edges.
So
that's
like
a
network
type
of
analysis,
so
they
use
graphs.
We
can
generalize.
The
idea
of
graphs
by
adding
triangles
at
linked.
Edges
are
even
tetrahedrons
at
linked
triangles.
More
formally,
we
can
think
of
our
data
is
composed
of
different
building
blocks
called
simplices
and
that's
a
mathematical
term.
A
Vertices,
edges
and
triangles
are
0
1,
&
2
dimensional,
simplices,
respectively.
A
collection
of
multiple
simplices
makes
a
simple,
complex
or
complex
for
short,
so
these
now
you're
building
from
networks
to
these
simplices
to
these
simple
complexes,
and
then
this
is
how
you
proceed
with
topological
data
analysis.
A
A
This
is
a
complex
where
you
have
one
loop,
which
is
this
and
one
void,
which
is
this
triangle
three-dimensional
triangle,
this
pyramid
and
then
they're
connected
by
this
connected
component,
so
you
have
or
well.
These
are
the
connected
components,
but
this
is
a
connection
here
between
them
and
there's
a
similar
concept
in
graph
theory,
but
in
this
case
they're
just
talking
about
basically
creating
a
data
or
a
network
out
of
the
data,
and
then
you
know
analyzing
it
like
a
network
or
like
a
mathematical
object.
A
So
they
talk
about
the
via
torus
rips
complex,
which
is
something
very
technical,
so
the
VR
complex
starts
with
data
and
a
metric
space
and
a
fixed
non-negative
parameter
R,
which
is
the
radius.
If
the
two
vertices
are
close
enough,
that
is,
the
distance
between
them
is
less
than
R.
The
V
are
complex
will
have
an
edge
between
those
two
vertices.
A
So
this
is
a
criterion
for
forming
edges
from
a
bunch
of
nodes,
and
there
are
other
ways
you
can
actually
do
this
in
graph
theory,
people
will
have
done
this
in
different
ways,
but
this
is
the
way
they
are
suggesting
that
it
be
done
in
TDA,
so
they
walk
through
an
example
of
how
to
apply
this
to
a
data
set.
So
you
have
these
points
in
your.
Like
you
know.
A
In
our
case,
we
have
points
that
are
the
center
of
a
centroid
of
a
of
a
biological
cell
in
an
embryo,
and
you
would
take
those
points
and
you
would
join
them.
And
so
we
actually
wrote
a
paper
on
embryo
networks,
and
this
is
a
similar
thing
that
we've
done
already
in
the
lab.
But
now
you're,
you
can
take
those
networks
and
you
can
find
shapes
within
them
and
so.
A
Then
they
they
take
these
V
R
complexes
and
they
create
persistence,
barcodes,
which
are
these
structures
here.
That
kind
of
demonstrate
like
the
distance
from
the
rate.
You
know
the
distance
of
the
radius
and
different
objects,
and
they
create
this
visualization
here
that
describes
it
and
then
representing
persistent
features.
A
So
all
observations
described
above
can
be
summarized
using
two
topological
features
connected
components
and
holes,
and
so
connected
components
are
the
things
that
are
connected
like
a
graph
and
holes
are
the
things
that
aren't
and
again
that
has
a
parallel
with
network
theory
where
they
talk
about
connected
components
that
goes
back
to
Rennie
who's,
the
one
of
the
as
a
mathematician
from
a
long
time
ago,
and
he's
described
connected
components
as
something
that
was
a
feature
of
grab
a
large
networks.
And
so
you
can
use
a
similar
concept
here.
A
Whether
things
parts
of
the
network
are
connected
or
not
to
describe
its
structure,
and
so
we
can
also
visualize
a
connected
components
and
I
mean
this
I
mean
I'm
not
going
to
like
walk
through
it.
Much
more,
but
I
just
wanted
to
give
people
a
taste
of
what
this.
What
this
is
about,
and
so
now
you
get
into
applied
to
apology.
So
this
is
the
topological
analysis
or
you
have
the
different
shapes
you
can
transform
between
two
different
shapes
or
understand
this.
A
What
are
the
features
in
a
shape
and
I
think
this
is
actually
quite
useful
to
machine
learning
as
well,
because
we're
talking
about
feature,
selection
and
feature
discovery,
and
this
is
kind
of
what
they're
doing
here,
but
they're
doing
in
a
little
bit,
maybe
more
rigorous
way
for
three-dimensional
objects.
There's
more
of
a
mathematical
bent,
so
there's
more
formality
to
it.
A
So
this
is
an
application
of
TDA
to
biology.
They
have
a
nice
figure
here,
so
structural
biology,
which
is
a
B,
is
evolution
so
they're
looking
at
I
guess
a
genetic
distance
between
samples
number
letter
C
is
an
application
to
cellular
architecture.
So
this
looks
rather
familiar
to
people
who
are
segmenting
cells.
A
A
A
So
you
know,
there's
so
many
different
techniques
in
here
I
don't
want
to
even
get
into
it
much
more
because
I
really
couldn't
explain
it
in
an
hour,
probably
what
they
are
or
probably
ever
for
some
of
them,
but
they
have
some
nice
figures
in
here
and
it.
You
know
it's
good.
If
you're
interested
in
this
more,
we
can
talk
about
it.
A
I
think
it's
a
very
interesting
approach
and
it
might
be
useful
to
the
machine,
learning
people
or
even
the
biology
people,
for
you
know
doing
some
analysis,
development
and
so
yeah,
and
then
they
end
this
paper
with
a
great
figure
here:
endless
forms
and
most
beautiful
x-ray
computed
tomography
scans
of
the
biological
specimens
specimens,
showing
the
diversity
of
morphology
in
the
natural
world.
So
these
are
all
these
images
from
from
different
plants
from
seeds.
In
other
parts
of
the
plant,
this
is
a
pepper
bell,
pepper.
A
You
know
you
have
all
these
different,
so
this
is
what
you
did
kind
of
daddy
collect.
We
actually
talked
I
think
it
was
freshmen
who
wants
to
build
this
general,
so
this
is
actually
quite
relevant
to
that
as
well.
We
have
this
gently
all
these
different
forms
that
we
can
maybe
unify
in
your
single
model,
and
so
this
might
be
good
for
Krishna
to
read
to
get
a
sense
of
like
what
people
are
thinking
in
terms
of
going
very
far
afield
and
doing
all
these
different.
A
A
A
Jessie
says
I'll
have
to
show
my
Darcy
Thompson
meme
about
Cookie
Monster
yeah,
it's
in
the
slag,
so
look
at
it
cool.
What
comes
up
again
here
also
lots
of
thoughts
with
regards
to
affordances
and
direct
perception.
Now
we
did
talk
about
that
link
between
morphology
or
morphometrics
and
direct
perception
and
affordances.
We
should
talk
more
about
that.
Yeah.
A
I
think
like
it's,
like
that
type
of
analysis,
topological
analysis
doesn't
run
as
serving
accessible
to
no
mathematicians
but
I
think
they're,
creating
tools
now
that
are
along
in
terms
of
opening
it
up
to
other
groups
of
people.
You
know
Christ,
don't
want
to
talk
to
a
mathematician
about
like
how
to
do
it
correctly
and
get
good
results,
but
I
mean
that
would
be
something
that
definitely
it
opens
up
new
avenues
for
a
lot
of
things,
and
so
I
mean
these
it
outside
biology.
They
have,
you
can
apply
perception,
I
suppose.