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From YouTube: Embryo Networks as Generative Divergent Integration
Description
Recorded talk (15 minutes) for Networks 2021 Conference. Slides are available here: https://figshare.com/articles/presentation/Embryo_Networks_as_Generative_Divergent_Integration/14773347
A
So
the
time
is
the
developmental
time
at
which
cells
are
in
the
embryo,
dividing
and
differentiating,
and
then
the
context
can
be
things
like.
The
angles
of
cell
division
were
other
features
that
we
might
want
to
add
into
the
model
and
we
have
a
get
a
jupiter
notebook
on
github.
That
contains
a
lot
of
the
details
for
that.
A
A
It's
a
point
cloud
where
you
have
data
from
like
300
and
some
embryos
that
are
the
different
cells
have
different
identities,
but
these
cells
are
tracked
in
different
embryos
over
time
and
the
idea
is
we
can
take
these
data
average
them
out
for
certain
cell
identities
and
find
the
location
space,
and
so
these
three
axes
are
x
y
z
and
then
on
the
right.
We
have
these
lineage
trees
that
in
and
we
work
in
c
elegans.
So
this
is
all
very
uniform
across
embryos
and
across
lineage
trees.
A
So
on
the
right,
we
have
a
lineage
tree
that
represents
time
over
time,
so
there's
cell
divisions
over
time
and
then
there's
this
parameter.
I,
which
is
sort
of
the
axial
organization
of
the
lineage
tree,
which
we
can
interpret
as
identity
and
other
you
know,
cell
identity
and
other
things.
So
we
have
a
lot
of
information
here
that
we
can
map
to
this
network,
and
so
cell
division
provides
a
number
of
challenges
for
looking
at
this
in
a
network
from
a
network
perspective.
A
The
first
is
that
the
graph
diameter
will
expand
or
grow
in
the
number
of
nodes
over
time,
so
as
cells
divide
by
on
orders
of
two,
they,
this
network
will
grow
both
in
size
but,
more
importantly,
in
its
density,
and
so
this
is.
The
consequence
of
this
is
that
local
connectivity
increases
over
time.
The
nodal
density
will
increase,
and
especially
as
you
get
differentiation
and
you
get
migration
of
cells,
certain
areas
will
tend
to
take
on
you
know,
modular
modular
form
and
so
global
modularity.
A
The
bus
increases-
and
this
is
due
to
differentiation
events
and
what
we
call
bifurcations
and
so
bifurcations
are
essentially
cell
divisions.
But
in
this
case
you
can
see
that
you
have
these
cells
that
start
out
as
a
single
cell
and
then
they
start
to
expand
and
something
that
looks
like
it's
going
to
divide
and
then
finally,
you
have
this
bipartite
structure.
This
bifurcation,
where
you
now
have
two
cells
where
you
had
one,
and
so
this
bifurcation
structure
this
at
least
the
questions.
How
many
parts
does
the
network
fragment
into
over
time?
A
A
So
in
this
example
of
the
interactome,
you
have
this
network
structure
in
anatomical
space
and
you
have
different
colored
connections.
Not
these
nodes,
don't
all
exist
at
the
same
point
in
time.
These
have
been
plotted
to
show
that
you
have
different
networks
at
different
points
in
time
and
the
connectivity
changes
as
you
have
different
levels
of
cell
division.
So
you
can
see
here
we
have
a
hairball
network
that
shows
what
the
embryo
network
will
look
like
over
time
and
different
with
the
anatomical
orientation.
A
Here
p1
is
the
posterior
and
ab
is
the
anterior
end,
and
we
can
also
then
connect
this
to
the
connectome,
the
the
neural
connector,
because
we
know,
for
example,
the
locations
of
all
the
cells
in
the
developing
embryo.
Well,
we
also
know
their
identity,
and
so
that
allows
us
to
look
at
neural
differentiation
over
time
and
the
emergence
of
this
connector.
A
So
this
is
what
our
generative
divergent
integration
is
is
referring
to
taking
these
embryo
networks
turning,
you
know,
turning
them
into
sort
of
these
hybrid
embryo
networks
and
connectomes,
and
then
looking
at
how
two
things
evolve
over
time,
and
so
here
you
can
see
an
example
of
the
connectome
that's
emerging
in
development.
This
is
at
about
300
minutes
of
development
of
embryonic
development,
and
you
can
see
that
you
can
track
the
different
neural
identities
based
on
their
lineage
tree
position.
A
A
So
in
this
case
we're
going
from
this
point
cloud
we're
creating
an
embryo
network
and
then
we're
trying
to
find,
within
the
embryo
network
or
within
a
sort
of
a
refined
point
cloud
where
those
neurons
are
located
and
you
can
see
that
they
take,
they
have
cert.
You
know
a
certain
axial
distribution
in
the
embryo,
and
so
we
can
integrate
those
two
networks
together
and
it's
it's
very
predictable
across
individuals.
A
And
so
again
you
can
see
this
in
three
dimensional
space.
You
can
see
this
in
two-dimensional
space
and
then
at
the
bottom.
Here
you
can
see
this
in
the
adult
where
these
neurons
are
located
within
the
organism,
and
so
you
have
two
networks
here.
You
have
the
connectome,
which
is
all
these
dots
here,
these
break
dots
and
then
you
have
every
cell
in
this
organism
which
also
forms
another
network.
A
So
this
is
an
example
of
generative
divergent
integration
and
we
can
look
at
the
eight
cell
example
in
the
24
cell
example.
So,
in
the
eight
cell
example,
we
can
look
at
only
the
embryo
network
because
the
neurons
haven't
differentiated
yet,
and
we
can
see
that
we
can
set
a
threshold
of
a
certain
distance
between
the
cells
or
the
cell
centroids.
To
give
us,
you
know
either
two
cells
are
connected
or
two
cells
are
not
connected.
A
But
you
can
see
here
the
eight
cell
embryo
in
this
case-
and
this
is
not
empirical-
it's
just
something
I
drew-
is
it's
a
bipartite
network?
It's
not
a
not
a
network,
that's
integrated
in
any
way.
It
has
little
pieces
that
are
it's
fragmented.
Essentially
so
we
say
for
all
developmental
cells,
blue,
the
distance
t
between
cell
centroids
and
that's
how
we
get
our
connectivity
and
there's
sparse
connectivity
due
to
the
larger
cell
size
and
sort
of
the
sparseness
of
this
embryo.
A
By
contrast,
we
go
to
this
24
cell
example
and
again
this
is
just
a
cartoon,
but
we
get
two
actually
at
this
point:
we're
getting
two
different
types
of
cell
we're
getting
the
somatic
cells
which
are
in
blue,
which
we
see
in
the
eight
cell,
and
we
get
these
light
green
cells
which
are
neurons
or
emerging
neurons.
And
so
now
we
can
make
the
connection
between
these
two
types
of
networks.
A
We
have
these
connectome
or
neural
networks
that
are
starting
to
form,
and
then
we
have
these
embryo
networks,
which
are
already
like
sort
of
becoming
more
dense
and
connecting
together,
there's
no
longer
this
fragmentation
of
the
network.
It's
totally
joined
together,
but
you
can
see
that
there
that
the
neural
network
and
the
somatic
network
are
joined
together
by
the
same
criterion,
and
so
we
actually
have
this
dual
network.
A
And
so
all
neurons
that
are
green
might
share
like
gap
junctions
and
have
a
special
sort
of
and
and
those
networks
are
at
this
point
fragmented,
but
they
share
the
you
know
properties
that
the
somatic
cells
do
not.
Nevertheless,
you
can
say
that
they're
connected,
because
we
have
this
criterion
of
distance,
which
is
of
course
important
in
signaling
and
other
things,
and
so
we
can
draw
this
network
in
a
number
of
ways.
But
the
idea
is:
is
that
they're
integrated
within
one
another
they're
embedded
within
one
another?
A
And
so
but
then
we
have
a
larger
question,
which
is
that,
with
the
in
terms
of
developmental
spatial
connectivity
and
connectomes,
what
kind
of
network
is
it?
Is
it
a
random
network?
Is
it
a
skill-free
network
or
is
it
a
small
world
network,
and
these
are
data
from
an
adult
zebrafish?
So
the
adult
zebrafish
exhibits
this
type
of
connectivity
and
it's
in
its
neural
network.
A
But
the
question
is:
is
what
do
we
expect
for
developmental
networks,
and
so
this
is
vexing,
because
it's
not
necessarily
going
to
yield
these
types
of
patterns
because
it
not
only
is
it
not
static,
but
it
also
has
certain
properties
that
maybe
we
need
to
figure
out
what
you
know:
there's
maybe
a
new
rule
or
a
new
set
of
rules
that
we
need
to
consider
for
this.
So
we've
have
a
number
of
candidates.
For
this.
We
have
the
new
world
networks,
which
are
small
world
networks.
With
expansion.
A
A
So
in
terms
of
new
world
embryo
networks,
these
are
multi-level
networks.
We
have
a
number
approximate
proximity
and
adjacency
measurements,
such
as
convex
hall
measurements
over
time,
and
we
can
understand
that
using
topological
data
analysis.
We
can
also
use
differential
network
diameter
and
look
at
the
network
diameter
between
t1
and
tn.
Whatever
that
time
is
so
we
can
get
an
accounting
of
how
these
things
grow
over
time.
We
can
also
measure
expansion
rate
in
different
ways,
so
we
can
look
at
differential
path,
link
ratios
so
between
time.
A
One
versus
time
in
we
can
look
at
the
difference
between
the
path
lengths
or
we
can
look
at
differential
clustering
again
between
time,
one
and
time
n.
So
we
can
see
how
much
clustering
is
gained
over
time.
We
assume
that
we
start
out
with
a
random
initial
condition
that
doesn't
have
much
structure,
so
the
clustering
will,
of
course
increase,
but
by
how
much?
A
We
can
also
look
for
new
types
of
topologies,
and
there
are
at
least
three
candidates
for
this.
One
are
feature-rich
networks,
so
these
are
topological
features
that
capture
emerging
tissues,
fluid
dynamics
and
gene
expression
cascades
a
second
one
are
multiple
worlds,
so
multiple
worlds
consists
of
different
pro
processes
and
structures
captured
in
an
impartite
network
with
weak
connectors.
A
So
this
is
more
relevant
to
the
combining
the
connectome
and
the
embryo
network
into
one's
single
system,
but
also
something
that
has
differential
functionality
and
then
finally
semi-integrated
networks,
which
of
course
are
interrelated
phenotypic
modules
and
functional
systems.
This
is
like
the
brain
and
the
body
problem,
but
this
is
actually
something
that
we
can
quantify
in
our
networks.
A
So
we've
come
up
with
one
thing
for
now
that
that
might
be
a
candidate
and
that's
something
we're
proposing
called
the
density
bifurcation
model,
so
the
process
of
increasing
connectivity
and
development
occurs
as
follows.
At
first,
you
get
cells
that
divide
and
migrate
and
as
a
result
of
that,
based
on
our
sort
of
criterion,
the
connectivity
increases.
A
Secondly,
cell
migration
enriches
local
communities
and
cliques,
so
you
get
this
enrichment
of
structure.
Thirdly,
the
function
of
cells
diverge
over
time.
So
there's
this
differentiation
function.
Not
only
do
you
get
connectomes
and
embryo
networks,
but
you
get
structure
within
embryo
networks.
You
get
different
organ
systems
and
things
that
emerge,
and
so
at
least
two
interconnected
networks
emerge
from
this,
but
probably
more
as
we
go
through
development.
A
Finally,
interconnected
networks
provide
weak
ties
and
these
are
functional
interdependencies
between
emerging
tissues.
So
these
interconnections
between
different
types
of
networks-
these
are
actually
weak
ties.
So
if
we
go
back
to
our
cartoon,
we
can
see
that
the
neural
networks
and
the
somatic
networks
are
connected,
but
these
are
weak
ties.
A
That
might
say
not
exhibit
all
of
the
features
of
t
cells
that
are
connected
within
the
somatic
network,
but
nevertheless
have
some
influence
and
we
use
the
term
weak
tie
because
weak
ties
are,
you
know
they
be
loosely
more
loosely
associated
but
still
associated
and
have
topological
effects,
so
future
directions
for
this
work.
We
want
to
capture
embryo
dynamics
more
effectively.
I
showed
an
image
of
a
hairball
network.
A
I
showed
images
of
where
you
can
look
at
multiple
layers
of
the
lineage
tree
simultaneously,
but
we
really
want
to
get
a
better
accounting
of
the
hemorrhoid
dynamics,
and
that
means
looking
at
time
series
and
looking
building
networks
that
are
dynamic
in
time
and
multi-level
in
time.
So
here
you
see
examples
of
embryos
that
are
evolving
over
time
that
are
changing
their
their
morphology
over
time,
and
this
is
the
sort
of
thing
we
want
to
pick
up
on.
A
We
want
to
be
able
to
identify
a
lot
of
these
movements
and
maybe
what
we
call
meta
features
which
we're
currently
kind
of
beginning
to
understand,
with
using
machine
learning
and
deep
learning,
where
you
get
different
movements
of
the
furrow
and
different
movements.
You
know
things
that
emerge
as
cells,
differentiate
and
move
around,
and
so
those
are
the
things
you
want
to
characterize
with
networks.