►
Description
One hour lecture on "Embryo Networks, Computational Development, and Neurosimulation". Presenter: Bradly Alicea, December 2022.
A
Today,
I'm
going
to
talk
to
you
about
embryo
Network's,
computational
development
and
neurosimulation,
this
is
representative
of
work
being
done
in
the
past
five
years.
In
the
diva
worm
group,
the
diva
worm
group
is
part
of
the
open
arm
foundation
and
the
orthogonal
research
and
education
lab.
We
started
in
2018
with
a
paper
on
embryo
networks
which
we'll
talk
about
and
then
talking
about,
Developmental
connectomes
and
then
more
recently,
we've
done
papers
on
hypergraphs
and
tensegrity
networks
and
we'll
talk
about
what
all
those
are
in
a
little
bit.
A
So
the
motivating
question
is:
how
do
we
characterize
the
process
of
proliferation,
cellular
interactions
and
functional
differentiation
in
embryogenesis?
And
here
you
can
see
an
example
of
a
c
elegans
embryo
developing
from
the
two
cell
stage,
and
when
you
get
to
about
200
minutes
of
development,
you
start
to
give
the
formation
of
this
comma,
which
is
the
second
morphology
from
the
right
and
then
at
the
very
right.
A
You
have
this
pretzel
phenotype,
which
is
where
the
what
starts
to
look
like
The
larva
worm,
starts
to
form
within
the
egg,
and
then
this
leads
to
the
structure
down
at
the
bottom
of
the
title
page
here
with
this
network
on
it,
but
you
can
clearly
see
that
that's
curled
up
C
elegans
larva
just
ready
to
patch
out
of
the
egg.
So
that's
the
core
Time
Force
of
C
elegans
development
and
we'll
be
using
examples
from
c
elegans,
as
well
as
other
organisms.
In
this
talk.
A
So
this
is
an
example
of
newly
hatched
C
elegans.
This
is
this
spiral
that
it
forms
the
larva
forms
just
before
the
egg
hatches
and
you
can
form
a
network
out
of
this
using
different
landmarks.
This.
This
is
a
microscopy
image.
You
can
take
that
microscopy
image,
find
landmarks
and
build
a
network.
And
of
course,
here
the
network
is
the
nearest
neighbor
Downstream
in
in
the
phenotype
or
in
the
anatomy
from
the
head.
So
you
can
see
that
there
that
works,
that
kind
of
spiral
outwards,
so
you
can
characterize
different
topologies
in
that
way.
A
You
can
also
look
at
something
like
the
mouse
blastocyst,
which
is
an
early
stage
of
mouse
development
where
you
have
this
Inner
Cell
mass
in
this
outer
edge
of
cells-
and
here
you
can
characterize
the
cells
in
different
in
different
classifications
depending
on
the
cell's
state.
So
if
they
were
interested
in
the
inner
saw
Mass
versus
the
outer
ring
of
cells
there,
we
want
to
maybe
map
out
some
of
the
connections.
Maybe
they
have
chemical
connections.
Maybe
they
have
other
types
of
relationships
that
we
want
to
characterize.
A
So
we
need
to
do
is
use
something
Akin
as
what
they
call
New
World
networks,
which
are
actually
networks
from
the
brain,
Network
literature,
and
these
are
networks
that
expand
when
in
terms
of
their
number
of
nodes
with
time.
So
as
time
goes
on,
you
get
especially
if
you're
characterizing
single
cells,
you
get
more
and
more
cells,
you
get
more
complexity
in
your
graph
and
you
need
to
account
for
that
in
your
representation.
A
So,
typically,
we
can
take
images
of
different
and
we'll
see
this
later
of
different
stages
of
development
and
compare
the
networks,
and
we
need
to
account
for
that
in
a
representation.
But
there
are
a
number
of
ways
to
do
that.
So,
if
you
think
just
about
the
connectivity,
though,
what
does
this
reveal?
Why
are
we
doing
this?
A
A
You
can
also
characterize
cells
with
a
common
function.
So
in
the
mouse
example
the
mouse
blastocyst,
the
Inner
Cell
Mass,
we
can
characterize
the
relationships
between
the
inner
cell
Mass,
but
also
with
other
cells
in
the
embryo,
and
so
we
can
actually
get
those
functional
categories
worked
out.
Finally,
you
find
connections
between
symmetrical
pairs
and
C
elegans.
A
So,
to
recap:
if
you're
not
familiar
with
how
cell
division
works,
but
especially
in
the
in
the
case
of
like
a
graft
theoretical
representation,
there's
a
term,
we
can
use
called
bifurcation,
and
this
is
going
from
a
single
Network
to
a
bar,
bipartite
Network,
and
so
this
asks
the
question:
how
many
parts
does
the
network
fragment
into
over
time?
So
you
can
see
here.
We
have
a
bipartite
structure.
We
have
a
bifurcation
of
one
cell
into
two
cells,
and
so
we
have
this
say.
A
For
example,
we
have
a
single
cell,
we
have
a
bunch
of
cells
around
it,
they
form
a
network
and
then
that
cell
divides
that's
a
bifurcation
of
that
node
in
the
in
the
network,
and
so
now
we
need
to
represent
that
bifurcation
event
going
from
a
single
Network
to
a
bipartite
network
in
that
area.
So
we
need
to
actually
account
for
this
in
the
representation.
A
So,
as
I
mentioned
before,
we
also
have
this
problem
of
the
graph
diameter
expanding
because
there's
a
growth
in
the
number
of
nodes.
So
as
the
cells
divide
and
they
differentiate,
but
especially
as
they
divide
and
proliferate.
The
number
of
nodes
increases
in
the
network,
and
so
we
need
to
have
a
good
accounting
for
that
and
the
new
world
networks
approach
is
this
one
possible
approach
to
that
local
connectivity
tends
to
increase
as
the
nodal
density
increases
and
Global
modularity
increases
as
we
get
differentiation
in
these
bifurcation
events.
A
A
So
this
is
our
mathematical
treatment
of
embryo
networks.
This
comes
from
our
work
in
2018.
This
is
a
basic
embryo
Network.
So
the
idea
is
you
get
this
Point
cloud
of
of
cell
centroids
and
you
characterize
the
relationships
between
those
cell
centroids
by
either.
You
know
some
sort
of
relationship
between
the
cells
in
terms
of
space
or
in
terms
of
time
or
in
terms
of
something
like
chemical
signaling,
but
regardless
we
need
to
have
some
sort
of
mathematical
representation.
A
So
we
can
use
cell
tracking
data,
which
scans
an
image.
It
produces
a
bunch
of
cell
centroids
from
microscopy
data
and
you
so
you
get
this
point
cloud
and
you
have
to
characterize
these
cells
in
3D
space
and,
of
course,
cell
tracking.
Does
that
automatically?
So
you
get
it
embedded
into
three-dimensional
anatomical
space
where
you
have
three
anatomical
Dimensions,
which
are
XYZ
in
this
representation?
A
So
as
we
move
through
development,
that
time
increases
and
context,
which
is
the
last
parameter
and
context,
is
interesting
because
it
can
be
anything
you
want
it
to
be,
can
be.
You
know
some
sort
of
relate
set
of
relationships,
some
sort
of
identity
marker,
some
sort
of
other
type
of
marker,
and
so
it's
it's
a
pretty
flexible
methodology.
We
have
a
Jupiter
notebook
that
divorce.github.io
you
can
find
more
about
it.
A
Also,
if
you
go
to
the
paper,
you
can
find
a
link
to
it
in
the
paper
in
the
methods.
So
this
gives
us
this
five-dimensional
data
structure,
and
this
is
an
example
of
how
you
can
use
context.
So
we
take
data
from
this
point
Cloud.
This
is
XYZ
coordinates.
These
XYZ
coordinates
are
anatomical,
so
it's
anterior,
posterior,
dorsal,
ventral
and
left
right,
and
so
you
put
these
in
a
context.
You
average
over
these
points
for
different
cells.
A
A
A
So
that's
that's
the
first
step,
and
then
we
move
on
to
characterizing
these
lineage
trees,
and
so
these
lineage
trees
and
C
elegans
are
again
very
simple:
they're
binary
trees
that
have
exhibit
division
events,
as
you
can
see,
we've
characterized
it
with
a
binary
code,
so
you
have
a
single
cell.
You
have
a
division
event
where
we
have
a
zero
lineage
in
a
one
lineage
and
then
sub
lineages
of
zero,
zero,
zero
one
and
then
one
zero
one
one,
and
so
these
are.
A
This
is
the
formation
of
these
sub
lineages,
which
will
eventually
contribute
to
these
sort
of
modules
that
this
modularity
that
results
eventually
in
the
in
the
lineage
trees
it
divides.
Well,
we
have
this
time
Dimension,
which
goes
down
to
one
of
each
tree.
So
it's
very
simple:
there
are
different
layers
to
the
lineage
tree
and
those
layers,
then,
can
be
characterized
with
t
and
then
I,
which
is
the
spatial
context
which
has
this.
The
lineage
between
C
elegans
is
organized
along
an
interior
posterior
axial
order.
A
It
doesn't
have
to
be
that
you
can
rearrange
it
in
different
ways.
You
can
build
trees
that
are
organized
based
on
their
spatial
or
more
explicit
spatial
locations,
or
maybe
some
of
the
you
know,
signaling
gradients
that
you
might
be
interested
in
and
and
once
you
get
outside
of
C
elegans,
these
conditions
change.
Sometimes
it's
harder
to
identify
single
song,
winning
edges
like
in
the
mouse
they
people
have
worked
on
approximating
so
many
edges,
but
they're
not
absolute.
So
this
is
a
an
issue
that
comes
up
also.
A
We
have
this
I,
which
is
the
context,
and
that
can
be
a
number
of
things.
So
you
know
this
is
a
flexible
approach,
but
it
also
comes
with
some
caveats,
so
we
take
the
five
dimensional
data
structure
and
we
can
build
these
networks,
and
so
this
is
an
example
of
spatial
connectivity,
and
this
is
an
example
of
perhaps
an
interactive
example
that
I
talked
about
before,
where
you
have
chemical,
signaling
locally
between
cells.
A
You
want
to
know
what
are
the
nearest
cells
not
only
in
a
single
static
example
of
a
stage
of
development
in
an
embryo
but
across
different
layers
of
that
lineage
tree?
So,
as
we
saw
before,
we
have
different
layers
of
the
lineage
tree,
and
here
we
can
see
that
these
different
layers
of
the
lineage
tree
are
embedded
in
this
network,
a
three-dimensional
Network
space.
A
So
this
topology
contains
not
only
lineage
tree
information
and
proximity
information,
but
other
types
of
information
that
you
can
mine
from
it,
and
so
this
is
an
example
on
the
right
of
these
two
subtrees
that
are
emerging,
what
they
call
a
b
and
P1
and
the
CL
against
embryo.
And
so,
as
those
emerge,
you
start
to
see
connectivity
differences.
A
P1
cells
tend
to
be
connected
to
P1
a
b
tend
to
be
connected
to
a
b,
but
there's
overlap,
as
you
can
see,
and
this
again
is
this
circular
graph
on
the
right
is
just
based
on
this
distance
metric
information.
So
that's
the
only
Criterion
we're
using
for
connectivity,
but
you
can
see
that
it
starts
to
form
two
modules
and
maybe
a
few
more
modules.
A
As
we
as
we
go
forward,
you
can
start
to
see
that
there's
local
connectivity
in
different
areas
because
the
cells
you
know
they're
they're
in
they're,
not
in
uniform
distributions
within
the
embryo,
so
they're
not
necessarily
uniform
sizes
either.
So
you
start
to
see
these
modules
start
to
emerge
and
we
can
describe
that
pretty
well
using
using
complex,
Network
Theory.
A
So
next
we
come
to
the
question
of
what
kind
of
a
network.
Is
it
if
you're
familiar
with
complex,
Network
Theory?
You
know
that
there
are
different
types
of
networks
that
emerge
from
data.
So
if
we
look
at
different
types
of
complex
networks,
you
know
we.
We
start
with
the
assumption
that
the
random
Network
has
nothing
like
has
no
structure.
Basically.
So
a
lot
of
times,
people
will
generate
these
random
Networks
to
represent
sort
of
a
sort
of
a
null
condition
or
sort
of
a
default
condition.
A
A
Now
we
can
assume
that
it's
random,
but
it's
probably
not
and
I,
know
from
doing
analysis
and-
and
you
can
see
this
in
some
of
the
papers-
that
the
cl
against
embryo
is
not
random-
it's
not
a
random
graph
and
it
continues
to
be
less
random
over
developmental
time.
So
you
know
very
early
on.
You
may
find
some
random
signature,
but
not
really
because
you
get
these.
You
already
start
to
get
these
two
anatomical
polls
very
early
in
development,
but
what
kind
of
a
network
is
it?
A
A
That's
that's
a
signal,
a
very
strong
modularity
and
if
you're
familiar
with
the
CL
against
connectome,
the
small
world
effect
has
been
described
in
the
CL
against
connect
open,
different
papers
that
small
world
connect
connectivity
emerges
in
the
developmental
connectome
and
it
takes
a
while
for
it
to
emerge.
So
the
very
first
steps
of
a
developmental
connectome.
You
don't
really
see
that
small
world
organization,
but
by
the
time
you
get
towards
a
mature
connectome.
You
do
begin
to
see
that
sort
of
organization,
so
we
can
actually
look
at
these
different
network
types.
A
So
we
can
actually
look
at
the
somatic
and
nervous
system
networks
in
adult
CL
again.
So
this
is
an
example
from
the
open
or
browser.
If
you're
not
familiar
with
it,
you
can
go
to
browser.openorg.org
and
you
can
explore
the
worm.
You
can
explore
the
muscles,
the
body
sort
of
the
body
wall
and
the
muscles
you
can
explore
the
nervous
system.
The
center
image
is,
is
an
image
of
the
nervous
system
with
its
connections
with
its
neurons
and
connections
and
then
below
you
see
another
version
of
that.
A
It
has
around
a
thousand
cells
in
the
body
in
the
somatic
Network
in
adulthood,
and
it
has
about
300
cells
in
the
adult
connectome
in
the
developmental
connect
Dome
and
the
develop,
and
the
embryo
Network
have
fewer
cells
to
deal
with.
So
this
is
a
tractable
kind
of
network
analysis.
We
can
do
plus
we
know
kind
of
what
the
path
is
from
development
to
adulthood.
A
We
also
know
that
these
organisms
are
utellic,
so
that
means
they
have
the
same
number
of
cells
from
organism
to
organism,
and
they
have
this
sort
of
deterministic
division
division
program
that
you
know
doesn't
like
vary.
So
unless
you
have
a
mute
on
your
hands,
they
generally
every
lineage
tree
produces
the
same
set
of
cells
in
the
same
roughly
the
same
position,
so
it's
a
very
easy
system
to
work
with
and
so
building
these
networks
from
C
elegans
is
especially
then.
A
So
I
told
you,
then,
that
we
have
these
somatic
networks,
these
embryo
networks,
and
we
have
these
connectomes
or
neuronal
Networks,
and
so
one
of
the
things
we
can
do
as
we
can
look
at
and
we
have
data
for
these
that
are
publicly
available.
Other
groups
have
collected
a
lot
of
data
on
this
and
we've.
The
diva
worm
group
has
been
involved
in
sort
of
mining
these
data
and
building
these
kind
of
models.
A
So
one
thing
we
have
is
this
Point
cloud
of
embryo
cells,
and
so
this
is
you
know
on
this
is
raw
that
I
just
wanted
to
show
that
it's
kind
of
the
shape
of
the
data
to
give
you
an
idea
of
what
we
have
and
then
we
average
those
cells
out
because
they
have
certain
identities
and
we
can
find
sort
of
a
mean
cell
centroid
and
then
build
these
embryo
networks
from
this.
This
is
just
a
raw
example.
A
So,
as
we
know
in
development,
we
first
get
a
neural
tube,
and
this
is
I'm
talking
about
manelion
development
and
vertebrate
development.
You
get
a
neural
tube,
which
is
a
folding
activity,
and
then
you
get
these.
You
get
like
a
notochord
or
a
you
know,
a
sort
of
a
neural
crest
and
then
that
it
forms
a
basis
for
most
of
the
connectome
in
in
vertebrates.
So
you
get
these,
you
know,
get
these
cells
at
the
top.
You
get
these
cells
down
the
down.
A
The
cord
and
that
that
forms
your
spinal
column
and
your
central
nervous
system,
and
then
everything
else,
builds
off
of
that
and
then
C
elegans.
You
can
see
that
there
are
these
sort
of
axes
of
neural
cells
and
these
are
newly
differentiated
neuronal
cells.
So
when
you
build
a
connectome
in
development,
You're
Building
from
these
embryonic
cells
and
they
differentiate
into
neural
cells,
and
then
they
form
these
two
along
these
two
axes
you
can
see
at
the
Top
This
is
a
along
the
left,
right,
Axis
and
the
anterior
posterior
axis.
A
So
you
have
two
axes
of
cells
and
then,
in
the
three-dimensional
view
you
see
that
there's
some
dorsal
ventral
bias
for
each
of
these.
That
kind
of
goes
diagonally,
dorsally
and
ventrally.
So
you
get
these
two
axes,
and
so
these
will
eventually
form
what
we
see
in
the
adult,
which
is
that
we
have
a
cluster
of
cells
at
the
head
cluster,
our
cells
at
the
tail
and
then
a
bunch
of
cells
along
this
midline
that
are
all
connected
by
long
distance
connections
or
short
distance
connections.
So
we've
written
well.
A
These
are
the
two
papers,
not
the
bottom,
the
first
one,
the
cell
differentiation
processes,
describes
how
we
build
these
embryo
networks,
so
this
was
in
biosystems
and
then,
in
the
same
issue
of
biosystems,
we
published
a
paper
on
the
emergent
connectome
and
C
elegans
embryogenesis.
So
this
is
the
paper
that
talks
about
the
neural
connect
element
development.
A
So
this
is
an
exam.
This
tree
just
kind
of
gives
us
these
distance
thresholds,
and
this
is
this
is
an
exercise
and
looking
at
the
different
sub
trees
that
we
can
build.
These
are
lineage
trees
that
we
can
build
from
these
networks,
so
we
can
map
the
lineage
trees
of
the
network
topologies
so
that
they
don't
look
like
these
hairballs.
That
don't
mean
anything,
and
so
we
can
see
that
they're
they're
these
sort
of
overlaps
between
lineage
trees.
A
Looking
at
these
different
Network
topology,
so
we
build
a
network
at
each
level
of
division
and
then
we
look
at
the
the
member,
their
memberships
in
different
developmental
or
lineage
tree
sub
trees,
and
so
we
can
see
that
there's
overlap.
But
it's
not
completely.
You
know
mushed
together,
but
it's
also
not
completely
separate.
A
So
that's
interesting
because
that
means
that
there's
a
lot
of-
and
this
is
a
again
this
distance
metric
so
we're
looking
at
like
the
intersection
of
these
two
sort
of
modules-
sometimes
they're
separate
and
sometimes
they're-
not
so
we,
but
we
can
find
all
sorts
of
new
types
of
topologies
doing
things
like
this.
So
you
know
we
talked
about
random
networks
versus
scale,
free
versus
small
world
and
those
are
fine
for
like
generic
networks.
A
So
when
people
look
at
like
Transportation
networks
or
connectums
or
you
know
social
networks,
they
find
these
three
types
of
network
topologies.
But
when
we're
dealing
with
connectomes
that
are
connected
to
say,
like
the
lineage
tree,
that
might
have
their
origins
in
a
very
few
cells,
so
very
few
number
of
cells
where
there
isn't
really
a
topology
to
speak
of.
But
then
you
get
the
emergence
of
this
complexity,
this
organization.
How
do
we
describe
those?
And
so
one
of
the
things
we've
done?
A
And
we
haven't
really
put
a
paper
out
on
this,
but
there
are
new
types
of
topologies
that
we
can
sort
of
hypothesize
exists
and
we
don't
really
know.
But
we
know
from
what
we
deal
with
in
the
embryo
we
deal
with
in
terms
of
cell
lineage
and
what
we
deal
with
in
terms
of
the
you
know
merging
these
two
types
of
networks
that
there
are
a
number
of
possible
new
types
of
connection
regimes.
So
one
of
them
is
this
feature-rich
network,
and
these
are
topological
features
that
capture
fractals
and
fluid
dynamics.
A
So
these
are
types
of
networks
that
are
like,
like
these
embryo
networks,
which
are
spatial
in
nature,
that
capture
spatial
relationships,
but
they
also
capture
other
things
that
are
reliant
on
spatial
relationships
like
fluid
dynamics
or
fractal
organization.
So
when
you
have
like
a
number
of
cells
that
are,
you
know,
kind
of
clustered
together,
maybe
that's
a
product
of
fluid
dynamics
or
maybe
there's
fractal
organization
where
you
get
a
ring
of
cells
and
then
a
smaller
ring
of
cells
and
a
smaller
ring
of
cells
and
so
forth.
A
We
can
capture
all
those
relationships
with
embryo
models,
because
they're
essentially
representations
of
spatial
organization,
and
by
that
for
that
matter,
solar
connectoms,
if
you,
if
you
use
a
certain
Criterion
for
them,
they
also
have
this
idea
of
multiple
world
topologies,
and
so
these
are
different
processes
and
structures
captured
in
an
end
partite
Network,
which
means
that
they
have
multiple
parts.
So
in
one
in
the
embryo
networks
paper,
you
know,
we've
talked
about
the
bipart
type
Network,
which
are
two
different.
A
You
know
two
different
sort
of
graphs
that
are
connected
together.
So
if
you
have
dividing
cells,
a
bipartite
network
makes
sense
there,
but
in
the
case
of
our
lineage
trees,
we
have
actually
C.
Elegans
has
eight
sub
lineage
trees
that
have
founder
cells
at
the
eight
cell
stage,
and
so
that's
important
in
the
development
of
tissues
in
the
development
of
subsystems
like
the
germline,
and
so
we
can
actually
look
at
those
those
sub
lineages
and
the
relationship
between
those
sub
lineages.
A
So
we
have
these
unpartite
networks
that
emerge
and
then
those
Empire
type
networks
have
weak
connectors.
So,
for
example,
the
germline
and
the
you
know
some
of
the
other
tissues
that
form
that
don't
necessarily
have
functional
connections
have
other
types
of
spatial
connections
or
other
types
of
signaling
connections
that
we
can
capture
using
this
type.
A
So
this
is
a
concept
called
Divergent
integration,
and
this
Divergent
integration
goes
back
to
these
two
last
two
types
of
topologies,
multiple
worlds
and
semi-integrated
networks.
It's
basically
capturing
the
overlap
between
different
types
of
networks,
the
overlap
between
lineage
trees
and
networks
and
then
representing
this
in
a
way
that
that
says,
you
know
there
there's
this
undifferentiated
mass
of
cells
that
then
emerge.
You
know
from
that.
A
You
get
different
functional
systems
that
emerge
like
a
connect,
Dome
and
maybe
a
set
of
tissues,
and
maybe
you
know
a
generic
somatic
module
that
you
know
of
different
types
of
cells.
So
there
are
different
types
of
so
Divergent
means
that
things
are
diverging,
but
integration
means
that
they
still
remain
connected
together
as
a
single
organism,
so
they
don't
just
form
their
own
organisms.
They
don't
form
their
own
subsystems
that
don't
communicate
with
one
another.
It's
an
important
concept,
because
these
networks
are
the
thing
about
Network
theory.
A
Is
it
often
is
good
at
characterizing
things
that
are
both
internally
connected
and
have
weaker
connections
with
other
subsystems,
and
that's
one
of
the
powerful
things
about
Network
Theory.
So
that
allows
you
to
capture
that
relationship
in
a
nice
visualization.
So
this
visualization
shows
you
single
cells.
This
is
a
three-dimensional
sort
of
animation
of
this
three-dimensional
graph.
I
showed
earlier.
So
this
is
a
network
at
different
levels
of
with
nodes
from
different
levels
of
the
lineage
tree.
A
A
So
that's
that
right
connection,
a
b,
a
r
p
and
a
b
are
connected
and
there's
a
long
connection,
because
they're,
a
long
distance
away,
they've
had
three
three
sort
of
cell
generations
to
move
apart,
and
so
indeed
that's
what
you
see
here,
you
see
these
cell
centroids
and
then
you
see
the
cell
bodies,
which
are
in
a
sort
of
approximations
of
where
they
are
in
the
embryo.
But
it
shows
that
these
cells
are
in
the
embryo
they're
moving
around.
They
have
relationships
at
different
levels
of
differentiation.
A
I
didn't
put
the
cell
for
a
b,
but
that's
like
the
sort
of
the
Anchor
Point
for
that
part
of
the
this
is
like
the
the
anterior
end
of
the
a
worm.
So
a
b
is
sort
of
the
Anchor
Point
there,
but
again
like
these
are
just
approximations
of
position
and
and
approximations
of
these
relationships.
So
this
is
what
this
looks
like
now.
This
is
a
regular
Network.
A
This
is
where
you,
each
node
represents
a
cell
and
there's
no
differentiation
of
function
or
of
category,
so
every
cell
has
its
own
node
and
they're
connected.
Usually
through
some.
You
know
very
simple
Criterion
like
distance
or
you
know
it
could
be
a
layer
of
the
lineage
tree
or
it
could
be
signaling
molecules
or
something
like
that
and
you
can
get
a
nice
topology.
That's
spatially,
you
know
relevant
and
you
know
interest.
A
A
This
is
Earth
distance
threshold
here
for
the
constructing
this
network,
so
you
can
see
that
if
you
take
all
cells
in
the
sort
of
at
the
top
end
of
our
data
set,
which
I
think
is
several
hundred
cells,
you
get
this
very
sparse
connectivity
and
these
cells
aren't
organized
that
I
think
the
a
b
ones
are
on
the
left.
The
P
one
cells
are
on
the
right,
so
there's
connectivity
across
the
posterior
anterior
divide
and
then
within
those
two
categories
you
get
the
32
cell.
A
At
the
middle,
the
same
threshold,
it
gets
a
little
bit
more
dense,
64
cell
gets
really
dense,
and
then
we
move
to
a
threshold
of
0.95
because
it
was
just
uninterpretable
at
the
128
cell
level.
But
you
get
this
again.
You
get
a
little
bit
more
localization
in
some
of
these.
You
know
regions
of
space,
but
you
also
get
strong
connectivity
between
those
two
anatomical
poles
and
then
the
256
cell,
which
is
much
more
dense
at
the
same
threshold.
A
A
You
know
they
might
change
their
connections
and
it
gives
you
a
distribution
of
those
connection
changes.
So
that's
where
the
power
of
hyper
no
hyper
graphs
come
in,
and
so,
but
before
we
move
on
to
that
type
of
model,
we
need
to
talk
about
the
density,
bifurcation
model
and
this
really
kind
of
lays
out.
This
idea
of
you
know
what
why
we're
interested
in
all
of
this
part
of
the
you
know,
building
a
network,
so
one
process
leading
to
a
semi-integrated
network
is
the
density
bifurcation
models.
A
So
this
process
of
density
bifurcation
is
basically
the
process
of
development,
but
this
is
described
in
terms
of
sort
of
development
and
then
also
Network,
complex,
Network
Theory.
So
the
first
step
is
that
cells
divide
and
migrate.
We've
seen
in
examples
of
that
in
our
graphs,
where
they
divide
and
they
move
around,
and
the
connectivity
generally
increases
over
time
as
we've
seen.
The
second
step
is
that
cell
migration
and
reaches
enriches
they'll,
take
a
local
communities
and
cliques.
So
cleaks
is
a
technical
term
from
from
complex
Network
theory.
A
In
the
paper
we
did
on
embryo
networks,
we
do
a
clique
analysis
of
the
embryo.
We
find
that
there
are
these
cliques
that
form
cliques
are
just
very
highly
connected
cells
or
nodes
that
have
are
fully
connected
and
they're,
usually
little
sub
modules
in
the
network
that
you
can
identify
using
an
algorithm.
There
are
also
local
communities,
which
you
know
typically
are
like
you
know,
functionally
related
where
they
form
clusters,
so
cell
migration
enriches
these
type
of
structures.
A
The
third
step
is
that
functional
function
of
the
function
of
cells
diverge,
which
is
differentiation,
so
you
have
a
bunch
of
cells
proliferating
and
then
they
start
to
take
on
new
functions
like
they
become
neuronal
cells
or
they
become
intestinal
cells
or
they
become
germ
cells,
and
so
that
Divergence
is
important
to
characterize.
So
two
interconnected
networks
emerge
or
maybe
more.
If
we're
talking
about
the
neural
connecto
versus
the
you
know
the
somatic
Network,
then
we
have
a
neural
connectome
and
a
somatic
Network
and
there's
communication
between
those
cells.
A
Eventually,
it
becomes
less
specific
between
those
networks
and
more
specific
within
each
Network.
But
you
still
have
you
know
they're
still
in
the
same
Market,
so
they
do
have
some
relationships
and
then
finally
interconnected.
Two
networks
provide
weak
ties,
so
these
interconnected
networks
provide
weak
ties.
There
are
connections
between
the
neural
connectome
and
the
somatic
cells.
Just
as
there's
a
connection
between
your
brain
and
other
tissues,
it
could
be
your
nerves.
It
could
be
through
other
types
of
things
going
on
in
the
body.
A
A
So
this
is
the
generative
Divergent
integration
model
and
I'm
just
going
to
lay
it
out
with
an
example
here
from
an
eight
cell.
This
is
a
just
an
embryo
that
I've
made
up
it's
kind
of
related
to
C
elegans,
but
it's
just
kind
of
a
Cartoon.
The
one
on
the
left
is
the
eight
cell.
The
one
on
the
right
is
the
24
so,
and
so
you
can
see
in
the
eight
cell,
we
have
fewer
connections
than
the
24
cell.
A
It's
based
on
distance,
so
the
more
cells
that
are
packed
into
the
embryo,
the
more
spatial
relationships,
are
going
to
be
drawn
out.
So
that's
maybe
cheating
a
little
bit,
but
it
shows
that
there's
this
change
in
connectivity
it
becomes
much
more
dense
and
then
the
24
cell
example.
We
start
to
get
a
neuronal
network
again,
not
something
we
see
in
the
C
elegans
embryo,
because
the
neurons
emerge
at
like
200
cells
or
something
but
well,
maybe
a
little
bit
less
than
that.
A
I
just
show
these
like
kind
of
centroids,
but
there's
more
distance
between
the
centroids
and
the
eight
cell,
and
then
the
24
cell
they're,
more
densely,
packed
in
and
a
word
about
that
you
get
a
lot
of
Gap
Junctions
between
cells
and
so
in
the
neural
connectum.
For
example,
there
are
a
lot
of
Gap
Junctions
that
are
formed
and
they're
functional,
Gap
Junctions.
They
do
things
they
exchange
information
between
cells,
it's
the
cell
is
the
the
embryo,
becomes
more
packed
in
cells,
opportunities
for
Gap
Junctions,
the
forms
increases.
A
So
with
that
kind
of
electrical
connection
or
direct
connection
between
cells,
you
get
this
a
higher
opportunity
for
connectivity,
so
just
putting
in
the
biological
context,
as
I
said
here,
all
neurons
green,
that's
your
Gap
Junction.
So
in
this
case
the
green
cells
are
defined
by
Gap,
Junctions
and
distance,
but
also
the
blue
cells
and
the
blue
cells
will
have
Gap
Junctions
too.
It's
just
that
they're,
not
this
network
isn't
being
defined
by
that.
So
that's
the
idea,
there's
actually
two
sub-modules
of
the
white
green,
but
that's
something
yeah.
A
So
in
any
case,
my
point
being
is
that
there
are
multiple
ways
to
have
connectivity
as
you
get
more
cells,
you
get
more
opportunities
for
connectivity
and
that's
where
we,
but
then
we
also
have
this
Divergent
integration,
where
different
cell
categories
emerge,
where
they're
connected
by
different
means,
other
means,
and
eventually
those
light.
Green
cells
will
join
together
into
a
unified,
Network
and
start
to
function
as
a
unified
Network.
This
is
actually
what
we
see
in
the
Clans
connectome.
A
We
see,
like
you,
know
a
bunch
of
things
happening
in
the
head,
a
bunch
of
cells
emerging
in
the
tail
and
then
there's
this
connection
between
the
two
later.
So
this
is
just
a
lesson
as
to
how
to
link
networks
to
anatomy
and
morphology,
but
also
how
they
diverge
in
terms
of
function
and
how
they
stay
connected
as
a
whole
organism.
A
A
What
if
the
correct
model
is
not
a
typical
complex,
Network
and
I
talked
about
their
different,
maybe
different
types
of
connectivity
regimes
in
an
earlier
slide,
but
this
may
not
even
be
like
the
right
way
to
think
about
it.
So
there
are
different
ways
that
people
have
kind
of
approached
Networks,
and
this
is
where
you
know
we're
thinking
about,
like
these
growing
networks,
we're
thinking
about
the
organization
very
broadly,
and
so
how
do
we
represent
these
things?
So
this
again,
this
is
going
back.
A
Stepping
back
from
this
hyper
graph
model
to
just
regular
old
hairball
Networks,
which
each
you
know
each
node
is
a
cell
and
everything.
So
we
have
new
world
networks
which
I
mentioned
before
we
have
chimeric
states
which
are
simultaneously
coherent
and
incoherent.
So
we
have
this
idea
of
Divergence
of
the
state
where
we
have
networks
of
two
different
states,
and
you
know
they're
coherent
in
Clarence
States,
then
we
have
network
connectivity
that
prefers
influences
or
network
connectivity
preferences
influences
later
activity
in
ways
that
affect
symmetry.
A
So
no
more,
you
know,
like
we
talk
about
small
world
networks,
that's
usually
an
efficient
type
of
organization
for
hierarchical
networks,
but
like
in
something
like
the
nervous
system,
something
like
the
visual
system.
Maybe
that's
not
the
best.
You
know
things
that
cost
the
least
to
to
develop.
So
we
think
about
this
in
terms
of
metabolism
and
evolution.
What
is
the
cheapest
type
of
network
to
evolve
or
show
up
in
development?
A
Is
it
something
that's
very
simple
and
local,
or
is
it
something
that's
distributed,
and
we
have
to
think
not
only
about
energetic
costs
but
like
the
cost
of
information
processing
as
well?
So
there
are
a
lot
of
considerations
here.
So
I
put
this
slide
in
to
just
drive
home
the
point
that
these
networks
can
be
weared
in
a
number
of
different
ways.
A
We've
just
shown
a
small
subset
of
this
work,
that's
possible,
and
so
one
of
the
things
we're
trying
to
capture
here
we
step
back
and
look
at
the
big
picture,
they're
trying
to
capture
a
lot
of
these
processes
that
are
occurring
in
the
embryo.
The
embryo
is
very
Dynamic
and
you
see
these
folding
and
buckling
events,
and
you
see
migration
of
cells
and
you
see
all
sorts.
This
is
from
the
zebrafish
neural
connectome
and
you
see
the
zebrafish
embryo.
The
cells
are
moving
around
forming
these.
A
You
know
like
things
like
neural
crest
and
then
buckling
and
they're
forming
different
structures.
This
is
all
like.
You
know
the
process
that
we're
trying
to
capture
these
networks,
so
it
looks
different.
Then
a
lot
of
the
networks
have
shown
because
it
doesn't
show
this
dynamical
aspect
to
it,
and
so
this
is
the
kind
of
thing
we
want
to
form,
and
so
we
can
see
that
as
this
zebrafish
embryo
is
developing,
you
not
only
get
cell
movement,
but
you
get
things
that
form
like
a
nervous
system.
A
You
get
different
structures
that
form,
and
that
may
or
may
not
be.
You
know
due
to
well.
There
may
be
a
lot
of
different
functional
processes
going
on
here,
but
at
the
end
of
the
day,
what
we
want
to
do
is
we
want
to
characterize
from
like
a
sort
of
a
homogeneous
set
of
Developmental
cells
to
all
these
different
structures.
A
So
how
do
we
do
that?
Well,
we
don't
do
anything
as
sexy
as
this
picture,
where
there's
this
animation
and
it's
very
attract
visually
attractive.
But
it's
not
telling
us
exactly
what
we
want
to
know.
So
we
developed
this
developmental
hypergraph
method,
so
these
developmental
hypergraphs
are
the
typographs
that
I
mentioned.
So
each
of
these
nodes
have
a
number
of
different
cells
in
them.
So
indeed,
you
can
see
the
numbers
next
to
the
nodes
and
the
the
bigger
the
node,
the
larger.
The
number
just
means
that
there
are
more
cells
in
it.
A
So
this
is
Mosaic
development,
so
this
is
again
restricted
to
this
type
of
deterministic
development.
Well,
we
know
what
lineage
tree,
what
kind
of
cells
the
lineage
tree
is
going
to
produce?
We
can
track
all
the
sulfates
and
we
we
can
start
embryogenesis
off
at
this
one.
That's
hop
right!
There's
this
tree!
That
starts
with
a
one
and
the
subtree
on
the
right
hand.
A
Side
of
that
starts
a
one,
and
that's
our
assumption
that
embryogenesis
there
may
be
a
sub
lineage
begins
at
a
single
hyper
node,
so
the
single
hypernode
is
a
single
cell
in
it,
and
so
that's
that's
where
we're
starting
from
and
then
sub
lineages
are
defined
by
cell
type.
So
when
a
new
cell
type
emerges
like
a
normal
cell
type,
this
graph
branches,
so
you
can
see
the
branching
here
at
in
at
the
top
right.
A
We
have
one
two
four
and
then
there's
a
branching,
seven
and
one
seven
being
one
type
of
cell
one
being
a
new
type
of
cell
this
germline
and
this
you
know
it
starts
with
the
developmental
stem
cell
for
that
sub.
You
know
that
new
branch
and
then
those
cells
start
to
proliferate
in
that
space.
So
that's
that's
how
these
are
set
up,
and
you
see
this
again
and
again.
You
see
this
on
the
bottom,
where
you
have
28
to
48
to
3,
so
that
represents
a
doubling
of
cells.
A
Roughly
it's
a
little
bit
more
a
little
bit
less
than
a
doubling.
But
it's
you
know
it's
basically
a
bunch
of
division
event
somewhere
asymmetrical,
but
most
are
you
know
like
a
binary
Division,
and
then
you
get
28
cells
to
51
cells.
So
you
get
this
Vision
event.
48
of
them
go
to
one
sub,
one,
each
three
go
to
a
new
sub
lineage
and
then
those
cells
divide
multiple
times
to
50,
and
actually
it
doesn't
divide
multiple
times.
A
Necessarily
it's
getting
an
exchange
from
48,
which
is
this
previous
sub
lineage,
and
these
cells
are
D,
differentiating
and
moving
into
this
new
sub
lineage.
So
you
can
see
that
there
there's
a
lot
of
stuff
going
on
development.
You
have
these
division
events
they're
contributing
to
these
new
categories.
Sometimes
there's
exchange
between
the
categories,
and
then
we
can
count
all
that
in
this
representation
and
so
cells
can
transition
between
subgraphs
what
we
call
anastomoses,
which
are
these
connections
between
two
different
systems,
as
shown
here
on
the
right
which
I
just
explained.
A
So
one
of
the
ways
we've
also
been
able
to
characterize
is
especially
in
terms
of
the
formation
of
connectomes,
is
by
looking
at
first
plural
Dynamics
or
what
we
call
epigenetic
strategies
and
said
this
is
where
cells
are
actually
engaging
in
different
strategies,
and
we
don't
want
to
assume
that
they
have
cognition,
but
they
do
have
these
rules
that
they
use
to
sort
of
sort
themselves
and
Connect
into
these
networks.
The
emails
to
sort
themselves
into
these
hyper
graphs
as
well.
In
this
way-
and
so
this
is
based
on
the
idea.
A
First
mover
Advantage
stack
of
work
competition
if
you're
familiar
with
that
economic
concept
is
what
it's
based
on
the
idea
that
there
are
things
that
go
first
and
Things
That
Go
second,
and
that
sort
of
forms
this
constraints
on
the
rest
of
the
cells,
so
in
this
case
we're
looking
at
their
time
of
origin.
So
you
know
these
are
in
minutes,
so
these
cells
have,
you
know,
they're
different
ways
that
these
cells
are
organized.
A
There's
a
network
of
cells
that
emerge
at
different
times
in
development,
and
they
Connect
into
this
network
by
you
know
Simple
Rules.
So
maybe
the
one
that's
first
born
has
to
connect,
make
the
first
connection
into
whoever
they
want
to
connect
to,
and
then
you
get
the
next
first
point
that
connects
and
so
forth,
and
so
this
is
in
in
Game
Theory.
This
is
called
a
first
player
advantage
or
you
know,
and
it
constrains
a
second
player
in
a
constrained
subsequent
players.
A
So
what
you
do
is
you
get
these
different
strategies
that
emerge,
and
these
are
just
like
xnor
xor
exclusive
or
these
are
based
on
logic,
gates
and
PN.
Coupling
is
based
on
the
terminality
in
this
paper
Frontiers
and
cellular
Neuroscience.
That
was
from
2020,
and
it
kind
of
lays
all
this
out.
So
this
isn't.
This
doesn't
make
a
lot
of
sense
right
now,
but
if
you
read
the
paper,
it'll
make
more
sense,
but
what
it
does
in
the
connectome
is
it.
A
It
identifies
potential,
pre
and
post-synaptic
relationships
and
it
yields
various
strategies
for
establishing
connections
between
cells,
and
so
we
can
do
this
with
individual
cells
or
hypergraphs
or
sorting
cells
into
hypergraphs.
Using
different
rules.
We
can
observe,
like
you,
know,
different
cell
differentiation,
but
we
don't
necessarily.
You
know
that
that
kind
of
data
is
kind
of
hard
to
understand
a
lot
in
C
elegans.
It's
not
necessarily
hard
to
understand,
but
in
other
organisms,
sulfate
is
very,
very
fluid,
and
so
you
know
we
we
want
to
understand.
A
A
So
these
subsequent
moves
constrain
the
what
happens
in
the
embryo.
So
what
I'm
saying
here
is
that
one
of
the
take-home
messages
is
that
if
you
start
off
with
a
first
move,
that's
asymmetrical,
it
will
shape
what
happens
in
the
rest
of
embryogenesis.
If
you
start
off
with
a
symmetrical
sort
of
strategy,
where
there's
no
asymmetry,
then
you
know
that
doesn't
necessarily
have
an
effect
on
later
development.
But
it's
interesting
thinking
about
like
different
modes
of
development
and
thinking
about
what
ifs
and
development
so
yeah.
A
What
if
we
have
this
sort
of
early
asymmetrical
event,
what
would
happen
to
the
embryo
or
what
would
happen
if
there
were
no
asymmetric
events?
Would
it
just
basic?
Would
the
lineages
and
supplementing
just
be
evenly
matched,
and
would
we
even
get
any
structure
at
all,
so
this
is
work
again
from
this
biosystems
paper
in
2018
and
it's
very
relevant
to
Networks.
A
So,
along
with
networks,
we're
going
to
capture
embryo
Dynamics
and
I
showed
the
example
of
the
zebrafish
embryo
before
this
is
an
image
of
an
embryo,
that's
defined.
This
is
a
on
the
right.
We
have
a
drosophila
embryo,
which
is
this
long
germ,
which
is
different
than
the
zebrafish
or
the
C
elegans,
in
terms
of
how
it
differentiates
and
forms
an
a
putative
embryo
Network.
A
So
you
get
these
different
things
like
furrows
forming
in
the
body
of
the
embryo
that
are,
they
have
to
be
dealt
with
differently,
I
guess
then
C,
elegans
or
zebrafish
there's
different
structures
and
different
embryos,
but
we
want
to
understand
the
spatially
localized
differentiation.
These
patterns
are
actually
you
know,
we
want
to
be
able
to
characterize
them.
We've
talked
about
maybe
game
theoretic
models.
A
We've
talked
about
Network
models,
we've
talked
about
hypergraph
models,
so
these
are
all
kind
of
the
reason
I'm
throwing
these
models
out
here
and
talking
about
all
these
different
concepts
is
because
we
have
a
lot
of
variation.
We
need
to
capture.
So
this
is
what
we
want
to
capture
embryo
Dynamics.
We
also
want
to
capture
spatial
Dynamics
and
and
what's
happening
in
space
and
time,
so
this
is
where
we
get
into
and
embodied
hyper
or
in
body
developmental
networks.
So
you
know
it's
enough
just
to
say
that
this
is
a
generic
development.
A
It's
another
thing
when
you
have
a
specific
type
of
body,
that's
we're
trying
to
capture
recapitulate
so
in
this
drosophila
embryo,
it's
very
specific
to
drosophila
and
maybe
some
other
flies
that
are
like
drosophila,
but
it's
very
different
from
our
other
organisms.
So
having
an
embodied
development
network
is
actually
important
because
it
allows
us
to
embody
this
process
in
a
specific
anatomy
in
a
specific
set
of
rules
and
so
an
embodied
hyper
node,
which
is
something
that
we're
drawing
from
our
work
on
hypergraphs.
A
An
embodied
hyper
node
is
a
generic
reservoir
for
individual
nodes
context,
dependent
spatio
temporal
unit
or
an
epistemological
container.
So
these
dots
in
this
in
the
circle
represent
these
embodied
hypertos,
and
these
contain
different
cells
or
different
things.
It's
a
context,
dependent
unit.
It
exists
in
space
that
exists
in
time
and
it
has
some
context.
It
either
has
like
cells
from
a
specific
functional
category
or
specific
structural
category
or
whatever.
A
This
kind
of
underscores.
These
connections
between
Network
science,
category
Theory
and
branching
theory
that
we've
discussed
connected
hyper
nodes
is
linked
processes
of
Internet
interactions.
So
this
goes
to
the
idea
that
we
have
these
linked
processes,
they're,
Divergent
and
yet
they're
linked
together,
and
so
we've
described
that
using
sort
of
a
qualitative,
Network
Theory
approach,
and
we
can
attach
statistics
to
that.
A
They
have
other,
they
exhibit
a
lot
of
diversity
in
terms
of
what
other
cells
are
connected
to,
or
you
know
what
other
kinds
of
things
that
they
express-
maybe
gene,
expression,
wise
or
you
know
behaviorally,
so
there's
a
lot
of
variation
in
their
why
these
nodes-
and
we
can
look
at
that
with
these
power
Spectrum
again
more
around
in
body
developmental
networks.
These
are
networks
that
are
embodied
with
major
anatomical
features,
so
they're
embedded
with
me
within
major
anatomical
features,
so
it
could
be
this
neural
network,
but
the
somatic
Network.
A
A
As
we've
mentioned,
and
so
our
networks
are
defined
by
the
head
and
the
tail
and
the
different
sides
of
the
anatomy,
and
we
sort
of
did
that
with
our
standard
embryo
networks,
except
for
the
fact
that
we
really
want
to
focus
on
this
information
about
which
end
is
up
which
end
is
down
and
then
maybe
the
function
of
these
cells
so
we'll
see
I
think
in
the
next
slide.
Where
how
this
function
works.
A
So
that's
important
neurodevelopment
then
ties
that,
together
by
modeling,
a
small
connectome
and
an
embodied
agent
as
it
grows
and
initiates
sensory
motor
Behavior.
So
we
can
actually
embed
this
small
connecto
into
an
agent,
not
just
a
network
and
see
what
it
looks
like
when
it's
moving
around.
So
it's
not
just
the
network
that
we
want
to
embody.
You
know
in
a
anatomical
context
and
then
maybe
ask
the
question:
what
happens
when
this
embryo
moves
around
or
what
happens
in
the
cells
move
around
the
embryo?
What
what
kind
of
Transformations
are
possible?
A
So
this
next
slide
is
an
example
of
an
embodied
hyper
graph
in
terms
of
the
lineage
tree,
and
so
we
can
see
that
we
start
with
a
single
cell
and
chemical
structure
type
is
along
this
axis,
so
we
have
a
somatic
phenotype,
a
neural
connectome
and
a
reproductive
tract.
We
have
neural
precursors
in
the
middle
here
we
have
an
embryo
Network
down
here,
which
is
the
precursor
of
the
somatic
phenotype,
and
then
we
have
this
germ
line,
which
is
a
precursor
of
the
reproductive
tract.
A
This
comes
from
even
a
more
generic
set
of
divisions,
so
the
32
cell
embryo
and
the
eight
cell
embryo,
and
so,
as
you
can
see,
the
all
of
these
circles
have
a
number
of
cells
in
them.
The
cells
are
connected
to
other
cells,
but
we
don't
make
that
differentiation
in
this
graph.
This
is
just
like
a
tree
that
goes
upward
in
branches,
but
they're
little
networks
in
in
each
of
these
nodes
and
they're
actually
connected,
maybe
to
things
like
the
neural
connectome,
and
so
that
we
have
these
exchange
points
here.
A
So
this
is
what
this
looks
like
this
is
over
time,
so
this
is
going
upwards
in
time.
So
this
is
what
these
hyper
graphs
look
like
these
hyper
networks
and
then
this
is
an
example
of
a
spatial
hypograph.
So
this
is
where
we
have
two
different
layers,
where
we
have
a
cell
division,
128
cell
stage
to
256
cell
stage,
and
we
go
from
one
layer
to
another,
and
you
can
see
it's
not
just
that.
A
So
this
is
what
we
talk
about
when
we
talk
about
these
anastomoses
These
are
subgraphs
of
selected
connectivity.
So
if
we
look
at
the
human
heart,
we
see
that
there
are
different
chambers
of
the
human
heart
they're
connected
through
little
passageways
and
that's
exactly
what
we
see
with
graphs.
We
have
these
different
functional
units
and
these
are
hyper
graphs,
so
these
all
contain
cells
within
them.
A
They're
connected
these
cell
groups
are
connected,
and
then
there
are
these
subgraphs
that
are
connected
through
these
selective
connections
that
are
much
like
the
anastomo
season
and
anatomical
object,
and
this
is
a
drosophila
embryo
showing
this
in
a
an
in
body
context
where
we
have
different
structures
that
are
connected
together,
your
different
means,
but
also
separate,
and
so
this
is
an
example
finally
of
how
these
embodied
networks
are
embodied
in
an
individual,
a
sort
of
functional
Network.
So
this
is
an
example
of
sort
of
an
embodied
agent
where
we
have
an
input
and
an
output.
A
We
have
these
hyper
nodes
that
have
cells
within
them,
they're
connected
between
one
another,
and
these
numbers
just
represent
the
number
of
cells
in
each
node.
So
these
number
of
cells
increase,
but
you
also
get
new
intermediate
nodes
as
development
proceeds
and
then
finally,
you
get
this
very
densely
connected
hypergraph.
Here,
that's
functionally,
you
know
much
more
complex
than
this
first
graph.
This
is
the
growth
of
a
simple
connectome
between
sensors
ion
effect
or
zo.
A
So
you
can
build
these
in
body
networks
as
a
way
to
look
at
information
processing,
and
so
here
we
have
these
different
types
of
relationships
between
the.
As
this
network
grows,
how
the
number
of
cells
you
know
doubles
and
quadruples
over
time.
This
is
so.
We
have
a
couple
of
rules
that
come
from
this.
The
first
is
proportional
temporal
branching,
which
is
where
we
have
this
ranching
event
from
35
cells
to
a
doubling
roughly,
and
we
have
contributions
of
this
doubling
to
each
of
these
hyper
notes.
A
So
we
have
in
the
first
net
node
we
have
35
cells
in
the
second
node
we
have
54
cells
and
16
cells.
These
are
distributed
in
different
amounts
over
this.
This
doubling
is
distributed
in
different
amounts
across
these
different
hyper
nodes,
and
you
can
see
this
in
an
example
from
a
network.
So
we
start
at
28
go
to
48
and
we
go
to
three
and
we
have
two
different
sub
networks
here
that
originate
from
a
single
Network.
So
this
is
proportional
temporal
branching.
A
So
finally,
we
talk
about
connect
ohms
and
we
talk
about
tensegrity
Networks,
so
tensegrity
networks
are
networks
of
cells
that
are
joined
together
and
they're,
held
together
in
a
structural
stability
in
a
sort
of
a
superstructural
stability
by
the
forces
that
are
sort
of
acting
against
them.
So
if
we
compare
connectome
and
a
tensegrity
network,
a
connectome
is
connected
by
neuroactivity,
so
it
could
be
a
gap
Junction.
It
could
be
a
synaptic
connection
and
it's
basically
communication
between
the
cells
either
electrical
or
chemical
in
its
Integrity
Network.
A
We
have
a
structure
that
is
structurally
super
stable
and
it's
held
together
by
different
elements
in
the
network
being
held
together
by
connections,
but
these
connections
transmit
forces.
So
the
structural
Elements,
which
are
the
nodes,
have
this
sort
of
the
existing
compression
and
then
the
connections
exist
in
tension,
so
in
cells.
This
is
often
where
we
have
things
like
microtubules,
that
are
the
nodes
that
act
in
compression
and
then
actin
molecules
act
in
tension.
They
hold
together
everything.
So
this
is
a
concept
from
architecture.
A
A
So
we
can
actually
merge
all
these
types
of
networks.
Together.
We
can
merge
connectomes
and
integrity
networks,
they're,
basically,
two
different
types
of
connection
matrices.
The
connectome
is
wisfij,
which
is
the
co-activation
between
neurons.
The
tensegrity
network
is
C
sub.
I
j,
which
is
the
force
trans
mineral
long,
biological
struts,
and
these
two
different
types
of
networks
can
coexist
in
the
same
Anatomy.
A
We
can
also
have
our
embryo
networks
and
lineage
hypographs
within
this
network,
so
this
is
a
little
bit
different.
In
this
case
we
have
W
sub,
I
j,
which
are
the
spatial
proximity
developmental
cells,
so
our
embryo
networks
can
be
generic
with
single
cells
representing
in
the
nodes
or
hyper
graphs
with
Hyper
nodes,
which
are
multiple
cells
or
multiple
classical
nodes
in
a
single
hypergraph
node.
A
So
we
can
do
all
those
types
of
representations
to
represent,
what's
going
on
in
the
body
and
or
more
morphogenesis,
and
things
like
that,
but
you
can
also
use
these
tensegrity
networks,
which
again
are
these.
You
know
they
they
bring.
They
sort
of
describe
the
state
of
stability
of
this
organism,
and
so
we
can
put
all
this
together.
A
We're
working
also
on
graph
neural
networks
and
looking
at
how
we
can
build
graph
neural
networks
from
embryo
data
and
graph
neural
networks
are
interesting
because
of
these
embeddings
that
you
can
develop
from
the
data
and
they
can
represent
different
spatial
relationships
or
other
types
of
relationships
from
the
data
that
we
couldn't
necessarily
come
up
with
on
our
own,
as
we
abstract
away
the
phenotype
to
get
these
build.
These
networks
that
we
just
talked
about
so
gnns
actually
can
discover
new
network
relationships
within
the
data
and
so
we're
working
on
this.
A
It's
we
have
a
platform
and
open
source
development
for
this,
and
it's
based
on
the
cell
tracker
GNN
that's
been
published,
but
this
is
something
that
is
really
an
interesting
New
Direction.
It
basically
generates
the
nodes
dynamically
and
then
generates
the
connections
between
them,
and
so
this
is
something
that
we
can
use
for
a
number
of
different
network
applications
as
we
move
forward.