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From YouTube: DevoWorm #42: Modeling biological tensegrity networks, chemical perceptrons, Neural Operators.
Description
Modeling tensegrity networks in MATLAB/SciLab and COMSOL. From a 3-D structure to a connectivity matrix. Components of biological tensegrity and structural propagation. Neural operators and solving for reaction-diffusion morphogenesis. Attendees: Richard Gordon, Susan Crawford-Young, Jesse Parent, Bradly Alicea, and Morgan Hough
A
A
B
B
B
A
B
So
that
was
nice
because
Dr
Zhang,
who
I'm
working
with
he
he's
very
intuitive
about
mechanics
and
he
said
yeah
yeah.
He
wanted
as
a
tension
structure
only
and
so
I'm
going
yeah.
It's
the
tension,
structured,
no
compression
whatsoever
and
no
elasticity
well
have
there
is
some
elasticity
in
any
material
so,
but
it
just
needs
to
be
a
material.
C
A
A
A
B
A
Mean
I
don't
know
like
I,
don't
have
a
good
like
drawing
of
it
or
an
animation,
but
I
guess
the
microtubules
are
sort
of
things
that
hold
the
structure
to
get
so
like
the
cytop,
the
the
membrane
it
holds
things
together.
There
holds
the
structure,
you
know
in
a
certain
confirmation
and
it
also
plays
a
role
in
some
of
the
other
structures.
Like
the
you
know,
the
nucleus
and
and
other
things
that
are
sort
of
I
guess.
Whenever
you
need
structure
in
a
Cell
I
know
they
have.
B
They
do
a
lot
of
things
there,
hello,
the
microtubules
and
the
neurons,
certainly
crazy
acts
and
and
in
that
yeah
I
just
asked.
So
where
are
the
microtubules?
In
the
cell
like
I,
know
the
actin
in
a
normal
non-dividing
cell
Etc
is
on
the
outside
of
like
it
forms
an
outside
layer,
there's
stuff
inside
too,
yes,
okay,
but
but
it
does
does
tend
to
the
outside
of
the
cell.
At
least
I
have
a
paper
on
that
and
they
like
I,
said
they're
biologists
and
they
took
a
picture
of
it.
B
C
C
C
B
B
B
C
C
B
Yeah
so
n
yeah,
all
right:
okay,
okay,
all
right,
Chris
Martin's!
He
didn't
talk
to
me
much
when
I
visited
him.
Oh
he
didn't.
No.
He
didn't
want
to
talk
about
science,
no
yeah,
no
he's
out
of
it
yeah.
He
has
been
wanting
and
I
said.
Well,
you
know.
I
came
all
the
way,
basically
all
the
way
here
to
talk
to
you
about
this,
so
we
can
spend
five
minutes
that
I'm
talking
about
this
I,
don't
think.
B
B
B
A
So
we
talked
a
few
weeks
ago
about
something
called
morphological
waves
and
we
had
some
skepticism
in
the
group
about
the
concept
and
how
it's
similar
to
differentiation
waves.
So
this
idea
goes
actually
back
I
think
to
discussions
with
Kristoff
teacher.
It
was
actually
a
pretty
interesting
person
in
the
field
of
a
wife
and
I
I've
gathered
some
papers
of
his
on
chemical
computational
perceptron.
A
So
let
me
take
a
look:
let's
take
a
look
at
some
of
these
papers,
so
the
first
paper
is
online
learning
in
a
chemical
perceptron
and,
of
course,
perceptrons
are
very
early
neural
networks.
There
are
systems
where
you
have
a
lot
of
inputs
that
are
summed
into
a
single
unit
or
neuron,
and
then
there's
an
output,
so
you're,
taking
in
a
lot
of
different
inputs
and
you're
producing
classifications
from
that
and
perceptrons
go
back
to
the
1960s
and
they've
been
used
in
as
toy
models.
A
A
lot
for
different
things
in
this
case
we're
looking
at
a
chemical
perceptron
and
so
we're
looking
at
biological
learning
such
as
it
is,
and
so
this
is
a
Kristoff
teacher,
is
the
second
author
on
this
paper
is
at
Portland.
State
University,
so
the
abstract
of
this
paper
reads:
autonomous
learning,
implemented
purely
by
means
of
a
synthetic
chemical
system
has
not
been
previously
realized,
so
we're
interested
in
autonomous
learning
in
a
chemical
system
in
a
synthetic
chemical
system.
A
This
is
a
lot
to
do
with
like
synthetic
biology
and
other
applications
like
that.
Learning
promotes
reusability
and
minimizes
the
system
design
to
simple
input,
output
specification.
So
again
you
have
this
perceptron,
where
you
have
multiple
inputs
to
a
single
unit
which
either
sums
the
inputs
or
filters
the
inputs
using
some
learning
Rule
and
then
gives
you
outputs
this
article
we
introduce
a
chemical
perceptron,
the
First
full
featured
implementation
of
a
perceptron
in
an
artificial
chemistry.
A
So
artificial
chemistries
are
actually
an
interesting
area
of
a
life
research
and
it
involves
taking
chemical
worlds
or
chemistry
systems
and
simulating
them
in
silico.
So
you
can
simulate
a
chemistry
system,
say
to
understand
the
origins
of
life
or
to
understand
how
to
design
different
types
of
chemical
biochemical
structures.
Things
like
that.
A
A
A
A
We
present
two
models,
so
this
is
these
are
the
properties
at
the
top
and
then
the
second
sentence
they
talk
about.
There
are
different
types
of
perceptron
that
they're
using
for
those
the
weight,
Loop
perceptron
and
the
weight
race
perceptron,
which
represents
two
possible
strategies
for
a
chemical
implementation
of
linear
integration
and
threshold.
Both
chemical
perceptrons
can
be
successfully
identified
or
cancer
successfully
identify
all
14
linearly.
Separable
geel
input
logic
functions,
so
these
are
things
they
throw
at
the
perceptron
to
get
it
to
classify
correctly
or
to
test
to
see.
A
If
it
can
do
this
and
maintain
High
robustness
against
rate
constant
perturbations,
we
suggest
the
DNA
strand.
Displacement
could,
in
principle,
provide
an
implementation
substrate
for
our
model,
allowing
the
chemical
perceptor
on
a
perform,
reusable
programmable
and
adaptable,
wet
biochemical
computing.
A
So
one
of
the
criticisms
of
the
morpha
I
guess
morpha
morphological
waves
was
that
it
was
sort
of
like
it
had
a
sort
of
a
mysterious
component
to
it.
So
there
was
a
learning
component
to
the
reaction.
Diffusion
equations,
for
example.
Does
that
occur
by
magic
or
is
there
some
sort
of
underlying
sort
of?
Is
there
maybe
an
underlying
intelligence?
And
even
that
seemed
a
little
bit
outlandish?
A
But
this
is
sort
of
addressing
this
issue
where
you
have
a
chemical
system
or
a
biochemical
system
that
has
its
learning
capability,
so
you
can
actually
create
perceptrons
in
natural
systems.
Using
a
variety
of
techniques,
I
mean
the
perceptron
is
just
an
abstraction.
You
can
use
this
sort
of
model
in
chemical
systems,
so,
for
example,
if
you
have
a
lot
of
different
combinations
of
something
that
go
into
a
process
and
there's
a
simple
input,
output
that
would
be
considered
a
perceptron.
A
Even
though
it's
not
a
perceptron
or
a
biological
neuron
per
se,
it's
that
sort
of
structure
of
the
problem
or
the
structure
of
the
system
where
things
get
processed.
So
this
is
a
I
think
this
is
a
useful
mechanism,
or
at
least
a
useful
model
for
looking
at
some
of
these
chemical
or
biochemical
mechanisms.
A
So,
let's
see
if
we
can
get
down
to
the
bottom
here,
the
contributions
of
their
model
here
are
as
follows.
Our
system
is
the
first
full-featured
implementation
of
online
learning
in
simulated,
artificial
chemistry
called
the
chemical
perceptra,
so
learning
as
well
as
linear
integration
of
weights
and
inputs,
which
are
integration
at
that
same
single
unit
that
we
mentioned
before
is
handled
internally.
A
A
The
chemical
perceptron
learns
perfectly
all
14
linearly
separable
logic
functions
after
200
learning
iterations,
so
it
doesn't
necessarily
take
that
long
to
work.
The
chemical
perceptron
is
reusable
since
it
recovers
its
internal
ready
state
after
each
processing
event,
and
they
so
I
want
to
get
down
to
this
weight,
Loop
and
weight
race
perceptrons
to
give
an
idea,
because
they
talk
about
the
artificial
chemistry
here
and
their
details
to
that
and
there's
a
lot
of
kinetics
in
this
Peart
official
chemistry.
Really
it's
really
based
on
Michelle
Smith
and
enzyme
kinetics.
A
And
so
you
have
this
great,
limiting
aspect
to
it
that
you
can
use
to
understand
both
sort
of
you
know
if
you're
doing
chemistry,
experiments
or
you
have
these
self-assembling
chemistries
as
well,
and
so
they
kind
of
show
some
of
these
concentration
versus
time
step
Dynamics,
and
this
is
the
model
of
the
perceptron.
So
you
have
these
multiple
inputs
coming
into
this
single
unit.
That
summarizes
things
according
to
some
sort
of
rule
or
conditional
and
then
there's
an
output.
A
D
A
Fuel
species
e,
so
this
is
the
weight,
Loop
receptor
and
computes
the
weight
sum
directly
by
transforming
weights
W
into
outs,
but
species
y
ep.
The
problem
is
that
the
weights
encode
the
state
of
the
perceptron,
so
their
concentration
must
be
preserved.
Apart
from
my
species,
the
perceptron
must
also
create
back
of
copies
of
the
weights.
The
perceptron
can
then
restore
its
weights
after
the
output
production
is
over,
and
so
that
you
know
this
kind
of
works
by
preserving
information
and
re-encoding
it.
A
So
they
give
a
table
with
all
these
different
weights
in
it,
then
the
weight
raise
perceptron
is
the
second
model,
so
the
functioning
of
the
weight
Loop
perceptron
is
based
on
rather
conservatively
designed
phases
working
in
sequence.
This
approach
works
well
since
there's
almost
a
one-to-one
relation
between
the
routines
of
a
formal
perceptron
and
those
of
a
chemical
perceptron,
then.
Nevertheless,
the
idea
of
a
direct
calculation
of
the
weight
sum
and
recovering
the
original
state
seems
unnecessarily
cumbersome
for
a
chemical
system.
A
The
weight
race
perceptron
improves
upon
the
weight
Loop
perceptron
by
switching
the
chemical
rules
of
inputs
and
weights.
That
is,
instead
of
having
inputs
catalyzing
a
transformation
of
weights
to
a
weight
sum
which
determines
an
output
weight,
simply
catalyze
the
input
to
Output
reactions,
as
presented
in
figure
four,
which
is
this
figure.
D
A
Which
shows
this
process
where,
in
a
in
a
binary
mode,
function
the
weights,
W
catalyze
or
compete
on
the
input
output,
reactions
of
X
and
Y,
so
X
and
W
compete
and
then
there's
an
output
y
in
the
learning
mode,
which
is
B
the
desired
output
species
d,
0
and
D1
transforms
to
weights
W.
The
provided
variant
does
not
match
the
actual
output.
So
in
this
case
your
species
transforms
to
the
weights
W.
A
So
that's
this
paper
that
the
second
paper
is
this
feed
forward
chemical
neural
network,
an
in
silicochemical
system
that
learns
exclusive
or
so
xor
is
exclusive,
or
this
is
usually
used
as
a
logic
gate,
but
this
is-
and
this
is
also
Kristoff
teacher-
is
the
third
author
on
this
paper,
and
this
also
has
you
know
chemical
neural
network.
So
this
is
a
similar
type
of
system
inspired
by
natural
biochemicals
that
perform
complex
information
processing
within
living
cells.
A
We
design
and
simulate
a
chemically
implemented
feed
forward
neural
network,
which
learns
by
novel
chemical
reaction-based
analog
of
back
propagation.
Our
network
is
implemented
in
a
simulated
chemical
system
where
individual
neurons
are
separated
from
each
other
by
semi-permeable
cell-like
membranes.
A
So
this
is
where
we
have
neurons
that
have
these
semi-permeable
membranes,
which
is
an
interesting
design
feature
because
most
neural
network
neurons,
don't
worry
about
this
too
much.
They
worry
about
mathematical
functions,
so
this
is
an
interesting.
This
is
a
compartmentalized
modular
design
that
allows
a
variety
of
network
topologies
to
be
constructed
from
the
same
building
blocks.
A
So
they
talk
about
this.
As
you
know,
sort
of
an
embodied
system
having
developed
a
family
one
family
of
individual
chemical
perceptrons,
we
wish
to
design
a
method
for
connecting
these
in
a
more
computationally,
powerful
Network,
so
the
network
should
be
modular
and
allow
for
different
topologies
to
be
reconstructed.
We
achieved
this
goal
of
the
feed
forward:
chemical
neural
network
or
an
fcnn,
which
is
a
network
of
cellulite
compartments.
Each
containing
a
chemical
neuron
as
a
module
communication
between
nodes
in
the
network
is
achieved
the
permeation
through
the
walls
of
these
compartments.
A
So
these
part
compartments
have
walls,
walls
are
selectively
permeable
and
things
pass
between
the
walls
which
allows
the
Network's
feed
forward
and
back
propagation
mechanisms
to
function.
So
this
is
a
little
bit
different
than
the
way
we
usually
think
about
neural
networks,
which
is
that
they
have
connections
that
have
weights
and
then
those
weights
determine
whether
the
message
is
passed
on
to
the
next
Network
or
neuron
in
the
network.
Okay,
like
standard
single
layer
perceptrons
each
of
our
individual
chemical
perceptrons
can
learn
linearly,
separable
binary,
two
input
logic
functions
such
as,
and
or
so.
A
These
are
the
simplest
logic
functions
and
or
it's
that
you
have
a
logic
gate
that
says
I'm
going
to.
If,
if
such
is
true,
there
are
two
things
that
are
activated
in
and
in
or
if
something
is
true,
one
thing
or
the
other
thing
are
activated,
so
there
are
different
ways,
different
rules
that
we
can
use
to
when,
when
a
logic
function
is
performed
to
pass
on
information
to
the
next
unit.
A
These
simple
logic
functions,
however,
incapable
of
learning
will
linearly
Inseparable
functions,
xor
and
xnor,
which
is
exclusive
or
her
exclusive.
Nor
so
this
is
where
you
have
exclusivity
in
some
of
these
functions.
These
are
linearly
inseparable
here
we
demonstrate
the
fcnn
learns
each
of
these
functions
to
our
knowledge.
A
This
is
a
major
motivation
behind
the
modern
study
of
Proto
cells,
which
we
talked
about
last
week
in
a
couple
weeks
ago,
as
being
something
that
people
use
to
study,
minimal
cells
and
the
origins
of
life,
and
it's
actually
something
they
do
in
artificial
life
a
lot
they
work
with
protocells,
which
are
these
things
these
these
vesicles,
that
you
can
load
up
with
different
things.
You
can
boot
them
up
with
biochemicals
or
other
proteins,
and
you
can
get
them
to
do
things
behave
like
minimal
cells
with
enough.
A
You
know
enough
stuff
in
it
to
get
it
to
do
things,
and
the
analogy
of
the
cell
is
a
self-contained.
Self-Sustaining
regulatory
machine
is
a
familiar
one
and
the
most
basic
requirement
for
such
a
machinist
compartmentalization,
so
compartmentalization
actually
is
interesting,
because
it
enables
a
lot
of
things.
It
enables
local
information
processing.
A
It
enables,
by
extension,
what
we
call
modularity
or
the
specialization
of
functions
in
a
certain
place.
It's
bounded
by
something
like
a
boundary
or
a
membrane,
and
it
allows
for
things
higher
order,
things
like
redundancies
and
other
things
where
you
have
multiple
copies
of
something,
so
that
if
one
thing
is
damaged
or
one
thing
goes
offline,
the
other
things
can
take
over
and
you
can
only
get
these
sorts
of
properties
with
compartmentalization
because
you
need
to
have
specialization.
A
You
need
to
have
individual
units
instead
of
having
things
as
kind
of
as
a
generic
system,
and
we
don't
see
a
lot
of
that
neural
networks.
You
see
some
like.
We
see
layers
of
neural
networks
and
we
see
some
specialization
of
of
different
layers,
but
we
don't
people,
don't
really
talk
too
much
about
modularity.
A
So
this
is
an
interesting
way
to
approach
this
problem,
foreign
things
here
they
talk
about
their
networks
as
modular
and
having
these
compartments,
but
that
also
implies
that
they
have
boundaries,
and
so
the
membrane
boundaries
are
permeable
they
have
to
be
in.
Of
course,
actual
cells
are
permeable.
A
We
have
ion
channels,
we
have
Gap
Junctions,
we
have
other
types
of
passageways
in
and
out
of
the
cell,
and
these
things
are
specialized
for
different
functions,
so
you
can
think
about
like
an
ion
channel,
it's
very
selective
for
certain
ions
to
pass
through
and
it
has
a
function.
So
this
is
something
that
is
can
be
highly
specialized
for
a
certain
thing
that
you
want
to
do
and,
of
course,
in
neural
networks.
We
don't
really
talk
too
much
about.
We
don't
talk
about
like
ion
channels
very
much
when
we
model
real
neurons.
A
So
they
modeled
this
mathematically
and
you
can
see
the
math
here.
The
chemical
neurons,
the
chemical
neuron
we
chose
is
the
building
block
for
fcnns.
Is
the
analog
asymmetric
signal
and
perceptron
or
aasp,
and
these
are
two
new
variants
of
the
aasp-
are
used,
one
for
hidden,
neurons
and
one
for
the
output
neuron
as
a
reference
throughout
the
section,
whereas
the
article
table
one
list
of
chemical
species
and
the
fcnn.
So
this
is
in
the
subliminal
materials.
A
This
is
an
artificial
life
article.
So
it's
at
their
artificial
wave
Journal
website,
so
they
go
on
they
talk.
This
is
the
table
here
with
the
inputs,
outputs
weights
and
the
different
chemical
species
that
are
associated
with
these
things
and
they
kind
of
go
through
these
things.
Inputs
input,
weight
integration
and
they
talked
about
basically
the
mathematical
mapping
of
these
things.
A
So
this
is
a
reaction,
the
a
map
of
the
reactions
and
the
input
weight,
integration
step
in
a
two
input
aasp,
so
you
can
see
that
the
dotted
arrow
is
denote
a
catalyst.
So
this
is
a
catalyst
here,
for
example,
or
this
one,
and
then
this
signifies
it
reaction
in
the
network
between
I
x
sub,
1
and
y
each
week,
catalyzes
a
reaction
turning
its
Associated
input
into
y,
so
everything
goes
gets
turned
into
y,
well
that
input
y
simultaneously
annihilate
each
other
at
a
different
rate.
So.
C
A
Is
where
you
get
these
sort
of
Dynamics,
these
kinetic
Dynamics
and
you
can
classify
it
or
you
can
characterize
it
in
a
network.
So
then
they
get
to
the
learning
part
or
they
go
through
some
of
this.
They
have
these
aasp
networks
and
they
show
kind
of
how
these
work,
positive,
weight,
adaptation,
negative
weight
adaptation
and
an
output
comparison,
so
the
different
types
of
learning
that
they
propose
and
then
finally
we
can
talk
about
some.
A
You
know
what
these
are
useful
for,
which
is
that
you
have
these
fcnns
and
they
have
a
true
like
topology,
so
you
can
take
a
tree
of
these
compartments,
so
you
can
take
these
compartments,
in
a
say,
a
cell
or
a
structure,
and
you
can
map
them
to
a
tree,
so
you
can
show
how
these
things
sort
of
operate
or
maybe
even
evolve,
and
so
this
is
a
nice
way
of
representing
this
okay.
So
thank
you
for
listening
to
that.
A
C
Know
I
think
I.
Think
Thomas
has
finally
gotten
my
point
the
to
what
it's
based
on
a
very
bad
experience,
which
Susan
might
remember,
I
bought
the
first
Apple
camera.
It
was
a.
It
was
a.
It
was
separate
from
the
computer
okay,
so
you
plugged
it
into
the
computer
and
we
took
Axolotl
eggs
and
dropped
them
in
a
a
tube
and
after
the
initial
transient
they
should
fall
very
smoothly.
C
So
I
took
movies
of
this,
and
the
movies
were
completely
jittery.
I
mean
time.
Interval
between
frames
was
very,
very
bad.
Okay,
so
based
on
that
I,
don't
trust.
Digital
cameras,
digital
movie,
cameras,
okay
and
I.
Think
I
think
that
Thomas
has
finally
got
my
point
and
we'll
try
to
do
an
experiment
where
the
motion
of
something
under
the
microscope
slide
that
approximates
the
size
of
the
diatom
and
does
not
have
does
not
undergo
stop,
stop
go
friction
with
the
slide.
B
C
D
C
B
C
The
guy
who
was
a
high
school
teacher,
spent
a
year
with
us.
Yes,
what
Ross?
What
was
his
name?
Flint
Flint
Flint?
What
was
his
first
name?
Russ
Russ
Flint,
oh
okay,
yeah!
What
we
did
is
we
hard-boiled
an
axolotl
egg?
Okay,
you
can
do
it
just
by
cooking
it
a
little
bit
and
then
we
sliced
it
vertically.
C
B
C
B
B
C
B
Actually
do
this
and
then
they
do
that
it's
going
over
inside
and
then
they
fall.
Then
they
become
better
interesting
at
this
point
when
they
have
risen,
that's
when
they
want
to
get
out
so
the
optical
clearance
tomography
and
take
an
image
of
the
blastocycle.
That's
I
want
to
do
this
experiment
but,
like
I
said,
I
have
to
wait
until
I
finished
my
other
stuff
for
for
my
PhD,
but
he
said
I
could
do
that.
He
said
I
could
do
this
at
the
end.
I
go
okay,
it's
a
promise!
This
is
the
carrot.
B
B
B
C
C
A
C
C
A
A
A
C
A
C
B
B
A
So
this
is
the
book
that
Susan
sent
to
me,
and
this
is
a
let's
see
if
it
comes
up,
not
computational
modeling
of
tensegrity
structures,
and
this
is
where
I
got
a
lot
of
the
Matlab
code
for
this.
For
this
example,
oh
okay,
so
in
the
book
I
think
it's
like
chapter
two.
They
lay
out
Matlab
code
for
simulating
10,
segregate
Network
and
it's
like.
A
Basically,
you
define
the
network,
you
define
the
nodes,
you
define
the
edges,
you
assign
you
basically
build
a
matrix
and
then
that
Matrix
is
it's
it's
the
way
they
have
it
set
up.
It's
like
negative
one,
zero
and
one.
Those
are
the
three
states
and
then
like
it's
either
there's
neutral
tension,
there's
positive
tension
or
negative
tension.
They
Define
that
in
the
book
as
to
what
those.
A
A
C
C
C
A
You
have
this
a
I
I
sub
IJ,
which
is
a
connectivity
Matrix
where
you
have
yeah,
I
and
J,
and
then
you
have
you
have
three
states,
plus
one
zero
and
negative
one,
and
you
can
make
different
assumptions
about
the
connectivity
like
whether
the
con
connections
are
linear
or
not.
But
you
end
up
with
these
three
states
of
force
and
then
those
states
are
foreign.
C
A
A
A
So
this
is
just
these
are
the
values
of
these
states,
so
this
is
I,
guess
your
set
of
you
know
your
three
things
and
that
is
actually
I
think
these
are
your
spatial
coordinates
of
the
different
of
the
nodes,
and
then
these
are
the
force.
This
is
the
force
vect.
These
are
the
force
vectors
as
a
matrix,
and
then
this
is
and
then
you
work
through
this-
you
do
some
Matrix
algebra
to
get
to
down
to
the
bottom
here.
C
A
A
B
B
C
A
A
Them
right
right,
you
need
to
generate
them.
They
need
to
figure
out
like
what
the
you
know,
how
it
behaves
physically.
Well,
I!
Guess
that's
something
to
be
doing
like
a
physics
simulator
like
com,
Soul
or
something
where
you
have
you
can
actually
evaluate.
If
something
is
in
a
position
in
a
three-dimensional
space,
how
does
it
behave?
Yeah,
yeah,.
B
B
Have
enough
I
have
another
paper
about
material
for
wearable
electronics
that
has
a
J
curve
like
Stephen
Levin
says
that
all
10
seconds,
10
security
structures
have
and
they've
taken
a
close-up
look
at
this
material
and
it
looks
sort
of
tensegrity-like
okay,
so
I
have
that
paper
too.
So
maybe
I
should
send
you
those
too
papers
yeah.
A
A
B
A
B
C
A
C
A
A
D
A
A
A
I
think
if
the
rank
is
above
a
certain
value,
it
gives
you
like.
Basically
what
they're
trying
to
do
with
this
code
is
evaluate
the
state
of
the
structure
if
it's
stable
or
not,
and
so
I
think
at
certain
levels
of
the
like.
If
the
rank
is
above
a
certain
number,
it's
stable
and
if
it's
below
a
certain
number,
it's
not.
A
Basically,
that's
I
mean
that's
that's
what
I
got
out
of
it
and
I
think
that
would
be
the
most
heuristic,
but
I
think
there's
probably
a
better
way
to
to
figure
out
whether
what
what
you
know
a
summary
statistic
for
the
structure.
That's
basically
what
this
is,
but
yeah
yeah.
So
that
was
the.
So
that's
one
option
for
computing
this
stuff
and
it's
you
know
they're,
probably
maybe
better
options,
but
you
know-
or
things
could
be
added
to
this,
as
we
you
know-
would
want.
C
C
A
C
D
C
A
B
A
B
B
B
C
B
C
D
B
C
B
C
B
C
C
C
C
C
B
B
Yeah
true
and
I'm,
going
with
the
engineers
on
this,
we
really
just
want
something
that
mimics
part
of
the
behavior
of
the
cells
to
build
the
material
that
covers
part
of
the
J
curve
that
that
he's
talking
about
is
the
best
strain.
The
stress
strain
curve,
the
covers
part
of
it.
That's
good,
I'll
get
another
material
for
the
other
part
of
it
thicker
and
a
third
one
for
the
top
part
or
something
so
then
I
can
cover
the
whole
like
curve
stretch
drain
curve,
and
then
we
can
improve
Optical
elastography,
not.
B
B
D
A
We
have
the
well
Susan
shared
that
paper
see
if
I
can
share
my
screen
here.
Okay,
so
this
is
the
paper
she
shared
equivalent
mechanical
properties
of
tensegrity
trust
structures
with
self-stress
included.
So
this
is
the
let's
see
if
there
are
any
figures
in
this
paper.
Well,
these
are
the
major
well,
these
are
the
block
matrices
here.
Where
did
they
define?
A
A
B
D
B
A
Lot
of
this
stuff,
like
if
you're
simulating
it,
gets
pretty
deep
into
Matrix
algebra
and
Matrix
manipulation.
So
the
mechanical
properties
of
five
typical
tensegrity
modules
inscribed
in
the
cube
of
edgelink
a,
are
determined
and
evaluated
using
the
proposed
Continuum
model.
So
they
have
things
like
force:
strut,
simplexes,
three
strut,
simplexes,
an
octahedron,
a
tetrahedron
and
X
module.
So
these
a
series
of
different
structures
to
do
this,
and
then
they
just
they
analyze
structures
consisting
of
cables
and
struts
again.
A
So
these
are
not
biological
structures,
they're,
just
generic
structures
that
form
this
network,
then
they
have.
This
parameter
K,
which
is
the
EAS
cable
over
EA,
strut,
EA
strut,
where
EA
is
e,
is
the
Young's
modulus,
which
is
defined
by
well,
it's
a
yeah
and
then
a
is
the
cross
section
and
then
the
selfie
deliberated
system
of
the
forces
is
represented
by
this
parameter
s
over
EA,
where
s
is
a
free
multiplier
and
the
EA
is
that
quantity
there.
So
this
is.
A
These
are
the
matrices
that
they
derived
from
this
and
they
do
the
calculations.
And
then
this
is
what
they
look
like
these,
these
four
stroke,
Simplex
modules.
So
they
have
this
structure
here
and
again
they
have
this
XYZ
and
these
coordinates.
They
have
the
forces
acting
upon
the
nodes
and
then
you
know
those
are
transmitted
throughout
the
structure
and
then
you
do
the
calculations
and
you
can
figure
out
whether
it's
stable
or
not.
B
B
A
A
A
D
D
D
D
D
A
Yeah
yeah
so
they're
yeah,
they're,
they're,
learning
the
mappings
between
finite
dimensional,
euclidean
spaces
and
they're,
predicting
these
outputs
for
yeah
they're,
solving
equations,
basically
and
then
there's
a
4A
interval
operator,
which
does
a
similar
thing.
It's
doing,
I
guess
a
4A
analysis,
yeah,
okay,
so
this
is
yeah.
This
is
and
then
this
shows
you
kind
of
the
diagram
of
the
system
where
you
have
an
input.
You
wouldn't
put
it
into
this
inner
operator
and
you
go
to
Output.
A
A
B
B
A
D
B
Besides,
my
niece
might
know
something
about
some
of
the
neural
Nets
because
she
was
she
was
looking
at
quasars
and
how
nebula
that's
it.
She
was
trying
to
figure
out
the
shape
of
a
nebula
from
Just,
One
Direction,
so
she's
you
only
have
a
image
of
a
nebula
for
One
Direction,
because
that's
where
we
are
in
the
universe
and
she
was
trying
to
figure
out
their
3D
shape
from
from
just
looking
at
it
from
One
Direction.
Okay,
oh
boy,
so
that's
that
was
her
PhD
thesis,
okay,.