►
Description
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A
B
A
A
B
B
B
B
C
B
Individual
themselves
have
different
farming
races,
specific
points
in
an
environment,
so
the
greediness
today,
others
on
top
of
that
there's
an
extra
layer
of
information
about
the
rate
of
farming,
the
middle
of
a
cell
at
different
points
in
its
barnacles
and
the
idea.
So
I
guess.
If
I
get
been
known
for
holidays.
B
B
Presenting
some
map
of
the
world,
it
should
be
relatively
super,
a
uniform
in
size,
number
of
spikes
and
peak
firing
rate.
However,
it's
been
suggested
that
this
was
not
in
fact
the
case
specifically
they're
talking
about
different
fine
lines
and
then,
and
they
kind
of
concluded
a
grid
field,
we're
a
less
uniform
intensity
than
expected,
meaning
they
fire
a
cell
five
different
rates
at
different
points
and
the
paddle
strong,
weak
fields
are
spatially
stable
and
recruit
across
trials.
B
B
They
maintain
this
differential
firing
rate,
but
if,
if
they
remapped,
then
the
cells
they
showed
on
the
virus
conditions,
if
they
remap
themselves,
the
where
the
cell
is
preferentially
fire
more
or
less
changes
as
well,
so
sort
of
the
this
preferential
firing
rate
changes
with
remapping,
but
it's
consistent
as
long
as
the
grid
cell
firing
fields
are
consistent.
That's
the
basic
result
of
this
paper.
B
Mistake
here
these
are
the
actual
raw
spikes.
These
are
the
numbers.
The
spikes
divided
by
the
mount
of
tiny
animals
spent
in
that
particular
area,
so
there's
actual
number
of
spikes
would
be
biased
by
how
much
time
you
spend
in
different
areas.
So
this
is
sort
of
a
what
they
call
a
rate
map.
This
is
essentially
the
same
as
the
rate
map,
but
it's
just
they
put
a
threshold
on
it,
so
they
only
show
fields
that
are
above
a
certain
rate.
That's
just
clipping
it.
B
It's
it's
actually
not
gone.
It's
there.
It's
there.
You
can't
see
it
very
well
here
it's
actually
quite
noticeable
on
this
one
and
they
picked
a
darker
color.
It's
a
there's,
a
really
dark
dark
red
a
little
here.
They
picked
that
really
regular
dark
red.
So
it
is
the
same
it's
there,
and
this
is
the
ORAC
correlation
matching
to
matrix.
I
am
always
confused
by
that
someone's
gonna
have
to
sit
down.
Explain
it
to
me
again,
I
just
find
it.
B
This
is
basically
showing
the
0
through
10,
here
or
sort
of
representing
these
different
10
different
spaces,
where
the
cells
active
and
just
also
the
different,
just
sorting
them
by
firing
rate.
So
you
can
see
that
in
some
some
places,
that
cell
doesn't
fire
much
at
all
I'm
on
doing
it
and
they're
all
said
in
one
place,
this
fires
a
lot
more,
so
it's
individual
cells,
firing
rate
by
different
place,
fields,
these
different
circles
and
and
how
there's
a
preferential
there's
a
difference
between
them.
B
B
D
B
D
D
B
This
be
here
again,
this
is
not
looking
at
all
cells
in
this,
this,
this
correlation
for
all
cells
and
the
number
of
cells
that
were
into
each
of
these
buckets
there's
a
fair
amount
of
information,
and
this
thing
about
how
they
eliminated
cells
from
the
study,
because
there
are
many
souls
that
they
they
start
out
with
many
cells
that
they
were
recorded
from,
but
they
had
to
eliminate
many
of
them.
So
there's
a
huge
sort
of
bias
in
this,
but
they
try
to
eliminate
that
bias.
B
For
example,
they
say:
well,
some
cells
may
fire
differentiate
because
they're
there
they're
partially
representing
pen
direction.
So
they
had
a
method
for
saying
how
do
we
determine
if
the
cells
actually
just
representing
a
direction
a
you
know,
a
combination
of
head
direction
and
location?
How
do
we
remove
those
cells
because
we
don't
want
them
biasing
the
data.
D
D
B
Know
I
mean
maybe
I
think
what
they
with
the
implications.
They
just
basically
summed
up
all
the
spikes
right
and.
C
A
B
B
So
this
is
the
real
date
of
all
these
cells,
and
then
they
ran
asunder
by
some
sort
of
simulation
and
I
did
I
didn't
understand
exactly
the
simulation,
but
they're,
basically
showing
that
through
basically
looking
at
the
data
through
a
simulation,
they
got
the
same
sort
of
separation
between
oh,
they
know
they
got
separation
between
these
two.
So
this
is
the
real
data
and
then
they
did
a
more
basic
simulation
which
did
not
show
that
that
that
hi
CB
you
follow
I'm
saying
they
did
some
kind
of
simulation
to
say:
hey
our
simulations.
B
Don't
show
this
to
the
real
data,
it's
different
than
a
simulation
and
I
apologize
for
not
understand
that
exactly
how
they
did
that
simulation.
If
you
care,
we
can
go
into
that,
but
again,
they're
all
they're,
basically
just
trying
to
say
this
result
is
real.
It's
in
the
it's
in
the
data:
it's
not
something
that
can
you
be
explained
by
any
of
our
current
methods
of
thinking
about
grid
cells.
B
This
next
figure
here,
they're
showing
the
same
results
if
they
take
okay,
here's
a
single
animal
in
a
single
environment
and
they
split
the
data
into
the
first
half
and
the
second
half
to
show
that
of
their
over
the
time
the
animals
than
that
in
that
space
that
you
get
the
same
results.
So
there's
not
a
bias
towards
the
beginning
of
they're,
just
they're,
just
looking
for
ways
of
proving
that
that
it's
the
correct
data,
this
one
is
I,
I,
didn't
quite
understand.
B
I
think
context
is
they're,
basically
like
changing
the
color
of
the
room
or
the
change
in
the
scent
of
the
room.
So
it's
the
same
room,
but
now
they've
changed
the
context
and
the
cells
do
not
remap
and
the
preference
all
a
firing
exists
there
as
well,
and
then
here
they're,
showing
the
same
thing
with
scaling.
They're
basically
saying
if
we
scale
the
room,
but
not
so
much
that
there's
remapping,
that
the
same
preferential
thing
occurs,
and
these
are
also
fine-tuning
of
the
same
basic
idea.
B
So
they're
really
just
saying
that
this
preferential
firing
is
tied
to
the
mapping
and
if
the
mapping
doesn't
change
you,
because
if
you
change
the
context
and
mapping
doesn't
change
or
rescale
the
mapping
doesn't
change.
These
things
still
exist.
So
it's
you
know,
it's
not
that
super
important
to
you,
but
they're.
Just
working
around
the
concept
again.
B
This
one
I'm
not
gonna
go.
This
is
basically
looking
at
populations
of
cells
and
doing
the
same
thing
with
us
with
a
shuffling
thing.
So
and
again,
all
these
are
just
flavors
of
the
same
basic
idea,
proving
that
this
condition
exists
under
different
ways
of
testing
and
looking
at
the
data,
and
so
they
down
here,
they
even
say
write
it
here.
It
says
this
reveals
that
the
inter
field
variability
of
stable
across
them
sessions
in
the
fields,
ten
tubes
to
be
retained,
similar
relative
peak
for
arguments
across
time.
B
So
here's
the
here's,
the
summary
what
they
do
finding
is
a
three-fold
grid
cells
possess
larger
than
larger,
into
field
firing
variability
than
expected
by
chance
or
anything
else.
So
there's
something
there:
the
grid
cells,
the
grid
shows,
reproducible,
heterogeneity
and
the
right,
such
local,
as
well
as
distributed.
Spatial
modulation
and
grid
cells
reaction
context
changed
by
remapping,
their
peak
field
firing
distribution.
So
it
seems
to
go
with
the
rig
mapping.
B
B
C
B
B
Their
preferred
answer
to
what
causes
this
hemorrhage
energy
is
the
following:
you've
got,
you
got
place,
cells
and
you've
got
grid
cells
and
there
are
basic,
they
said.
Well,
maybe
this
heterogeneity
in
these
grid
cells
are
coming
from
that
maybe
two
things
that
maybe
it's
coming
from
an
input
to
the
good
cells
may
be
coming
from
the
grid
cells
connecting
themselves
or
maybe
it's
coming
from
the
place
off,
projecting
back
to
Rizzo
and
they
kind
of
they
kind
of
preferred.
B
What
which
place
cells
are
active,
so
the
unique
and
they're
saying
well
that
that
could
be
the
source
of
the
uniqueness
here.
That
is,
if
I,
have
a
unique
place
representation
here-
and
this
is
projecting
down
to
here,
then,
if
I
look
at
individual
plate,
the
grid
cells
and
how
they're
connected
place
cells
that
they
could
have
differential
connectivity
here
and
therefore
one
unique
place
out
here,
it's
going
to
form
a
unique
it's
sort.
B
These
cells,
as
two
things,
there's
an
inherent
grittiness
to
what
bridge
they'll
do,
but
there's
also
this
additional
information
on
top
of
it,
which
is
coming
from
play,
cells
and
I
kind
of
like
that
idea.
It's
it's
sort
of
it's
almost
like
saying.
Imagine
imagine
you
could
say
the
grid
cells
are
always
going
to
have
their
grid,
but
there's
going
to
be
a
sparsity
enforced
upon
that
that
doesn't
get
really
bad,
but
causes
causes
the
grid
cells
themselves
to
have
different.
B
You
know
something
to
be
acting
more
than
others,
so
it's
like
there's
a
sparsity
to
them,
there's
extra
activity
and-
and
therefore
you
know
you
have
a
sparse
pattern
here
and
it's
being
learned
by
being
associated
with
sparse
pattern
here
and
back
and
forth.
So
that
was
a
basically
saying
is
well
rich
Hills
know,
uniquely
where
they
are,
then
then
we
could
encode
place
uniquely
in
grid
cells.
As
you
know,
they
Brits
are
modeled
by
this
differential
activity.
B
B
Nice
way
of
looking
at
it
is
it's
like.
We
always
taught
about
sparsity
representation
in
someplace
driving,
another
smart
representation.
So
it's
Allison.
You
can
learn
those
two
and
it's
like
R
itself.
Might
this
Myra,
where
you
need
to
put
that
on
here,
but
the
green
sauce
has
these
two
basic
representations?
One
is
a
sparse
coding
related
place,
but
that's
on
top
of
in
this.
It
has
to
sit
on
top
of
the
bumps,
and
they
make
a
point
of
paper
that
that
this
requires
to
be
multiple
bumps.
B
A
B
A
B
Heavily,
they
did
not
talk
about
that.
Little
here
will
be
around
it.
So
their
conclusion
other
between
such
a
good
way
for
the
system
to
accumulate
you
can
let
the
outputs
of
play
cells.
That's
what
I
was
just
talking
about
here
are
active
in
that
place
and
feed
them
back
to
the
individual
play
cells.
Oh,
they
were
saying
this
was
just
allowing
the
system
to
combine
focal
place,
information
and
self,
mostly
related
path.
Integration
signals
in
order
to
derive
an
unambiguous
estimation
of
current
location,
so
they're.
B
D
B
B
D
B
You
could
go
to
large
one,
but
is
it
large
enough?
I
mean
we
we've
done
that
we
do
yeah
and
we
talked
about
having
this
grid
cell
space
being
really
really
huge
right.
Huge
I
mean
you
know.
Unlimited
number
of
you
have
enough
vigil
modules.
You
you
have
this.
You
know
monster
space
where
if
it
was
as
simple
as
what
tank
had-
and
you
say
let's
say:
I
have
six
phase
quadrants
and
five
six
pumps
moving
around
and
two
of
them
are
more
active
than
the
other
and
might
think
of
it
as
a
binary.
D
A
B
B
But
we
don't
argue
in
the
past
the
modules
have
these
different
phases
right,
and
that
means
that
they
had
to
be
anchoring
uniquely,
like
I,
have
a
module
and
module
B.
You
know
they're
the
same
phase
spacing
they
would
have
different
route
anchoring
points
to
do
the
night
brings
yeah,
but
we
have
no
evidence
for
that.
It
could
be
happening,
but
but
well
I
guess
it
could
be
of
several
things.
For
example,
we
we
started
off
by
suing
for
this
to
work
for
our
system
to
work.
B
We
haven't
have
a
bunch
of
modules
and
you
get
a
large
in
each
one.
Has
these
one
had
the
same
space?
They
knew
everything
phase
space,
but
but
they
have
the
different
entries
and
you
get
a
really
large
space
and
a
bunch
of
these
right,
two
or
three
wouldn't
be
very
much,
and
then
these
things
are
saying,
given
a
single
module
which
has
my
v6
bumps
in
it,
as
in
the
tank
paper,
there's
there's
an
encoding
on
top
of
this.
That
gives
you
more
than
gives
you
some
specificity
and
maybe
you're
saying
there.
B
So
it
could
be
something
in
between
you
know.
You
could
have
perhaps
you
can
have
three
bottles
and
nearby
columns
of
something
that
each
have
the
same.
Spacing,
and
this
is
you
know
six
three,
two
and
and
then
you
line
them
up
to
get
something
in
bigger
space,
so
yeah
I
think
in
this
paper
they
were
just
talking
about
like
what
would
you
get
from
a
single
module
and.
B
C
B
B
This
was
one
that
was
talking
about
the
same
issue,
the
field,
the
field
variability,
but
then
they
were.
It
was
all
about
some
strange
response
of
inhibitory
neurons
into
neurons
that
they
had
reported
earlier
and
how
this
could.
This
could
explain
the
nature
of
these
inhibitory
neurons,
so
I
didn't
have
time
to
get
into
that.
That's
a
very
detail
than
sort
of
mathy
paper
on
trying
to
explain
some.
It
was
just
beyond
my
ability
to
read
them
an
interest
level,
and
then
there
was
another
one
here.
C
B
Is
the
thing
and
let
me
let's
describe
it
and
let's
go
through
what
am
I
causing
what
is
useful
so
and
as
I?
You
know
if
I
point
out
before
we
not
only
do
we
didn't
know
the
exact
location,
but
you
also
have
to
some
places
circuit
as
to
representing
the
particular
state
of
the
object
that
we
revisited
cortex
and
so
there's
going
to
be
an
even
an
additional
sort
of
a
representation
may
not
be
in
the
midst
of
themselves
and
maybe
some
but
there's
an
additional
representation.
B
D
I
think
this
is
probably
the
grid
cells
are
actually
coding,
something
additional
and
their
firing
rates
or
something
not
necessarily
the
rate
itself,
but
something
else
which
that
we
see
it
experimentally
in
terms
of
funding.
It's
like.
Maybe
it's,
maybe
it's
mini
birds
or
something
like
that.
So
that's
probably
right.
The
other.
D
D
An
environment
this
is
this
is
the
module.
Oh,
that's.
A
type
of
funding
over
it
laughter
in
general,
like
the
certain
certain
parts
of
the
environment
are
I,
was
just
to
finish
this.
Certain
parts
of
the
environment
are
pinning
certain
phases.
That's
that's
the
terminology
for
saying
that,
like
when
you're,
when
the
animal
is
like
along
this
boundary,
yeah,
it's
gonna,
it's
kind
of
kind
of
provide
some
initial
input
to
those
good
cells
right
there.
D
C
D
B
C
D
So
here
I'm
putting
out
that
like
well.
If
these
cells
I
mean
object,
vector
cells
are
in
entorhinal
cortex,
their
profit,
just
like
border
cells,
they're,
probably
helping
anchor
the
grid
cells.
They're,
probably
probably
like
one
that
cells
that
active
in
this
environment,
it
Technic
provides
input
to
the
grid
cells.
C
D
Green
cell
is
probably
providing
excited
excited
to
re-encode
to
this
black
cell,
and
so
it's
also
possible
that
these
differences
in
firing
rates
come
from
these,
like
maybe
certain
parts
of
the
room
have
stronger
anchoring
effects.
Maybe
certain
parts
of
the
environment
are
providing
more
more
of
this
excitatory
input
to
grid
cells
and
causing
them
to
that
those.
D
B
B
C
B
Those
are
projecting
to
the
grid
cells,
yeah
and,
and
that
we're
saying
what
they're
saying
here
when
I,
what
I
try
to
say
again
was
that
they
don't
do
that
uniformly
right,
there's
a
that
that
causes
certain
grid
cells
get
more
input
than
others,
and
that
leads
to
this
thing,
but
but
that
would
still
be
consistent,
saying
now
now
we
can
think
about
them
as
coding.
The
grid
cells
is
coding
a
specific
place,
because
if
I
now
update
my
if
I
move
my
grid
cells
by
movement,
they
will
now
predict
different
set
of
play
cells.
D
C
B
C
D
B
A
A
B
Because
because
we
need
to
happen,
we
have
the
reverse
process.
The
first
process
is
once
I.
Have
these
grid
cells
active
and
I
move
and
I
have
move?
My
bumps
I
now
need
to
predict
which
place
cells
are
gonna,
be
active,
I
mean
it's
my
that's
like
part
of
the
whole
system,
so
this
is
bi-directional,
and
so
these
place
cells
over.
B
B
B
D
B
C
C
C
D
B
I,
don't
think
they
look
for
that.
They
just
had
this
big
collection
of
grid
cells
and
100
of
them,
and
they
said.
Okay,
where
is
that
cell
firing
now
give
her?
There
were
hundreds
of
these
I
I,
don't
think
they
said.
I
could
be
wrong,
but
I
don't
recall
anything.
They
are
about
them.
Saying:
okay,
let's
find
two
cells
apart
at
the
same
spot,
so.
D
I'm
not
saying
anything
about
I'm,
not
I'm,
not
saying
that
there's
differential
can
connecting
like
some
grid
cells
connect
to
the
place
cells.
Some
don't
I'm,
saying
that
the
places
where
these
green
circles
are
sparsely
spread
through
the
environment
and
wherever
those
land
on
a
grid
cell
there's
stronger
firing
and
whenever
they
don't
there's
weaker
fire.
Oh.
C
B
B
B
You
know
I,
don't
know
who's
in
the
paper
or
not.
I
didn't
seem
like
it
was
called
out
explicitly,
but
am
I've
been
in
the
data
again
I'm
thinking
about
the
tank
paper
where
they
show
these
six
phase
modules
and
they
showed
how
like
two
out
of
the
six,
were
highly
active
in
integrated
response.
It's
not
binary,
but
you
know
what.
B
Is
that
sparsity
of
hyerin,
always
probably
in
this
data
in
this
paper?
I
just
didn't,
expect
it.
You
know,
for
example,
is
there
a
consistent
level
of
sparsity
or
encoding
power
in
the
differential
activity
of
the
grid
cells
they're,
showing
that
this
there's
this
different
track
to
reading
the
grid
cells?
They
say:
that's
always
there
it's
consistent,
but
it's
that
level
I
mean
if
I'm
going
to
use
that
to
encode
something
you
would
want
it
to
be
just
like
any
sparse
representation.
B
If
you
wanted
to
have
a
similar
sparsity
of
that
encoding
mechanism,
I
can
we
want
in
one
place
for
the
four
out
of
six
bridge
cells
to
be
highly
active
in
another
place?
Only
one
out
of
six
to
be
highly
active
you'd
always
want
like
two
out
of
six
behind
that.
So
that's
my
immediately
jump
to
that
conclusion.
Here,
let's
say
like
oh
I
have
a
bunch
of
little
good
cell
phase
modules.
B
All
these
little
bumps
moving
around
and
I
would
want
to
have
some
certain
level
of
subset
of
a
more
active
than
others,
and
that
would
be
at
a
consistent
coding
scheme
and
sim,
presumably
on
the.
If
it
is
bi-directional
like
this,
as
I
suggested,
you
would
it's
interesting
how
to
play
cell,
because
all
the
grid
cells
are
active
right
there,
just
differentially
active
so
somehow
the
play
cells.
Maybe
this
gets
back
to
your
your
question
so
tidy
about
bursting
the
place
that
you
wanted
preferentially
to
connect
to
the
ones
that
are
highly
active?
B
Not
so
how
do
they
know
to
do
that?
You
know
it
could
be
a
phase.
It
could
be
a
burst.
It
could
be
all
right.
Well,
I,
think
it's
fascinating
idea
that
that
this
is
an
encoding
scheme
that
can
be
used
to
much
more
high
certainty
code,
location
and
not
not
just
the
idea
that
multiple
modules
at
different
phases-
I
guess
we
can
leave
it
at
that-
that's
the
something
else
to
be.