<s>
In	O
computational	O
neuroscience	O
,	O
the	O
Wilson	B-Algorithm
–	I-Algorithm
Cowan	I-Algorithm
model	I-Algorithm
describes	O
the	O
dynamics	O
of	O
interactions	O
between	O
populations	O
of	O
very	O
simple	O
excitatory	O
and	O
inhibitory	O
model	O
neurons	O
.	O
</s>
<s>
neural	B-Algorithm
oscillations	I-Algorithm
,	O
and	O
stimulus-dependent	O
evoked	O
responses	O
are	O
predicted	O
.	O
</s>
<s>
The	O
Wilson	B-Algorithm
–	I-Algorithm
Cowan	I-Algorithm
model	I-Algorithm
considers	O
a	O
homogeneous	O
population	O
of	O
interconnected	O
neurons	O
of	O
excitatory	O
and	O
inhibitory	O
subtypes	O
.	O
</s>
<s>
The	O
equations	O
that	O
describes	O
this	O
evolution	O
are	O
the	O
Wilson-Cowan	B-Algorithm
model	I-Algorithm
:	O
</s>
<s>
If	O
denotes	O
a	O
cell	O
's	O
threshold	B-Algorithm
potential	I-Algorithm
and	O
is	O
the	O
distribution	O
of	O
thresholds	O
in	O
all	O
cells	O
,	O
then	O
the	O
expected	O
proportion	O
of	O
neurons	O
receiving	O
an	O
excitation	O
at	O
or	O
above	O
threshold	O
level	O
per	O
unit	O
time	O
is	O
:	O
</s>
<s>
that	O
is	O
a	O
function	O
of	O
sigmoid	B-Algorithm
form	O
if	O
is	O
unimodal	O
.	O
</s>
<s>
A	O
canonical	O
analysis	O
of	O
these	O
issues	O
,	O
developed	O
in	O
2008	O
by	O
Shusterman	O
and	O
Troy	O
using	O
the	O
Wilson	B-Algorithm
–	I-Algorithm
Cowan	I-Algorithm
model	I-Algorithm
,	O
predicts	O
qualitative	O
and	O
quantitative	O
features	O
of	O
epileptiform	O
activity	O
.	O
</s>
<s>
In	O
particular	O
,	O
it	O
accurately	O
predicts	O
the	O
propagation	O
speed	O
of	O
epileptic	O
seizures	O
(	O
which	O
is	O
approximately	O
4	O
–	O
7	O
times	O
slower	O
than	O
normal	O
brain	B-Algorithm
wave	I-Algorithm
activity	O
)	O
in	O
a	O
human	O
subject	O
with	O
chronically	O
implanted	O
electroencephalographic	O
electrodes	O
.	O
</s>
<s>
In	O
waking	O
adults	O
this	O
state	O
is	O
commonly	O
associated	O
with	O
alpha	O
rhythm	O
,	O
whereas	O
slower	O
(	O
theta	B-Algorithm
and	O
delta	B-Algorithm
)	O
rhythms	O
are	O
usually	O
observed	O
during	O
deeper	O
relaxation	O
and	O
sleep	O
.	O
</s>
<s>
To	O
describe	O
this	O
general	O
setting	O
,	O
a	O
3-variable	O
spatially	O
dependent	O
extension	O
of	O
the	O
classical	O
Wilson	B-Algorithm
–	I-Algorithm
Cowan	I-Algorithm
model	I-Algorithm
can	O
be	O
utilized	O
.	O
</s>
<s>
The	O
ratio	O
in	O
formula	O
(	O
1	O
)	O
shows	O
that	O
the	O
leading	O
edge	O
of	O
the	O
region	O
of	O
synchronous	O
seizure	O
activity	O
migrates	O
approximately	O
4	O
–	O
7	O
times	O
more	O
slowly	O
than	O
normal	O
brain	B-Algorithm
wave	I-Algorithm
activity	O
,	O
which	O
is	O
in	O
agreement	O
with	O
the	O
experimental	O
data	O
described	O
above	O
.	O
</s>
<s>
It	O
might	O
be	O
also	O
useful	O
for	O
predicting	O
migration	O
and	O
spread	O
of	O
electrical	O
activity	O
over	O
large	O
regions	O
of	O
the	O
brain	O
that	O
occur	O
during	O
deep	B-Application
sleep	I-Application
(	O
Delta	B-Algorithm
wave	I-Algorithm
)	O
,	O
cognitive	O
activity	O
and	O
in	O
other	O
functional	O
settings	O
.	O
</s>
