<s>
Transition	B-Algorithm
path	I-Algorithm
sampling	I-Algorithm
(	O
TPS	O
)	O
is	O
a	O
Rare	O
Event	O
Sampling	O
method	O
used	O
in	O
computer	B-Application
simulations	I-Application
of	O
rare	O
events	O
:	O
physical	O
or	O
chemical	O
transitions	O
of	O
a	O
system	O
from	O
one	O
stable	O
state	O
to	O
another	O
that	O
occur	O
too	O
rarely	O
to	O
be	O
observed	O
on	O
a	O
computer	O
timescale	O
.	O
</s>
<s>
Examples	O
include	O
protein	O
folding	O
,	O
chemical	O
reactions	O
and	O
nucleation	B-Algorithm
.	O
</s>
<s>
Once	O
a	O
probability	O
is	O
assigned	O
to	O
each	O
of	O
the	O
many	O
pathways	O
,	O
one	O
can	O
construct	O
a	O
Monte	B-Algorithm
Carlo	I-Algorithm
random	O
walk	O
in	O
the	O
path	O
space	O
of	O
the	O
transition	O
trajectories	O
,	O
and	O
thus	O
generate	O
the	O
ensemble	O
of	O
all	O
transition	O
paths	O
.	O
</s>
<s>
As	O
in	O
all	O
Monte	B-Algorithm
Carlo	I-Algorithm
walks	O
,	O
the	O
new	O
path	O
will	O
then	O
be	O
accepted	O
or	O
rejected	O
in	O
order	O
to	O
have	O
the	O
correct	O
path	O
probability	O
.	O
</s>
<s>
The	O
factor	O
C(t' )	O
at	O
this	O
specific	O
time	O
can	O
be	O
computed	O
with	O
a	O
combination	O
of	O
path	O
sampling	O
and	O
umbrella	B-Algorithm
sampling	I-Algorithm
.	O
</s>
<s>
TPS/TIS	O
as	O
normally	O
implemented	O
can	O
be	O
acceptable	O
for	O
non-equilibrium	O
calculations	O
provided	O
that	O
the	O
interfacial	O
fluxes	O
are	O
time-independent	O
(	O
stationary	B-Algorithm
)	O
.	O
</s>
<s>
To	O
treat	O
non-stationary	B-Algorithm
systems	O
in	O
which	O
there	O
is	O
time	O
dependence	O
in	O
the	O
dynamics	O
,	O
due	O
either	O
to	O
variation	O
of	O
an	O
external	O
parameter	O
or	O
to	O
evolution	O
of	O
the	O
system	O
itself	O
,	O
then	O
other	O
rare	O
event	O
methods	O
may	O
be	O
needed	O
,	O
such	O
as	O
Stochastic	O
Process	O
Rare	O
Event	O
Sampling	O
.	O
</s>
