
324 Modeling and Inverse Problems in the Presence of Uncertainty
the s et of critical transitions by
J
cr
= {j ∈ {1, 2, . . . , l} | the jth transition is a critical one},
and the set of non-critica l ones by
J
ncr
= {j ∈ {1, 2, . . . , l}| the jth transition is a non-critical one}.
S3. Compute ∆t
1
according to the following formula:
∆t
1
= min
{1≤i≤n}
(
max {ǫx
i
/̟
i
, 1}
|ˆµ
i
(x)|
,
max {ǫx
i
/̟
i
, 1}
2
ˆσ
2
i
(x)
)
, (8.22)
where ǫ is the error control parameter (in our calculations below, we set
ǫ = 0.03), ̟
i
is chosen such that the relative changes in all the transition
rates will be bounded by ǫ at least to the first-order approximation (as
described in the text), and
ˆµ
i
(