Hardware Reference
In-Depth Information
3.8
Simulation Results
In this section, we first proof that the actuation matrices for bioassays are sparse.
Next, we present simulation results for four widely used laboratory protocols,
namely exponential dilution of a protein sample, interpolation dilution of a protein
sample, mixing tree bioassay, and PCR bioassay, respectively [
16
,
23
]. Then
the simulation result of a new benchmark for a flash chemistry application is
presented [
33
].
The error dictionaries for these four bioassays are generated, and the compaction
algorithms for error dictionaries are applied. Fault simulation to mimic the occur-
rences of errors are also carried out.
3.8.1
Exponential Dilution of a Protein Sample
3.8.1.1
Generating Error Dictionaries
The exponential dilution bioassay contains 103 operations. The sequencing graph
is shown in Fig.
2.20
b and the detailed description of the bioassay can be found
in [
16
].
By applying the PRSA-based synthesis algorithm [
16
], the synthesis result for
the bioassay can be derived. When running the bioassay on a 10
10 electrode
array and no erroneous operation occurs, the completion time is 208 s. Based on the
synthesis result for the error-free case, the dynamic re-synthesis algorithm proposed
in [
35
] is applied to generate the error dictionary.
In order to generate entries of the error dictionary, erroneous operations are
inserted into the bioassay. By considering each operation as a possible erroneous
operation, 103 dictionary entries with single error that occurs in the bioassay are
generated. If we set the upper limit for the number of erroneous operations to be
two, the number of possible combinations of errors that must be considered is
10
2
,
i.e., .103
102/=2 (here we assume that errors will not occur in error recovery
operations). Therefore, the total number of entries
N
e
in the dictionary is given by:
N
e
D
103
C
.103
102/=2
D
5356.
The fault simulation is run on a 2.30 GHz Intel i3 dual-core processor with 8 GB
of memory. The CPU time is 1,925.7 s for generating the error dictionary. The
histogram for the numbers of extra droplets consumed in these 5,356 dictionary
entries is shown in Fig.
3.7
a. The maximum number of additional droplets consumed
in the process of error-recovery is 8.
When we consider the cost of error recovery, not all these 5,356 dictionary entries
will be selected as “effective entries” in the error dictionary. For some biochemistry
experiments, the cost of precious samples and reagents can be greater than the cost
of the biochips. If “too many” droplets are consumed in recovering from the error,
running the bioassay on a new biochip can be more cost-effective. In this situation,
the corresponding synthesis results will not be recorded in the error dictionary.
