Hardware Reference
In-Depth Information
Figure
3.4
b shows the actuation signals applied on electrodes when a droplet
is being moved. We can find that the destination electrode of the droplet will be
actuated, while all the other surrounding electrodes are deactivated.
Similarly, we can analyze the actuation signals that need to be applied on elec-
trodes when a dispensing/mixing/splitting operation is executed. We can find that,
usually an actuated electrode is surrounded by a group of deactivated electrodes.
When we convert the actuation signals applied on electrodes to a vector or a matrix,
we find that non-zero elements (that corresponds to actuated electrodes) are much
fewer than zero elements (that corresponds to deactivated electrodes). In this way,
we also find that actuation matrices in error dictionaries are sparse.
From the above discussion, we find that the size of the dictionary can be reduced
by compacting the actuation matrices. Two data-compaction algorithms for sparse
matrices will be introduced in Sect.
3.5
.
3.5
Compaction of the Error Dictionary
In this section, we describe two algorithms to compact actuation matrices of
synthesis results for bioassay. Corresponding algorithms for de-compaction of error
dictionary also will be discussed.
3.5.1
Compaction of the Actuation Matrix
Suppose the actuation matrix
non-
zero elements, where M and N refer to the array dimensions and T is the number of
clock circles for the bioassay. We describe two algorithms for the compaction of the
actuation matrix. The compaction ratio is defined as the number of elements before
compaction divided by the number of elements in the matrix after compaction.
A
is an .M
N/-by-T sparse matrix with
K
Method I:
three-
tuples. Each tuple records the row indices, column indices and numerical values
of a non-zero element in the matrix. Thus the number of elements in the
actuation matrix is compacted from
NMT
to 3
COO (coordinate list) compaction [
26
].
A
can be stored as
N
K
, and its compaction ratio R
I
. For example, the matrix M
Mix
1
in Sect.
3.3
has 36 elements, and seven of them are non-zero elements. Thus M
Mix
1
can
be compacted to 7 three-tuples, which have 21 elements in total: .1; 1 ;
v
1
/,
.2; 2 ;
v
1
/; :::; .6; 4;
v
2
/, .6; 6 ;
v
2
/. The compaction ratio for matrix M
Mix
1
is
equal to 1:71.
Method II: Run-length encoding [
27
]. The actuation matrix of each dictionary
entry can be reformatted to a signal sequence. The actuation sequence in which
the same status value occurs in consecutive clock cycles can be compacted
according to the single status value and the corresponding count number. For the
can be calculated as
NMT
=3
K
