13th International Conference on Membrane Computing - MTA Sztaki

T. Ahmed, G. DeLancy, A. Paun
Table 6. Error Calculation for an SNR of 25
A B C Average
0.026050201 64.57143304 6.32E+011 2.11E+011
Original Functions Flux Functions when SNR = 10
F 0: 0.000002 * A * B * C 0.037418924438467255 - 0.00666065409056642*A*B*C
F 1: 0.00003 * B * C 0.03739589061548739 - 0.6660734345363942*B*C
F 2: 0.00004 * C * A 5.97325907520103E-5 - 8.615188297155205E-4*C*A
F 3: 0.0005 * B
1.3867825429805325E-14 + 4.958777189347849E-4*B
F 4: 0.007 * C
-5.371722788640667E-19 + 0.007036948200220921*C
Table 7. SNR 10 Results
and what we know the true ux-dynamics to be is caused by introducing noise
into the time series.
As shown by the above results, log-gain theory fails to generate accurate ux
dynamics for our substances when the data becomes suciently noisy. This was
expected; using enough noise will break even the most robust models. What
was not expected was just how quickly the model began to fall apart. Biological
data is said to have relatively low SNR values due in part to the sensitivity
of the equipment required to record the data and the randomness inherent in
all biological processes. Our experimentation nds that there is sucient noise
present in SNR values of 40 and below to break the process.
Also shown are the ux functions derived from the log-gain theory. These
functions are shown to deviate further from their actual values as SNR decreases.
Like the ux dynamics and error, this is expected as noise is interfering with
our data set. Once again these results are disproportionately disturbed for the
amount of noise present in the data at many steps.
5 Conclusion
Based on the data derived from these tests we have determined that the log-gain
procedure fails to account for noise and begins to break down at when the SNR
drops below 40. This corresponds to the signal being 40 times stronger than
the noise, or 2.5 percent observed noise in the recorded data. Since biological
processes are often considered to have low SNR values (and are therefore fairly
Table 8. Error Calculation for an SNR of 10
A B C Average
0.016546042 1109.035792 1.16E+012 3.87E+011
80