13th International Conference on Membrane Computing - MTA Sztaki

A case-study on the influence of noise to log-gain principles for flux dynamic
discovery
With the data we constructed about the ux functions, our model (see appendix),
initial concentrations, molar weights, and the appropriate multiplicity
of each edge we were able to run Simulation Plugin 2 plugin for MetaPlab and
obtain the time series for each substance.Next, we took this data and used Matlab
to plot the time series for each substance (shown below).These are the time
series that we expect the log-gain theory to yield for perfect, noiseless data.
Simulation Plugin 2 is a plugin that simply runs the computations for the
given inputs of a given model.Using this plugin we can quickly and easily determine
the time series for various substances in a model, given that we know
sucient data (initial values and regulation functions) of the substances.Since
this data is assumed for our experiment, we already have it.
As such, our next step is to add noise to the data.To this end we made use of
the genSignalForSNR function of Matlab, which allows us to specify a particular
value for the SNR to be applied to a time series of our choosing.Through the
use of this function we can approximate what in vivo biological data may look
like by applying noise to the time series we have generated.
Worth noting is that genSignalForSNR will be adding Gaussian noise to our
data set.Gaussian noise is a statical noise that is normally distributed.The
choice to add Gaussian noise was made in an attempt to have an ideal mix of
data with noise.The uniform distribution of Gaussian was believed to aid in this
area.
Figure 30 (see appendix) shows the genSignalForSNR inputs for our three
time series with an SNR parameter of 20.An SNR of 20 implies that the signal
strength will be 20 times greater than the strength of the noise.In our original
research we considered all SNR values less than or equal to 80 in increments of
5; for the purposes of this paper, we will only consider SNR values of 40, 25, and
10.The purpose for this choice will become apparent later.
This genSignalForSNR function must be run for every substance at every
SNR value we wish to test.The substance inputs take the form of three .txt les
(A.txt, B.txt, and C.txt) which contain the time series of the three substances
as shown above.The raw time series data used to create these .txt les was
obtained by exporting the time series data for each of the three substances.
Figure 31 (see appendix) simply shows the body of the actual genSignal-
ForSNR function in Matlab.While Fig.30 shows how we call the function in
Matlab, Fig.31 shows what is happening behind the scenes.As we can see,
the genSignalForSNR function generates Gaussian noise, scales the input signal
according to the given SNR, calculates the signal power and noise power, calculates
the SNR for the scaled signal and generated noise, and nally applies the
generated noise to the input signal.For the purpose of this research, the signal
used in this function was our time series data.
The genSignalForSNR gives us the modied time series data values that we
would see if the data collection process had contained noise.We can now take
this noisy data that we have generated using genSignalForSNR and use Matlab
to plot these new noisy time series.
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