The main processing steps of the SVDSolarLikeSOSRotationalModulation pipeline are
the following:

•
selection of the input sources

•
segmentation of the photometric timeseries

•
estimate of the linear correlation degree between gmag and ${G}_{\mathrm{BP}}{G}_{\mathrm{RP}}$ observations in each timeseries segment

•
search for outliers in timeseries segments

•
search for a periodic signal in each timeseries segment

•
modelling of the $G$ timeseries

•
estimate of a magnetic activity index in each timeseries segment

•
estimate of the stellar rotation period.
The first four tasks are performed by the SVD package whereas the others are performed
by the SOS package. The selection of the input candidates is performed according the
criteria outlines in Section 7.5.2. The segmentation of
photometric timeserie is required because the typical lifetime of spots and faculae
is of the order of several months
(see e.g. Lanza et al. 2003; Messina et al. 2003, and reference therein). A
detailed description of the adopted segmentation algorithm can be found in
Lanzafame et al. (2018). A well defined linear correlation between colour and magnitude
measurements is expected for variability due rotational modulation in solarlike
stars (see e.g. Messina et al. 2006). The SVDSolarLike package estimates
the Pearson Correlation Coefficient $r$ between $G$ and ${G}_{\mathrm{BP}}{G}_{\mathrm{RP}}$ observations in
each timeseries segment. This index can be regarded as an indicator of variability
due to rotational modulation. The closer $r$ is to $\pm 1$ the higher the probability
that rotational modulation is occurring. The SVDSolarLike package performs also a
robust linear regression between $G$ and ${G}_{\mathrm{BP}}{G}_{\mathrm{RP}}$ observations. The robust
regression procedure permits also to identify possible outliers i.e. points whose
location in the $G$ vs. ${G}_{\mathrm{BP}}{G}_{\mathrm{RP}}$ scatter plot, is significantly distant from the
straightline bestfitting the data. The identification of photometric outliers is
also performed by searching for the observations satisfying the condition
The points identified as outliers can be regarded as candidate flareevents. The
SOSRotationalModulation package performs a period search in each timeseries
segment by computing the generalised LombScargle periodogram as implemented by
Zechmeister and Kürster (2009). The period with the highest power in the periodogram is
selected by the pipeline and a False Alarm Probability (FAP) is associated with it.
The formulation used to compute the FAP is that prescribed by Baluev (2008).
A period is flagged as valid if the associated FAP is less then 0.05.
If a significant period is detected in a given segment, the pipeline performs also a
data modelling and fits the timeseries segment to the function:

$$G(t)=A+B\mathrm{sin}\left(\frac{2\pi t}{P}\right)+C\mathrm{cos}\left(\frac{2\pi t}{P}\right)$$ 

(7.3) 
where t is the observation time referred to the reference epoch ${t}_{start}$
that is the time at which starts the segment and $P$ is the period detected in the
segment. The SOSRotationalModulation package estimates the rotation period of a
solarlike candidate by analysing the distribution of the periods recovered in the
different timeseries segments. The mode of the distribution is taken as best
estimate of the stellar rotation period. The amplitude of rotational modulation can
be regarded as an index of the stellar magnetic activity and is widely used to study
solarlike activity cycles
(see e.g. Rodonò et al. 2000; Ferreira Lopes et al. 2015; Lehtinen et al. 2016). For
a given we computed an estimate of this Activity Index (AI) by means of the
equation:

$$AI={G}_{95th}{G}_{5th}$$ 

(7.4) 
where ${G}_{95th}$ and ${G}_{5th}$ are the 95th and 5th percentiles of the $G$ magnitudes measured in the segment. Note that an alternative estimate of the
amplitude associate with rotational modulation can be inferred from the fit
coefficients of Equation 7.3 through the relationship:

$${A}_{fit}=2\sqrt{{B}^{2}+{C}^{2}}$$ 

(7.5) 
A more detailed description of the reduction pipeline can be found in Lanzafame et al. (2018).