La AMH como marcador endocrino de la reserva folicular

The Sun is definitely the most observed star in our Universe. We continuously

increase our knowledge about the origin and development of the solar activity, inner structure of the Sun and solar dynamo, influence of the solar activity on the terrestrial environment and formation of the Space Weather. The most critical component for such progress in understanding of the Sun is tremendous amounts of observational data acquired by the space-based and ground-based facilities. For example, the Atmospheric and Imaging Assembly telescope onboard the Solar Dynamics Observatory makes 4K-resolution images of the Sun faster than each two

seconds, which results in around 1 TB of scientific data per day. I do not think that there is a person who looked through all SDO/AIA images.

At the same time, the fast development of realistic 3D simulations also results in large data volumes. As an example, let us consider the widely-used Bifrost simulation

results of the enhanced network of the Sun [78]. One of the publicly-available

results of these simulations cover the region of the solar atmosphere of the size 24 Mm×24 Mm×17 Mm for less than 30 min with 10 s temporal resolution, which already results in 1.5 TB of scientific data. These are also the data volumes which are very hard to handle manually.

Growing amounts of data from ground and space observing instruments and realistic 3D simulations, together with the demand on the reliable operational forecasts of solar activity and space weather, require implementation of new approaches for analysis of multidimensional data sets. A cross-disciplinary synergy based on machine learning and data mining becomes a necessity rather than a desired research direction. The machine learning techniques are already applied for prediction of solar and heliospheric events on certain timescales (strong solar flares, coronal mass ejections, solar energetic particles), reconstruction of coronal mass ejections, deconvolution of the solar observational images, similarity search among multidimensional spectroscopic data sets. Moreover, applications of such techniques not only deliver the results but allow us to understand better the physics behind the studied processes. Thus, the number of works containing “machine learning” term in the title or abstract increases continuously, and this trend will continue to exist.

In conclusion, it is very probable that the future solar and heliospheric physicists will have a fundamental knowledge from and understand both physics and data science disciplines. And it is a very proper time to anticipate that direction and prepare the next generation of solar scientists for the bright future full of discoveries in our interdisciplinary area.

APPENDIX A

MAGNETOGRAM SEGMENTATION AND PIL DETECTION ALGORITHM

Suppose B is a magnetic field strength map (magnetogram), Zi is a class of

pixel i of the magnetogram (i.e., “positive”, “negative” or “neutral”), N is the total number of pixels in the magnetogram, ε(i) is a neighborhood (e.g., the closest 8 pixels) of pixel i. The magnetogram segmentation can be formulated as the following optimization procedure to maximize function p(Z, B) for a given B by finding optimal classification Zmax [42]: p(Zmax, B) = max Z p(Z, B) ∝ N Y i=1 φi(Zi, Bi) Y j∈ε(i) φ(Zi, Zj)

Here φi(Zi, Bi) and φ(Zi, Zj) are the scoring functions for each pixel depending

on the magnetic field strength and assumed classes of pixels. The choice of the scoring function defines segmentation characteristics and, in fact, should do the following: separate the segments of positive and negative magnetic field polarity, and avoid very small segments with weak field probably coming from noise in the data. We use the scoring functions suggested by Chernyshov et al. [42]:

φi(Zi, Bi) = e−C1 √ |B0−Bi|_{, for Z} i “positive” φi(Zi, Bi) = e−C1 √ |B0+Bi|_{, for Z} i “negative” φi(Zi, Bi) = e−C2|Bi|, for Zi “neutral” φ(Zi, Zj) = eCpair[Zi6=Zj],

where parameters C1 = 1.0, C2 = 1.0, Cpair = 20, B0 = 1000 G are chosen to

obtain a stable segmentation of magnetic polarities in strong field regions. Here [Zi 6=

Zj] is equal 1 if Zi 6= Zj, and zero otherwise. Following Chernyshov et al. [42], the

is approximated by the factorized probability density function q(Z) = Qn

i=1qi(Zi).

To measure how strongly the factorized distribution deviates from the actual, one can use the Kullback-Leibler (KL) divergence Bishop [18]. In order to find the best approximating factorized distribution, q(Z), one can minimize the KL divergence:

min

q(Z) KL(q||p) = −

Z

q(Z)logp(Z|B)

q(Z) dZ

Here we keep the original notation for KL-divergence KL(q||p) between distributions q and p introduced in Bishop [18]. The optimal q(Z) is given by solution of the equation [42]: qi(Zi) = 1 Cexp(log(φi(Zi)) − Cpair X t∈ε(i) X j6=i qj(Zj))

This solution can be found iteratively [42]: q_inew(Zi) = 1 Cexp(log(φi(Zi)) − Cpair X t∈ε(i) X j6=i q_jold(Zj))

Using this equation, one can calculate the factorized distribution multiplier qifor

each pixel i and its assumed class Zi (“positive”, “negative”, or “neutral”). Because

the factorized distribution represents the product of multipliers for each pixel, one can simply maximize qi(Zi) for each pixel i separately and obtain Zmax.

For identification of PIL in active regions, we smooth the original HMI magne- togram using the Gaussian filter with width σ =1.5′′_{, and apply the segmentation}

algorithm. Then, we apply a morphological dilation procedure separately for positive and negative segments (i.e., expand each segment to include neighboring pixels), and find the PIL as an intersection of the dilated positive and negative segments. Finally, we filter all small islands of the PIL with the number of pixels less than 3% of the total number of pixels occupied by PIL. This approach is quite robust, and allows us to automatically identify the PIL and calculate magnetic field properties.

APPENDIX B

DESCRIPTION OF CLASSIFIERS