  New relationships between the orbital period and some parameters of W Ursae
Majoris (W UMa) type systems are presented in this study. To investigate the
relationships, we calculated the absolute parameters of a sample of 118
systems. For this purpose, we used the parallax values obtained from the Gaia
Early Data Release 3 (Gaia EDR3) star catalog for more precise calculations.
The other required parameters, including the light curve solutions and the
orbital period were derived from previous research. For some relationships, we
added 86 systems from another study with an orbital period of less than 0.6
days to our sample, allowing us to increase the number of systems to 204.
Therefore, the mass (M) values of each component along with all the other
absolute parameters were recalculated for these contact systems. We used the
Markov Chain Monte Carlo (MCMC) approach in order to gain the new orbital
period-mass relations (P-M) per component, and added the temperature (T) to the
process to acquire the new orbital period-temperature (P-T1) relation. We
presented the orbital period behavior in terms of log(g) by new relations for
each component. We have also obtained a model between the orbital period, the
mass of the primary component and temperature (P-M1-T1) using the Artificial
Neural Networks (ANN) method. Additionally, we present a model for the
relationship between the orbital period and the mass ratio (P-q) by fitting a
Multi-Layer Perceptron (MLP) regression model to a sample of the data collected
from the literature.
