## 4 Conclusions  
In this work, we have studied indoor air quality related to important, but more rarely continuously measured parameters: small ion concentration and its association with radon and PM concentration in two elementary schools' indoor environments. We have analyzed the association using two approaches: descriptive statistical analysis coupled with linear modelling and artificial neural network predictive modelling. The following conclusions can be made. * Descriptive statistics showed that for similar median radon concentrations larger number of nanosized particles corresponds to smaller number of small ions. This observation is coherent with the balance equation. * The linear model derived directly from balance equation allowed estimation of balance equation parameters. The parameters corresponding to the radon term were similar in both schools, indicating similar increase in small ion concentration with radon concentration in both schools. Regarding particulate matter parameters, it was observed that attachment coefficients become larger for particle aggregations corresponding to larger particle diameters, in accordance to theoretical expectations. However, these parameters were different in two schools, possibly due to different air pollution composition. * The hypothesis that small ion concentration, which may have certain impact on human health and wellbeing, can be predicted based on radon and particulate matter measurements predictors was successfully tested. * Explained variance for the linear predictive model was under 0.5, and for the artificial neural network (ANN) predictive model with similar predictors was around 0.7. ANN predictive model has achieved median absolute error of about 40 ions/cm\({}^{3}\) on test data. These modelling efforts enable several future work directions and applications that may be of wider interest for indoor air quality monitoring. Since small ions can be an important part of air quality consideration, their concentration could be to a certain extent modelled based on several more easily obtained/measured predictors. We have showed that the ANN model successfully helped in harmonizing inputs from several instruments of different grade (low cost radon and lab grade particulate matter monitors) and enabled predictions of small ions concentration of comparable quality to the lab grade Gerdien type instrument. Furthermore, since the particulate matter concentration was one of the important predictors, and having in mind recent uptake of low-cost PM monitors, data  
Figure 5: Comparison of an artificial neural network (ANN) model based on radon and 2 PCA particle components for School 1 (solid line) and a measurement of small ions (dotted line). Unit is [#/cm\({}^{3}\)]. Training/test score 0.69/0.69. driven solution for estimating small ions concentration based on these sensors as supporting predictors is an interesting future research topic. Conceptualization, M.D. ([PERSON]); data curation, M.D. ([PERSON]) and M.J.-S.; formal analysis, M.D. ([PERSON]) and M.D. ([PERSON]); funding acquisition, M.D. ([PERSON]), M.D. ([PERSON]) and M.J.-S.; investigation, M.D. ([PERSON]), P.K. and M.J.-S.; methodology, M.D. ([PERSON]), P.K., M.J.-S. and Z.R. ; project administration, M.D. ([PERSON]); resources, P.K. and M.J.-S.; software, M.D. ([PERSON]); supervision, M.J.-S. and Z.R. ; validation, M.D. ([PERSON]) and M.D. ([PERSON]); visualization, M.D. ([PERSON]); writing--original draft, M.D. ([PERSON]), M.D. ([PERSON]), R.J., P.K., M.J.-S. and Z.R. ; writing--review and editing, M.D. ([PERSON]), M.D. ([PERSON]), R.J., P.K., M.J.-S. and Z.R. All authors have read and agreed to the published version of the manuscript. The research was funded by the Ministry of Education, Science and Technological Development of the Republic of Serbia. We would like to thank the participating pupils and staff of Elementary School \"Aleksa Santic\" in Kaluderica, Belgrade, and Elementary School \"20. oktobar\" New Belgrade, Belgrade, for helping with the smooth realization of the experiments.