## 1 Introduction
[12] claim that the reports where the presence of negative ions is credited for increasing psychological health are without reliable evidence in therapeutic practice. The studies showing that negative ions could help people with symptoms of allergies to dust, mold spores, and other allergens need additional confirmations. However, it is encouraging that there are no known negative effects of negative ions, so positive effect should be studied further. On the other hand, adverse health effects of radon [13] and particulate matter [14] are long well known. Since all three quantities (radon, SI and PM concentration) are linked via a balance equation, even though the health effects are only firmly established for radon and PM [8], it is useful to consider all three simultaneously. Understanding the way in which various air quality variables interact can be beneficial for developing predictive models, and also enable obtaining more knowledge about air quality based only on several key predictor measurements. Children spend a large part of their time at school microenvironment. In the last decade several large studies conducted within the framework of European projects BREATHE and SINPHONIE addressed the topics of level and chemical composition of particulate matter fractions including ultrafine particulate matter and gaseous air pollutants, also addressing differences during teaching and non-teaching hours and periods when there are no occupants in schools [15; 16]. In the framework of numerous studies at national and international level radon concentration was measured in school classrooms, usually by utilizing passive samplers. The objectives of this paper are the following. The first objective was to bring additional insight into indoor air quality by measuring a number of important air quality variables including quantities that are somewhat more rarely measured with higher temporal resolution namely SI concentration and radon concentration in two elementary schools' indoor environments. In addition, we have measured PM concentration and size with high temporal and size resolution. Descriptive statistics of the measured parameters is presented and discussed. We then proceed to studying association between SI, radon and PM concentrations, based on a balance equation. Parameters of the balance equation are estimated from the data in two schools. We investigate the hypothesis that small ion concentration can be predicted based on radon and particulate matter measurements predictors, by using artificial neural network model. If successful, this kind of modelling effort could enable obtaining more knowledge about air quality based only on several key predictor measurements. This could potentially enable more simple measurement campaigns, where a smaller number of parameters would be measured, but still allowing for similar insights. The outline of this paper is as follows. First, we provide a brief explanation of the physical processes involved in creation of small ions, and then utilize balance equation to describe it quantitatively. We then discuss the link between small ion concentration, volumetric production rate and particulate matter concentration. Following this discussion, we describe the method that was used in the indoor measuring campaign, in which a number of relevant parameters appearing in the balance equation are measured either directly or via an important proxy. We study an interplay between concentrations of radon, SI and PM. For this purpose, we utilize two approaches. The first approach is based on a balance equation which is used to derive approximate relation between concentration of small ions and particulate matter. The form of the obtained relation is transformed via Taylor expansion to enable meaningful linear regression modelling with several predictors.