In recent decades, numerous efforts were taken towards the surveillance and mitigation of harmful emissions at a global scale. The undeniable adverse effects of various pollutants on the overall health of citizens have reached a consensus among researchers and policymakers. Additionally, the issue of their impact on climate change has been extensively researched.The current paper introduces the use of connectivity to in-situ air quality measurements for determining what are the most influential locations within a given area of interest. This assessment relies upon constructing and analyzing multiplex networks from a multitude of geolocated sensors that actively monitor PM2.5, PM10 and NO2emissions within the region of Lombardy, Italy covering a temporal span of 55 years.

We display an application of the notions of kernelization and data reduction from parameterized complexity to proof complexity: Specifically, we show that the existence of data reduction rules for a parameterized problem having (a). a small-length reduction chain, and (b). small-size (extended) Frege proofs certifying the soundness of reduction steps implies the existence of subexponential size (extended) Frege proofs for propositional formalizations of the given problem. We apply our result to infer the existence of subexponential Frege and extended Frege proofs for a variety of problems. Improving earlier results of Aisenberg et al. (ICALP 2015), we show that propositional formulas expressing (a stronger form of) the Kneser-Lovász Theorem have quasipolynomial size Frege proofs for each constant value of the parameter k. Another notable application of our framework is to impossibility results in computational social choice: we show that, for any fixed number of agents, propositional translations of the Arrow and Gibbard-Satterthwaite impossibility theorems have subexponential size Frege proofs.