Stochastic Solution of a KPP-Type Nonlinear Fractional Differential Equation

Mathematics Subject Classification: 26A33, 76M35, 82B31A stochastic solution is constructed for a fractional generalization of the KPP (Kolmogorov, Petrovskii, Piskunov) equation. The solution uses a fractional generalization of the branching exponential process and propagation processes which are spectral integrals of Levy processes

The effects of amalgamations on voter turnout: evidence from sub-municipal governments in Portugal

The 2013 territorial reform of sub-municipal units (SMUs) of government in Portugal presents an interesting opportunity to understand the effect of amalgamations on democratic outcomes. Like other reforms of its kind, the Portuguese amalgamation reform was triggered by economic motivations, aimed at improving local services but seeking mostly to reduce the level of public expenditures. Much less relevance was given to the political impacts of territorial consolidation. The aim of this research is to assess the impacts of the Portuguese territorial reform on political participation measured as voter turnout in SMU elections. We use data from five election cycles (2001–2017) to compare turnout levels in amalgamated jurisdictions vis-à-vis the ones that did not amalgamate as a result of the process of territorial reform. The results of this quasi-experimental design indicate that turnout levels after the reform have decreased in the 2013 election and recovered in the 2017 election, but the negative effects were much more pronounced in amalgamated SMUs than in non-amalgamated SMUs.Previous versions of this paper were presented at the 2018 European Urban and Regional Association conference in Tilburg, The Netherlands and at the 2018 European Consortium of Political Research meeting in Hamburg, Germany. The authors would like to thank our colleagues Adam Gendzwill, Kurt Houlberg, Pawel Swianiewicz, and Filipe Teles for providing useful comments to these earlier versions of this manuscript. This research is partially supported by the "Programa Operacional da Regiao Norte", NORTE2020, in the context of project NORTE-01-0145-FEDER-000037 (SmartEGOV) and by the Portuguese Science and Technology Foundation (Fundacao para a Ciencia e Tecnologia) [grant no PEst-OE/CJP/UI0758/2019]. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the Portuguese Science and Technology Foundation