About the Authors

Georgios Papantonopoulos

ppntnpls@otenet.gr

Affiliation Center for Research and Applications of Nonlinear Systems, Department of Mathematics, University of Patras, Patras, Greece

Keiso Takahashi

Affiliation Department of Conservative Dentistry, School of Dentistry, Ohu University, Fukushima, Japan

Tasos Bountis

Affiliation Laboratory of Nonlinear Systems and Applied Analysis, Department of Mathematics, University of Patras, Patras, Greece

Bruno G. Loos

Affiliation Department of Periodontology, Academic Center for Dentistry Amsterdam (ACTA), University of Amsterdam and VU University, Amsterdam, The Netherlands

Competing Interests

The authors have declared that no competing interests exist.

Author Contributions

Conceived and designed the experiments: GP BGL. Performed the experiments: GP BGL KT. Analyzed the data: GP TB. Contributed reagents/materials/analysis tools: BGL KT. Wrote the paper: GP BGL TB.