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Supplemental Information

Supplementary Text

Supplementary Text (includes mathematical proofs of the theorems/properties)

DOI: 10.7287/peerj.preprints.382v3/supp-1

Additional Information

Competing Interests

The authors declare that there are no conflicts of interest.

Author Contributions

Jomar Rabajante conceived and designed the experiments, analyzed the data, wrote the paper, prepared figures and/or tables, reviewed drafts of the paper.

Cherryl O. Talaue conceived and designed the experiments, wrote the paper, reviewed drafts of the paper.


This work was financially supported by the Philippine Council for Industry, Energy and Emerging Technology Research and Development (PCIEERD) of the Department of Science and Technology (DOST), and by the University of the Philippines. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

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