English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In the commented paper, the authors declare an analogy with the quantummechanical pure states established through the application of thehigh-dimensional combinatorial Laplacian considering that the simplicialcomplex is in the pure state when it is formed by collection of the purestates. In their work, besides giving a completely erroneous analogy for thepure quantum mechanical state, which contradicts to very basic postulates ofquantum mechanic, the authors clearly fail to provide and explain mathematicalformalism behind their claims. Their intention is to rigorously prove that theexistence of opinion space in all considered cases consists of the pure quantumstates using incorrect normalization constant which does not produce traceequal to one. In this comment we prove out that their claims are erroneous. Inorder to show incorrectness of Maletic & Rajkovic model and conclusions wecalculated and examined connections between different combinatorial structuresof q- dimensional simplicial complexes and their Laplacian spectra and analyzedresulting symmetric and positive semidefinite matrices in the context of thedensity matrix of a quantum mechanical system. Importance of presented researchis to further develop accurate quantitative topological-based characterizationmethod for convertibility and distillation of density matrix.

Comment on Consensus formation on a simplicial complex of opinions (arXiv:1212.1940, Physica A, Vol. 397 (1), pp. 111-120, 2014)