Planck–Shannon Classifier: A Novel Method to Discriminate Between Sonified Raman Signals from Cancer and Healthy Cells

The Planckian distribution equation (PDE), also called blackbody radiation-like equation, BRE, was derived from the Planck radiation formula by replacing its universal constants and temperature with free parameters, A, B, and C, resulting in y = A/(x + B)⁵/(e^C/(x+B)Â −Â 1), where x is bin variable and y is frequency. PDE has been found to fit many long-tailed asymmetric histograms (LAHs) reported in various fields, including atomic physics, protein folding, single-molecule enzymology, whole-cell metabolism, brain neurophysiology, electrophysiology, decision-making psychophysics, glottometrics (quantitative study of words and texts), sociology, econometrics, and cosmology (http://www.conformon.net/wp-content/uploads/2016/09/PDE_Vienna_2015.pdf ). The apparent universality of PDE is postulated to be due to the principle of wave-particle duality embodied in PDE that applies not only to quantum mechanics but also to macrophysics regardless of scales. In this paper, the new classification method referred to as the Planck–Shannon classifier (PSC) or the Planck–Shannon plot (PSP) is formulated based on the two functions, i.e., (i) the Planckian information of the second kind, I_PS, and (ii) the Shannon entropy, H, that can be computed from PDE. PSC has been shown to successfully distinguish between the digital CymaScopic images generated from the sonified Raman signals measured from normal and cancer cells in human brain tissues. PSC is a general purpose classifier and can be applied to classifying long-tailed asymmetric histograms generated by many physical, chemical, biological, physiological, psychological, and socioeconomical processes called Planckian processes, i.e., those processes that generate long-tailed asymmetric histograms fitting PDE.