A mathematical addendum. Quantifying energetic dynamics in physical and biological systems through a simple geometric tool and geodetic curves

Cellular Gauge Symmetry and the Li organization principle: A mathematical addendum. Quantifying energetic dynamics in physical and biological systems through a simple geometric tool and geodetic curves

 
 
 
Alexander Yurkin a, , Arturo Tozzi, b,c, James F. Peters d, e, f, c, , Pedro C. Marijuán g, 
 
a Russian Academy of Sciences, Moscow, Puschino, Russia
b Center for Nonlinear Science, University of North Texas, 1155 Union Circle, #311427, Denton, TX 76203-5017, USA
c Computational Intelligence Laboratory, University of Manitoba, Winnipeg R3T 5V6 Manitoba, Canada
d Department of Electrical and Computer Engineering, University of Manitoba, 75A Chancellor's Circle, Winnipeg, MB R3T 5V6, Canada
e Department of Mathematics, Adıyaman University, 02040 Adıyaman, Turkey
f Department of Mathematics, Faculty of Arts and Sciences, Adıyaman University, 02040 Adıyaman, Turkey
g Grupo de Bioinformación / Bioinformation Group, Instituto Aragonés de Ciencias de la Salud (IACS), Instituto de Investigación Sanitaria Aragón (IIS), Edificio CIBA. Avda. San Juan Bosco, 13, 50009 Zaragoza, Spain
Received 28 April 2017, Revised 9 June 2017, Accepted 16 June 2017, Available online 17 June 2017
 
 
 
 
 

The present Addendum complements the accompanying paper “Cellular Gauge Symmetry and the Li Organization Principle”; it illustrates a recently-developed geometrical physical model able to assess electronic movements and energetic paths in atomic shells. The model describes a multi-level system of circular, wavy and zigzag paths which can be projected onto a horizontal tape. This model ushers in a visual interpretation of the distribution of atomic electrons’ energy levels and the corresponding quantum numbers through rather simple tools, such as compasses, rulers and straightforward calculations. Here we show how this geometrical model, with the due corrections, among them the use of geodetic curves, might be able to describe and quantify the structure and the temporal development of countless physical and biological systems, from Langevin equations for random paths, to symmetry breaks occurring ubiquitously in physical and biological phenomena, to the relationships among different frequencies of EEG electric spikes. Therefore, in our work we explore the possible association of binomial distribution and geodetic curves configuring a uniform approach for the research of natural phenomena, in biology, medicine or the neurosciences.

 

 

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Cellular Gauge Symmetry and the Li organization principle: A mathematical addendum. Quantifying energetic dynamics in physical and biological systems through a simple geometric tool and geodetic curves
 
Alexander Yurkina, , Arturo Tozzib, c, , James F. Petersd, e, f, c, , Pedro C. Marijuáng, , 
a Russian Academy of Sciences, Moscow, Puschino, Russia
b Center for Nonlinear Science, University of North Texas, 1155 Union Circle, #311427, Denton, TX 76203-5017, USA
c Computational Intelligence Laboratory, University of Manitoba, Winnipeg R3T 5V6 Manitoba, Canada
d Department of Electrical and Computer Engineering, University of Manitoba, 75A Chancellor's Circle, Winnipeg, MB R3T 5V6, Canada
e Department of Mathematics, Adıyaman University, 02040 Adıyaman, Turkey
f Department of Mathematics, Faculty of Arts and Sciences, Adıyaman University, 02040 Adıyaman, Turkey
g Grupo de Bioinformación / Bioinformation Group, Instituto Aragonés de Ciencias de la Salud (IACS), Instituto de Investigación Sanitaria Aragón (IIS), Edificio CIBA. Avda. San Juan Bosco, 13, 50009 Zaragoza, Spain
Received 28 April 2017, Revised 9 June 2017, Accepted 16 June 2017, Available online 17 June 2017
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https://doi.org/10.1016/j.pbiomolbio.2017.06.007
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Abstract
The present Addendum complements the accompanying paper “Cellular Gauge Symmetry and the Li Organization Principle”; it illustrates a recently-developed geometrical physical model able to assess electronic movements and energetic paths in atomic shells. The model describes a multi-level system of circular, wavy and zigzag paths which can be projected onto a horizontal tape. This model ushers in a visual interpretation of the distribution of atomic electrons’ energy levels and the corresponding quantum numbers through rather simple tools, such as compasses, rulers and straightforward calculations. Here we show how this geometrical model, with the due corrections, among them the use of geodetic curves, might be able to describe and quantify the structure and the temporal development of countless physical and biological systems, from Langevin equations for random paths, to symmetry breaks occurring ubiquitously in physical and biological phenomena, to the relationships among different frequencies of EEG electric spikes. Therefore, in our work we explore the possible association of binomial distribution and geodetic curves configuring a uniform approach for the research of natural phenomena, in biology, medicine or the neurosciences.