Special Issue "Coexistence of Complexity Metrics and Machine-Learning Approaches for Understanding Complex Biological Phenomena"

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Entropy and Biology".

Deadline for manuscript submissions: 30 September 2021.

Special Issue Editors

Dr. Leonidas P. Karakatsanis
E-Mail Website
Guest Editor
Department of Environmental Engineering, Democritus University of Thrace, 671 00 Xanthi, Greece
Interests: complexity; nonlinear systems; Tsallis non-extensive statistics; machine learning; coding DNA; non-coding DNA; biological complexity; complexity metrics; phase space
Prof. Dr. Dimitrios S. Monos
E-Mail Website
Guest Editor
Department of Pathology and Laboratory Medicine, The Children’s Hospital of Philadelphia and Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA 19104, USA
Interests: functional–structural aspects of histocompatibility molecules

Special Issue Information

Dear Colleagues,

The dynamics of complex systems and the ways in which they influence a number of biological processes are one of the most interesting physical problems through which current developments in the independent fields of physics and biology/genomics can be brought together and that they can attempt to address more effectively. These dynamics include the hierarchy of complex and self-organized phenomena such as intermittent turbulence, fractal structures, long-range correlations, far-from-equilibrium phase transitions, anomalous diffusion–dissipation and strange kinetics, the reduction of dimensionality in phase space etc. At equilibrium, the dynamical attractive phase space is practically infinitely dimensional, as the system state evolves in all dimensions according to the famous ergodic theorem of Boltzmann–Gibbs statistics. Far from equilibrium, the statistics of the dynamics follow the q-Gaussian generalization of the B–G statistics or other more generalized statistics. In Tsallis q-statistics, even for the case of q = 1 (corresponding to the Gaussian process), the non-extensive character permits the development of long-range correlations produced by equilibrium phase-transition multi-scale processes.

Many scientists have used complexity metrics such as generalized entropies, multifractal analysis, q-triplet of Tsallis statistics, complex networks, fractal dimension etc. to understand the complex behaviour of complex phenomena in biology/genomics. The projection of the dynamics to the statistics in the phase space develops a complete picture that can be integrated to the variations of the complexity metrics. This picture of dynamics can be identified from machine-learning tools for clustering, classification and prediction. The merging of complexity theory and machine-learning approaches can provide semantic results enabling a deeper understanding and promotion of the fundamental laws of complex biological phenomena.

This Special Issue emphasizes the merging of the complexity metrics and the machine-learning approaches, hoping to attain a deeper understanding of complex biological phenomena. The analysis and study of complex biological phenomena based on the aforementioned statistical approaches fall within the scope of this Special Issue.

Dr. Leonidas P. Karakatsanis

Prof. Dr. Dimitrios S. Monos
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.


  • complexity metrics
  • generalized entropies
  • Tsallis q-triplet
  • Tsallis entropy
  • machine learning
  • phase space
  • biological complexity
  • coding DNA
  • non-coding DNA
  • genomics
  • evolutional biology

Published Papers (1 paper)

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Semicovariance Coefficient Analysis of Spike Proteins from SARS-CoV-2 and Other Coronaviruses for Viral Evolution and Characteristics Associated with Fatality
Entropy 2021, 23(5), 512; https://doi.org/10.3390/e23050512 - 23 Apr 2021
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Complex modeling has received significant attention in recent years and is increasingly used to explain statistical phenomena with increasing and decreasing fluctuations, such as the similarity or difference of spike protein charge patterns of coronaviruses. Different from the existing covariance or correlation coefficient [...] Read more.
Complex modeling has received significant attention in recent years and is increasingly used to explain statistical phenomena with increasing and decreasing fluctuations, such as the similarity or difference of spike protein charge patterns of coronaviruses. Different from the existing covariance or correlation coefficient methods in traditional integer dimension construction, this study proposes a simplified novel fractional dimension derivation with the exact Excel tool algorithm. It involves the fractional center moment extension to covariance, which results in a complex covariance coefficient that is better than the Pearson correlation coefficient, in the sense that the nonlinearity relationship can be further depicted. The spike protein sequences of coronaviruses were obtained from the GenBank and GISAID databases, including the coronaviruses from pangolin, bat, canine, swine (three variants), feline, tiger, SARS-CoV-1, MERS, and SARS-CoV-2 (including the strains from Wuhan, Beijing, New York, German, and the UK variant B.1.1.7) which were used as the representative examples in this study. By examining the values above and below the average/mean based on the positive and negative charge patterns of the amino acid residues of the spike proteins from coronaviruses, the proposed algorithm provides deep insights into the nonlinear evolving trends of spike proteins for understanding the viral evolution and identifying the protein characteristics associated with viral fatality. The calculation results demonstrate that the complex covariance coefficient analyzed by this algorithm is capable of distinguishing the subtle nonlinear differences in the spike protein charge patterns with reference to Wuhan strain SARS-CoV-2, which the Pearson correlation coefficient may overlook. Our analysis reveals the unique convergent (positive correlative) to divergent (negative correlative) domain center positions of each virus. The convergent or conserved region may be critical to the viral stability or viability; while the divergent region is highly variable between coronaviruses, suggesting high frequency of mutations in this region. The analyses show that the conserved center region of SARS-CoV-1 spike protein is located at amino acid residues 900, but shifted to the amino acid residues 700 in MERS spike protein, and then to amino acid residues 600 in SARS-COV-2 spike protein, indicating the evolution of the coronaviruses. Interestingly, the conserved center region of the spike protein in SARS-COV-2 variant B.1.1.7 shifted back to amino acid residues 700, suggesting this variant is more virulent than the original SARS-COV-2 strain. Another important characteristic our study reveals is that the distance between the divergent mean and the maximal divergent point in each of the viruses (MERS > SARS-CoV-1 > SARS-CoV-2) is proportional to viral fatality rate. This algorithm may help to understand and analyze the evolving trends and critical characteristics of SARS-COV-2 variants, other coronaviral proteins and viruses. Full article
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