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Mathematics
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Discrete and Algebraic Mathematical Biology
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Discrete and Algebraic Mathematical Biology

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Algebra, Geometry and Topology".

Deadline for manuscript submissions: closed (15 June 2022) | Viewed by 7712

Special Issue Editor

Dr. Matthew Macauley

E-Mail Website
Guest Editor
School of Mathematical & Statistical Sciences, Clemson University, Clemson, SC, USA
Interests: Mathematical biology; discrete mathematics

Special Issue Information

Dear Colleagues,

Over the past several decades, biological problems have seen an infusion of discrete mathematical structures and algebraic techniques. What started in the 1960s with several scientists independently modeling gene regulatory networks with basic logical rules instead of differential equations has blossomed into entire subfields of discrete and algebraic mathematical biology. Algebraic geometry is the backbone of topics such as biochemical reaction networks, phylogenetics, algebraic statistics, combinatorial neural codes, and algebraic modeling of biological networks. Graphs and networks feature prominently in many agent-based models, and structural models on a variety of scales, from molecular structures (the micro) to macro scales such as food-webs and evolutionary trees. Computational problems such as reverse-engineering biological networks, folding protein or RNA strands, aligning and reconstructing DNA sequences, or solving an optimization problem often prominently involve discrete and algebraic techniques.

In recent years, many biological problems have utilized mathematical tools from algebra and discrete mathematics. In some cases, this has given birth to brand new subfields within pure and computational mathematics, such as algebraic geometry, graph theory, and discrete dynamical systems. This Special Issue will welcome submissions from a wide variety of topics—everything from applied work, to theoretical and pure mathematical topics that are off-shoots of biological problems. Examples of areas that this Special Issue can cover include but are not limited to the following:

  • Boolean, logical, or agent-based models;
  • Biochemical reaction networks;
  • Discrete dynamical systems and cellular automata;
  • Algebraic statistics;
  • Neural codes;
  • Genomics;
  • Phylogenetics;
  • Polytopes and optimization;
  • Molecular structures;
  • Protein and RNA folding;
  • Analysis of Boolean functions;
  • Dynamic processes over graphs;
  • Topological data analysis;
  • Problems from discrete mathematics and graph theory inspired by biology;
  • Algebraic problems inspired by biology;
  • Topological problems inspired by biology.

Dr. Matthew Macauley
Guest Editor

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 submissions that pass pre-check are 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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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.

Keywords

  • Mathematical biology
  • Mathematical modeling
  • Discrete mathematics
  • Algebraic geometry
  • Computational algebra
  • Graph theory

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Further information on MDPI's Special Issue polices can be found here.

Published Papers (3 papers)

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24 pages, 68462 KiB  
Article
Space: The Re-Visioning Frontier of Biological Image Analysis with Graph Theory, Computational Geometry, and Spatial Statistics
by John R. Jungck, Michael J. Pelsmajer, Camron Chappel and Dylan Taylor
Mathematics 2021, 9(21), 2726; https://doi.org/10.3390/math9212726 - 27 Oct 2021
Cited by 1 | Viewed by 2040
Abstract
Every biological image contains quantitative data that can be used to test hypotheses about how patterns were formed, what entities are associated with one another, and whether standard mathematical methods inform our understanding of biological phenomena. In particular, spatial point distributions and polygonal [...] Read more.
Every biological image contains quantitative data that can be used to test hypotheses about how patterns were formed, what entities are associated with one another, and whether standard mathematical methods inform our understanding of biological phenomena. In particular, spatial point distributions and polygonal tessellations are particularly amendable to analysis with a variety of graph theoretic, computational geometric, and spatial statistical tools such as: Voronoi polygons; Delaunay triangulations; perpendicular bisectors; circumcenters; convex hulls; minimal spanning trees; Ulam trees; Pitteway violations; circularity; Clark-Evans spatial statistics; variance to mean ratios; Gabriel graphs; and, minimal spanning trees. Furthermore, biologists have developed a number of empirically related correlations for polygonal tessellations such as: Lewis’s law (the number of edges of convex polygons are positively correlated with the areas of these polygons): Desch’s Law (the number of edges of convex polygons are positively correlated with the perimeters of these polygons); and Errara’s Law (daughter cell areas should be roughly half that of their parent cells’ areas). We introduce a new Pitteway Law that the number of sides of the convex polygons in a Voronoi tessellation of biological epithelia is proportional to the minimal interior angle of the convex polygons as angles less than 90 degrees result in Pitteway violations of the Delaunay dual of the Voronoi tessellation. Full article
(This article belongs to the Special Issue Discrete and Algebraic Mathematical Biology)
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22 pages, 997 KiB  
Article
COVID-19 Mortality Prediction Using Machine Learning-Integrated Random Forest Algorithm under Varying Patient Frailty
by Erwin Cornelius, Olcay Akman and Dan Hrozencik
Mathematics 2021, 9(17), 2043; https://doi.org/10.3390/math9172043 - 25 Aug 2021
Cited by 19 | Viewed by 2987
Abstract
The abundance of type and quantity of available data in the healthcare field has led many to utilize machine learning approaches to keep up with this influx of data. Data pertaining to COVID-19 is an area of recent interest. The widespread influence of [...] Read more.
The abundance of type and quantity of available data in the healthcare field has led many to utilize machine learning approaches to keep up with this influx of data. Data pertaining to COVID-19 is an area of recent interest. The widespread influence of the virus across the United States creates an obvious need to identify groups of individuals that are at an increased risk of mortality from the virus. We propose a so-called clustered random forest approach to predict COVID-19 patient mortality. We use this approach to examine the hidden heterogeneity of patient frailty by examining demographic information for COVID-19 patients. We find that our clustered random forest approach attains predictive performance comparable to other published methods. We also find that follow-up analysis with neural network modeling and k-means clustering provide insight into the type and magnitude of mortality risks associated with COVID-19. Full article
(This article belongs to the Special Issue Discrete and Algebraic Mathematical Biology)
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22 pages, 4597 KiB  
Article
On the Loop Homology of a Certain Complex of RNA Structures
by Thomas J. X. Li and Christian M. Reidys
Mathematics 2021, 9(15), 1749; https://doi.org/10.3390/math9151749 - 24 Jul 2021
Cited by 1 | Viewed by 1699
Abstract
In this paper, we establish a topological framework of τ-structures to quantify the evolutionary transitions between two RNA sequence–structure pairs. τ-structures developed here consist of a pair of RNA secondary structures together with a non-crossing partial matching between the two backbones. [...] Read more.
In this paper, we establish a topological framework of τ-structures to quantify the evolutionary transitions between two RNA sequence–structure pairs. τ-structures developed here consist of a pair of RNA secondary structures together with a non-crossing partial matching between the two backbones. The loop complex of a τ-structure captures the intersections of loops in both secondary structures. We compute the loop homology of τ-structures. We show that only the zeroth, first and second homology groups are free. In particular, we prove that the rank of the second homology group equals the number γ of certain arc-components in a τ-structure and that the rank of the first homology is given by γ−χ+1, where χ is the Euler characteristic of the loop complex. Full article
(This article belongs to the Special Issue Discrete and Algebraic Mathematical Biology)
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