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Mathematics
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Mathematical Modelling in Biology
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Mathematical Modelling in Biology

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematical Biology".

Deadline for manuscript submissions: 30 June 2024 | Viewed by 9907

Special Issue Editors

Dr. Saurav Mallik

E-Mail Website
Guest Editor
Harvard T.H. Chan School of Public Health, Harvard University, Boston, MA 02138, USA
Interests: computational biology; biostatistics; machine learning; mathematical biology
Special Issues, Collections and Topics in MDPI journals
Dr. Yashika Rustagi

E-Mail Website
Guest Editor
Dana-Farber Cancer Institute, Harvard University, Boston, MA 02138, USA
Interests: biotechnology
Dr. Guimin Qin

E-Mail Website
Guest Editor
School of Computer Science and Technology, Xidian University, Xi’an 710071, China
Interests: bioinformatics; machine learning; computational biology; system biology
Dr. Aimin Li

E-Mail Website
Guest Editor
School of Computer Science and Engineering, Xi’an University of Technology, Xi’an 710048, China
Interests: machine learning; computation mathematics; bioinformatics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

For understanding complex bio-systems, it is required to determine and characterize the biomolecules individually along with identifying the interaction between those biomolecules and respective pathways/Gene-Ontologies. Recent trends include so-called “complex diseases” such as COVID-19, cancer, Parkinson’s disease, Alzheimer’s disease, etc. those need to be detected in earlier stage.

With the recent advancement on various emerging techniques, the main aim of the current biomedical research has shifted toward interpreting the big data generated by single/multi-omics technologies. Various mathematical, statistical and other machine learning-based computational models allow the researchers to investigate how the complex regulatory processes are linked and how their disruptions might lead to the development of those diseases. Those models might cover the number theory, probability and biostatistics, integral and differential systems, optimization, algebra, geometry, game theory, topology, graph theory, machine learning, automata, soft computing, etc.

Various biological problems that associated with the models, fall under following categories: cell organization, genomic organization and gene expression (next generation sequence data), epigenetics (DNA methylation), immune system and disease diagnosis, neurobiology and behavioral science, plant biology and agriculture, industrial biotechnology, radiology (viz., MRI and biomedical imaging), tomography and models of physiological systems, systems biology, etc. Specially, some of the computational challenges might include gene signature discovery, regression model finding, classification model, clustering, network centrality finding, correlation study, feature selection or extraction, network motif discovery, statistical hypothesis test (differential expression analysis), but not limited to that.    

So far, many interesting ongoing research have been conducted on “Mathematical Modelling in Biology”, but still there exit many diversities and numerous challenges. Hence, new mathematical and other computational models are welcome and greatly appreciable that are beneficial for human in many ways being specially in disease diagnosis and therapeutic value.

The purpose of this Topical Collection is to choose and publish review articles, original research articles as well as other perspective article representing novel theory, algorithms and applications of computation modeling applied to various fields of biology especially biomedical areas.

Dr. Saurav Mallik
Dr. Yashika Rustagi
Dr. Guimin Qin
Dr. Aimin Li
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 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
  • biostatistical and machine learning models
  • complex biological systems
  • multi-omics data
  • cancer biology

Published Papers (5 papers)

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Research

15 pages, 9808 KiB  
Article
Hierarchical Symmetry-Breaking Model for Stem Cell Differentiation
by Nikolaos K. Voulgarakis
Mathematics 2024, 12(9), 1380; https://doi.org/10.3390/math12091380 - 01 May 2024
Viewed by 343
Abstract
Waddington envisioned stem cell differentiation as a marble rolling down a hill, passing through hierarchically branched valleys representing the cell’s temporal state. The terminal valleys at the bottom of the hill indicate the possible committed cells of the multicellular organism. Although originally proposed [...] Read more.
Waddington envisioned stem cell differentiation as a marble rolling down a hill, passing through hierarchically branched valleys representing the cell’s temporal state. The terminal valleys at the bottom of the hill indicate the possible committed cells of the multicellular organism. Although originally proposed as a metaphor, Waddington’s hypothesis establishes the fundamental principles for characterizing the differentiation process as a dynamic system: the generated equilibrium points must exhibit hierarchical branching, robustness to perturbations (homeorhesis), and produce the appropriate number of cells for each cell type. This article aims to capture these characteristics using a mathematical model based on two fundamental hypotheses. First, it is assumed that the gene regulatory network consists of hierarchically coupled subnetworks of genes (modules), each modeled as a dynamical system exhibiting supercritical pitchfork or cusp bifurcation. Second, the gene modules are spatiotemporally regulated by feedback mechanisms originating from epigenetic factors. Analytical and numerical results show that the proposed model exhibits self-organized multistability with hierarchical branching. Moreover, these branches of equilibrium points are robust to perturbations, and the number of different cells produced can be determined by the system parameters. Full article
(This article belongs to the Special Issue Mathematical Modelling in Biology)
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16 pages, 1564 KiB  
Article
Is Drug Delivery System a Deterministic or Probabilistic Approach? A Theoretical Model Based on the Sequence: Electrodynamics–Diffusion–Bayes
by Huber Nieto-Chaupis
Mathematics 2023, 11(21), 4528; https://doi.org/10.3390/math11214528 - 03 Nov 2023
Viewed by 593
Abstract
Commonly, it is accepted that oncology treatment would yield outcomes with a certain determinism without any quantitative support or mathematical model that establishes such determinations. Nowadays, with the advent of nanomedicine, the targeting drug delivery scheme has emerged, whose central objective is the [...] Read more.
Commonly, it is accepted that oncology treatment would yield outcomes with a certain determinism without any quantitative support or mathematical model that establishes such determinations. Nowadays, with the advent of nanomedicine, the targeting drug delivery scheme has emerged, whose central objective is the uptake of nanoparticles by tumors. Once they are injected into the bloodstream, it is unclear as to which process governs the directing of nanoparticles towards the desired target, deterministic or stochastic. In any scenario, an optimal outcome, small toxicity and minimal dispersion of drugs is expected. Commonly, it is expected that an important fraction of them can be internalized into tumor. In this manner, due to the fraction of nanoparticles that have failed to uptake, the success of the drug delivery scheme might be at risk. In this paper, a theory based on the sequence electrodynamics–diffusion–Bayes theorem is presented. The Bayesian probability that emerges at the end of the sequence might be telling us that dynamical processes based on the injection of electrically charged nanoparticles might be dictated by stochastic formalism. Thus, rather than expecting a deterministic process, the chain of events would convert the drug delivery scheme to be dependent on a sequence of conditional probabilities. Full article
(This article belongs to the Special Issue Mathematical Modelling in Biology)
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22 pages, 1600 KiB  
Article
A Game-Theoretic Approach for Rendering Immersive Experiences in the Metaverse
by Anjan Bandyopadhyay, Ansh Sarkar, Sujata Swain, Debajyoty Banik, Aboul Ella Hassanien, Saurav Mallik, Aimin Li and Hong Qin
Mathematics 2023, 11(6), 1286; https://doi.org/10.3390/math11061286 - 07 Mar 2023
Cited by 6 | Viewed by 1964
Abstract
The metaverse is an upcoming computing paradigm aiming towards blending reality seamlessly with the artificially generated 3D worlds of deep cyberspace. This giant interactive mesh of three-dimensional reconstructed realms has recently received tremendous attention from both an academic and commercial point of view [...] Read more.
The metaverse is an upcoming computing paradigm aiming towards blending reality seamlessly with the artificially generated 3D worlds of deep cyberspace. This giant interactive mesh of three-dimensional reconstructed realms has recently received tremendous attention from both an academic and commercial point of view owing to the curiosity instilled by its vast possible use cases. Every virtual world in the metaverse is controlled and maintained by a virtual service provider (VSP). Interconnected clusters of LiDAR sensors act as a feeder network to these VSPs which then process the data and reconstruct the best quality immersive environment possible. These data can then be leveraged to provide users with highly targeted virtual services by building upon the concept of digital twins (DTs) representing digital analogs of real-world items owned by parties that create and establish the communication channels connecting the DTs to their real-world counterparts. Logically, DTs represent data on servers where postprocessing can be shared easily across VSPs, giving rise to new marketplaces and economic frontiers. This paper presents a dynamic and distributed framework to enable high-quality reconstructions based on incoming data streams from sensors as well as to allow for the optimal allocation of VSPs to users. The optimal synchronization intensity control problem between the available VSPs and the feeder network is modeled using a simultaneous differential game, while the allocation of VSPs to users is modeled using a preference-based game-theoretic approach, where the users give strict preferences over the available VSPs. Full article
(This article belongs to the Special Issue Mathematical Modelling in Biology)
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19 pages, 1544 KiB  
Article
HistoSSL: Self-Supervised Representation Learning for Classifying Histopathology Images
by Xu Jin, Teng Huang, Ke Wen, Mengxian Chi and Hong An
Mathematics 2023, 11(1), 110; https://doi.org/10.3390/math11010110 - 26 Dec 2022
Cited by 2 | Viewed by 2714
Abstract
The success of image classification depends on copious annotated images for training. Annotating histopathology images is costly and laborious. Although several successful self-supervised representation learning approaches have been introduced, they are still insufficient to consider the unique characteristics of histopathology images. In this [...] Read more.
The success of image classification depends on copious annotated images for training. Annotating histopathology images is costly and laborious. Although several successful self-supervised representation learning approaches have been introduced, they are still insufficient to consider the unique characteristics of histopathology images. In this work, we propose the novel histopathology-oriented self-supervised representation learning framework (HistoSSL) to efficiently extract representations from unlabeled histopathology images at three levels: global, cell, and stain. The model transfers remarkably to downstream tasks: colorectal tissue phenotyping on the NCTCRC dataset and breast cancer metastasis recognition on the CAMELYON16 dataset. HistoSSL achieved higher accuracies than state-of-the-art self-supervised learning approaches, which proved the robustness of the learned representations. Full article
(This article belongs to the Special Issue Mathematical Modelling in Biology)
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11 pages, 3954 KiB  
Article
WAVECNV: A New Approach for Detecting Copy Number Variation by Wavelet Clustering
by Yang Guo, Shuzhen Wang, A. K. Alvi Haque and Xiguo Yuan
Mathematics 2022, 10(12), 2151; https://doi.org/10.3390/math10122151 - 20 Jun 2022
Cited by 1 | Viewed by 1597
Abstract
Copy number variation (CNV) detection based on second-generation sequencing technology is the basis of much gene research, but the read depth is affected by mapping errors, repeated reads, and GC bias. The existing methods have low sensitivity to variation regions with a short [...] Read more.
Copy number variation (CNV) detection based on second-generation sequencing technology is the basis of much gene research, but the read depth is affected by mapping errors, repeated reads, and GC bias. The existing methods have low sensitivity to variation regions with a short length and small variation range. Therefore, it is necessary to improve the sensitivity of algorithms to short-variation fragments. This study proposes a new CNV-detection method named WAVECNV to solve this issue. The algorithm uses wavelet clustering to process the read depth and determine the normal cluster and abnormal cluster according to the size of the cluster. Then, according to the distance between genome bins and normal clusters, the outlier of each genome bin is evaluated. Finally, a statistical model is established, and the p-value test is used for calling CNVs. Through this method, the information of the short variation region is retained. WAVECNV was tested and compared with peer methods in terms of simulated data and real cancer-sequencing data. The results show that the sensitivity of WAVECNV is better than the existing methods. It also has high precision in data with low purity and coverage. In real data experiments, WAVECNV can detect more cancer genes than existing methods. Therefore, this method can be regarded as a conventional method in the field of genomic mutation analysis of cancer samples. Full article
(This article belongs to the Special Issue Mathematical Modelling in Biology)
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