Special Issue "Mathematical Models: Methods and Applications"

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics and Symmetry/Asymmetry".

Deadline for manuscript submissions: 15 October 2022 | Viewed by 3001

Special Issue Editors

Dr. OPhir Nave
E-Mail Website
Guest Editor
Department of Mathematics and Computer Science, Jerusalem College of Technology (JCT), Jerusalem, Israel
Interests: mathematical models of cancer; asymptotic analysis; method of integral invariant manifold; fixed point; numerical analysis; singular perturbe; gradient algorithms
Dr. Svetlana Bunimovich-Mendrazitsky
E-Mail Website
Co-Guest Editor
Department of Mathematics, Ariel University, Ariel, Israel
Interests: mathematical modelling

Special Issue Information

Dear Colleagues,

The Special Issue “Mathematical Modeling: Methods and Applications” aims to publish papers that provide new concepts, ideas, insight, or new understanding of biological systems using a mathematical model. The mathematical models can be of a theoretical or practical nature.

In order to study models in the natural sciences, various methods of mathematics can be applied, such as: moving beyond a dimensionless model and using symmetry, various asymptotic methods, numerical methods, system decomposition methods providing a fast system and a slow subsystem, approximation by columns, use of beads and more. We are interested in mathematical models implemented to analyze the phenomenon under investigation in order to advance science and discover new phenomena and knowledge.

Papers submitted to the journal should provide a deep, biological insight as a result of mathematical analysis using numerical analysis by new algorithms. The papers should identify and open up challenging new types of mathematical problems that are derived from biological knowledge.

Please note that all submitted papers must be within the general scope of the Symmetry journal.

Dr. OPhir Nave
Guest Editor
Dr. Svetlana Bunimovich-Mendrazitsky
Co-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. Symmetry 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.

Keywords

  • Computer algorithms
  • Symmetry
  • Mathematical modeling
  • Numerical analysis
  • Asymptotic analysis
  • ODE and PDE
  • Biology
  • Multiscale and multiphysics modeling.

Published Papers (6 papers)

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Research

Article
Double Penalized Expectile Regression for Linear Mixed Effects Model
Symmetry 2022, 14(8), 1538; https://doi.org/10.3390/sym14081538 - 27 Jul 2022
Viewed by 161
Abstract
This paper constructs the double penalized expectile regression for linear mixed effects model, which can estimate coefficient and choose variable for random and fixed effects simultaneously. The method based on the linear mixed effects model by cojoining double penalized expectile regression. For this [...] Read more.
This paper constructs the double penalized expectile regression for linear mixed effects model, which can estimate coefficient and choose variable for random and fixed effects simultaneously. The method based on the linear mixed effects model by cojoining double penalized expectile regression. For this model, this paper proposes the iterative Lasso expectile regression algorithm to solve the parameter for this mode, and the Schwarz Information Criterion (SIC) and Generalized Approximate Cross-Validation Criterion (GACV) are used to choose the penalty parameters. Additionally, it establishes the asymptotic normality of the expectile regression coefficient estimators that are suggested. Though simulation studies, we examine the effects of coefficient estimation and the variable selection at varying expectile levels under various conditions, including different signal-to-noise ratios, random effects, and the sparsity of the model. In this work, founding that the proposed method is robust to various error distributions at every expectile levels, and is superior to the double penalized quantile regression method in the robustness of excluding inactive variables. The suggested method may still accurately exclude inactive variables and select important variables with a high probability for high-dimensional data. The usefulness of doubly penalized expectile regression in applications is illustrated through a case study using CD4 cell real data. Full article
(This article belongs to the Special Issue Mathematical Models: Methods and Applications)
Article
On Filters of Bitonic Algebras
Symmetry 2022, 14(8), 1509; https://doi.org/10.3390/sym14081509 (registering DOI) - 23 Jul 2022
Viewed by 220
Abstract
With the deep study in this work, we introduce the concept of filters of a bitonic algebra A. We study some fundamental structures of such determined filters. We also focus on features of filters with respect to homomorphisms. With the help of [...] Read more.
With the deep study in this work, we introduce the concept of filters of a bitonic algebra A. We study some fundamental structures of such determined filters. We also focus on features of filters with respect to homomorphisms. With the help of the idea of upper sets, we investigate basic ideas of filters in a bitonic algebra, and we also state some important theorems related to them. We obtain some relations between filters of bitonic algebras and upper sets. We obtain an equivalent condition of the filters with the help of the notion of upper sets. Full article
(This article belongs to the Special Issue Mathematical Models: Methods and Applications)
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Article
Improve Stock Price Model-Based Stochastic Pantograph Differential Equation
Symmetry 2022, 14(7), 1358; https://doi.org/10.3390/sym14071358 - 01 Jul 2022
Viewed by 277
Abstract
Although the concept of symmetry is widely used in many fields, it is almost not discussed in finance. This concept appears to be relevant in relation, for example, to mathematical models that can predict stock prices to contribute to the decision-making process. This [...] Read more.
Although the concept of symmetry is widely used in many fields, it is almost not discussed in finance. This concept appears to be relevant in relation, for example, to mathematical models that can predict stock prices to contribute to the decision-making process. This work considers the stock price of European options with a new class of the non-constant delay model. The stochastic pantograph differential equation (SPDE) with a variable delay is provided in order to overcome the weaknesses of using stochastic models with constant delay. The proposed model is constructed to improve the evaluation process and prediction accuracy for stock prices. The feasibility of the proposed model is introduced under relatively weak conditions imposed on its volatility function. Furthermore, the sensitivity of time lag is discussed. The robust stochastic theta Milstein (STM) method is combined with the Monte Carlo simulation to compute asset prices within the proposed model. In addition, we prove that the numerical solution can preserve the non-negativity of the solution of the model. Numerical experiments using real financial data indicate that there is an increasing possibility of prediction accuracy for the proposed model with a variable delay compared to non-linear models with constant delay and the classical Black and Scholes model. Full article
(This article belongs to the Special Issue Mathematical Models: Methods and Applications)
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Article
Differential Response to Cytotoxic Drugs Explains the Dynamics of Leukemic Cell Death: Insights from Experiments and Mathematical Modeling
Symmetry 2022, 14(6), 1269; https://doi.org/10.3390/sym14061269 - 20 Jun 2022
Cited by 1 | Viewed by 353
Abstract
This study presents a framework whereby cancer chemotherapy could be improved through collaboration between mathematicians and experimentalists. Following on from our recently published model, we use A20 murine leukemic cells transfected with monomeric red fluorescent proteins cells (mCherry) to compare the simulated and [...] Read more.
This study presents a framework whereby cancer chemotherapy could be improved through collaboration between mathematicians and experimentalists. Following on from our recently published model, we use A20 murine leukemic cells transfected with monomeric red fluorescent proteins cells (mCherry) to compare the simulated and experimental cytotoxicity of two Federal Drug Administration (FDA)-approved anticancer drugs, Cytarabine (Cyt) and Ibrutinib (Ibr) in an in vitro model system of Chronic Lymphocytic Leukemia (CLL). Maximum growth inhibition with Cyt (95%) was reached at an 8-fold lower drug concentration (6.25 μM) than for Ibr (97%, 50 μM). For the proposed ordinary differential equations (ODE) model, a multistep strategy was used to estimate the parameters relevant to the analysis of in vitro experiments testing the effects of different drug concentrations. The simulation results demonstrate that our model correctly predicts the effects of drugs on leukemic cells. To assess the closeness of the fit between the simulations and experimental data, RMSEs for both drugs were calculated (both RMSEs < 0.1). The numerical solutions of the model show a symmetrical dynamical evolution for two drugs with different modes of action. Simulations of the combinatorial effect of Cyt and Ibr showed that their synergism enhanced the cytotoxic effect by 40%. We suggest that this model could predict a more personalized drug dose based on the growth rate of an individual’s cancer cells. Full article
(This article belongs to the Special Issue Mathematical Models: Methods and Applications)
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Article
Experimental Validation of a Mathematical Model to Describe the Drug Cytotoxicity of Leukemic Cells
Symmetry 2021, 13(10), 1760; https://doi.org/10.3390/sym13101760 - 22 Sep 2021
Cited by 3 | Viewed by 542
Abstract
Chlorambucil (Chl), Melphalan (Mel), and Cytarabine (Cyt) are recognized drugs used in the chemotherapy of patients with advanced Chronic Lymphocytic Leukemia (CLL). The optimal treatment schedule and timing of Chl, Mel, and Cyt administration remains unknown and has traditionally been decided empirically and [...] Read more.
Chlorambucil (Chl), Melphalan (Mel), and Cytarabine (Cyt) are recognized drugs used in the chemotherapy of patients with advanced Chronic Lymphocytic Leukemia (CLL). The optimal treatment schedule and timing of Chl, Mel, and Cyt administration remains unknown and has traditionally been decided empirically and independently of preclinical in vitro efficacy studies. As a first step toward mathematical prediction of in vivo drug efficacy from in vitro cytotoxicity studies, we used murine A20 leukemic cells as a test case of CLL. We first found that logistic growth best described the proliferation of the cells in vitro. Then, we tested in vitro the cytotoxic efficacy of Chl, Mel, and Cyt against A20 cells. On the basis of these experimental data, we found the parameters for cancer cell death rates that were dependent on the concentration of the respective drugs and developed a mathematical model involving nonlinear ordinary differential equations. For the proposed mathematical model, three equilibrium states were analyzed using the general method of Lyapunov, with only one equilibrium being stable. We obtained a very good symmetry between the experimental results and numerical simulations of the model. Our novel model can be used as a general tool to study the cytotoxic activity of various drugs with different doses and modes of action by appropriate adjustment of the values for the selected parameters. Full article
(This article belongs to the Special Issue Mathematical Models: Methods and Applications)
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Article
Novel Method to Analytically Obtain the Asymptotic Stable Equilibria States of Extended SIR-Type Epidemiological Models
Symmetry 2021, 13(7), 1120; https://doi.org/10.3390/sym13071120 - 23 Jun 2021
Cited by 2 | Viewed by 787
Abstract
We present a new analytical method to find the asymptotic stable equilibria states based on the Markov chain technique. We reveal this method on the Susceptible-Infectious-Recovered (SIR)-type epidemiological model that we developed for viral diseases with long-term immunity memory. This is a large-scale [...] Read more.
We present a new analytical method to find the asymptotic stable equilibria states based on the Markov chain technique. We reveal this method on the Susceptible-Infectious-Recovered (SIR)-type epidemiological model that we developed for viral diseases with long-term immunity memory. This is a large-scale model containing 15 nonlinear ordinary differential equations (ODEs), and classical methods have failed to analytically obtain its equilibria. The proposed method is used to conduct a comprehensive analysis by a stochastic representation of the dynamics of the model, followed by finding all asymptotic stable equilibrium states of the model for any values of parameters and initial conditions thanks to the symmetry of the population size over time. Full article
(This article belongs to the Special Issue Mathematical Models: Methods and Applications)
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