AppliedMath最新文献

Mathematical Modelling of Cancer Treatments, Resistance, Optimization 癌症治疗的数学模型，耐药性，优化

AppliedMath Pub Date : 2025-04-04 DOI: 10.3390/appliedmath5020040

Tahmineh Azizi

{"title":"Mathematical Modelling of Cancer Treatments, Resistance, Optimization","authors":"Tahmineh Azizi","doi":"10.3390/appliedmath5020040","DOIUrl":"https://doi.org/10.3390/appliedmath5020040","url":null,"abstract":"Mathematical modeling plays a crucial role in the advancement of cancer treatments, offering a sophisticated framework for analyzing and optimizing therapeutic strategies. This approach employs mathematical and computational techniques to simulate diverse aspects of cancer therapy, including the effectiveness of various treatment modalities such as chemotherapy, radiation therapy, targeted therapy, and immunotherapy. By incorporating factors such as drug pharmacokinetics, tumor biology, and patient-specific characteristics, these models facilitate predictions of treatment responses and outcomes. Furthermore, mathematical models elucidate the mechanisms behind cancer treatment resistance, including genetic mutations and microenvironmental changes, thereby guiding researchers in designing strategies to mitigate or overcome resistance. The application of optimization techniques allows for the development of personalized treatment regimens that maximize therapeutic efficacy while minimizing adverse effects, taking into account patient-related variables such as tumor size and genetic profiles. This study elaborates on the key applications of mathematical modeling in oncology, encompassing the simulation of various cancer treatment modalities, the elucidation of resistance mechanisms, and the optimization of personalized treatment regimens. By integrating mathematical insights with experimental data and clinical observations, mathematical modeling emerges as a powerful tool in oncology, contributing to the development of more effective and personalized cancer therapies that improve patient outcomes.","PeriodicalId":477867,"journal":{"name":"AppliedMath","volume":"5 2","pages":"40-40"},"PeriodicalIF":0.0,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.mdpi.com/2673-9909/5/2/40/pdf?version=1743767276","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147896458","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

From Algebro Geometric Solutions of the Toda Equation to Sato Formulas 从户田方程的 Algebro 几何解到佐藤公式

AppliedMath Pub Date : 2024-07-09 DOI: 10.3390/appliedmath4030046

Pierre Gaillard

引用次数: 0

Long- and Medium-Term Financial Strategies on Equities Using Dynamic Bayesian Networks 使用动态贝叶斯网络的股票中长期财务策略

AppliedMath Pub Date : 2024-07-03 DOI: 10.3390/appliedmath4030045

Karl Lewis, M. Caruana, David Paul Suda

引用次数: 0

Network Goodness Calculus Propositions 网络良性计算命题

AppliedMath Pub Date : 2024-07-02 DOI: 10.3390/appliedmath4030044

Marina Bershadsky, Božidar Ivanković, Marko Pušić

引用次数: 0

Some Comments about the p-Generalized Negative Binomial (NBp) Model 关于 p-广义负二项（NBp）模型的一些评论

AppliedMath Pub Date : 2024-06-11 DOI: 10.3390/appliedmath4020039

Daniel A. Griffith

引用次数: 0

Introducing a Parallel Genetic Algorithm for Global Optimization Problems 为全局优化问题引入并行遗传算法

AppliedMath Pub Date : 2024-06-10 DOI: 10.3390/appliedmath4020038

Vasileios Charilogis, Ioannis G. Tsoulos

{"title":"Introducing a Parallel Genetic Algorithm for Global Optimization Problems","authors":"Vasileios Charilogis, Ioannis G. Tsoulos","doi":"10.3390/appliedmath4020038","DOIUrl":"https://doi.org/10.3390/appliedmath4020038","url":null,"abstract":"The topic of efficiently finding the global minimum of multidimensional functions is widely applicable to numerous problems in the modern world. Many algorithms have been proposed to address these problems, among which genetic algorithms and their variants are particularly notable. Their popularity is due to their exceptional performance in solving optimization problems and their adaptability to various types of problems. However, genetic algorithms require significant computational resources and time, prompting the need for parallel techniques. Moving in this research direction, a new global optimization method is presented here that exploits the use of parallel computing techniques in genetic algorithms. This innovative method employs autonomous parallel computing units that periodically share the optimal solutions they discover. Increasing the number of computational threads, coupled with solution exchange techniques, can significantly reduce the number of calls to the objective function, thus saving computational power. Also, a stopping rule is proposed that takes advantage of the parallel computational environment. The proposed method was tested on a broad array of benchmark functions from the relevant literature and compared with other global optimization techniques regarding its efficiency.","PeriodicalId":477867,"journal":{"name":"AppliedMath","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141362792","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

An Efficient Algorithm for Basic Elementary Matrix Functions with Specified Accuracy and Application 具有指定精度的基本初等矩阵函数的高效算法及其应用

AppliedMath Pub Date : 2024-06-05 DOI: 10.3390/appliedmath4020037

Huizeng Qin, Youmin Lu

{"title":"An Efficient Algorithm for Basic Elementary Matrix Functions with Specified Accuracy and Application","authors":"Huizeng Qin, Youmin Lu","doi":"10.3390/appliedmath4020037","DOIUrl":"https://doi.org/10.3390/appliedmath4020037","url":null,"abstract":"If the matrix function f(At) posses the properties of f(At)=gf(tkA, then the recurrence formula fi−1=gfi,i=N,N−1,⋯,1,f(tA)=f0, can be established. Here, fN=f(AN)=∑j=0majANj,AN=tkNA. This provides an algorithm for computing the matrix function f(At). By specifying the calculation accuracy p, a method is presented to determine m and N in a way that minimizes the time of the above algorithm, thus providing a fast algorithm for f(At). It is important to note that m only depends on the calculation accuracy p and is independent of the matrix A and t. Therefore, f(AN) has a fixed calculation format that is easily computed. On the other hand, N depends not only on A, but also on t. This provides a means to select t such that N is equal to 0, a property of significance. In summary, the algorithm proposed in this article enables users to establish a desired level of accuracy and then utilize it to select the appropriate values for m and N to minimize computation time. This approach ensures that both accuracy and efficiency are addressed concurrently. We develop a general algorithm, then apply it to the exponential, trigonometric, and logarithmic matrix functions, and compare the performance with that of the internal system functions of Mathematica and Pade approximation. In the last section, an example is provided to illustrate the rapid computation of numerical solutions for linear differential equations.","PeriodicalId":477867,"journal":{"name":"AppliedMath","volume":"89 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141385090","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Exploratory Analysis of Distributional Data Using the Quantile Method 使用定量法对分布数据进行探索性分析

AppliedMath Pub Date : 2024-02-17 DOI: 10.3390/appliedmath4010014

Manabu Ichino

引用次数: 0

Convergence and Stability Improvement of Quasi-Newton Methods by Full-Rank Update of the Jacobian Approximates 通过雅各布近似值的全角更新改进准牛顿方法的收敛性和稳定性

AppliedMath Pub Date : 2024-01-26 DOI: 10.3390/appliedmath4010008

Peter Berzi

{"title":"Convergence and Stability Improvement of Quasi-Newton Methods by Full-Rank Update of the Jacobian Approximates","authors":"Peter Berzi","doi":"10.3390/appliedmath4010008","DOIUrl":"https://doi.org/10.3390/appliedmath4010008","url":null,"abstract":"A system of simultaneous multi-variable nonlinear equations can be solved by Newton’s method with local q-quadratic convergence if the Jacobian is analytically available. If this is not the case, then quasi-Newton methods with local q-superlinear convergence give solutions by approximating the Jacobian in some way. Unfortunately, the quasi-Newton condition (Secant equation) does not completely specify the Jacobian approximate in multi-dimensional cases, so its full-rank update is not possible with classic variants of the method. The suggested new iteration strategy (“T-Secant”) allows for a full-rank update of the Jacobian approximate in each iteration by determining two independent approximates for the solution. They are used to generate a set of new independent trial approximates; then, the Jacobian approximate can be fully updated. It is shown that the T-Secant approximate is in the vicinity of the classic quasi-Newton approximate, providing that the solution is evenly surrounded by the new trial approximates. The suggested procedure increases the superlinear convergence of the Secant method φS=1.618… to super-quadratic φT=φS+1=2.618… and the quadratic convergence of the Newton method φN=2 to cubic φT=φN+1=3 in one-dimensional cases. In multi-dimensional cases, the Broyden-type efficiency (mean convergence rate) of the suggested method is an order higher than the efficiency of other classic low-rank-update quasi-Newton methods, as shown by numerical examples on a Rosenbrock-type test function with up to 1000 variables. The geometrical representation (hyperbolic approximation) in single-variable cases helps explain the basic operations, and a vector-space description is also given in multi-variable cases.","PeriodicalId":477867,"journal":{"name":"AppliedMath","volume":"4 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140493459","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A Mathematical Structure Underlying Sentences and Its Connection with Short–Term Memory 句子的数学结构及其与短时记忆的联系

AppliedMath Pub Date : 2024-01-18 DOI: 10.3390/appliedmath4010007

E. Matricciani

{"title":"A Mathematical Structure Underlying Sentences and Its Connection with Short–Term Memory","authors":"E. Matricciani","doi":"10.3390/appliedmath4010007","DOIUrl":"https://doi.org/10.3390/appliedmath4010007","url":null,"abstract":"The purpose of the present paper is to further investigate the mathematical structure of sentences—proposed in a recent paper—and its connections with human short–term memory. This structure is defined by two independent variables which apparently engage two short–term memory buffers in a series. The first buffer is modelled according to the number of words between two consecutive interpunctions—variable referred to as the word interval, IP—which follows Miller’s 7±2 law; the second buffer is modelled by the number of word intervals contained in a sentence, MF, ranging approximately for one to seven. These values result from studying a large number of literary texts belonging to ancient and modern alphabetical languages. After studying the numerical patterns (combinations of IP and MF) that determine the number of sentences that theoretically can be recorded in the two memory buffers—which increases with the use of IP and MF—we compare the theoretical results with those that are actually found in novels from Italian and English literature. We have found that most writers, in both languages, write for readers with small memory buffers and, consequently, are forced to reuse sentence patterns to convey multiple meanings.","PeriodicalId":477867,"journal":{"name":"AppliedMath","volume":"116 31","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139615134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0