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First-Stage Dynamics of the Immune System and Cancer 免疫系统与癌症的第一阶段动态变化
AppliedMath Pub Date : 2023-12-12 DOI: 10.3390/appliedmath3040052
Roberto Herrero, Joan Nieves, Augusto Gonzalez
{"title":"First-Stage Dynamics of the Immune System and Cancer","authors":"Roberto Herrero, Joan Nieves, Augusto Gonzalez","doi":"10.3390/appliedmath3040052","DOIUrl":"https://doi.org/10.3390/appliedmath3040052","url":null,"abstract":"The innate immune system is the first line of defense against pathogens. Its composition includes barriers, mucus, and other substances as well as phagocytic and other cells. The purpose of the present paper is to compare tissues with regard to their immune response to infections and to cancer. Simple ideas and the qualitative theory of differential equations are used along with general principles such as the minimization of the pathogen load and economy of resources. In the simplest linear model, the annihilation rate of pathogens in any tissue should be greater than the pathogen’s average replication rate. When nonlinearities are added, a stability condition emerges, which relates the strength of regular threats, barrier height, and annihilation rate. The stability condition allows for a comparison of immunity in different tissues. On the other hand, in cancer immunity, the linear model leads to an expression for the lifetime risk, which accounts for both the effects of carcinogens (endogenous or external) and the immune response. The way the tissue responds to an infection shows a correlation with the way it responds to cancer. The results of this paper are formulated in the form of precise statements in such a way that they could be checked by present-day quantitative immunology.","PeriodicalId":477867,"journal":{"name":"AppliedMath","volume":"30 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139007751","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 Bi-Parametric With-Memory Iterative Method for Solving Nonlinear Equations 求解非线性方程的高效双参数内存迭代法
AppliedMath Pub Date : 2023-12-11 DOI: 10.3390/appliedmath3040051
Ekta Sharma, Shubham Kumar Mittal, J. P. Jaiswal, S. Panday
{"title":"An Efficient Bi-Parametric With-Memory Iterative Method for Solving Nonlinear Equations","authors":"Ekta Sharma, Shubham Kumar Mittal, J. P. Jaiswal, S. Panday","doi":"10.3390/appliedmath3040051","DOIUrl":"https://doi.org/10.3390/appliedmath3040051","url":null,"abstract":"New three-step with-memory iterative methods for solving nonlinear equations are presented. We have enhanced the convergence order of an existing eighth-order memory-less iterative method by transforming it into a with-memory method. Enhanced acceleration of the convergence order is achieved by introducing two self-accelerating parameters computed using the Hermite interpolating polynomial. The corresponding R-order of convergence of the proposed uni- and bi-parametric with-memory methods is increased from 8 to 9 and 10, respectively. This increase in convergence order is accomplished without requiring additional function evaluations, making the with-memory method computationally efficient. The efficiency of our with-memory methods NWM9 and NWM10 increases from 1.6818 to 1.7320 and 1.7783, respectively. Numeric testing confirms the theoretical findings and emphasizes the superior efficacy of suggested methods when compared to some well-known methods in the existing literature.","PeriodicalId":477867,"journal":{"name":"AppliedMath","volume":"1 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138584647","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
Assessing Antithetic Sampling for Approximating Shapley, Banzhaf, and Owen Values 评估用于逼近沙普利、班扎夫和欧文值的反抽样
AppliedMath Pub Date : 2023-12-06 DOI: 10.3390/appliedmath3040049
Jochen Staudacher, Tim Pollmann
{"title":"Assessing Antithetic Sampling for Approximating Shapley, Banzhaf, and Owen Values","authors":"Jochen Staudacher, Tim Pollmann","doi":"10.3390/appliedmath3040049","DOIUrl":"https://doi.org/10.3390/appliedmath3040049","url":null,"abstract":"Computing Shapley values for large cooperative games is an NP-hard problem. For practical applications, stochastic approximation via permutation sampling is widely used. In the context of machine learning applications of the Shapley value, the concept of antithetic sampling has become popular. The idea is to employ the reverse permutation of a sample in order to reduce variance and accelerate convergence of the algorithm. We study this approach for the Shapley and Banzhaf values, as well as for the Owen value which is a solution concept for games with precoalitions. We combine antithetic samples with established stratified sampling algorithms. Finally, we evaluate the performance of these algorithms on four different types of cooperative games.","PeriodicalId":477867,"journal":{"name":"AppliedMath","volume":"51 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138596657","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
Interval Quadratic Equations: A Review 区间二次方程：回顾
AppliedMath Pub Date : 2023-12-01 DOI: 10.3390/appliedmath3040048
Isaac Elishakoff, Nicolas Yvain
{"title":"Interval Quadratic Equations: A Review","authors":"Isaac Elishakoff, Nicolas Yvain","doi":"10.3390/appliedmath3040048","DOIUrl":"https://doi.org/10.3390/appliedmath3040048","url":null,"abstract":"In this study, we tackle the subject of interval quadratic equations and we aim to accurately determine the root enclosures of quadratic equations, whose coefficients constitute interval variables. This study focuses on interval quadratic equations that contain only one coefficient considered as an interval variable. The four methods reviewed here in order to solve this problem are: (i) the method of classic interval analysis used by Elishakoff and Daphnis, (ii) the direct method based on minimizations and maximizations also used by the same authors, (iii) the method of quantifier elimination used by Ioakimidis, and (iv) the interval parametrization method suggested by Elishakoff and Miglis and again based on minimizations and maximizations. We will also compare the results yielded by all these methods by using the computer algebra system Mathematica for computer evaluations (including quantifier eliminations) in order to conclude which method would be the most efficient way to solve problems relevant to interval quadratic equations.","PeriodicalId":477867,"journal":{"name":"AppliedMath","volume":"69 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138622715","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
The Role of the Volatility in the Option Market 波动率在期权市场中的作用
AppliedMath Pub Date : 2023-12-01 DOI: 10.3390/appliedmath3040047
Ivan Arraut, Ka-I Lei
{"title":"The Role of the Volatility in the Option Market","authors":"Ivan Arraut, Ka-I Lei","doi":"10.3390/appliedmath3040047","DOIUrl":"https://doi.org/10.3390/appliedmath3040047","url":null,"abstract":"We review some general aspects about the Black–Scholes equation, which is used for predicting the fair price of an option inside the stock market. Our analysis includes the symmetry properties of the equation and its solutions. We use the Hamiltonian formulation for this purpose. Taking into account that the volatility inside the Black–Scholes equation is a parameter, we then introduce the Merton–Garman equation, where the volatility is stochastic, and then it can be perceived as a field. We then show how the Black–Scholes equation and the Merton–Garman one are locally equivalent by imposing a gauge symmetry under changes in the prices over the Black–Scholes equation. This demonstrates that the stochastic volatility emerges naturally from symmetry arguments. Finally, we analyze the role of the volatility on the decisions taken by the holders of the options when they use the solution of the Black–Scholes equation as a tool for making investment decisions.","PeriodicalId":477867,"journal":{"name":"AppliedMath","volume":" 974","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138610694","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
Unimodality of Parametric Linear Programming Solutions and Efficient Quantile Estimation 参数线性规划解的单模性与有效分位数估计
AppliedMath Pub Date : 2023-11-07 DOI: 10.3390/appliedmath3040044
Sara Mollaeivaneghi, Allan Santos, Florian Steinke
{"title":"Unimodality of Parametric Linear Programming Solutions and Efficient Quantile Estimation","authors":"Sara Mollaeivaneghi, Allan Santos, Florian Steinke","doi":"10.3390/appliedmath3040044","DOIUrl":"https://doi.org/10.3390/appliedmath3040044","url":null,"abstract":"For linear optimization problems with a parametric objective, so-called parametric linear programs (PLP), we show that the optimal decision values are, under few technical restrictions, unimodal functions of the parameter, at least in the two-degrees-of-freedom case. Assuming that the parameter is random and follows a known probability distribution, this allows for an efficient algorithm to determe the quantiles of linear combinations of the optimal decisions. The novel results are demonstrated with probabilistic economic dispatch. For an example setup with uncertain fuel costs, quantiles of the resulting inter-regional power flows are computed. The approach is compared against Monte Carlo and piecewise computation techniques, proving significantly reduced computation times for the novel procedure. This holds especially when the feasible set is complex and/or extreme quantiles are desired. This work is limited to problems with two effective degrees of freedom and a one-dimensional uncertainty. Future extensions to higher dimensions could yield a key tool for the analysis of probabilistic PLPs and, specifically, risk management in energy systems.","PeriodicalId":477867,"journal":{"name":"AppliedMath","volume":"92 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135539679","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
Advanced Technologies and Artificial Intelligence in Agriculture 农业中的先进技术和人工智能
AppliedMath Pub Date : 2023-11-01 DOI: 10.3390/appliedmath3040043
Alexander Uzhinskiy
{"title":"Advanced Technologies and Artificial Intelligence in Agriculture","authors":"Alexander Uzhinskiy","doi":"10.3390/appliedmath3040043","DOIUrl":"https://doi.org/10.3390/appliedmath3040043","url":null,"abstract":"According to the Food and Agriculture Organization, the world’s food production needs to increase by 70 percent by 2050 to feed the growing population. However, the EU agricultural workforce has declined by 35% over the last decade, and 54% of agriculture companies have cited a shortage of staff as their main challenge. These factors, among others, have led to an increased interest in advanced technologies in agriculture, such as IoT, sensors, robots, unmanned aerial vehicles (UAVs), digitalization, and artificial intelligence (AI). Artificial intelligence and machine learning have proven valuable for many agriculture tasks, including problem detection, crop health monitoring, yield prediction, price forecasting, yield mapping, pesticide, and fertilizer usage optimization. In this scoping mini review, scientific achievements regarding the main directions of agricultural technologies will be explored. Successful commercial companies, both in the Russian and international markets, that have effectively applied these technologies will be highlighted. Additionally, a concise overview of various AI approaches will be presented, and our firsthand experience in this field will be shared.","PeriodicalId":477867,"journal":{"name":"AppliedMath","volume":"42 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135271193","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
Some Comments about Zero and Non-Zero Eigenvalues from Connected Undirected Planar Graph Adjacency Matrices 关于连通无向平面图邻接矩阵零特征值和非零特征值的若干注释
AppliedMath Pub Date : 2023-11-01 DOI: 10.3390/appliedmath3040042
Daniel A. Griffith
{"title":"Some Comments about Zero and Non-Zero Eigenvalues from Connected Undirected Planar Graph Adjacency Matrices","authors":"Daniel A. Griffith","doi":"10.3390/appliedmath3040042","DOIUrl":"https://doi.org/10.3390/appliedmath3040042","url":null,"abstract":"Two linear algebra problems implore a solution to them, creating the themes pursued in this paper. The first problem interfaces with graph theory via binary 0-1 adjacency matrices and their Laplacian counterparts. More contemporary spatial statistics/econometrics applications motivate the second problem, which embodies approximating the eigenvalues of massively large versions of these two aforementioned matrices. The proposed solutions outlined in this paper essentially are a reformulated multiple linear regression analysis for the first problem and a matrix inertia refinement adapted to existing work for the second problem.","PeriodicalId":477867,"journal":{"name":"AppliedMath","volume":"82 12","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135271623","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
Dynamic Analysis of Neuron Models 神经元模型的动态分析
AppliedMath Pub Date : 2023-10-30 DOI: 10.3390/appliedmath3040041
Yiqiao Wang, Guanghong Ding, Wei Yao
{"title":"Dynamic Analysis of Neuron Models","authors":"Yiqiao Wang, Guanghong Ding, Wei Yao","doi":"10.3390/appliedmath3040041","DOIUrl":"https://doi.org/10.3390/appliedmath3040041","url":null,"abstract":"Based on the Hodgkin–Huxley theory, this paper establishes several nonlinear system models, analyzes the models’ stability, and studies the conditions for repetitive discharge of neuronal membrane potential. Our dynamic analysis showed that the main channel currents (the fast transient sodium current, the potassium delayed rectifier current, and the fixed leak current) of a neuron determine its dynamic properties and that the GHK formula will greatly widen the stimulation current range of the repetitive discharge condition compared with the Nernst equation. The model including the change in ion concentration will lead to spreading depression (SD)-like depolarization, and the inclusion of a Na-K pump will weaken the current stimulation effect by decreasing the extracellular K accumulation. The results indicate that the Hodgkin–Huxley model is suitable for describing the response to initial stimuli, but due to changes in ion concentration, it is not suitable for describing the response to long-term stimuli.","PeriodicalId":477867,"journal":{"name":"AppliedMath","volume":"147 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136022635","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
Quantum Computing in Insurance Capital Modelling under Reinsurance Contracts 再保险合同下保险资本模型中的量子计算
AppliedMath Pub Date : 2023-10-26 DOI: 10.3390/appliedmath3040040
Muhsin Tamturk, Marco Carenzo
{"title":"Quantum Computing in Insurance Capital Modelling under Reinsurance Contracts","authors":"Muhsin Tamturk, Marco Carenzo","doi":"10.3390/appliedmath3040040","DOIUrl":"https://doi.org/10.3390/appliedmath3040040","url":null,"abstract":"In this study, we design an algorithm to work on gate-based quantum computers. Based on the algorithm, we construct a quantum circuit that represents the surplus process of a cedant under a reinsurance agreement. This circuit takes into account a variety of factors: initial reserve, insurance premium, reinsurance premium, and specific amounts related to claims, retention, and deductibles for two different non-proportional reinsurance contracts. Additionally, we demonstrate how to perturb the actuarial stochastic process using Hadamard gates to account for unpredictable damage. We conclude by presenting graphs and numerical results to validate our capital modelling approach.","PeriodicalId":477867,"journal":{"name":"AppliedMath","volume":"36 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134908590","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
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