Study on Mathematical Modeling Software MATLAB Teaching in Higher Vocational Colleges

The present situation of the mathematics teaching in higher vocational colleges is not optimistic. In the new education system, it is an urgent problem for the mathematics teachers in higher vocational colleges to bring forth new ideas for the teaching methods, improve the students＇ interest in learning, and train the application-oriented talented personnel needed by the society. MATLAB software package can help set up a bridge and link for the mathematics teaching and the practical application. Its powerful numerical calculation ability can quickly solve all kinds of calculation problems, so that the basic thinking methods are more closely focused in mathematics teaching and also more conditions are created for mathematics teaching to combine the actual major conditions and life conditions. In this paper, the related problems in the implementation of mathematical modeling software MATLAB and model in higher vocational colleges are discussed.

Edge detection and mathematic fitting for corneal surface with Matlab software

AIM：To select the optimal edge detection methods to identify the corneal surface,and compare three fitting curve equations with Matlab software. METHODS：Fifteen subjects were recruited. The corneal images from optical coherence tomography（OCT）were imported into Matlab software. Five edge detection methods（Canny,Log,Prewitt,Roberts,Sobel）were used to identify the corneal surface. Then two manual identifying methods（ginput and getpts）were applied to identify the edge coordinates respectively. The differences among these methods were compared. Binomial curve（y=Ax2＋Bx＋C）,Polynomial curve [p（x）=p1xn＋p2x（n-1）＋....＋pnx＋pn＋1] and Conic section（Ax2＋Bxy＋Cy2＋Dx＋Ey＋F=0）were used for curve fitting the corneal surface respectively. The relative merits among three fitting curves were analyzed. Finally,the eccentricity（e）obtained by corneal topography and conic section were compared with paired t-test. RESULTS：Five edge detection algorithms all had continuous coordinates which indicated the edge of the corneal surface. The ordinates of manual identifying were close to the inside of the actual edges. Binomial curve was greatly affected by tilt angle. Polynomial curve was lack of geometrical properties and unstable. Conic section could calculate the tilted symmetry axis,eccentricity,circle center,etc. There were no significant differences between ＇e＇ values by corneal topography and conic section（t=0.9143,P=0.3760 〉0.05）.CONCLUSION：It is feasible to simulate the corneal surface with mathematical curve with Matlab software. Edge detection has better repeatability and higher efficiency. The manual identifying approach is an indispensable complement for detection. Polynomial and conic section are both the alternative methods for corneal curve fitting. Conic curve was the optimal choice based on the specific geometrical properties.

Mathematical Modeling and Software Application of Blood Flow for Therapeutic Management of Stroke

People in the rural areas do not have access to specialist medical care, and when they have complications of stroke, they do not have specialists to look at them and they cannot afford to travel to the cities. The primary health care centers are not equipped with sophisticated equipments. Medicine is about medication, treatment and management. In rural areas treatment is not available either because of accessibility or affordability. Even the few doctors that are available are not in primary health care centres. Well conserved one-dimensional non-linear equations of blood flow describing blood flow in distensible blood vessels were used to develop software. This model could describe discontinuities and disruption in blood flow. The computer software can be used for detecting artherosclerosis, stenosis and differentiation of haemorrhagic and ischaemic strokes for stroke management from simple measurements. The software developed is capable of computing the Siriraj and the Allen clinical scores. These scores have been proposed to help clinicians in making decisions while waiting for results of computerized tomography, hence clinicians can start anti-thrombotic treatment while waiting for the scan results. It is capable of simulating stenosis at different position and depth of flow along the arterial length, and can be used for diagnosis. The medical emphasis is on avoiding possible occurrence, every individual can know his status by inputting the required data such as flow and geometry of their arteries into the developed interface and such measurements can be obtained from simple Doppler measurements.

MATHEMATICAL MODELING AND BIFURCATION ANALYSIS FOR A BIOLOGICAL MECHANISM OF CANCER DRUG RESISTANCE

Drug resistance is one of the most intractable issues in targeted therapy for cancer diseases.It has also been demonstrated to be related to cancer heterogeneity,which promotes the emergence of treatment-refractory cancer cell populations.Focusing on how cancer cells develop resistance during the encounter with targeted drugs and the immune system,we propose a mathematical model for studying the dynamics of drug resistance in a conjoint heterogeneous tumor-immune setting.We analyze the local geometric properties of the equilibria of the model.Numerical simulations show that the selectively targeted removal of sensitive cancer cells may cause the initially heterogeneous population to become a more resistant population.Moreover,the decline of immune recruitment is a stronger determinant of cancer escape from immune surveillance or targeted therapy than the decay in immune predation strength.Sensitivity analysis of model parameters provides insight into the roles of the immune system combined with targeted therapy in determining treatment outcomes.

Combining reinforcement learning with mathematical programming:An approach for optimal design of heat exchanger networks

Heat integration is important for energy-saving in the process industry.It is linked to the persistently challenging task of optimal design of heat exchanger networks(HEN).Due to the inherent highly nonconvex nonlinear and combinatorial nature of the HEN problem,it is not easy to find solutions of high quality for large-scale problems.The reinforcement learning(RL)method,which learns strategies through ongoing exploration and exploitation,reveals advantages in such area.However,due to the complexity of the HEN design problem,the RL method for HEN should be dedicated and designed.A hybrid strategy combining RL with mathematical programming is proposed to take better advantage of both methods.An insightful state representation of the HEN structure as well as a customized reward function is introduced.A Q-learning algorithm is applied to update the HEN structure using theε-greedy strategy.Better results are obtained from three literature cases of different scales.

Mathematical Modeling of Cell Polarity Establishment of Budding Yeast

The budding yeast Saccharomyces cerevisiae is a powerful model system for studying the cell polarity establishment.The cell polarization process is regulated by signaling molecules,which are initially distributed in the cytoplasm and then recruited to a proper location on the cell membrane in response to spatial cues or spontaneously.Polarization of these signaling molecules involves complex regulation,so the mathematical models become a useful tool to investigate the mechanism behind the process.In this review,we discuss how mathematical modeling has shed light on different regulations in the cell polarization.We also propose future applications for the mathematical modeling of cell polarization and morphogenesis.

An Implementation of Multiscale Line Detection and Mathematical Morphology for Efficient and Precise Blood Vessel Segmentation in Fundus Images

Diagnosing various diseases such as glaucoma,age-related macular degeneration,cardiovascular conditions,and diabetic retinopathy involves segmenting retinal blood vessels.The task is particularly challenging when dealing with color fundus images due to issues like non-uniformillumination,low contrast,and variations in vessel appearance,especially in the presence of different pathologies.Furthermore,the speed of the retinal vessel segmentation system is of utmost importance.With the surge of now available big data,the speed of the algorithm becomes increasingly important,carrying almost equivalent weightage to the accuracy of the algorithm.To address these challenges,we present a novel approach for retinal vessel segmentation,leveraging efficient and robust techniques based on multiscale line detection and mathematical morphology.Our algorithm’s performance is evaluated on two publicly available datasets,namely the Digital Retinal Images for Vessel Extraction dataset(DRIVE)and the Structure Analysis of Retina(STARE)dataset.The experimental results demonstrate the effectiveness of our method,withmean accuracy values of 0.9467 forDRIVE and 0.9535 for STARE datasets,aswell as sensitivity values of 0.6952 forDRIVE and 0.6809 for STARE datasets.Notably,our algorithmexhibits competitive performance with state-of-the-art methods.Importantly,it operates at an average speed of 3.73 s per image for DRIVE and 3.75 s for STARE datasets.It is worth noting that these results were achieved using Matlab scripts containing multiple loops.This suggests that the processing time can be further reduced by replacing loops with vectorization.Thus the proposed algorithm can be deployed in real time applications.In summary,our proposed system strikes a fine balance between swift computation and accuracy that is on par with the best available methods in the field.

Aggravation of Cancer,Heart Diseases and Diabetes Subsequent to COVID-19 Lockdown via Mathematical Modeling

The global populationhas beenandwill continue to be severely impacted by theCOVID-19 epidemic.The primary objective of this research is to demonstrate the future impact of COVID-19 on those who suffer from other fatal conditions such as cancer,heart disease,and diabetes.Here,using ordinary differential equations(ODEs),two mathematical models are developed to explain the association between COVID-19 and cancer and between COVID-19 and diabetes and heart disease.After that,we highlight the stability assessments that can be applied to these models.Sensitivity analysis is used to examine how changes in certain factors impact different aspects of disease.The sensitivity analysis showed that many people are still nervous about seeing a doctor due to COVID-19,which could result in a dramatic increase in the diagnosis of various ailments in the years to come.The correlation between diabetes and cardiovascular illness is also illustrated graphically.The effects of smoking and obesity are also found to be significant in disease compartments.Model fitting is also provided for interpreting the relationship between real data and the results of thiswork.Diabetic people,in particular,need tomonitor their health conditions closely and practice heart health maintenance.People with heart diseases should undergo regular checks so that they can protect themselves from diabetes and take some precautions including suitable diets.The main purpose of this study is to emphasize the importance of regular checks,to warn people about the effects of COVID-19(including avoiding healthcare centers and doctors because of the spread of infectious diseases)and to indicate the importance of family history of cancer,heart diseases and diabetes.The provision of the recommendations requires an increase in public consciousness.

Learning to represent 2D human face with mathematical model

How to represent a human face pattern?While it is presented in a continuous way in human visual system,computers often store and process it in a discrete manner with 2D arrays of pixels.The authors attempt to learn a continuous surface representation for face image with explicit function.First,an explicit model(EmFace)for human face representation is pro-posed in the form of a finite sum of mathematical terms,where each term is an analytic function element.Further,to estimate the unknown parameters of EmFace,a novel neural network,EmNet,is designed with an encoder-decoder structure and trained from massive face images,where the encoder is defined by a deep convolutional neural network and the decoder is an explicit mathematical expression of EmFace.The authors demonstrate that our EmFace represents face image more accurate than the comparison method,with an average mean square error of 0.000888,0.000936,0.000953 on LFW,IARPA Janus Benchmark-B,and IJB-C datasets.Visualisation results show that,EmFace has a higher representation performance on faces with various expressions,postures,and other factors.Furthermore,EmFace achieves reasonable performance on several face image processing tasks,including face image restoration,denoising,and transformation.

Practical Use of the Subjective Mathematical Model of Bayes and Its External Validation in Dental Medicine & Dentistry

Objective: Our study aims to validate the subjective Bayes mathematical model using the mathematical model of logistic regression. Expert systems are being utilized increasingly in medical fields for the purposes of assisting diagnosis and treatment planning in Dentistry. Existing systems used few symptoms for dental diagnosis. In Dentistry, few symptoms are not enough for diagnosis. In this research, a conditional probability model (Bayes rule) was developed with increased number of symptoms associated with a disease for diagnosis. A test set of recurrent cases was then used to test the diagnostic capacity of the system. The generated diagnosis matched that of the human experts. The system was also tested for its capacity to handle uncommon dental diseases and the system portrayed useful potential. Method: The study used the Subjective Mathematical Bayes Model (SBM) approach and employed Logistic Regression Mathematical Model (LMR) techniques. The external validation of the subjective mathematical Bayes model (MSB) concerns the real cases of 625 patients who developed alveolar osteitis (OA). We propose strategies for reproducibility and reporting standards, outlining an updated WAMBS (when to Worry and how to Avoid the Misuse of Bayesian Statistics) checklist. Finally, we outline the impact of Bayesian analysis Logistic Regression Mathematical Model (LMR) techniques and on artificial intelligence, a major goal in the next decade. Results: The internal validation had identified seven (7) etiological factors of OA, which will be compared to the cases of MRL, for the external validation which retained six (6) etiological factors of OA. The experts in the internal validation of the MSB had generated 40 cases of OA and a COP of (0.5), which will be compared to the MRL that collected 625 real cases of OA to produce a Cop of (0.6) in the external validation, which discriminates between healthy patients (Se) and sick patients (Sp). Compared to real cases and the logistic regression model, the Bayesian model is efficient and its validity is established.

MATLAB软件辅助高等数学教学——以计算机类专业为例

鉴于在高等数学相关函数和定积分的教学中缺少应用场景介绍和学生空间想象力弱等问题,采用MATLAB软件辅助高等数学教学,通过图形直观展示其应用场景和自行编写代码计算定积分。结果表明:将MATLAB软件融入课堂教学不仅提高学生学习积极性,还加深学生对概念及定义的理解,使学生获得直观的感性认识和理性认识,提高了课堂的教学质量和效果。

Mathematical Modeling of HIV Investigating the Effect of Inconsistent Treatment

HIV is a retrovirus that infects and impairs the cells and functions of the immune system. It has caused a great challenge to global public health systems and leads to Acquired Immunodeficiency Syndrome (AIDS), if not attended to in good time. Antiretroviral therapy is used for managing the virus in a patient’s lifetime. Some of the symptoms of the disease include lean body mass and many opportunistic infections. This study has developed a SIAT mathematical model to investigate the impact of inconsistency in treatment of the disease. The arising non-linear differential equations have been obtained and analyzed. The DFE and its stability have been obtained and the study found that it is locally asymptotically stable when the basic reproduction number is less than unity. The endemic equilibrium has been obtained and found to be globally asymptotically stable when the basic reproduction number is greater than unity. Numerical solutions have been obtained and analyzed to give the trends in the spread dynamics. The inconsistency in treatment uptake has been analyzed through the numerical solutions. The study found that when the treatment rate of those infected increases, it leads to an increase in treatment population, which slows down the spread of HIV and vice versa. An increase in the rate of treatment of those with AIDS leads to a decrease in the AIDS population, the reverse happens when this rate decreases. The study recommends that the community involvement in advocating for consistent treatment of HIV to curb the spread of the disease.

Critical Analysis of Increasingly Mathematical Economics in the Modern Society

This paper critically examines the escalating trend of mathematization in economics,highlighting its implications and controversies in contemporary economic research.While the application of sophisticated mathematical models and statistical techniques has enhanced the precision,rigor,and status of economics within academia and practical application,concerns arise regarding the potential oversimplification and detachment from real-world complexities.The adoption of mathematical tools has arguably led to a focus on theoretically tractable problems at the expense of those more relevant to practical economic and social issues.This paper explores both the benefits and limitations of this trend,discussing how the reliance on quantitative methods affects the innovation,comprehensibility,and application of economic theories.We argue for a balanced approach that fosters innovation by integrating qualitative insights and embracing interdisciplinary methods to ensure economics remains both rigorous and relevant to societal needs.

Mathematical Modeling of the Co-Infection Dynamics of HIV and Tuberculosis Incorporating Inconsistency in HIV Treatment

A non-linear HIV-TB co-infection has been formulated and analyzed. The positivity and invariant region has been established. The disease free equilibrium and its stability has been determined. The local stability was determined and found to be stable under given conditions. The basic reproduction number was obtained and according to findings, co-infection diminishes when this number is less than unity, and persists when the number is greater than unity. The global stability of the endemic equilibrium was calculated. The impact of HIV on TB was established as well as the impact of TB on HIV. Numerical solution was also done and the findings indicate that when the rate of HIV treatment increases the latent TB increases while the co-infected population decreases. When the rate of HIV treatment decreases the latent TB population decreases and the co-infected population increases. Encouraging communities to prioritize the consistent treatment of HIV infected individuals must be emphasized in order to reduce the scourge of HIV-TB co-infection.

Integration of Mathematics History into Junior Middle School Education: A Pedagogical Approach to Enhance Mathematical Literacy

The integration of the history of mathematics into junior middle school mathematics education represents a significant focus of international research in mathematics and education.The mathematics curriculum standards for compulsory education have emphasized the importance of incorporating the history of mathematics,aiming to gradually integrate it into the mathematics classroom.However,in the practical implementation of junior middle school mathematics education,the effective combination of the history of mathematics with teaching methodologies remains largely unexplored.This article explores the integration of junior middle school mathematics education and the history of mathematics,aiming to provide classroom teaching recommendations for teachers and promote the formation of students’mathematical literacy.

Teaching Reform and Practice of “Mathematical Analysis” under the New Engineering Education Paradigm

With the advent and promotion of the new engineering education paradigm,university mathematics courses face new challenges and opportunities.As a fundamental course for engineering majors,the reform of“Mathematical Analysis”is particularly crucial.This paper explores the necessity,specific practices,and outcomes of teaching reform in“Mathematical Analysis”within the context of the new engineering education.By reforming teaching content,methods,and assessment approaches,this study aims to enhance students’mathematical literacy and comprehensive abilities to meet the demands of the new engineering education development.

Integration of Ideological and Political Education into the Probability Theory and Mathematical Statistics Course:A Teaching Design Based on Estimation and Hypothesis Testing

With the rapid development of higher education in China,colleges and universities are facing new challenges and impacts in talent training.Probability Theory and Mathematical Statistics is one of the important courses in higher education for science and engineering majors and economics and management majors.Its critical role in cultivating students’thinking skills and improving their problem-solving skills is self-evident.Course ideological and political education construction is an important link in college talent training work.Combining ideological and political education with course teaching can help students establish correct value concepts and play a certain role in improving their comprehensive ability and quality.At present,the construction of ideological and political education in the Probability Theory and Mathematical Statistics course still faces some problems,mainly manifested in the lack of attention paid by teachers to course ideological and political education,insufficient exploitation of ideological and political elements,and the simplification of ideological and political education implementation methods.In order to comprehensively deepen the construction of course ideological and political education in line with the actual needs of Probability Theory and Mathematical Statistics course teaching,we should strengthen the construction of teacher teams,improve teachers’ability to carry out course ideological and political education,integrate educational resources,develop educational resources for ideological and political education,and innovate teaching methods to improve the overall effect of ideological and political education integration.

Analysis of the Impact of Inductive Reasoning on the Mathematical Thinking Style of Deaf and Hard-of-Hearing Students

In this paper,we combine the teaching and learning situation of deaf and hard-of-hearing students in the Linear Algebra course of the Computer Science and Technology major at the Nanjing Normal University of Special Education.Based on the cognitive style of deaf and hard-of-hearing students,we apply example induction,exhaustive induction,and mathematical induction to the teaching of Linear Algebra by utilizing specific course content.The aim is to design comprehensive teaching that caters to the cognitive style characteristics of deaf and hard-of-hearing students,strengthen their mathematical thinking styles such as quantitative thinking,algorithmic thinking,symbolic thinking,visual thinking,logical thinking,and creative thinking,and enhance the effectiveness of classroom teaching and learning outcomes in Linear Algebra for deaf and hard-of-hearing students.

基于MATLAB/Simulink对光伏电池建立模型与仿真

基于光伏电池数学模型,对光伏电池板的工作原理进行简要分析并给出其等效电路,使用MATLAB/Simulink对其建立仿真模型,并且通过在不同的环境下来测试光伏电池模型的特性,仿真结果与理论上的光伏电池P-V、I-V特性曲线基本吻合,证明所建立模型的合理性,对光伏电池在现实中的应用具有实际意义并对找到光伏电池合适的工作环境和实现其的最大功率提供了理论依据.

信息化背景下高等数学教学MATLAB软件辅助研究——以计算机类专业为例

本研究以计算机类专业为背景,探讨了信息化时代下高等数学教学中MATLAB软件的应用及其辅助效果。文章首先概述了高等数学的基本概念,并阐述了MATLAB软件在高等数学教学中应用的重要性。接着,详细分析了MATLAB软件在图像处理、三重积分计算、微分方程求解、定积分教学及幂级数逼近教学等多个高等数学领域中的具体教学方式。研究表明,MATLAB软件的有效融入能够帮助学生更直观地理解抽象的高等数学概念,提高计算效率,同时培养了学生的编程技能和实践能力。本文旨在为高等数学的教学改革提供新的思路和方法,推动教育信息化进程,提高教学质量。