Train Students to Solve the Practical Problem by Building Mathematics Models

It focuses on that students must be developed the ability to solve the practical problem by building the mathematics models and the ability to combine the theory with the practice. It also states that students must be improved the learning interests and practical experience.

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.

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.

Residual subsidence time series model in mountain area caused by underground mining based on GNSS online monitoring

The residual subsidence caused by underground mining in mountain area has a long subsidence duration time and great potential harm,which seriously threatens the safety of people's production and life in the mining area.Therefore,it is necessary to use appropriate monitoring methods and mathematical models to effectively monitor and predict the residual subsidence caused by underground mining.Compared with traditional level survey and InSAR(Interferometric Synthetic Aperture Radar)technology,GNSS(Global Navigation Satellite System)online monitoring technology has the advantages of long-term monitoring,high precision and more flexible monitoring methods.The empirical equation method of residual subsidence in mining subsidence is effectively combined with the rock creep equation,which can not only describe the residual subsidence process from the mechanism,but also predict the residual subsidence.Therefore,based on GNSS online monitoring technology,combined with the mining subsidence model of mountain area and adding the correlation coefficient of the compaction degree of caving broken rock and the Kelvin model of rock mechanics,this paper constructs the residual subsidence time series model of arbitrary point on the ground in mountain area.Through the example,the predicted results of the model in the inversion parameter phase and the dynamic prediction phase are compared with the measured data sequence.The results show that the model can carry out effective numerical calculation according to the GNSS monitoring data of any point on the ground,and the model prediction effect is good,which provides a new method for the prediction of residual subsidence in mountain mining.

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.

A Vertex Network Model of Arabidopsis Leaf Growth

Biology provides many examples of complex systems whose properties allow organisms to develop in a highly reproducible,or robust,manner.One such system is the growth and development of flat leaves in Arabidopsis thaliana.This mechanistically challenging process results from multiple inputs including gene interactions,cellular geometry,growth rates,and coordinated cell divisions.To better understand how this complex genetic and cellular information controls leaf growth,we developed a mathematical model of flat leaf production.This two-dimensional model describes the gene interactions in a vertex network of cells which grow and divide according to physical forces and genetic information.Interestingly,the model predicts the presence of an unknown additional factor required for the formation of biologically realistic gene expression domains and iterative cell division.This two-dimensional model will form the basis for future studies into robustness of adaxial-abaxial patterning.

A framework for dynamic modelling of railway track switches considering the switch blades,actuators and control systems

The main contribution of this paper is the development and demonstration of a novel methodology that can be followed to develop a simulation twin of a railway track switch system to test the functionality in a digital environment.This is important because,globally,railway track switches are used to allow trains to change routes;they are a key part of all railway networks.However,because track switches are single points of failure and safety-critical,their inability to operate correctly can cause significant delays and concomitant costs.In order to better understand the dynamic behaviour of switches during operation,this paper has developed a full simulation twin of a complete track switch system.The approach fuses finite element for the rail bending and motion,with physics-based models of the electromechanical actuator system and the control system.Hence,it provides researchers and engineers the opportunity to explore and understand the design space around the dynamic operation of new switches and switch machines before they are built.This is useful for looking at the modification or monitoring of existing switches,and it becomes even more important when new switch concepts are being considered and evaluated.The simulation is capable of running in real time or faster meaning designs can be iterated and checked interactively.The paper describes the modelling approach,demonstrates the methodology by developing the system model for a novel“REPOINT”switch system,and evaluates the system level performance against the dynamic performance requirements for the switch.In the context of that case study,it is found that the proposed new actuation system as designed can meet(and exceed)the system performance requirements,and that the fault tolerance built into the actuation ensures continued operation after a single actuator failure.

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.

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.

Data-driven intelligent modeling framework for the steam cracking process

Steam cracking is the dominant technology for producing light olefins,which are believed to be the foundation of the chemical industry.Predictive models of the cracking process can boost production efficiency and profit margin.Rapid advancements in machine learning research have recently enabled data-driven solutions to usher in a new era of process modeling.Meanwhile,its practical application to steam cracking is still hindered by the trade-off between prediction accuracy and computational speed.This research presents a framework for data-driven intelligent modeling of the steam cracking process.Industrial data preparation and feature engineering techniques provide computational-ready datasets for the framework,and feedstock similarities are exploited using k-means clustering.We propose LArge-Residuals-Deletion Multivariate Adaptive Regression Spline(LARD-MARS),a modeling approach that explicitly generates output formulas and eliminates potentially outlying instances.The framework is validated further by the presentation of clustering results,the explanation of variable importance,and the testing and comparison of model performance.

Experiments and model development of p-nitrochlorobenzene and naphthalene purification in a continuous tower melting crystallizer

With the increasing demand for high-purity products,the industrial application of melt crystallization technology has been highly concerned.In this study,the purification process of nitrochlorobenzene binary eutectic system(NBES)and naphthalene–benzothiophene solid solution system(NBSSS)in tower melting crystallizer is analyzed,and a mathematical model of crystallization process is established.The key parameters in terms of feed concentration,crystal bed height,reflux ratio and stirring speed effi-ciency on purification effects were discussed by the established model.The results show that the concentration of p-nitrochlorobenzene was purified from 90.85%to 99.99%,when the crystal bed height is 600 mm,the reflux ratio is 2.5,and the stirring speed is 12 rmin^(-1).The naphthalene concentration is purified from 95.89%to 99.99%,when the crystal bed height is 400 mm,the reflux ratio is 1.43,and the stirring speed is 16 rmin^(-1).The quality of the model is evaluated by the ARD(average relative deviation).The minimum ARD values of the NBES and NBSSS are 2.39%and 5.22%,respectively,indicating the model satisfactorily explains the purification process.

The calculation and optimal allocation of transmission capacity in natural gas networks with MINLP models

The transmission capacity of gas pipeline networks should be calculated and allocated to deal with the capacity booking with shippers. Technical capacities, which depend on the gas flow distribution at routes or interchange points, are calculated with a multiobjective optimization model and form a Pareto solution set in the entry/exit or point-to-point regime. Then, the commercial capacities, which can be directly applied in capacity booking, are calculated with single-objective optimization models that are transformed from the above multiobjective model based on three allocation rules and the demand of shippers.Next, peak-shaving capacities, which are daily oversupply or overdelivery amounts at inlets or deliveries,are calculated with two-stage transient optimization models. Considering the hydraulic process of a pipeline network and operating schemes of compressor stations, all the above models are mixed-integer nonlinear programming problems. Finally, a case study is made to demonstrate the ability of the models.

Refined mathematical model for the breaching of concrete-face sand-gravel dams due to overtopping failure

Overtopping is one of the main reasons for the breaching of concrete-face sand-gravel dams(CFSGDs).In this study,a refined mathematical model was established based on the characteristics of the overtopping breaching of CFSGDs.The model characteristics were as follows:(1)Based on the Renormailzation Group(RNG)k-εturbulence theory and volume of fluid(VOF)method,the turbulent characteristics of the dam-break flow were simulated,and the erosion surface of the water and soil was tracked;(2)In consideration of the influence of the change in the sediment content on the dam-break flow,the dam material transport equation,which could reflect the characteristics of particle settlement and entrainment motion,was used to simulate the erosion process of the sand gravels;(3)Based on the bending moment balance method,a failure equation of the concrete face slab under dead weight and water load was established.The proposed model was verified through a case study on the failure of the Gouhou CFSGD.The results showed that the proposed model could well simulate the erosion mode of the special vortex flow of the CFSGD scouring the support body of the concrete face slab inward and reflect the mutual coupling relationship between the dam-break flow,sand gravels,and concrete face slabs.Compared with the measured values,the relative errors of the peak discharge,final breach average width,dam breaching duration,and maximum failure length of the face slab calculated using the proposed model were all less than 12%,thus verifying the rationality of the model.The proposed model was demonstrated to perform better and provide more detailed results than three selected parametric models and three simplified mathematical models.The study results can aid in establishing the risk level and devising early warning strategies for CFSGDs.

A Study on the Nonlinear Caputo-Type Snakebite Envenoming Model with Memory

In this article,we introduce a nonlinear Caputo-type snakebite envenoming model with memory.The well-known Caputo fractional derivative is used to generalize the previously presented integer-order model into a fractionalorder sense.The numerical solution of the model is derived from a novel implementation of a finite-difference predictor-corrector(L1-PC)scheme with error estimation and stability analysis.The proof of the existence and positivity of the solution is given by using the fixed point theory.From the necessary simulations,we justify that the first-time implementation of the proposedmethod on an epidemicmodel shows that the scheme is fully suitable and time-efficient for solving epidemic models.This work aims to show the novel application of the given scheme as well as to check how the proposed snakebite envenoming model behaves in the presence of the Caputo fractional derivative,including memory effects.

Tight gas charging and accumulation mechanisms and mathematical model

The gas-water distribution and production heterogeneity of tight gas reservoirs have been summarized from experimental and geological observations, but the charging and accumulation mechanisms have not been examined quantitatively by mathematical model. The tight gas charging and accumulation mechanisms were revealed from a combination of physical simulation of nuclear magnetic resonance coupling displacement, numerical simulation considering material and mechanical equilibria, as well as actual geological observation. The results show that gas migrates into tight rocks to preferentially form a gas saturation stabilization zone near the source-reservoir interface. When the gas source is insufficient, gas saturation reduction zone and uncharged zone are formed in sequence from the source-reservoir interface. The better the source rock conditions with more gas expulsion volume and higher overpressure, the thicker the gas saturation stabilization and reduction zones, and the higher the overall gas saturation. When the source rock conditions are limited, the better the tight reservoir conditions with higher porosity and permeability as well as larger pore throat, the thinner the gas saturation stabilization and reduction zones, but the gas saturation is high. The sweet spot of tight gas is developed in the high-quality reservoir near the source rock, which often corresponds to the gas saturation stabilization zone. The numerical simulation results by mathematical model agree well with the physical simulation results by nuclear magnetic resonance coupling displacement, and reasonably explain the gas-water distribution and production pattern of deep reservoirs in the Xujiaweizi fault depression of the Songliao Basin and tight gas reservoirs in the Linxing-Huangfu area of the Ordos Basin.

Quantification of Ride Comfort Using Musculoskeletal Mathematical Model Considering Vehicle Behavior

This research aims to quantify driver ride comfort due to changes in damper characteristics between comfort mode and sport mode,considering the vehicle’s inertial behavior.The comfort of riding in an automobile has been evaluated in recent years on the basis of a subjective sensory evaluation given by the driver.However,reflecting driving sensations in design work to improve ride comfort is abstract in nature and difficult to express theoretically.Therefore,we evaluated the human body’s effects while driving scientifically by quantifying the driver’s behavior while operating the steering wheel and the behavior of the automobile while in motion using physical quantities.To this end,we collected driver and vehicle data using amotion capture system and vehicle CAN and IMU sensors.We also constructed a three-dimensional musculoskeletal mathematical model to simulate driver movements and calculate the power and amount of energy per unit of time used for driving the joints and muscles of the human body.Here,we used comfort mode and sport mode to compare damper characteristics in terms of hardness.In comfort mode,damper characteristics are soft and steering stability is mild,but vibration from the road is not easily transmitted to the driver making for a lighter load on the driver.In sport mode,on the other hand,damper characteristics are hard and steering stability is comparatively better.Still,vibration from the road is easily transmitted to the driver,whichmakes it easy for a load to be placed on the driver.As a result of this comparison,it was found that a load was most likely to be applied to the driver’s neck.This result in relation to the neck joint can therefore be treated as an objective measure for quantifying ride comfort.

Stochastic Framework for Solving the Prey-Predator Delay Differential Model of Holling Type-Ⅲ

The current research aims to implement the numerical resultsfor the Holling third kind of functional response delay differential modelutilizing a stochastic framework based on Levenberg-Marquardt backpropagationneural networks (LVMBPNNs). The nonlinear model depends uponthree dynamics, prey, predator, and the impact of the recent past. Threedifferent cases based on the delay differential system with the Holling 3^(rd) type of the functional response have been used to solve through the proposedLVMBPNNs solver. The statistic computing framework is provided byselecting 12%, 11%, and 77% for training, testing, and verification. Thirteennumbers of neurons have been used based on the input, hidden, and outputlayers structure for solving the delay differential model with the Holling 3rdtype of functional response. The correctness of the proposed stochastic schemeis observed by using the comparison performances of the proposed and referencedata-based Adam numerical results. The authentication and precision ofthe proposed solver are approved by analyzing the state transitions, regressionperformances, correlation actions, mean square error, and error histograms.

Statistical Time Series Forecasting Models for Pandemic Prediction

COVID-19 has significantly impacted the growth prediction of a pandemic,and it is critical in determining how to battle and track the disease progression.In this case,COVID-19 data is a time-series dataset that can be projected using different methodologies.Thus,this work aims to gauge the spread of the outbreak severity over time.Furthermore,data analytics and Machine Learning(ML)techniques are employed to gain a broader understanding of virus infections.We have simulated,adjusted,and fitted several statistical time-series forecasting models,linearML models,and nonlinear ML models.Examples of these models are Logistic Regression,Lasso,Ridge,ElasticNet,Huber Regressor,Lasso Lars,Passive Aggressive Regressor,K-Neighbors Regressor,Decision Tree Regressor,Extra Trees Regressor,Support Vector Regressions(SVR),AdaBoost Regressor,Random Forest Regressor,Bagging Regressor,AuoRegression,MovingAverage,Gradient Boosting Regressor,Autoregressive Moving Average(ARMA),Auto-Regressive Integrated Moving Averages(ARIMA),SimpleExpSmoothing,Exponential Smoothing,Holt-Winters,Simple Moving Average,Weighted Moving Average,Croston,and naive Bayes.Furthermore,our suggested methodology includes the development and evaluation of ensemble models built on top of the best-performing statistical and ML-based prediction methods.A third stage in the proposed system is to examine three different implementations to determine which model delivers the best performance.Then,this best method is used for future forecasts,and consequently,we can collect the most accurate and dependable predictions.

Simulation Analysis of New Energy Vehicle Engine Cooling System Based on K-E Turbulent Flow Mathematical Model

New energy vehicles have better clean and environmental protection characteristics than traditional fuel vehicles.The new energy engine cooling technology is critical in the design of new energy vehicles.This paper used oneand three-way joint simulation methods to simulate the refrigeration system of new energy vehicles.Firstly,a k-εturbulent flow model for the cooling pump flow field is established based on the principle of computational fluid dynamics.Then,the CFD commercial fluid analysis software FLUENT is used to simulate the flow field of the cooling pump under different inlet flow conditions.This paper proposes an optimization scheme for new energy vehicle engines’“boiling”phenomenon under high temperatures and long-time climbing conditions.The simulation results show that changing the radiator’s structure and adjusting the thermostat’s parameters can solve the problem of a“boiling pot.”The optimized new energy vehicle engine can maintain a better operating temperature range.The algorithm model can reference each cryogenic system component hardware selection and control strategy in the new energy vehicle’s engine.

Problem-based Learning Combining Seminar Teaching Method for the Practice of Mathematical Modeling Course's Teaching Reform for Computer Discipline

Mathematical modeling course has been one of the fast development courses in China since 1992,which mainly trains students’innovation ability.However,the teaching of mathematical modeling course is quite difficult since it requires students to have a strong mathematical foundation,good ability to design algorithms,and programming skills.Besides,limited class hours and lack of interest in learning are the other reasons.To address these problems,according to the outcome-based education,we adopt the problem-based learning combined with a seminar mode in teaching.We customize cases related to computer and software engineering,start from simple problems in daily life,step by step deepen the difficulty,and finally refer to the professional application in computer and software engineering.Also,we focus on ability training rather than mathematical theory or programming language learning.Initially,we prepare the problem,related mathematic theory,and core code for students.Furtherly,we train them how to find the problem,and how to search the related mathematic theory and software tools by references for modeling and analysis.Moreover,we solve the problem of limited class hours by constructing an online resource learning library.After a semester of practical teaching,it has been shown that the interest and learning effectiveness of students have been increased and our reform plan has achieved good results.