scholarly journals Parameter estimation in mathematical models of viral infections using R

2017 ◽  
Author(s):  
Van Kinh Nguyen ◽  
Esteban A. Hernandez-Vargas
Keyword(s):  
Mathematical Modeling ◽  
Parameter Estimation ◽  
Mathematical Models ◽  
Viral Infections ◽  
Free Software ◽  
Virus Dynamics ◽  
Biological Applications ◽  
Simulation Results ◽  
Underlying Mechanisms ◽  
Mathematical Relations

AbstractIn recent years, mathematical modeling approaches have played a central role to understand and to quantify mechanisms in different viral infectious diseases. In this approach, biological-based hypotheses are expressed via mathematical relations and then tested based on empirical data. The simulation results can be used to either identify underlying mechanisms, provide predictions on infection outcomes, or evaluate the efficacy of a treatment.Conducting parameter estimation for mathematical models is not an easy task. Here we detail an approach to conduct parameter estimation and to evaluate the results using the free software R. The method is applicable to influenza virus dynamics at different complexity levels, widening experimentalists capabilities in understanding their data. The parameter estimation approach presented here can be also applied to other viral infections or biological applications.

scholarly journals Modeling and Parameter Identification of the Vibration Characteristics of Armature Assembly in a Torque Motor of Hydraulic Servo Valves under Electromagnetic Excitations

2014 ◽  
Vol 6 ◽  
pp. 247384 ◽  
Author(s):  
Jinghui Peng ◽  
Songjing Li ◽  
Yongbo Fan
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Models ◽  
Natural Frequencies ◽  
Experimental Studies ◽  
Vibration Characteristics ◽  
Mode Shapes ◽  
The Finite Element Method ◽  
Hydraulic Servo ◽  
Simulation Results ◽  
Vibration Modal

The resonance of the armature assembly is the main problem leading to the fatigue of the spring pipe in a torque motor of hydraulic servo valves, which can cause the failure of servo valves. To predict the vibration characteristics of the armature assembly, this paper focuses on the mathematical modeling of the vibration characteristics of armature assembly in a hydraulic servo valve and the identification of parameters in the models. To build models more accurately, the effect of the magnetic spring is taken into account. Vibration modal analysis is performed to obtain the mode shapes and natural frequencies, which are necessary to implement the identification of damping ratios in the mathematical models. Based on the mathematical models for the vibration characteristics, the harmonic responses of the armature assembly are analyzed using the finite element method and measured under electromagnetic excitations. The simulation results agree well with the experimental studies.

scholarly journals Evasion guidance for air-breathing hypersonic vehicles against unknown pursuer dynamics

2021 ◽  
Author(s):  
Tian Yan ◽  
Yuanli Cai ◽  
Bin Xu
Keyword(s):  
Parameter Estimation ◽  
Gradient Descent ◽  
Rapid Development ◽  
Energy Optimization ◽  
Hypersonic Vehicles ◽  
Air Breathing ◽  
Related Research ◽  
Practical Guidance ◽  
Simulation Results ◽  
Guidance Algorithm

AbstractThe rapid development of hypersonic vehicles has motivated the related research dramatically while the evasion of the hypersonic vehicles becomes one of the challenging issues. Different from the work based on the premise that the pursuers’ information is fully known, in this paper the evasion guidance for air-breathing hypersonic vehicles (AHVs) against unknown pursuer dynamics is studied. The gradient descent is employed for parameter estimation of the unknown dynamics of the pursuer. The energy-optimized evasion guidance algorithm is further developed by taking the acceleration constraint and energy optimization into consideration. Under the proposed algorithm, the system can deal with the unknown pursuer dynamics effectively and provide more practical guidance for the evasion process. The simulation results show that the proposed method can enable the AHV to achieve successful evasion.

scholarly journals A Tool for the Analysis and Characterization of School Mathematical Models

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1569
Author(s):  
Jesús Montejo-Gámez ◽  
Elvira Fernández-Ahumada ◽  
Natividad Adamuz-Povedano
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Models ◽  
Educational Research ◽  
Analysis Procedure ◽  
Real System ◽  
The Real ◽  
School Model ◽  
Corresponding Analysis ◽  
Three Components

This paper shows a tool for the analysis of written productions that allows for the characterization of the mathematical models that students develop when solving modeling tasks. For this purpose, different conceptualizations of mathematical models in education are discussed, paying special attention to the evidence that characterizes a school model. The discussion leads to the consideration of three components, which constitute the main categories of the proposed tool: the real system to be modeled, its mathematization and the representations used to express both. These categories and the corresponding analysis procedure are explained and illustrated through two working examples, which expose the value of the tool in establishing the foci of analysis when investigating school models, and thus, suggest modeling skills. The connection of this tool with other approaches to educational research on mathematical modeling is also discussed.

Call for Manuscripts for the 2015 Focus Issue: Mathematical Modeling

2013 ◽  
Vol 18 (9) ◽  
pp. 571
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Models ◽  
Real World ◽  
The Real

This call for manuscripts is requesting articles that address how to use mathematical models to analyze, predict, and resolve issues arising in the real world.

A RELAX Based Method for Spotlight SAR Imaging

2012 ◽  
Vol 500 ◽  
pp. 362-367
Author(s):  
Xiao Zhen Ren ◽  
Yao Qin ◽  
Hong Liang Fu
Keyword(s):  
Parameter Estimation ◽  
Estimation Problem ◽  
Noisy Environment ◽  
Parameter Estimation Problem ◽  
Imaging Algorithm ◽  
Imaging Results ◽  
Sar Imaging ◽  
Simulation Results ◽  
Noisy Condition

The imaging problem of spotlight SAR is converted to a parameter estimation problem of several monochromatic signals in additive white Gaussian noisy condition in this paper. Moreover, a spotlight SAR imaging algorithm based on RELAX is presented in detail. Traditional polar format algorithm and the presented method are applied to spotlight SAR imaging respectively, and the imaging results are compared. Simulation results show that the polar format algorithm doesn’t give satisfactory imaging results, while the proposed method adapts the noisy environment better and obtains better results.

Methods of Mathematical Modeling of the Leaching Process of Cobalt-Containing Solutions

2021 ◽  
Vol 316 ◽  
pp. 661-666
Author(s):  
Nataliya V. Mokrova
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Chemical Kinetics ◽  
Group Method ◽  
Data Handling ◽  
Multistage Processes ◽  
Leaching Process ◽  
Proposed Model ◽  
Simulation Results ◽  
The Mathematical Model

Current cobalt processing practices are described. This article discusses the advantages of the group argument accounting method for mathematical modeling of the leaching process of cobalt solutions. Identification of the mathematical model of the cascade of reactors of cobalt-producing is presented. Group method of data handling is allowing: to eliminate the need to calculate quantities of chemical kinetics; to get the opportunity to take into account the results of mixed experiments; to exclude the influence of random interference on the simulation results. The proposed model confirms the capabilities of the group method of data handling for describing multistage processes.

Mathematical Alternatives to Standard Probability that Provide Selectable Degrees of Precision

2017 ◽  
Author(s):  
Terrence Fine
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Models ◽  
Theory Of Measurement ◽  
Belief Functions ◽  
Standard Practice ◽  
Mathematical Probability ◽  
Comparative Probability ◽  
The Relationship ◽  
Standard Probability

This chapter challenges the nearly universal reliance upon standard mathematical probability for mathematical modeling of chance and uncertain phenomena, and offers four alternatives. In standard practice, precise assignments are made inappropriately, even to the occurrences of events that may be unobservable in principle. Four familiar examples of chance or uncertain phenomena are discussed, about which this is true. The theory of measurement provides an understanding of the relationship between the accuracy of information and the precision with which the phenomenon under examination should be modeled mathematically. The model of modal or classificatory probability offers the least precision. Comparative probability, plausibility/belief functions and upper/lower probabilities are carefully considered. The selectable precision of these alternative mathematical models of chance and uncertainty makes for an improved range of levels of accuracy in modeling the empirical domain phenomena of chance, uncertainty, and indeterminacy. Knowledge of such models encourages further thought in this direction.

Fractal analysis and control of the competition model

2016 ◽  
Vol 09 (03) ◽  
pp. 1650045 ◽  
Author(s):  
Mianmian Zhang ◽  
Yongping Zhang
Keyword(s):  
Feedback Control ◽  
Mathematical Models ◽  
Fractal Analysis ◽  
Fractal Geometry ◽  
Julia Set ◽  
Julia Sets ◽  
Competition Model ◽  
Simulation Results ◽  
Population Competition ◽  
And Control

Lotka–Volterra population competition model plays an important role in mathematical models. In this paper, Julia set of the competition model is introduced by use of the ideas and methods of Julia set in fractal geometry. Then feedback control is taken on the Julia set of the model. And synchronization of two different Julia sets of the model with different parameters is discussed, which makes one Julia set change to be another. The simulation results show the efficacy of these methods.

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