Learn to Integrate Mathematical Models in Human Performance Modeling

2017 ◽  
Vol 61 (1) ◽  
pp. 776-780 ◽  
Author(s):  
Yiqi Zhang ◽  
Changxu Wu
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Mathematical Models ◽  
Human Performance ◽  
Performance Modeling ◽  
Model Integration ◽  
Braking Performance ◽  
Research Gap ◽  
Warning Response

The current paper provided a tutorial of the integration of mathematical models in human performance modeling. It introduced the unique features of mathematical modeling in human performance, and the steps in mathematical model integration, including how the literature of models was reviewed, how a research gap was identified, and how a mathematical model was developed and integrated based on existing models, and how a model was validated via an experimental study. A case study was presented by following each step to illustrate the integration of several existing models to derive a new model of drivers’ braking performance in warning response with its integration with the existing mathematical models of driver speed control in normal situations and the model of humans’ warning response time. This is the first tutorial work that provided a detailed explanation of the steps in mathematical model integration with a case study in human performance modeling. It could be used as guidance for human factors professionals to learn the mathematical modeling approaches and will benefit the field of human performance modeling.

Human performance modeling: A case study

2010 ◽  
Vol 49 (8) ◽  
pp. 36-41 ◽  
Author(s):  
Jerry L. Harbour
Keyword(s):  
Human Performance ◽  
Performance Modeling

scholarly journals Applied Mathematical Approach for Decision-Making in Building Plan Design

2018 ◽  
Vol 3 (9) ◽  
pp. 39
Author(s):  
Grit Ngowtanasuwan
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Publishing House ◽  
Unit Cost ◽  
Construction Cost ◽  
Model Unit ◽  
International Publishing ◽  
Plan Design ◽  
The Mathematical Model

This article presents a method for solving decision in building plan design by using a mathematical model (nonlinear programming). First objective is to formulate mathematical models for analysis in dividing rooms and dimensions in a building plan. Secondly, to calculate the dimensions and room sizes which have minimum construction cost. A case study of a condominium building plan was analyzed in this research. The results found application of the mathematical model was applicable. The mathematical models were formulated, the minimum construction cost was ฿723,000 (US$24,100) and usable area in the condominium was 67.5 m2 and followed the assigned design constraints.Keywords: Building plan design; Mathematical model; Unit cost;eISSN 2398-4295 © 2018. The Authors. Published for AMER ABRA cE-Bs by e-International Publishing House, Ltd., UK. This is an open-access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer–review under responsibility of AMER (Association of Malaysian Environment-Behaviour Researchers), ABRA (Association of Behavioural Researchers on Asians) and cE-Bs (Centre for Environment-Behaviour Studies), Faculty of Architecture, Planning & Surveying, Universiti Teknologi MARA, Malaysia. DOI:

scholarly journals Countering reproducibility issues in mathematical models with software engineering techniques: A case study using a one-dimensional mathematical model of the atrioventricular node

PLoS ONE ◽  
2021 ◽  
Vol 16 (7) ◽  
pp. e0254749
Author(s):  
Christopher Schölzel ◽  
Valeria Blesius ◽  
Gernot Ernst ◽  
Alexander Goesmann ◽  
Andreas Dominik
Keyword(s):  
Mathematical Model ◽  
Software Engineering ◽  
Mathematical Models ◽  
Modular Design ◽  
Atrioventricular Node ◽  
Unit Testing ◽  
Development Environment ◽  
One Dimensional ◽  
Model Code

One should assume that in silico experiments in systems biology are less susceptible to reproducibility issues than their wet-lab counterparts, because they are free from natural biological variations and their environment can be fully controlled. However, recent studies show that only half of the published mathematical models of biological systems can be reproduced without substantial effort. In this article we examine the potential causes for failed or cumbersome reproductions in a case study of a one-dimensional mathematical model of the atrioventricular node, which took us four months to reproduce. The model demonstrates that even otherwise rigorous studies can be hard to reproduce due to missing information, errors in equations and parameters, a lack in available data files, non-executable code, missing or incomplete experiment protocols, and missing rationales behind equations. Many of these issues seem similar to problems that have been solved in software engineering using techniques such as unit testing, regression tests, continuous integration, version control, archival services, and a thorough modular design with extensive documentation. Applying these techniques, we reimplement the examined model using the modeling language Modelica. The resulting workflow is independent of the model and can be translated to SBML, CellML, and other languages. It guarantees methods reproducibility by executing automated tests in a virtual machine on a server that is physically separated from the development environment. Additionally, it facilitates results reproducibility, because the model is more understandable and because the complete model code, experiment protocols, and simulation data are published and can be accessed in the exact version that was used in this article. We found the additional design and documentation effort well justified, even just considering the immediate benefits during development such as easier and faster debugging, increased understandability of equations, and a reduced requirement for looking up details from the literature.

scholarly journals Mathematical modeling in economics for selection of optimum investment solution

2021 ◽  
Vol 273 ◽  
pp. 08003
Author(s):  
Arthur Alukhanyan ◽  
Olga Panfilova
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Linear Programming ◽  
Mathematical Models ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Target Function ◽  
Investment Portfolio ◽  
Monetary Relations ◽  
Selection Of

This work is devoted to development of economic and mathematical models for selection of the optimum investment solution. Moreover, it states the basis for development of model examples and correction of the model considering the results obtained in the examples. In the work the problem is set for selection of the investment sources and objects, which is limited to the linear programming problem. The controlled variable and basic limitations simulating real credit and monetary relations are distinguished in the provided model. The discounted profit obtained from implementation of the optimum investment portfolio is considered as a target function. The economic and mathematical model presented in the article allows finding the optimum investment solution within the limits of the credit and monetary relations taking place both at the micro- and macroeconomic level.

Mathematical Modeling of the Anaerobic Filter Process

1983 ◽  
Vol 15 (8-9) ◽  
pp. 197-207 ◽  
Author(s):  
M Lindgren
Keyword(s):  
Mathematical Modeling ◽  
Waste Water ◽  
Mathematical Model ◽  
Mathematical Models ◽  
Efficient Tool ◽  
Anaerobic Filter ◽  
Filter Process

A dilute synthetic waste water was anaerobica1ly treated in a filter. A mathematical model of the anaerobic filter process was also developed and analyzed. Analysis showed that mathematical models are an efficient tool for system understanding and design.

scholarly journals A Mathematical Model for Top Nutation Based on Inertial Forces of Distributed Masses

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Ryspek Usubamatov ◽  
Albina Omorova
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Angular Momentum ◽  
Mathematical Models ◽  
Vibration Analysis ◽  
Analytical Approach ◽  
Main Property ◽  
Inertial Forces ◽  
Applied Torque ◽  
Dynamics And Vibration

The main property of gyroscopic devices is maintaining the axis of a spinning rotor, a mathematical model formulated on the principle of the change in the angular momentum. This principle is used for mathematical modeling of the motions of a top at known publications. Nevertheless, practical tests of gyroscopic devices do not correspond to this analytical approach. Recent investigations have demonstrated that the origin of gyroscope properties is more complex than that represented in known publications. The applied torque on a gyroscope produces internal torques of the spinning rotor based on the action of the several inertial forces. These forces are the centrifugal, Coriolis, and common inertial forces as well as the change in the angular momentum generated by the mass elements and center-mass of the spinning rotor. The action of these torques manifests itself in the resistance and precession torques of the gyroscopic devices. These inertial torques act simultaneously and interdependently around two axes and represent the fundamental principles of the gyroscope theory. The new inertial torques enable deriving mathematical models for the motions of well-known top that is the simplest form of gyroscopic devices. The novelty of the work is mathematical models for the motions of the top based on action of eight inertial forces acting around its two axes. The obtained mathematical models for the top nutation and self-stabilization are represented in terms of machine dynamics and vibration analysis. The new analytical approach for motions of the well-balanced top and top with eccentricity of the center-mass definitely responds to the practical results.

Mathematical Modeling of Biofilms

1997 ◽  
Vol 11 (1) ◽  
pp. 127-132 ◽  
Author(s):  
George H. Dibdin
Keyword(s):  
Mathematical Modeling ◽  
Complex System ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Mathematical Models ◽  
Diffusion Coefficients ◽  
Theoretical Basis ◽  
Reversible Reaction ◽  
Mathematical Equations ◽  
Insight Into

A set of mathematical equations constitutes a mathematical model if it aims to represent a real system and is based on some theory of that system's operation. On this definition, mathematical models, some very simple, are everywhere in science. A complex system like a biofilm requires modeling by numerical methods and, because of inevitable uncertainties in its theoretical basis, may not be able to make precise predictions. Nevertheless, such models almost always give new insight into the mechanisms involved, and stimulate further investigation. The way in which diffusion coefficients are measured for use in a model, particularly whether they include effects of reversible reaction, is a key element in the modeling. Reasons are given for separating diffusion from reversible reaction effects and dealing with them in a separate subroutine of the model.

Modeling Human Performance with Environmental Stressors: A Case Study of the Effect of Vehicle Motion

2007 ◽  
Vol 51 (12) ◽  
pp. 780-783
Author(s):  
Josephine Q. Wojciechowski
Keyword(s):  
Human Performance ◽  
Performance Modeling ◽  
Environmental Stressors ◽  
Modeling Tools ◽  
Moving Vehicle ◽  
Task Time ◽  
Improved Performance ◽  
And Performance ◽  
The Impact

Human performance modeling tools are used to predict mission performance as a function of human performance. The U.S. Army Research Laboratory has developed a human performance modeling tool, the Improved Performance Research Integration Tool (IMPRINT), for investigation of the impact on a Soldier's performance when the Soldier subjected to environmental stressors such as heat and cold. IMPRINT has the capability to create user-defined stressors to study the stressors' effect on human performance and therefore system performance. This case study used data from literature to create a user-defined stressor in IMPRINT to predict the effect of riding in a moving vehicle on task time and performance. This capability can provide useful information to system designers.

scholarly journals Mathematical Modeling to Perform an Analysis of Social Isolation Periods in the Dissemination of COVID-19

2021 ◽  
Vol 22 (4) ◽  
pp. 595-608
Author(s):  
A. Molter ◽  
R. S. Quadros ◽  
M. Rafikov ◽  
D. Buske ◽  
G. A. Gonçalves
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Mathematical Models ◽  
Social Isolation ◽  
Computer Simulations ◽  
The Other ◽  
Stable Level ◽  
The Social ◽  
The World ◽  
Second Peak

The outbreak of COVID-19 has made scientists from all over the world do not measureefforts to understand the dynamics of the disease caused by this coronavirus. Several mathematical models have been proposed to describe the dynamics and make predictions. This work proposes a mathematical model that includes social isolation of susceptible individuals as a strategy of suppression and mitigation of the disease. The Susceptible-Infectious-Isolated-Recovered-Dead (SIQRD) model is proposed to analyze three important issues about the dynamics of the disease taking into account social isolation: when the isolation should begin? How long to keep the isolation? How to get out of this isolation? To get answers, computer simulations are provided and their results discussed. The results obtained show that beginning social isolation on the 10th or 15th days, after confirmation of the 50th case, and with 70% of the population in isolation, seems to be promising, since the infected curve does not grow much until it enters the isolation and remains at a stable level during the isolation. On the other hand an abrupt release of the social isolation will imply a second peak of infected individuals above the first one, which is not desired. Therefore, the release from social isolation should be gradual.

scholarly journals METHODOLOGY OF DEVELOPMENT OF MATHEMATICAL MODELS OF INFORMATION PROCESSING SYSTEMS

2021 ◽  
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Information System ◽  
Information Processing ◽  
Mathematical Models ◽  
System Approach ◽  
Research Method ◽  
Literary Sources ◽  
History Of ◽  
The Mathematical Model

Modeling as a research method is a powerful cognitive tool throughout the history of human development. The article describes the methodology for the development of mathematical models of information systems, based on materials from various literary sources, author's developments on the system approach, mathematical modeling and programming. The mathematical model of the information system is described and all the characteristics of the IS are given.

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