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

2021 ◽  
Author(s):  
Christopher Schölzel ◽  
Valeria Blesius ◽  
Gernot Ernst ◽  
Alexander Goesmann ◽  
Andreas Dominik
Keyword(s):  
Mathematical Model ◽  
Software Engineering ◽  
Mathematical Models ◽  
Biological Systems ◽  
Atrioventricular Node ◽  
Version Control ◽  
Mathematical Representation ◽  
Missing Information ◽  
One Dimensional

AbstractOne 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 features almost all common types of reproducibility issues including missing information, errors in equations and parameters, a lack in available data files, non-executable code, missing or incomplete experiment protocols, and missing semantic information about the rationale behind equations. Many of these issues seem similar to problems that have already 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 can be applied to any mathematical model. 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. While the increased attention to design aspects and documentation required considerable effort, we found it 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.Author summaryReproducibility is one of the cornerstones of the scientific method. In order to draw reliable conclusions, an experiment must yield the same results when it is repeated using the same methods. However, biological systems are complex, which makes experiments cumbersome. It is therefore desirable to build a mathematical representation of the biological system, which captures its essential behavior in a set of variables and equations and allows for easier and faster experimentation. Unfortunately, recent studies have shown that half of the published mathematical models are not immediately reproducible due to missing information, mathematical errors, and incomplete documentation. These issues are similar to those faced in software engineering: A single missing file or a buggy line of code can render any kind of software useless. Software engineering has turned to rigorous software testing, automated development pipelines, and version control systems to overcome these challenges, but these techniques are not yet widely applied to mathematical modeling. In this paper we demonstrate their benefit for the reproducibility of a large mathematical model of the atrioventricular node. The software engineering solutions that we employ can be applied to any mathematical model and could therefore facilitate scientific progress by encouraging and simplifying model reuse.

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 PIPELINE ROBOTS WITH ELASTIC ELEMENTS

Transport ◽  
2002 ◽  
Vol 17 (5) ◽  
pp. 177-181 ◽  
Author(s):  
Arvydas Matuliauskas ◽  
Bronislovas Spruogis
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Degrees Of Freedom ◽  
Vibration Exciter ◽  
Motion Equations ◽  
Two Degrees Of Freedom ◽  
One Dimensional ◽  
The Mathematical Model ◽  
Original Construction ◽  
Elastic Elements

In the article constructions of the pipeline robots with elastic elements are reviewed and the scheme of new original construction is presented. The mathematical models of a robot with one-dimensional vibration exciter with two degrees of freedom were developed and the equations of movement were formed and written. The mathematical model of the pipeline robot with circular elements is formed and its motion equations are presented.

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.

DATA MINING FOR PREDICTORS OF SOFTWARE QUALITY

1999 ◽  
Vol 09 (05) ◽  
pp. 547-563 ◽  
Author(s):  
TAGHI M. KHOSHGOFTAAR ◽  
EDWARD B. ALLEN ◽  
WENDELL D. JONES ◽  
JOHN P. HUDEPOHL
Keyword(s):  
Software Engineering ◽  
Software Development ◽  
Software Quality ◽  
Configuration Management ◽  
Data Bases ◽  
Development Environment ◽  
Quality Modeling ◽  
Problem Reporting ◽  
Misclassification Rates

"Knowledge discovery in data bases" (KDD) for software engineering is a process for finding useful information in the large volumes of data that are a byproduct of software development, such as data bases for configuration management and for problem reporting. This paper presents guidelines for extracting innovative process metrics from these commonly available data bases. This paper also adapts the Classification And Regression Trees algorithm, CART, to the KDD process for software engineering data. To our knowledge, this algorithm has not been used previously for empirical software quality modeling. In particular, we present an innovative way to control the balance between misclassification rates. A KDD case study of a very large legacy telecommunications software system found that variables derived from source code, configuration management transactions, and problem reporting transactions can be useful predictors of software quality. The KDD process discovered that for this software development environment, out of forty software attributes, only a few of the predictor variables were significant. This resulted in a model that predicts whether modules are likely to have faults discovered by customers. Software developers need such predictions early in development to target software enhancement techniques to the modules that need improvement the most.

On the Big-R Notation for Describing Iterative and Recursive Behaviors

2011 ◽  
pp. 292-307
Author(s):  
Yingxu Wang
Keyword(s):  
Mathematical Model ◽  
Software Engineering ◽  
Mathematical Models ◽  
Programming Languages ◽  
Real Time ◽  
Mathematical Treatment ◽  
Time Process ◽  
Control Structures ◽  
Fundamental Properties ◽  
The Mathematical Model

Iterative and recursive control structures are the most fundamental mechanisms of computing that make programming more effective and expressive. However, these constructs are perhaps the most diverse and confusable instructions in programming languages at both syntactic and semantic levels. This article introduces the big-R notation that provides a unifying mathematical treatment of iterations and recursions in computing. Mathematical models of iterations and recursions are developed using logical inductions. Based on the mathematical model of the big-R notation, fundamental properties of iterative and recursive behaviors of software are comparatively analyzed. The big-R notation has been adopted and implemented in Real-Time Process Algebra (RTPA) and its supporting tools. Case studies demonstrate that a convenient notation may dramatically reduce the difficulty and complexity in expressing a frequently used and highly recurring concept and notion in computing and software engineering.

A mathematical model of biological resource dynamics, using Caspian/Ural sturgeon as a case study

2007 ◽  
Vol 65 (1) ◽  
pp. 103-110
Author(s):  
Mars B. Gabbasov ◽  
Nurbolat Zh. Jaichibekov ◽  
Daniel V. Lebedev
Keyword(s):  
Mathematical Model ◽  
Population Dynamics ◽  
Mathematical Models ◽  
Caspian Basin ◽  
Biological Parameters ◽  
Biological Resource ◽  
Graphic Form ◽  
Management Application ◽  
Resource Dynamics

Abstract Gabbasov, M. B., Jaichibekov, N. Zh., and Lebedev, D. V. 2008. A mathematical model of biological resource dynamics, using Caspian/Ural sturgeon as a case study. – ICES Journal of Marine Science, 65: 103–110. Some of the general principles involved in constructing mathematical models of biological resource dynamics are presented along with some of the requirements of such models for them to have value in terms of management application. A case study of sturgeon population dynamics in the Caspian Basin, using physical and biological parameters, is used to show theoretically how such a model can be developed and applied. The results of the case study are presented in graphic form, and the influence of different processes on the outcome of the calculation is discussed.

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