Sample records for accurate mathematical models

  1. Simple Mathematical Models Do Not Accurately Predict Early SIV Dynamics

    PubMed Central

    Noecker, Cecilia; Schaefer, Krista; Zaccheo, Kelly; Yang, Yiding; Day, Judy; Ganusov, Vitaly V.

    2015-01-01

    Upon infection of a new host, human immunodeficiency virus (HIV) replicates in the mucosal tissues and is generally undetectable in circulation for 1–2 weeks post-infection. Several interventions against HIV including vaccines and antiretroviral prophylaxis target virus replication at this earliest stage of infection. Mathematical models have been used to understand how HIV spreads from mucosal tissues systemically and what impact vaccination and/or antiretroviral prophylaxis has on viral eradication. Because predictions of such models have been rarely compared to experimental data, it remains unclear which processes included in these models are critical for predicting early HIV dynamics. Here we modified the “standard” mathematical model of HIV infection to include two populations of infected cells: cells that are actively producing the virus and cells that are transitioning into virus production mode. We evaluated the effects of several poorly known parameters on infection outcomes in this model and compared model predictions to experimental data on infection of non-human primates with variable doses of simian immunodifficiency virus (SIV). First, we found that the mode of virus production by infected cells (budding vs. bursting) has a minimal impact on the early virus dynamics for a wide range of model parameters, as long as the parameters are constrained to provide the observed rate of SIV load increase in the blood of infected animals. Interestingly and in contrast with previous results, we found that the bursting mode of virus production generally results in a higher probability of viral extinction than the budding mode of virus production. Second, this mathematical model was not able to accurately describe the change in experimentally determined probability of host infection with increasing viral doses. Third and finally, the model was also unable to accurately explain the decline in the time to virus detection with increasing viral dose. These results

  2. Mathematical models of cell motility.

    PubMed

    Flaherty, Brendan; McGarry, J P; McHugh, P E

    2007-01-01

    Cell motility is an essential biological action in the creation, operation and maintenance of our bodies. Developing mathematical models elucidating cell motility will greatly advance our understanding of this fundamental biological process. With accurate models it is possible to explore many permutations of the same event and concisely investigate their outcome. While great advancements have been made in experimental studies of cell motility, it now has somewhat fallen on mathematical models to taking a leading role in future developments. The obvious reason for this is the complexity of cell motility. Employing the processing power of today's computers will give researches the ability to run complex biophysical and biochemical scenarios, without the inherent difficulty and time associated with in vitro investigations. Before any great advancement can be made, the basics of cell motility will have to be well-defined. Without this, complicated mathematical models will be hindered by their inherent conjecture. This review will look at current mathematical investigations of cell motility, explore the reasoning behind such work and conclude with how best to advance this interesting and challenging research area.

  3. Mathematical Modeling and Pure Mathematics

    ERIC Educational Resources Information Center

    Usiskin, Zalman

    2015-01-01

    Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…

  4. Mathematical Modelling Approach in Mathematics Education

    ERIC Educational Resources Information Center

    Arseven, Ayla

    2015-01-01

    The topic of models and modeling has come to be important for science and mathematics education in recent years. The topic of "Modeling" topic is especially important for examinations such as PISA which is conducted at an international level and measures a student's success in mathematics. Mathematical modeling can be defined as using…

  5. Mathematical modeling in realistic mathematics education

    NASA Astrophysics Data System (ADS)

    Riyanto, B.; Zulkardi; Putri, R. I. I.; Darmawijoyo

    2017-12-01

    The purpose of this paper is to produce Mathematical modelling in Realistics Mathematics Education of Junior High School. This study used development research consisting of 3 stages, namely analysis, design and evaluation. The success criteria of this study were obtained in the form of local instruction theory for school mathematical modelling learning which was valid and practical for students. The data were analyzed using descriptive analysis method as follows: (1) walk through, analysis based on the expert comments in the expert review to get Hypothetical Learning Trajectory for valid mathematical modelling learning; (2) analyzing the results of the review in one to one and small group to gain practicality. Based on the expert validation and students’ opinion and answers, the obtained mathematical modeling problem in Realistics Mathematics Education was valid and practical.

  6. Annual Perspectives in Mathematics Education 2016: Mathematical Modeling and Modeling Mathematics

    ERIC Educational Resources Information Center

    Hirsch, Christian R., Ed.; McDuffie, Amy Roth, Ed.

    2016-01-01

    Mathematical modeling plays an increasingly important role both in real-life applications--in engineering, business, the social sciences, climate study, advanced design, and more--and within mathematics education itself. This 2016 volume of "Annual Perspectives in Mathematics Education" ("APME") focuses on this key topic from a…

  7. Mathematical and Numerical Techniques in Energy and Environmental Modeling

    NASA Astrophysics Data System (ADS)

    Chen, Z.; Ewing, R. E.

    Mathematical models have been widely used to predict, understand, and optimize many complex physical processes, from semiconductor or pharmaceutical design to large-scale applications such as global weather models to astrophysics. In particular, simulation of environmental effects of air pollution is extensive. Here we address the need for using similar models to understand the fate and transport of groundwater contaminants and to design in situ remediation strategies. Three basic problem areas need to be addressed in the modeling and simulation of the flow of groundwater contamination. First, one obtains an effective model to describe the complex fluid/fluid and fluid/rock interactions that control the transport of contaminants in groundwater. This includes the problem of obtaining accurate reservoir descriptions at various length scales and modeling the effects of this heterogeneity in the reservoir simulators. Next, one develops accurate discretization techniques that retain the important physical properties of the continuous models. Finally, one develops efficient numerical solution algorithms that utilize the potential of the emerging computing architectures. We will discuss recent advances and describe the contribution of each of the papers in this book in these three areas. Keywords: reservoir simulation, mathematical models, partial differential equations, numerical algorithms

  8. Antioxidant Capacity: Experimental Determination by EPR Spectroscopy and Mathematical Modeling.

    PubMed

    Polak, Justyna; Bartoszek, Mariola; Chorążewski, Mirosław

    2015-07-22

    A new method of determining antioxidant capacity based on a mathematical model is presented in this paper. The model was fitted to 1000 data points of electron paramagnetic resonance (EPR) spectroscopy measurements of various food product samples such as tea, wine, juice, and herbs with Trolox equivalent antioxidant capacity (TEAC) values from 20 to 2000 μmol TE/100 mL. The proposed mathematical equation allows for a determination of TEAC of food products based on a single EPR spectroscopy measurement. The model was tested on the basis of 80 EPR spectroscopy measurements of herbs, tea, coffee, and juice samples. The proposed model works for both strong and weak antioxidants (TEAC values from 21 to 2347 μmol TE/100 mL). The determination coefficient between TEAC values obtained experimentally and TEAC values calculated with proposed mathematical equation was found to be R(2) = 0.98. Therefore, the proposed new method of TEAC determination based on a mathematical model is a good alternative to the standard EPR method due to its being fast, accurate, inexpensive, and simple to perform.

  9. Teaching Mathematical Modeling in Mathematics Education

    ERIC Educational Resources Information Center

    Saxena, Ritu; Shrivastava, Keerty; Bhardwaj, Ramakant

    2016-01-01

    Mathematics is not only a subject but it is also a language consisting of many different symbols and relations. Taught as a compulsory subject up the 10th class, students are then able to choose whether or not to study mathematics as a main subject. The present paper discusses mathematical modeling in mathematics education. The article provides…

  10. Using Mathematics, Mathematical Applications, Mathematical Modelling, and Mathematical Literacy: A Theoretical Study

    ERIC Educational Resources Information Center

    Mumcu, Hayal Yavuz

    2016-01-01

    The purpose of this theoretical study is to explore the relationships between the concepts of using mathematics in the daily life, mathematical applications, mathematical modelling, and mathematical literacy. As these concepts are generally taken as independent concepts in the related literature, they are confused with each other and it becomes…

  11. Rigorous mathematical modelling for a Fast Corrector Power Supply in TPS

    NASA Astrophysics Data System (ADS)

    Liu, K.-B.; Liu, C.-Y.; Chien, Y.-C.; Wang, B.-S.; Wong, Y. S.

    2017-04-01

    To enhance the stability of beam orbit, a Fast Orbit Feedback System (FOFB) eliminating undesired disturbances was installed and tested in the 3rd generation synchrotron light source of Taiwan Photon Source (TPS) of National Synchrotron Radiation Research Center (NSRRC). The effectiveness of the FOFB greatly depends on the output performance of Fast Corrector Power Supply (FCPS); therefore, the design and implementation of an accurate FCPS is essential. A rigorous mathematical modelling is very useful to shorten design time and improve design performance of a FCPS. A rigorous mathematical modelling derived by the state-space averaging method for a FCPS in the FOFB of TPS composed of a full-bridge topology is therefore proposed in this paper. The MATLAB/SIMULINK software is used to construct the proposed mathematical modelling and to conduct the simulations of the FCPS. Simulations for the effects of the different resolutions of ADC on the output accuracy of the FCPS are investigated. A FCPS prototype is realized to demonstrate the effectiveness of the proposed rigorous mathematical modelling for the FCPS. Simulation and experimental results show that the proposed mathematical modelling is helpful for selecting the appropriate components to meet the accuracy requirements of a FCPS.

  12. Mathematical Modeling in Mathematics Education: Basic Concepts and Approaches

    ERIC Educational Resources Information Center

    Erbas, Ayhan Kürsat; Kertil, Mahmut; Çetinkaya, Bülent; Çakiroglu, Erdinç; Alacaci, Cengiz; Bas, Sinem

    2014-01-01

    Mathematical modeling and its role in mathematics education have been receiving increasing attention in Turkey, as in many other countries. The growing body of literature on this topic reveals a variety of approaches to mathematical modeling and related concepts, along with differing perspectives on the use of mathematical modeling in teaching and…

  13. Mathematical model for gyroscope effects

    NASA Astrophysics Data System (ADS)

    Usubamatov, Ryspek

    2015-05-01

    Gyroscope effects are used in many engineering calculations of rotating parts, and a gyroscope is the basic unit of numerous devices and instruments used in aviation, space, marine and other industries. The primary attribute of a gyroscope is a spinning rotor that persists in maintaining its plane of rotation, creating gyroscope effects. Numerous publications represent the gyroscope theory using mathematical models based on the law of kinetic energy conservation and the rate of change in angular momentum of a spinning rotor. Gyroscope theory still attracts many researchers who continue to discover new properties of gyroscopic devices. In reality, gyroscope effects are more complex and known mathematical models do not accurately reflect the actual motions. Analysis of forces acting on a gyroscope shows that four dynamic components act simultaneously: the centrifugal, inertial and Coriolis forces and the rate of change in angular momentum of the spinning rotor. The spinning rotor generates a rotating plane of centrifugal and Coriols forces that resist the twisting of the spinning rotor with external torque applied. The forced inclination of the spinning rotor generates inertial forces, resulting in precession torque of a gyroscope. The rate of change of the angular momentum creates resisting and precession torques which are not primary one in gyroscope effects. The new mathematical model for the gyroscope motions under the action of the external torque applied can be as base for new gyroscope theory. At the request of the author of the paper, this corrigendum was issued on 24 May 2016 to correct an incomplete Table 1 and errors in Eq. (47) and Eq. (48).

  14. A Weibull statistics-based lignocellulose saccharification model and a built-in parameter accurately predict lignocellulose hydrolysis performance.

    PubMed

    Wang, Mingyu; Han, Lijuan; Liu, Shasha; Zhao, Xuebing; Yang, Jinghua; Loh, Soh Kheang; Sun, Xiaomin; Zhang, Chenxi; Fang, Xu

    2015-09-01

    Renewable energy from lignocellulosic biomass has been deemed an alternative to depleting fossil fuels. In order to improve this technology, we aim to develop robust mathematical models for the enzymatic lignocellulose degradation process. By analyzing 96 groups of previously published and newly obtained lignocellulose saccharification results and fitting them to Weibull distribution, we discovered Weibull statistics can accurately predict lignocellulose saccharification data, regardless of the type of substrates, enzymes and saccharification conditions. A mathematical model for enzymatic lignocellulose degradation was subsequently constructed based on Weibull statistics. Further analysis of the mathematical structure of the model and experimental saccharification data showed the significance of the two parameters in this model. In particular, the λ value, defined the characteristic time, represents the overall performance of the saccharification system. This suggestion was further supported by statistical analysis of experimental saccharification data and analysis of the glucose production levels when λ and n values change. In conclusion, the constructed Weibull statistics-based model can accurately predict lignocellulose hydrolysis behavior and we can use the λ parameter to assess the overall performance of enzymatic lignocellulose degradation. Advantages and potential applications of the model and the λ value in saccharification performance assessment were discussed. Copyright © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  15. Mathematical, Constitutive and Numerical Modelling of Catastrophic Landslides and Related Phenomena

    NASA Astrophysics Data System (ADS)

    Pastor, M.; Fernández Merodo, J. A.; Herreros, M. I.; Mira, P.; González, E.; Haddad, B.; Quecedo, M.; Tonni, L.; Drempetic, V.

    2008-02-01

    Mathematical and numerical models are a fundamental tool for predicting the behaviour of geostructures and their interaction with the environment. The term “mathematical model” refers to a mathematical description of the more relevant physical phenomena which take place in the problem being analyzed. It is indeed a wide area including models ranging from the very simple ones for which analytical solutions can be obtained to those more complicated requiring the use of numerical approximations such as the finite element method. During the last decades, mathematical, constitutive and numerical models have been very much improved and today their use is widespread both in industry and in research. One special case is that of fast catastrophic landslides, for which simplified methods are not able to provide accurate solutions in many occasions. Moreover, many finite element codes cannot be applied for propagation of the mobilized mass. The purpose of this work is to present an overview of the different alternative mathematical and numerical models which can be applied to both the initiation and propagation mechanisms of fast catastrophic landslides and other related problems such as waves caused by landslides.

  16. Mathematization Competencies of Pre-Service Elementary Mathematics Teachers in the Mathematical Modelling Process

    ERIC Educational Resources Information Center

    Yilmaz, Suha; Tekin-Dede, Ayse

    2016-01-01

    Mathematization competency is considered in the field as the focus of modelling process. Considering the various definitions, the components of the mathematization competency are determined as identifying assumptions, identifying variables based on the assumptions and constructing mathematical model/s based on the relations among identified…

  17. Mathematical-Artificial Neural Network Hybrid Model to Predict Roll Force during Hot Rolling of Steel

    NASA Astrophysics Data System (ADS)

    Rath, S.; Sengupta, P. P.; Singh, A. P.; Marik, A. K.; Talukdar, P.

    2013-07-01

    Accurate prediction of roll force during hot strip rolling is essential for model based operation of hot strip mills. Traditionally, mathematical models based on theory of plastic deformation have been used for prediction of roll force. In the last decade, data driven models like artificial neural network have been tried for prediction of roll force. Pure mathematical models have accuracy limitations whereas data driven models have difficulty in convergence when applied to industrial conditions. Hybrid models by integrating the traditional mathematical formulations and data driven methods are being developed in different parts of world. This paper discusses the methodology of development of an innovative hybrid mathematical-artificial neural network model. In mathematical model, the most important factor influencing accuracy is flow stress of steel. Coefficients of standard flow stress equation, calculated by parameter estimation technique, have been used in the model. The hybrid model has been trained and validated with input and output data collected from finishing stands of Hot Strip Mill, Bokaro Steel Plant, India. It has been found that the model accuracy has been improved with use of hybrid model, over the traditional mathematical model.

  18. A mathematical model of insulin resistance in Parkinson's disease.

    PubMed

    Braatz, Elise M; Coleman, Randolph A

    2015-06-01

    This paper introduces a mathematical model representing the biochemical interactions between insulin signaling and Parkinson's disease. The model can be used to examine the changes that occur over the course of the disease as well as identify which processes would be the most effective targets for treatment. The model is mathematized using biochemical systems theory (BST). It incorporates a treatment strategy that includes several experimental drugs along with current treatments. In the past, BST models of neurodegeneration have used power law analysis and simulation (PLAS) to model the system. This paper recommends the use of MATLAB instead. MATLAB allows for more flexibility in both the model itself and in data analysis. Previous BST analyses of neurodegeneration began treatment at disease onset. As shown in this model, the outcomes of delayed, realistic treatment and full treatment at disease onset are significantly different. The delayed treatment strategy is an important development in BST modeling of neurodegeneration. It emphasizes the importance of early diagnosis, and allows for a more accurate representation of disease and treatment interactions. Copyright © 2015 Elsevier Ltd. All rights reserved.

  19. Modeling small cell lung cancer (SCLC) biology through deterministic and stochastic mathematical models.

    PubMed

    Salgia, Ravi; Mambetsariev, Isa; Hewelt, Blake; Achuthan, Srisairam; Li, Haiqing; Poroyko, Valeriy; Wang, Yingyu; Sattler, Martin

    2018-05-25

    Mathematical cancer models are immensely powerful tools that are based in part on the fractal nature of biological structures, such as the geometry of the lung. Cancers of the lung provide an opportune model to develop and apply algorithms that capture changes and disease phenotypes. We reviewed mathematical models that have been developed for biological sciences and applied them in the context of small cell lung cancer (SCLC) growth, mutational heterogeneity, and mechanisms of metastasis. The ultimate goal is to develop the stochastic and deterministic nature of this disease, to link this comprehensive set of tools back to its fractalness and to provide a platform for accurate biomarker development. These techniques may be particularly useful in the context of drug development research, such as combination with existing omics approaches. The integration of these tools will be important to further understand the biology of SCLC and ultimately develop novel therapeutics.

  20. Mathematical Modeling: A Structured Process

    ERIC Educational Resources Information Center

    Anhalt, Cynthia Oropesa; Cortez, Ricardo

    2015-01-01

    Mathematical modeling, in which students use mathematics to explain or interpret physical, social, or scientific phenomena, is an essential component of the high school curriculum. The Common Core State Standards for Mathematics (CCSSM) classify modeling as a K-12 standard for mathematical practice and as a conceptual category for high school…

  1. Primary School Pre-Service Mathematics Teachers' Views on Mathematical Modeling

    ERIC Educational Resources Information Center

    Karali, Diren; Durmus, Soner

    2015-01-01

    The current study aimed to identify the views of pre-service teachers, who attended a primary school mathematics teaching department but did not take mathematical modeling courses. The mathematical modeling activity used by the pre-service teachers was developed with regards to the modeling activities utilized by Lesh and Doerr (2003) in their…

  2. Transient Mathematical Modeling for Liquid Rocket Engine Systems: Methods, Capabilities, and Experience

    NASA Technical Reports Server (NTRS)

    Seymour, David C.; Martin, Michael A.; Nguyen, Huy H.; Greene, William D.

    2005-01-01

    The subject of mathematical modeling of the transient operation of liquid rocket engines is presented in overview form from the perspective of engineers working at the NASA Marshall Space Flight Center. The necessity of creating and utilizing accurate mathematical models as part of liquid rocket engine development process has become well established and is likely to increase in importance in the future. The issues of design considerations for transient operation, development testing, and failure scenario simulation are discussed. An overview of the derivation of the basic governing equations is presented along with a discussion of computational and numerical issues associated with the implementation of these equations in computer codes. Also, work in the field of generating usable fluid property tables is presented along with an overview of efforts to be undertaken in the future to improve the tools use for the mathematical modeling process.

  3. Transient Mathematical Modeling for Liquid Rocket Engine Systems: Methods, Capabilities, and Experience

    NASA Technical Reports Server (NTRS)

    Martin, Michael A.; Nguyen, Huy H.; Greene, William D.; Seymout, David C.

    2003-01-01

    The subject of mathematical modeling of the transient operation of liquid rocket engines is presented in overview form from the perspective of engineers working at the NASA Marshall Space Flight Center. The necessity of creating and utilizing accurate mathematical models as part of liquid rocket engine development process has become well established and is likely to increase in importance in the future. The issues of design considerations for transient operation, development testing, and failure scenario simulation are discussed. An overview of the derivation of the basic governing equations is presented along with a discussion of computational and numerical issues associated with the implementation of these equations in computer codes. Also, work in the field of generating usable fluid property tables is presented along with an overview of efforts to be undertaken in the future to improve the tools use for the mathematical modeling process.

  4. DMPy: a Python package for automated mathematical model construction of large-scale metabolic systems.

    PubMed

    Smith, Robert W; van Rosmalen, Rik P; Martins Dos Santos, Vitor A P; Fleck, Christian

    2018-06-19

    Models of metabolism are often used in biotechnology and pharmaceutical research to identify drug targets or increase the direct production of valuable compounds. Due to the complexity of large metabolic systems, a number of conclusions have been drawn using mathematical methods with simplifying assumptions. For example, constraint-based models describe changes of internal concentrations that occur much quicker than alterations in cell physiology. Thus, metabolite concentrations and reaction fluxes are fixed to constant values. This greatly reduces the mathematical complexity, while providing a reasonably good description of the system in steady state. However, without a large number of constraints, many different flux sets can describe the optimal model and we obtain no information on how metabolite levels dynamically change. Thus, to accurately determine what is taking place within the cell, finer quality data and more detailed models need to be constructed. In this paper we present a computational framework, DMPy, that uses a network scheme as input to automatically search for kinetic rates and produce a mathematical model that describes temporal changes of metabolite fluxes. The parameter search utilises several online databases to find measured reaction parameters. From this, we take advantage of previous modelling efforts, such as Parameter Balancing, to produce an initial mathematical model of a metabolic pathway. We analyse the effect of parameter uncertainty on model dynamics and test how recent flux-based model reduction techniques alter system properties. To our knowledge this is the first time such analysis has been performed on large models of metabolism. Our results highlight that good estimates of at least 80% of the reaction rates are required to accurately model metabolic systems. Furthermore, reducing the size of the model by grouping reactions together based on fluxes alters the resulting system dynamics. The presented pipeline automates the

  5. Mathematical Modeling in Science: Using Spreadsheets to Create Mathematical Models and Address Scientific Inquiry

    ERIC Educational Resources Information Center

    Horton, Robert M.; Leonard, William H.

    2005-01-01

    In science, inquiry is used as students explore important and interesting questions concerning the world around them. In mathematics, one contemporary inquiry approach is to create models that describe real phenomena. Creating mathematical models using spreadsheets can help students learn at deep levels in both science and mathematics, and give…

  6. The 24-Hour Mathematical Modeling Challenge

    ERIC Educational Resources Information Center

    Galluzzo, Benjamin J.; Wendt, Theodore J.

    2015-01-01

    Across the mathematics curriculum there is a renewed emphasis on applications of mathematics and on mathematical modeling. Providing students with modeling experiences beyond the ordinary classroom setting remains a challenge, however. In this article, we describe the 24-hour Mathematical Modeling Challenge, an extracurricular event that exposes…

  7. Mathematical Models of Elementary Mathematics Learning and Performance. Final Report.

    ERIC Educational Resources Information Center

    Suppes, Patrick

    This project was concerned with the development of mathematical models of elementary mathematics learning and performance. Probabilistic finite automata and register machines with a finite number of registers were developed as models and extensively tested with data arising from the elementary-mathematics strand curriculum developed by the…

  8. Mathematical modelling in developmental biology.

    PubMed

    Vasieva, Olga; Rasolonjanahary, Manan'Iarivo; Vasiev, Bakhtier

    2013-06-01

    In recent decades, molecular and cellular biology has benefited from numerous fascinating developments in experimental technique, generating an overwhelming amount of data on various biological objects and processes. This, in turn, has led biologists to look for appropriate tools to facilitate systematic analysis of data. Thus, the need for mathematical techniques, which can be used to aid the classification and understanding of this ever-growing body of experimental data, is more profound now than ever before. Mathematical modelling is becoming increasingly integrated into biological studies in general and into developmental biology particularly. This review outlines some achievements of mathematics as applied to developmental biology and demonstrates the mathematical formulation of basic principles driving morphogenesis. We begin by describing a mathematical formalism used to analyse the formation and scaling of morphogen gradients. Then we address a problem of interplay between the dynamics of morphogen gradients and movement of cells, referring to mathematical models of gastrulation in the chick embryo. In the last section, we give an overview of various mathematical models used in the study of the developmental cycle of Dictyostelium discoideum, which is probably the best example of successful mathematical modelling in developmental biology.

  9. An Investigation of Mathematical Modeling with Pre-Service Secondary Mathematics Teachers

    ERIC Educational Resources Information Center

    Thrasher, Emily Plunkett

    2016-01-01

    The goal of this thesis was to investigate and enhance our understanding of what occurs while pre-service mathematics teachers engage in a mathematical modeling unit that is broadly based upon mathematical modeling as defined by the Common Core State Standards for Mathematics (National Governors Association Center for Best Practices & Council…

  10. Understanding Prospective Teachers' Mathematical Modeling Processes in the Context of a Mathematical Modeling Course

    ERIC Educational Resources Information Center

    Zeytun, Aysel Sen; Cetinkaya, Bulent; Erbas, Ayhan Kursat

    2017-01-01

    This paper investigates how prospective teachers develop mathematical models while they engage in modeling tasks. The study was conducted in an undergraduate elective course aiming to improve prospective teachers' mathematical modeling abilities, while enhancing their pedagogical knowledge for the integrating of modeling tasks into their future…

  11. Mathematical Modelling in the Junior Secondary Years: An Approach Incorporating Mathematical Technology

    ERIC Educational Resources Information Center

    Lowe, James; Carter, Merilyn; Cooper, Tom

    2018-01-01

    Mathematical models are conceptual processes that use mathematics to describe, explain, and/or predict the behaviour of complex systems. This article is written for teachers of mathematics in the junior secondary years (including out-of-field teachers of mathematics) who may be unfamiliar with mathematical modelling, to explain the steps involved…

  12. Mathematical Models of Continuous Flow Electrophoresis

    NASA Technical Reports Server (NTRS)

    Saville, D. A.; Snyder, R. S.

    1985-01-01

    Development of high resolution continuous flow electrophoresis devices ultimately requires comprehensive understanding of the ways various phenomena and processes facilitate or hinder separation. A comprehensive model of the actual three dimensional flow, temperature and electric fields was developed to provide guidance in the design of electrophoresis chambers for specific tasks and means of interpreting test data on a given chamber. Part of the process of model development includes experimental and theoretical studies of hydrodynamic stability. This is necessary to understand the origin of mixing flows observed with wide gap gravitational effects. To insure that the model accurately reflects the flow field and particle motion requires extensive experimental work. Another part of the investigation is concerned with the behavior of concentrated sample suspensions with regard to sample stream stability particle-particle interactions which might affect separation in an electric field, especially at high field strengths. Mathematical models will be developed and tested to establish the roles of the various interactions.

  13. Science modelling in pre-calculus: how to make mathematics problems contextually meaningful

    NASA Astrophysics Data System (ADS)

    Sokolowski, Andrzej; Yalvac, Bugrahan; Loving, Cathleen

    2011-04-01

    'Use of mathematical representations to model and interpret physical phenomena and solve problems is one of the major teaching objectives in high school math curriculum' (National Council of Teachers of Mathematics (NCTM), Principles and Standards for School Mathematics, NCTM, Reston, VA, 2000). Commonly used pre-calculus textbooks provide a wide range of application problems. However, these problems focus students' attention on evaluating or solving pre-arranged formulas for given values. The role of scientific content is reduced to provide a background for these problems instead of being sources of data gathering for inducing mathematical tools. Students are neither required to construct mathematical models based on the contexts nor are they asked to validate or discuss the limitations of applied formulas. Using these contexts, the instructor may think that he/she is teaching problem solving, where in reality he/she is teaching algorithms of the mathematical operations (G. Kulm (ed.), New directions for mathematics assessment, in Assessing Higher Order Thinking in Mathematics, Erlbaum, Hillsdale, NJ, 1994, pp. 221-240). Without a thorough representation of the physical phenomena and the mathematical modelling processes undertaken, problem solving unintentionally appears as simple algorithmic operations. In this article, we deconstruct the representations of mathematics problems from selected pre-calculus textbooks and explicate their limitations. We argue that the structure and content of those problems limits students' coherent understanding of mathematical modelling, and this could result in weak student problem-solving skills. Simultaneously, we explore the ways to enhance representations of those mathematical problems, which we have characterized as lacking a meaningful physical context and limiting coherent student understanding. In light of our discussion, we recommend an alternative to strengthen the process of teaching mathematical modelling - utilization

  14. Mathematical Modeling: Convoying Merchant Ships

    ERIC Educational Resources Information Center

    Mathews, Susann M.

    2004-01-01

    This article describes a mathematical model that connects mathematics with social studies. Students use mathematics to model independent versus convoyed ship deployments and sinkings to determine if the British should have convoyed their merchant ships during World War I. During the war, the British admiralty opposed sending merchant ships grouped…

  15. A Primer for Mathematical Modeling

    ERIC Educational Resources Information Center

    Sole, Marla

    2013-01-01

    With the implementation of the National Council of Teachers of Mathematics recommendations and the adoption of the Common Core State Standards for Mathematics, modeling has moved to the forefront of K-12 education. Modeling activities not only reinforce purposeful problem-solving skills, they also connect the mathematics students learn in school…

  16. Introducing Modeling Transition Diagrams as a Tool to Connect Mathematical Modeling to Mathematical Thinking

    ERIC Educational Resources Information Center

    Czocher, Jennifer A.

    2016-01-01

    This study contributes a methodological tool to reconstruct the cognitive processes and mathematical activities carried out by mathematical modelers. Represented as Modeling Transition Diagrams (MTDs), individual modeling routes were constructed for four engineering undergraduate students. Findings stress the importance and limitations of using…

  17. A Mathematical Diet Model

    ERIC Educational Resources Information Center

    Toumasis, Charalampos

    2004-01-01

    Emphasis on problem solving and mathematical modeling has gained considerable attention in the last few years. Connecting mathematics to other subjects and to the real world outside the classroom has received increased attention in mathematics programs. This article describes an application of simple differential equations in the field of…

  18. Utility and translatability of mathematical modeling, cell culture and small and large animal models in magnetic nanoparticle hyperthermia cancer treatment research

    NASA Astrophysics Data System (ADS)

    Hoopes, P. J.; Petryk, Alicia A.; Misra, Adwiteeya; Kastner, Elliot J.; Pearce, John A.; Ryan, Thomas P.

    2015-03-01

    For more than 50 years, hyperthermia-based cancer researchers have utilized mathematical models, cell culture studies and animal models to better understand, develop and validate potential new treatments. It has been, and remains, unclear how and to what degree these research techniques depend on, complement and, ultimately, translate accurately to a successful clinical treatment. In the past, when mathematical models have not proven accurate in a clinical treatment situation, the initiating quantitative scientists (engineers, mathematicians and physicists) have tended to believe the biomedical parameters provided to them were inaccurately determined or reported. In a similar manner, experienced biomedical scientists often tend to question the value of mathematical models and cell culture results since those data typically lack the level of biologic and medical variability and complexity that are essential to accurately study and predict complex diseases and subsequent treatments. Such quantitative and biomedical interdependence, variability, diversity and promise have never been greater than they are within magnetic nanoparticle hyperthermia cancer treatment. The use of hyperthermia to treat cancer is well studied and has utilized numerous delivery techniques, including microwaves, radio frequency, focused ultrasound, induction heating, infrared radiation, warmed perfusion liquids (combined with chemotherapy), and, recently, metallic nanoparticles (NP) activated by near infrared radiation (NIR) and alternating magnetic field (AMF) based platforms. The goal of this paper is to use proven concepts and current research to address the potential pathobiology, modeling and quantification of the effects of treatment as pertaining to the similarities and differences in energy delivered by known external delivery techniques and iron oxide nanoparticles.

  19. Mathematical modeling and numerical simulation of the mitotic spindle orientation system.

    PubMed

    Ibrahim, Bashar

    2018-05-21

    The mitotic spindle orientation and position is crucial for the fidelity of chromosome segregation during asymmetric cell division to generate daughter cells with different sizes or fates. This mechanism is best understood in the budding yeast Saccharomyces cerevisiae, named the spindle position checkpoint (SPOC). The SPOC inhibits cells from exiting mitosis until the mitotic spindle is properly oriented along the mother-daughter polarity axis. Despite many experimental studies, the mechanisms underlying SPOC regulation remains elusive and unexplored theoretically. Here, a minimal mathematical is developed to describe SPOC activation and silencing having autocatalytic feedback-loop. Numerical simulations of the nonlinear ordinary differential equations (ODEs) model accurately reproduce the phenotype of SPOC mechanism. Bifurcation analysis of the nonlinear ODEs reveals the orientation dependency on spindle pole bodies, and how this dependence is altered by parameter values. These results provide for systems understanding on the molecular organization of spindle orientation system via mathematical modeling. The presented mathematical model is easy to understand and, within the above mentioned context, can be used as a base for further development of quantitative models in asymmetric cell-division. Copyright © 2018. Published by Elsevier Inc.

  20. Mathematical Modeling: Challenging the Figured Worlds of Elementary Mathematics

    ERIC Educational Resources Information Center

    Wickstrom, Megan H.

    2017-01-01

    This article is a report on a teacher study group that focused on three elementary teachers' perceptions of mathematical modeling in contrast to typical mathematics instruction. Through the theoretical lens of figured worlds, I discuss how mathematics instruction was conceptualized across the classrooms in terms of artifacts, discourse, and…

  1. Mathematics Teachers' Ideas about Mathematical Models: A Diverse Landscape

    ERIC Educational Resources Information Center

    Bautista, Alfredo; Wilkerson-Jerde, Michelle H.; Tobin, Roger G.; Brizuela, Bárbara M.

    2014-01-01

    This paper describes the ideas that mathematics teachers (grades 5-9) have regarding mathematical models of real-world phenomena, and explores how teachers' ideas differ depending on their educational background. Participants were 56 United States in-service mathematics teachers. We analyzed teachers' written responses to three open-ended…

  2. Mathematical modeling of a thermovoltaic cell

    NASA Technical Reports Server (NTRS)

    White, Ralph E.; Kawanami, Makoto

    1992-01-01

    A new type of battery named 'Vaporvolt' cell is in the early stage of its development. A mathematical model of a CuO/Cu 'Vaporvolt' cell is presented that can be used to predict the potential and the transport behavior of the cell during discharge. A sensitivity analysis of the various transport and electrokinetic parameters indicates which parameters have the most influence on the predicted energy and power density of the 'Vaporvolt' cell. This information can be used to decide which parameters should be optimized or determined more accurately through further modeling or experimental studies. The optimal thicknesses of electrodes and separator, the concentration of the electrolyte, and the current density are determined by maximizing the power density. These parameter sensitivities and optimal design parameter values will help in the development of a better CuO/Cu 'Vaporvolt' cell.

  3. Mathematical Modeling in the Undergraduate Curriculum

    ERIC Educational Resources Information Center

    Toews, Carl

    2012-01-01

    Mathematical modeling occupies an unusual space in the undergraduate mathematics curriculum: typically an "advanced" course, it nonetheless has little to do with formal proof, the usual hallmark of advanced mathematics. Mathematics departments are thus forced to decide what role they want the modeling course to play, both as a component of the…

  4. Teachers' Conceptions of Mathematical Modeling

    ERIC Educational Resources Information Center

    Gould, Heather

    2013-01-01

    The release of the "Common Core State Standards for Mathematics" in 2010 resulted in a new focus on mathematical modeling in United States curricula. Mathematical modeling represents a way of doing and understanding mathematics new to most teachers. The purpose of this study was to determine the conceptions and misconceptions held by…

  5. Mathematical Modeling: A Bridge to STEM Education

    ERIC Educational Resources Information Center

    Kertil, Mahmut; Gurel, Cem

    2016-01-01

    The purpose of this study is making a theoretical discussion on the relationship between mathematical modeling and integrated STEM education. First of all, STEM education perspective and the construct of mathematical modeling in mathematics education is introduced. A review of literature is provided on how mathematical modeling literature may…

  6. Mathematical models for plant-herbivore interactions

    USGS Publications Warehouse

    Feng, Zhilan; DeAngelis, Donald L.

    2017-01-01

    Mathematical Models of Plant-Herbivore Interactions addresses mathematical models in the study of practical questions in ecology, particularly factors that affect herbivory, including plant defense, herbivore natural enemies, and adaptive herbivory, as well as the effects of these on plant community dynamics. The result of extensive research on the use of mathematical modeling to investigate the effects of plant defenses on plant-herbivore dynamics, this book describes a toxin-determined functional response model (TDFRM) that helps explains field observations of these interactions. This book is intended for graduate students and researchers interested in mathematical biology and ecology.

  7. Mathematics teachers' conceptions about modelling activities and its reflection on their beliefs about mathematics

    NASA Astrophysics Data System (ADS)

    Shahbari, Juhaina Awawdeh

    2018-07-01

    The current study examines whether the engagement of mathematics teachers in modelling activities and subsequent changes in their conceptions about these activities affect their beliefs about mathematics. The sample comprised 52 mathematics teachers working in small groups in four modelling activities. The data were collected from teachers' Reports about features of each activity, interviews and questionnaires on teachers' beliefs about mathematics. The findings indicated changes in teachers' conceptions about the modelling activities. Most teachers referred to the first activity as a mathematical problem but emphasized only the mathematical notions or the mathematical operations in the modelling process; changes in their conceptions were gradual. Most of the teachers referred to the fourth activity as a mathematical problem and emphasized features of the whole modelling process. The results of the interviews indicated that changes in the teachers' conceptions can be attributed to structure of the activities, group discussions, solution paths and elicited models. These changes about modelling activities were reflected in teachers' beliefs about mathematics. The quantitative findings indicated that the teachers developed more constructive beliefs about mathematics after engagement in the modelling activities and that the difference was significant, however there was no significant difference regarding changes in their traditional beliefs.

  8. A Fuzzy mathematical model to estimate the effects of global warming on the vitality of Laelia purpurata orchids.

    PubMed

    Putti, Fernando Ferrari; Filho, Luis Roberto Almeida Gabriel; Gabriel, Camila Pires Cremasco; Neto, Alfredo Bonini; Bonini, Carolina Dos Santos Batista; Rodrigues Dos Reis, André

    2017-06-01

    This study aimed to develop a fuzzy mathematical model to estimate the impacts of global warming on the vitality of Laelia purpurata growing in different Brazilian environmental conditions. In order to develop the mathematical model was considered as intrinsic factors the parameters: temperature, humidity and shade conditions to determine the vitality of plants. Fuzzy model results could accurately predict the optimal conditions for cultivation of Laelia purpurata in several sites of Brazil. Based on fuzzy model results, we found that higher temperatures and lacking of properly shading can reduce the vitality of orchids. Fuzzy mathematical model could precisely detect the effect of higher temperatures causing damages on vitality of plants as a consequence of global warming. Copyright © 2017 Elsevier Inc. All rights reserved.

  9. Turbine Engine Mathematical Model Validation

    DTIC Science & Technology

    1976-12-01

    AEDC-TR-76-90 ~Ec i ? Z985 TURBINE ENGINE MATHEMATICAL MODEL VALIDATION ENGINE TEST FACILITY ARNOLD ENGINEERING DEVELOPMENT CENTER AIR FORCE...i f n e c e s e a ~ ~ d i den t i f y by b l ock number) YJI01-GE-100 engine turbine engines mathematical models computations mathematical...report presents and discusses the results of an investigation to develop a rationale and technique for the validation of turbine engine steady-state

  10. Thermodynamically accurate modeling of the catalytic cycle of photosynthetic oxygen evolution: a mathematical solution to asymmetric Markov chains.

    PubMed

    Vinyard, David J; Zachary, Chase E; Ananyev, Gennady; Dismukes, G Charles

    2013-07-01

    Forty-three years ago, Kok and coworkers introduced a phenomenological model describing period-four oscillations in O2 flash yields during photosynthetic water oxidation (WOC), which had been first reported by Joliot and coworkers. The original two-parameter Kok model was subsequently extended in its level of complexity to better simulate diverse data sets, including intact cells and isolated PSII-WOCs, but at the expense of introducing physically unrealistic assumptions necessary to enable numerical solutions. To date, analytical solutions have been found only for symmetric Kok models (inefficiencies are equally probable for all intermediates, called "S-states"). However, it is widely accepted that S-state reaction steps are not identical and some are not reversible (by thermodynamic restraints) thereby causing asymmetric cycles. We have developed a mathematically more rigorous foundation that eliminates unphysical assumptions known to be in conflict with experiments and adopts a new experimental constraint on solutions. This new algorithm termed STEAMM for S-state Transition Eigenvalues of Asymmetric Markov Models enables solutions to models having fewer adjustable parameters and uses automated fitting to experimental data sets, yielding higher accuracy and precision than the classic Kok or extended Kok models. This new tool provides a general mathematical framework for analyzing damped oscillations arising from any cycle period using any appropriate Markov model, regardless of symmetry. We illustrate applications of STEAMM that better describe the intrinsic inefficiencies for photon-to-charge conversion within PSII-WOCs that are responsible for damped period-four and period-two oscillations of flash O2 yields across diverse species, while using simpler Markov models free from unrealistic assumptions. Copyright © 2013 Elsevier B.V. All rights reserved.

  11. Mathematical Modeling and Computational Thinking

    ERIC Educational Resources Information Center

    Sanford, John F.; Naidu, Jaideep T.

    2017-01-01

    The paper argues that mathematical modeling is the essence of computational thinking. Learning a computer language is a valuable assistance in learning logical thinking but of less assistance when learning problem-solving skills. The paper is third in a series and presents some examples of mathematical modeling using spreadsheets at an advanced…

  12. Summer Camp of Mathematical Modeling in China

    ERIC Educational Resources Information Center

    Tian, Xiaoxi; Xie, Jinxing

    2013-01-01

    The Summer Camp of Mathematical Modeling in China is a recently created experience designed to further Chinese students' academic pursuits in mathematical modeling. Students are given more than three months to research on a mathematical modeling project. Researchers and teams with outstanding projects are invited to the Summer Camp to present…

  13. Strategies to Support Students' Mathematical Modeling

    ERIC Educational Resources Information Center

    Jung, Hyunyi

    2015-01-01

    An important question for mathematics teachers is this: "How can we help students learn mathematics to solve everyday problems, rather than teaching them only to memorize rules and practice mathematical procedures?" Teaching students using modeling activities can help them learn mathematics in real-world problem-solving situations that…

  14. Explorations in Elementary Mathematical Modeling

    ERIC Educational Resources Information Center

    Shahin, Mazen

    2010-01-01

    In this paper we will present the methodology and pedagogy of Elementary Mathematical Modeling as a one-semester course in the liberal arts core. We will focus on the elementary models in finance and business. The main mathematical tools in this course are the difference equations and matrix algebra. We also integrate computer technology and…

  15. Mathematical Modeling of Diverse Phenomena

    NASA Technical Reports Server (NTRS)

    Howard, J. C.

    1979-01-01

    Tensor calculus is applied to the formulation of mathematical models of diverse phenomena. Aeronautics, fluid dynamics, and cosmology are among the areas of application. The feasibility of combining tensor methods and computer capability to formulate problems is demonstrated. The techniques described are an attempt to simplify the formulation of mathematical models by reducing the modeling process to a series of routine operations, which can be performed either manually or by computer.

  16. The Effect of Instruction through Mathematical Modelling on Modelling Skills of Prospective Elementary Mathematics Teachers

    ERIC Educational Resources Information Center

    Ciltas, Alper; Isik, Ahmet

    2013-01-01

    The aim of this study was to examine the modelling skills of prospective elementary mathematics teachers who were studying the mathematical modelling method. The research study group was composed of 35 prospective teachers. The exploratory case analysis method was used in the study. The data were obtained via semi-structured interviews and a…

  17. A model-updating procedure to stimulate piezoelectric transducers accurately.

    PubMed

    Piranda, B; Ballandras, S; Steichen, W; Hecart, B

    2001-09-01

    The use of numerical calculations based on finite element methods (FEM) has yielded significant improvements in the simulation and design of piezoelectric transducers piezoelectric transducer utilized in acoustic imaging. However, the ultimate precision of such models is directly controlled by the accuracy of material characterization. The present work is dedicated to the development of a model-updating technique adapted to the problem of piezoelectric transducer. The updating process is applied using the experimental admittance of a given structure for which a finite element analysis is performed. The mathematical developments are reported and then applied to update the entries of a FEM of a two-layer structure (a PbZrTi-PZT-ridge glued on a backing) for which measurements were available. The efficiency of the proposed approach is demonstrated, yielding the definition of a new set of constants well adapted to predict the structure response accurately. Improvement of the proposed approach, consisting of the updating of material coefficients not only on the admittance but also on the impedance data, is finally discussed.

  18. Mathematical modeling improves EC50 estimations from classical dose-response curves.

    PubMed

    Nyman, Elin; Lindgren, Isa; Lövfors, William; Lundengård, Karin; Cervin, Ida; Sjöström, Theresia Arbring; Altimiras, Jordi; Cedersund, Gunnar

    2015-03-01

    The β-adrenergic response is impaired in failing hearts. When studying β-adrenergic function in vitro, the half-maximal effective concentration (EC50 ) is an important measure of ligand response. We previously measured the in vitro contraction force response of chicken heart tissue to increasing concentrations of adrenaline, and observed a decreasing response at high concentrations. The classical interpretation of such data is to assume a maximal response before the decrease, and to fit a sigmoid curve to the remaining data to determine EC50 . Instead, we have applied a mathematical modeling approach to interpret the full dose-response curve in a new way. The developed model predicts a non-steady-state caused by a short resting time between increased concentrations of agonist, which affect the dose-response characterization. Therefore, an improved estimate of EC50 may be calculated using steady-state simulations of the model. The model-based estimation of EC50 is further refined using additional time-resolved data to decrease the uncertainty of the prediction. The resulting model-based EC50 (180-525 nm) is higher than the classically interpreted EC50 (46-191 nm). Mathematical modeling thus makes it possible to re-interpret previously obtained datasets, and to make accurate estimates of EC50 even when steady-state measurements are not experimentally feasible. The mathematical models described here have been submitted to the JWS Online Cellular Systems Modelling Database, and may be accessed at http://jjj.bio.vu.nl/database/nyman. © 2015 FEBS.

  19. Mathematical modeling of fluxgate magnetic gradiometers

    NASA Astrophysics Data System (ADS)

    Milovzorov, D. G.; Yasoveev, V. Kh.

    2017-07-01

    Issues of designing fluxgate magnetic gradiometers are considered. The areas of application of fluxgate magnetic gradiometers are determined. The structure and layout of a two-component fluxgate magnetic gradiometer are presented. It is assumed that the fluxgates are strictly coaxial in the gradiometer body. Elements of the classical approach to the mathematical modeling of the spatial arrangement of solids are considered. The bases of the gradiometer body and their transformations during spatial displacement of the gradiometer are given. The problems of mathematical modeling of gradiometers are formulated, basic mathematical models of a two-component fluxgate gradiometer are developed, and the mathematical models are analyzed. A computer experiment was performed. Difference signals from the gradiometer fluxgates for the vertical and horizontal position of the gradiometer body are shown graphically as functions of the magnitude and direction of the geomagnetic field strength vector.

  20. Mathematical models of behavior of individual animals.

    PubMed

    Tsibulsky, Vladimir L; Norman, Andrew B

    2007-01-01

    This review is focused on mathematical modeling of behaviors of a whole organism with special emphasis on models with a clearly scientific approach to the problem that helps to understand the mechanisms underlying behavior. The aim is to provide an overview of old and contemporary mathematical models without complex mathematical details. Only deterministic and stochastic, but not statistical models are reviewed. All mathematical models of behavior can be divided into two main classes. First, models that are based on the principle of teleological determinism assume that subjects choose the behavior that will lead them to a better payoff in the future. Examples are game theories and operant behavior models both of which are based on the matching law. The second class of models are based on the principle of causal determinism, which assume that subjects do not choose from a set of possibilities but rather are compelled to perform a predetermined behavior in response to specific stimuli. Examples are perception and discrimination models, drug effects models and individual-based population models. A brief overview of the utility of each mathematical model is provided for each section.

  1. Quantitative dual-probe microdialysis: mathematical model and analysis.

    PubMed

    Chen, Kevin C; Höistad, Malin; Kehr, Jan; Fuxe, Kjell; Nicholson, Charles

    2002-04-01

    Steady-state microdialysis is a widely used technique to monitor the concentration changes and distributions of substances in tissues. To obtain more information about brain tissue properties from microdialysis, a dual-probe approach was applied to infuse and sample the radiotracer, [3H]mannitol, simultaneously both in agar gel and in the rat striatum. Because the molecules released by one probe and collected by the other must diffuse through the interstitial space, the concentration profile exhibits dynamic behavior that permits the assessment of the diffusion characteristics in the brain extracellular space and the clearance characteristics. In this paper a mathematical model for dual-probe microdialysis was developed to study brain interstitial diffusion and clearance processes. Theoretical expressions for the spatial distribution of the infused tracer in the brain extracellular space and the temporal concentration at the probe outlet were derived. A fitting program was developed using the simplex algorithm, which finds local minima of the standard deviations between experiments and theory by adjusting the relevant parameters. The theoretical curves accurately fitted the experimental data and generated realistic diffusion parameters, implying that the mathematical model is capable of predicting the interstitial diffusion behavior of [3H]mannitol and that it will be a valuable quantitative tool in dual-probe microdialysis.

  2. Mathematical modeling and experimental testing of three bioreactor configurations based on windkessel models

    PubMed Central

    Ruel, Jean; Lachance, Geneviève

    2010-01-01

    This paper presents an experimental study of three bioreactor configurations. The bioreactor is intended to be used for the development of tissue-engineered heart valve substitutes. Therefore it must be able to reproduce physiological flow and pressure waveforms accurately. A detailed analysis of three bioreactor arrangements is presented using mathematical models based on the windkessel (WK) approach. First, a review of the many applications of this approach in medical studies enhances its fundamental nature and its usefulness. Then the models are developed with reference to the actual components of the bioreactor. This study emphasizes different conflicting issues arising in the design process of a bioreactor for biomedical purposes, where an optimization process is essential to reach a compromise satisfying all conditions. Two important aspects are the need for a simple system providing ease of use and long-term sterility, opposed to the need for an advanced (thus more complex) architecture capable of a more accurate reproduction of the physiological environment. Three classic WK architectures are analyzed, and experimental results enhance the advantages and limitations of each one. PMID:21977286

  3. Issues and Importance of "Good" Starting Points for Nonlinear Regression for Mathematical Modeling with Maple: Basic Model Fitting to Make Predictions with Oscillating Data

    ERIC Educational Resources Information Center

    Fox, William

    2012-01-01

    The purpose of our modeling effort is to predict future outcomes. We assume the data collected are both accurate and relatively precise. For our oscillating data, we examined several mathematical modeling forms for predictions. We also examined both ignoring the oscillations as an important feature and including the oscillations as an important…

  4. Opinions of Secondary School Mathematics Teachers on Mathematical Modelling

    ERIC Educational Resources Information Center

    Tutak, Tayfun; Güder, Yunus

    2013-01-01

    The aim of this study is to identify the opinions of secondary school mathematics teachers about mathematical modelling. Qualitative research was used. The participants of the study were 40 secondary school teachers working in the Bingöl Province in Turkey during 2012-2013 education year. Semi-structured interview form prepared by the researcher…

  5. The Relationship between Students' Performance on Conventional Standardized Mathematics Assessments and Complex Mathematical Modeling Problems

    ERIC Educational Resources Information Center

    Kartal, Ozgul; Dunya, Beyza Aksu; Diefes-Dux, Heidi A.; Zawojewski, Judith S.

    2016-01-01

    Critical to many science, technology, engineering, and mathematics (STEM) career paths is mathematical modeling--specifically, the creation and adaptation of mathematical models to solve problems in complex settings. Conventional standardized measures of mathematics achievement are not structured to directly assess this type of mathematical…

  6. Current problems in applied mathematics and mathematical modeling

    NASA Astrophysics Data System (ADS)

    Alekseev, A. S.

    Papers are presented on mathematical modeling noting applications to such fields as geophysics, chemistry, atmospheric optics, and immunology. Attention is also given to models of ocean current fluxes, atmospheric and marine interactions, and atmospheric pollution. The articles include studies of catalytic reactors, models of global climate phenomena, and computer-assisted atmospheric models.

  7. Mathematical Models for Doppler Measurements

    NASA Technical Reports Server (NTRS)

    Lear, William M.

    1987-01-01

    Error analysis increases precision of navigation. Report presents improved mathematical models of analysis of Doppler measurements and measurement errors of spacecraft navigation. To take advantage of potential navigational accuracy of Doppler measurements, precise equations relate measured cycle count to position and velocity. Drifts and random variations in transmitter and receiver oscillator frequencies taken into account. Mathematical models also adapted to aircraft navigation, radar, sonar, lidar, and interferometry.

  8. An Experimental Approach to Mathematical Modeling in Biology

    ERIC Educational Resources Information Center

    Ledder, Glenn

    2008-01-01

    The simplest age-structured population models update a population vector via multiplication by a matrix. These linear models offer an opportunity to introduce mathematical modeling to students of limited mathematical sophistication and background. We begin with a detailed discussion of mathematical modeling, particularly in a biological context.…

  9. Beyond Motivation: Exploring Mathematical Modeling as a Context for Deepening Students' Understandings of Curricular Mathematics

    ERIC Educational Resources Information Center

    Zbiek, Rose Mary; Conner, Annamarie

    2006-01-01

    Views of mathematical modeling in empirical, expository, and curricular references typically capture a relationship between real-world phenomena and mathematical ideas from the perspective that competence in mathematical modeling is a clear goal of the mathematics curriculum. However, we work within a curricular context in which mathematical…

  10. Mathematical form models of tree trunks

    Treesearch

    Rudolfs Ozolins

    2000-01-01

    Assortment structure analysis of tree trunks is a characteristic and proper problem that can be solved by using mathematical modeling and standard computer programs. Mathematical form model of tree trunks consists of tapering curve equations and their parameters. Parameters for nine species were obtained by processing measurements of 2,794 model trees and studying the...

  11. ASTP ranging system mathematical model

    NASA Technical Reports Server (NTRS)

    Ellis, M. R.; Robinson, L. H.

    1973-01-01

    A mathematical model is presented of the VHF ranging system to analyze the performance of the Apollo-Soyuz test project (ASTP). The system was adapted for use in the ASTP. The ranging system mathematical model is presented in block diagram form, and a brief description of the overall model is also included. A procedure for implementing the math model is presented along with a discussion of the validation of the math model and the overall summary and conclusions of the study effort. Detailed appendices of the five study tasks are presented: early late gate model development, unlock probability development, system error model development, probability of acquisition and model development, and math model validation testing.

  12. The influence of mathematics learning using SAVI approach on junior high school students’ mathematical modelling ability

    NASA Astrophysics Data System (ADS)

    Khusna, H.; Heryaningsih, N. Y.

    2018-01-01

    The aim of this research was to examine mathematical modeling ability who learn mathematics by using SAVI approach. This research was a quasi-experimental research with non-equivalent control group designed by using purposive sampling technique. The population of this research was the state junior high school students in Lembang while the sample consisted of two class at 8th grade. The instrument used in this research was mathematical modeling ability. Data analysis of this research was conducted by using SPSS 20 by Windows. The result showed that students’ ability of mathematical modeling who learn mathematics by using SAVI approach was better than students’ ability of mathematical modeling who learn mathematics using conventional learning.

  13. Mathematical Modelling as a Professional Task

    ERIC Educational Resources Information Center

    Frejd, Peter; Bergsten, Christer

    2016-01-01

    Educational research literature on mathematical modelling is extensive. However, not much attention has been paid to empirical investigations of its scholarly knowledge from the perspective of didactic transposition processes. This paper reports from an interview study of mathematical modelling activities involving nine professional model…

  14. Using Covariation Reasoning to Support Mathematical Modeling

    ERIC Educational Resources Information Center

    Jacobson, Erik

    2014-01-01

    For many students, making connections between mathematical ideas and the real world is one of the most intriguing and rewarding aspects of the study of mathematics. In the Common Core State Standards for Mathematics (CCSSI 2010), mathematical modeling is highlighted as a mathematical practice standard for all grades. To engage in mathematical…

  15. Detecting Strengths and Weaknesses in Learning Mathematics through a Model Classifying Mathematical Skills

    ERIC Educational Resources Information Center

    Karagiannakis, Giannis N.; Baccaglini-Frank, Anna E.; Roussos, Petros

    2016-01-01

    Through a review of the literature on mathematical learning disabilities (MLD) and low achievement in mathematics (LA) we have proposed a model classifying mathematical skills involved in learning mathematics into four domains (Core number, Memory, Reasoning, and Visual-spatial). In this paper we present a new experimental computer-based battery…

  16. Automatic mathematical modeling for space application

    NASA Technical Reports Server (NTRS)

    Wang, Caroline K.

    1987-01-01

    A methodology for automatic mathematical modeling is described. The major objective is to create a very friendly environment for engineers to design, maintain and verify their model and also automatically convert the mathematical model into FORTRAN code for conventional computation. A demonstration program was designed for modeling the Space Shuttle Main Engine simulation mathematical model called Propulsion System Automatic Modeling (PSAM). PSAM provides a very friendly and well organized environment for engineers to build a knowledge base for base equations and general information. PSAM contains an initial set of component process elements for the Space Shuttle Main Engine simulation and a questionnaire that allows the engineer to answer a set of questions to specify a particular model. PSAM is then able to automatically generate the model and the FORTRAN code. A future goal is to download the FORTRAN code to the VAX/VMS system for conventional computation.

  17. On Fences, Forms and Mathematical Modeling

    ERIC Educational Resources Information Center

    Lege, Jerry

    2009-01-01

    The white picket fence is an integral component of the iconic American townscape. But, for mathematics students, it can be a mathematical challenge. Picket fences in a variety of styles serve as excellent sources to model constant, step, absolute value, and sinusoidal functions. "Principles and Standards for School Mathematics" (NCTM 2000)…

  18. Mathematical Modeling in the High School Curriculum

    ERIC Educational Resources Information Center

    Hernández, Maria L.; Levy, Rachel; Felton-Koestler, Mathew D.; Zbiek, Rose Mary

    2016-01-01

    In 2015, mathematics leaders and instructors from the Society for Industrial and Applied Mathematics (SIAM) and the Consortium for Mathematics and Its Applications (COMAP), with input from NCTM, came together to write the "Guidelines for Assessment and Instruction in Mathematical Modeling Education" (GAIMME) report as a resource for…

  19. Students' Mathematical Modeling of Motion

    ERIC Educational Resources Information Center

    Marshall, Jill A.; Carrejo, David J.

    2008-01-01

    We present results of an investigation of university students' development of mathematical models of motion in a physical science course for preservice teachers and graduate students in science and mathematics education. Although some students were familiar with the standard concepts of position, velocity, and acceleration from physics classes,…

  20. Mathematical Modeling Approaches in Plant Metabolomics.

    PubMed

    Fürtauer, Lisa; Weiszmann, Jakob; Weckwerth, Wolfram; Nägele, Thomas

    2018-01-01

    The experimental analysis of a plant metabolome typically results in a comprehensive and multidimensional data set. To interpret metabolomics data in the context of biochemical regulation and environmental fluctuation, various approaches of mathematical modeling have been developed and have proven useful. In this chapter, a general introduction to mathematical modeling is presented and discussed in context of plant metabolism. A particular focus is laid on the suitability of mathematical approaches to functionally integrate plant metabolomics data in a metabolic network and combine it with other biochemical or physiological parameters.

  1. Mathematical Modeling with Middle School Students: The Robot Art Model-Eliciting Activity

    ERIC Educational Resources Information Center

    Stohlmann, Micah S.

    2017-01-01

    Internationally mathematical modeling is garnering more attention for the benefits associated with it. Mathematical modeling can develop students' communication skills and the ability to demonstrate understanding through different representations. With the increased attention on mathematical modeling, there is a need for more curricula to be…

  2. Problem Posing and Solving with Mathematical Modeling

    ERIC Educational Resources Information Center

    English, Lyn D.; Fox, Jillian L.; Watters, James J.

    2005-01-01

    Mathematical modeling is explored as both problem posing and problem solving from two perspectives, that of the child and the teacher. Mathematical modeling provides rich learning experiences for elementary school children and their teachers.

  3. Examples of Mathematical Modeling

    PubMed Central

    Johnston, Matthew D.; Edwards, Carina M.; Bodmer, Walter F.; Maini, Philip K.; Chapman, S. Jonathan

    2008-01-01

    Mathematical modeling is being increasingly recognized within the biomedical sciences as an important tool that can aid the understanding of biological systems. The heavily regulated cell renewal cycle in the colonic crypt provides a good example of how modeling can be used to find out key features of the system kinetics, and help to explain both the breakdown of homeostasis and the initiation of tumorigenesis. We use the cell population model by Johnston et al.5 to illustrate the power of mathematical modeling by considering two key questions about the cell population dynamics in the colonic crypt. We ask: how can a model describe both homeostasis and unregulated growth in tumorigenesis; and to which parameters in the system is the model most sensitive? In order to address these questions, we discuss what type of modeling approach is most appropriate in the crypt. We use the model to argue why tumorigenesis is observed to occur in stages with long lag phases between periods of rapid growth, and we identify the key parameters. PMID:17873520

  4. Tools for Accurate and Efficient Analysis of Complex Evolutionary Mechanisms in Microbial Genomes. Final Report

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Nakhleh, Luay

    I proposed to develop computationally efficient tools for accurate detection and reconstruction of microbes' complex evolutionary mechanisms, thus enabling rapid and accurate annotation, analysis and understanding of their genomes. To achieve this goal, I proposed to address three aspects. (1) Mathematical modeling. A major challenge facing the accurate detection of HGT is that of distinguishing between these two events on the one hand and other events that have similar "effects." I proposed to develop a novel mathematical approach for distinguishing among these events. Further, I proposed to develop a set of novel optimization criteria for the evolutionary analysis of microbialmore » genomes in the presence of these complex evolutionary events. (2) Algorithm design. In this aspect of the project, I proposed to develop an array of e cient and accurate algorithms for analyzing microbial genomes based on the formulated optimization criteria. Further, I proposed to test the viability of the criteria and the accuracy of the algorithms in an experimental setting using both synthetic as well as biological data. (3) Software development. I proposed the nal outcome to be a suite of software tools which implements the mathematical models as well as the algorithms developed.« less

  5. DigitalHuman (DH): An Integrative Mathematical Model ofHuman Physiology

    NASA Technical Reports Server (NTRS)

    Hester, Robert L.; Summers, Richard L.; lIescu, Radu; Esters, Joyee; Coleman, Thomas G.

    2010-01-01

    Mathematical models and simulation are important tools in discovering the key causal relationships governing physiological processes and improving medical intervention when physiological complexity is a central issue. We have developed a model of integrative human physiology called DigitalHuman (DH) consisting of -5000 variables modeling human physiology describing cardiovascular, renal, respiratory, endocrine, neural and metabolic physiology. Users can view time-dependent solutions and interactively introduce perturbations by altering numerical parameters to investigate new hypotheses. The variables, parameters and quantitative relationships as well as all other model details are described in XML text files. All aspects of the model, including the mathematical equations describing the physiological processes are written in XML open source, text-readable files. Model structure is based upon empirical data of physiological responses documented within the peer-reviewed literature. The model can be used to understand proposed physiological mechanisms and physiological interactions that may not be otherwise intUitively evident. Some of the current uses of this model include the analyses of renal control of blood pressure, the central role of the liver in creating and maintaining insulin resistance, and the mechanisms causing orthostatic hypotension in astronauts. Additionally the open source aspect of the modeling environment allows any investigator to add detailed descriptions of human physiology to test new concepts. The model accurately predicts both qualitative and more importantly quantitative changes in clinically and experimentally observed responses. DigitalHuman provides scientists a modeling environment to understand the complex interactions of integrative physiology. This research was supported by.NIH HL 51971, NSF EPSCoR, and NASA

  6. Development of physical and mathematical models for the Porous Ceramic Tube Plant Nutrification System (PCTPNS)

    NASA Technical Reports Server (NTRS)

    Tsao, D. Teh-Wei; Okos, M. R.; Sager, J. C.; Dreschel, T. W.

    1992-01-01

    A physical model of the Porous Ceramic Tube Plant Nutrification System (PCTPNS) was developed through microscopic observations of the tube surface under various operational conditions. In addition, a mathematical model of this system was developed which incorporated the effects of the applied suction pressure, surface tension, and gravitational forces as well as the porosity and physical dimensions of the tubes. The flow of liquid through the PCTPNS was thus characterized for non-biological situations. One of the key factors in the verification of these models is the accurate and rapid measurement of the 'wetness' or holding capacity of the ceramic tubes. This study evaluated a thermistor based moisture sensor device and recommendations for future research on alternative sensing devices are proposed. In addition, extensions of the physical and mathematical models to include the effects of plant physiology and growth are also discussed for future research.

  7. The mathematics of cancer: integrating quantitative models.

    PubMed

    Altrock, Philipp M; Liu, Lin L; Michor, Franziska

    2015-12-01

    Mathematical modelling approaches have become increasingly abundant in cancer research. The complexity of cancer is well suited to quantitative approaches as it provides challenges and opportunities for new developments. In turn, mathematical modelling contributes to cancer research by helping to elucidate mechanisms and by providing quantitative predictions that can be validated. The recent expansion of quantitative models addresses many questions regarding tumour initiation, progression and metastases as well as intra-tumour heterogeneity, treatment responses and resistance. Mathematical models can complement experimental and clinical studies, but also challenge current paradigms, redefine our understanding of mechanisms driving tumorigenesis and shape future research in cancer biology.

  8. Mathematical modeling of laser lipolysis

    PubMed Central

    Mordon, Serge R; Wassmer, Benjamin; Reynaud, Jean Pascal; Zemmouri, Jaouad

    2008-01-01

    Background and Objectives Liposuction continues to be one of the most popular procedures performed in cosmetic surgery. As the public's demand for body contouring continues, laser lipolysis has been proposed to improve results, minimize risk, optimize patient comfort, and reduce the recovery period. Mathematical modeling of laser lipolysis could provide a better understanding of the laser lipolysis process and could determine the optimal dosage as a function of fat volume to be removed. Study design/Materials and Methods An Optical-Thermal-Damage Model was formulated using finite-element modeling software (Femlab 3.1, Comsol Inc). The general model simulated light distribution using the diffusion approximation of the transport theory, temperature rise using the bioheat equation and laser-induced injury using the Arrhenius damage model. Biological tissue was represented by two homogenous regions (dermis and fat layer) with a nonlinear air-tissue boundary condition including free convection. Video recordings were used to gain a better understanding of the back and forth movement of the cannula during laser lipolysis in order to consider them in our mathematical model. Infrared video recordings were also performed in order to compare the actual surface temperatures to our calculations. The reduction in fat volume was determined as a function of the total applied energy and subsequently compared to clinical data reported in the literature. Results In patients, when using cooled tumescent anesthesia, 1064 nm Nd:YAG laser or 980 nm diode laser: (6 W, back and forth motion: 100 mm/s) give similar skin surface temperature (max: 41°C). These measurements are in accordance with those obtained by mathematical modeling performed with a 1 mm cannula inserted inside the hypodermis layer at 0.8 cm below the surface. Similarly, the fat volume reduction observed in patients at 6-month follow up can be determined by mathematical modeling. This fat reduction depends on the applied

  9. Mathematical Model and Calibration Procedure of a PSD Sensor Used in Local Positioning Systems.

    PubMed

    Rodríguez-Navarro, David; Lázaro-Galilea, José Luis; Bravo-Muñoz, Ignacio; Gardel-Vicente, Alfredo; Domingo-Perez, Francisco; Tsirigotis, Georgios

    2016-09-15

    Here, we propose a mathematical model and a calibration procedure for a PSD (position sensitive device) sensor equipped with an optical system, to enable accurate measurement of the angle of arrival of one or more beams of light emitted by infrared (IR) transmitters located at distances of between 4 and 6 m. To achieve this objective, it was necessary to characterize the intrinsic parameters that model the system and obtain their values. This first approach was based on a pin-hole model, to which system nonlinearities were added, and this was used to model the points obtained with the nA currents provided by the PSD. In addition, we analyzed the main sources of error, including PSD sensor signal noise, gain factor imbalances and PSD sensor distortion. The results indicated that the proposed model and method provided satisfactory calibration and yielded precise parameter values, enabling accurate measurement of the angle of arrival with a low degree of error, as evidenced by the experimental results.

  10. Exploring Yellowstone National Park with Mathematical Modeling

    ERIC Educational Resources Information Center

    Wickstrom, Megan H.; Carr, Ruth; Lackey, Dacia

    2017-01-01

    Mathematical modeling, a practice standard in the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010), is a process by which students develop and use mathematics as a tool to make sense of the world around them. Students investigate a real-world situation by asking mathematical questions; along the way, they need to decide how to use…

  11. Pre-Service Teachers' Developing Conceptions about the Nature and Pedagogy of Mathematical Modeling in the Context of a Mathematical Modeling Course

    ERIC Educational Resources Information Center

    Cetinkaya, Bulent; Kertil, Mahmut; Erbas, Ayhan Kursat; Korkmaz, Himmet; Alacaci, Cengiz; Cakiroglu, Erdinc

    2016-01-01

    Adopting a multitiered design-based research perspective, this study examines pre-service secondary mathematics teachers' developing conceptions about (a) the nature of mathematical modeling in simulations of "real life" problem solving, and (b) pedagogical principles and strategies needed to teach mathematics through modeling. Unlike…

  12. Mathematical formalisms based on approximated kinetic representations for modeling genetic and metabolic pathways.

    PubMed

    Alves, Rui; Vilaprinyo, Ester; Hernádez-Bermejo, Benito; Sorribas, Albert

    2008-01-01

    There is a renewed interest in obtaining a systemic understanding of metabolism, gene expression and signal transduction processes, driven by the recent research focus on Systems Biology. From a biotechnological point of view, such a systemic understanding of how a biological system is designed to work can facilitate the rational manipulation of specific pathways in different cell types to achieve specific goals. Due to the intrinsic complexity of biological systems, mathematical models are a central tool for understanding and predicting the integrative behavior of those systems. Particularly, models are essential for a rational development of biotechnological applications and in understanding system's design from an evolutionary point of view. Mathematical models can be obtained using many different strategies. In each case, their utility will depend upon the properties of the mathematical representation and on the possibility of obtaining meaningful parameters from available data. In practice, there are several issues at stake when one has to decide which mathematical model is more appropriate for the study of a given problem. First, one needs a model that can represent the aspects of the system one wishes to study. Second, one must choose a mathematical representation that allows an accurate analysis of the system with respect to different aspects of interest (for example, robustness of the system, dynamical behavior, optimization of the system with respect to some production goal, parameter value determination, etc). Third, before choosing between alternative and equally appropriate mathematical representations for the system, one should compare representations with respect to easiness of automation for model set-up, simulation, and analysis of results. Fourth, one should also consider how to facilitate model transference and re-usability by other researchers and for distinct purposes. Finally, one factor that is important for all four aspects is the regularity

  13. Teaching Mathematical Modelling for Earth Sciences via Case Studies

    NASA Astrophysics Data System (ADS)

    Yang, Xin-She

    2010-05-01

    Mathematical modelling is becoming crucially important for earth sciences because the modelling of complex systems such as geological, geophysical and environmental processes requires mathematical analysis, numerical methods and computer programming. However, a substantial fraction of earth science undergraduates and graduates may not have sufficient skills in mathematical modelling, which is due to either limited mathematical training or lack of appropriate mathematical textbooks for self-study. In this paper, we described a detailed case-study-based approach for teaching mathematical modelling. We illustrate how essential mathematical skills can be developed for students with limited training in secondary mathematics so that they are confident in dealing with real-world mathematical modelling at university level. We have chosen various topics such as Airy isostasy, greenhouse effect, sedimentation and Stokes' flow,free-air and Bouguer gravity, Brownian motion, rain-drop dynamics, impact cratering, heat conduction and cooling of the lithosphere as case studies; and we use these step-by-step case studies to teach exponentials, logarithms, spherical geometry, basic calculus, complex numbers, Fourier transforms, ordinary differential equations, vectors and matrix algebra, partial differential equations, geostatistics and basic numeric methods. Implications for teaching university mathematics for earth scientists for tomorrow's classroom will also be discussed. Refereces 1) D. L. Turcotte and G. Schubert, Geodynamics, 2nd Edition, Cambridge University Press, (2002). 2) X. S. Yang, Introductory Mathematics for Earth Scientists, Dunedin Academic Press, (2009).

  14. Rival approaches to mathematical modelling in immunology

    NASA Astrophysics Data System (ADS)

    Andrew, Sarah M.; Baker, Christopher T. H.; Bocharov, Gennady A.

    2007-08-01

    In order to formulate quantitatively correct mathematical models of the immune system, one requires an understanding of immune processes and familiarity with a range of mathematical techniques. Selection of an appropriate model requires a number of decisions to be made, including a choice of the modelling objectives, strategies and techniques and the types of model considered as candidate models. The authors adopt a multidisciplinary perspective.

  15. Mathematical manipulative models: in defense of "beanbag biology".

    PubMed

    Jungck, John R; Gaff, Holly; Weisstein, Anton E

    2010-01-01

    Mathematical manipulative models have had a long history of influence in biological research and in secondary school education, but they are frequently neglected in undergraduate biology education. By linking mathematical manipulative models in a four-step process-1) use of physical manipulatives, 2) interactive exploration of computer simulations, 3) derivation of mathematical relationships from core principles, and 4) analysis of real data sets-we demonstrate a process that we have shared in biological faculty development workshops led by staff from the BioQUEST Curriculum Consortium over the past 24 yr. We built this approach based upon a broad survey of literature in mathematical educational research that has convincingly demonstrated the utility of multiple models that involve physical, kinesthetic learning to actual data and interactive simulations. Two projects that use this approach are introduced: The Biological Excel Simulations and Tools in Exploratory, Experiential Mathematics (ESTEEM) Project (http://bioquest.org/esteem) and Numerical Undergraduate Mathematical Biology Education (NUMB3R5 COUNT; http://bioquest.org/numberscount). Examples here emphasize genetics, ecology, population biology, photosynthesis, cancer, and epidemiology. Mathematical manipulative models help learners break through prior fears to develop an appreciation for how mathematical reasoning informs problem solving, inference, and precise communication in biology and enhance the diversity of quantitative biology education.

  16. An Examination of Pre-Service Mathematics Teachers' Approaches to Construct and Solve Mathematical Modelling Problems

    ERIC Educational Resources Information Center

    Bukova-Guzel, Esra

    2011-01-01

    This study examines the approaches displayed by pre-service mathematics teachers in their experiences of constructing mathematical modelling problems and the extent to which they perform the modelling process when solving the problems they construct. This case study was carried out with 35 pre-service teachers taking the Mathematical Modelling…

  17. Mathematical modeling of urea transport in the kidney.

    PubMed

    Layton, Anita T

    2014-01-01

    Mathematical modeling techniques have been useful in providing insights into biological systems, including the kidney. This article considers some of the mathematical models that concern urea transport in the kidney. Modeling simulations have been conducted to investigate, in the context of urea cycling and urine concentration, the effects of hypothetical active urea secretion into pars recta. Simulation results suggest that active urea secretion induces a "urea-selective" improvement in urine concentrating ability. Mathematical models have also been built to study the implications of the highly structured organization of tubules and vessels in the renal medulla on urea sequestration and cycling. The goal of this article is to show how physiological problems can be formulated and studied mathematically, and how such models may provide insights into renal functions.

  18. The (Mathematical) Modeling Process in Biosciences

    PubMed Central

    Torres, Nestor V.; Santos, Guido

    2015-01-01

    In this communication, we introduce a general framework and discussion on the role of models and the modeling process in the field of biosciences. The objective is to sum up the common procedures during the formalization and analysis of a biological problem from the perspective of Systems Biology, which approaches the study of biological systems as a whole. We begin by presenting the definitions of (biological) system and model. Particular attention is given to the meaning of mathematical model within the context of biology. Then, we present the process of modeling and analysis of biological systems. Three stages are described in detail: conceptualization of the biological system into a model, mathematical formalization of the previous conceptual model and optimization and system management derived from the analysis of the mathematical model. All along this work the main features and shortcomings of the process are analyzed and a set of rules that could help in the task of modeling any biological system are presented. Special regard is given to the formative requirements and the interdisciplinary nature of this approach. We conclude with some general considerations on the challenges that modeling is posing to current biology. PMID:26734063

  19. The (Mathematical) Modeling Process in Biosciences.

    PubMed

    Torres, Nestor V; Santos, Guido

    2015-01-01

    In this communication, we introduce a general framework and discussion on the role of models and the modeling process in the field of biosciences. The objective is to sum up the common procedures during the formalization and analysis of a biological problem from the perspective of Systems Biology, which approaches the study of biological systems as a whole. We begin by presenting the definitions of (biological) system and model. Particular attention is given to the meaning of mathematical model within the context of biology. Then, we present the process of modeling and analysis of biological systems. Three stages are described in detail: conceptualization of the biological system into a model, mathematical formalization of the previous conceptual model and optimization and system management derived from the analysis of the mathematical model. All along this work the main features and shortcomings of the process are analyzed and a set of rules that could help in the task of modeling any biological system are presented. Special regard is given to the formative requirements and the interdisciplinary nature of this approach. We conclude with some general considerations on the challenges that modeling is posing to current biology.

  20. Establishing an Explanatory Model for Mathematics Identity.

    PubMed

    Cribbs, Jennifer D; Hazari, Zahra; Sonnert, Gerhard; Sadler, Philip M

    2015-04-01

    This article empirically tests a previously developed theoretical framework for mathematics identity based on students' beliefs. The study employs data from more than 9,000 college calculus students across the United States to build a robust structural equation model. While it is generally thought that students' beliefs about their own competence in mathematics directly impact their identity as a "math person," findings indicate that students' self-perceptions related to competence and performance have an indirect effect on their mathematics identity, primarily by association with students' interest and external recognition in mathematics. Thus, the model indicates that students' competence and performance beliefs are not sufficient for their mathematics identity development, and it highlights the roles of interest and recognition. © 2015 The Authors. Child Development © 2015 Society for Research in Child Development, Inc.

  1. A continuous optimization approach for inferring parameters in mathematical models of regulatory networks.

    PubMed

    Deng, Zhimin; Tian, Tianhai

    2014-07-29

    The advances of systems biology have raised a large number of sophisticated mathematical models for describing the dynamic property of complex biological systems. One of the major steps in developing mathematical models is to estimate unknown parameters of the model based on experimentally measured quantities. However, experimental conditions limit the amount of data that is available for mathematical modelling. The number of unknown parameters in mathematical models may be larger than the number of observation data. The imbalance between the number of experimental data and number of unknown parameters makes reverse-engineering problems particularly challenging. To address the issue of inadequate experimental data, we propose a continuous optimization approach for making reliable inference of model parameters. This approach first uses a spline interpolation to generate continuous functions of system dynamics as well as the first and second order derivatives of continuous functions. The expanded dataset is the basis to infer unknown model parameters using various continuous optimization criteria, including the error of simulation only, error of both simulation and the first derivative, or error of simulation as well as the first and second derivatives. We use three case studies to demonstrate the accuracy and reliability of the proposed new approach. Compared with the corresponding discrete criteria using experimental data at the measurement time points only, numerical results of the ERK kinase activation module show that the continuous absolute-error criteria using both function and high order derivatives generate estimates with better accuracy. This result is also supported by the second and third case studies for the G1/S transition network and the MAP kinase pathway, respectively. This suggests that the continuous absolute-error criteria lead to more accurate estimates than the corresponding discrete criteria. We also study the robustness property of these three

  2. Mathematical modelling of intra-aortic balloon pump.

    PubMed

    Abdolrazaghi, Mona; Navidbakhsh, Mahdi; Hassani, Kamran

    2010-10-01

    Ischemic heart diseases now afflict thousands of Iranians and are the major cause of death in many industrialised countries. Mathematical modelling of an intra-aortic balloon pump (IABP) could provide a better understanding of its performance and help to represent blood flow and pressure in systemic arteries before and after inserting the pump. A mathematical modelling of the whole cardiovascular system was formulated using MATLAB software. The block diagram of the model consists of 43 compartments. All the anatomical data was extracted from the physiological references. In the next stage, myocardial infarction (MI) was induced in the model by decreasing the contractility of the left ventricle. The IABP was mathematically modelled and inserted in the model in the thoracic aorta I artery just before the descending aorta. The effects of IABP on MI were studied using the mathematical model. The normal operation of the cardiovascular system was studied firstly. The pressure-time graphs of the ventricles, atriums, aorta, pulmonary system, capillaries and arterioles were obtained. The volume-time curve of the left ventricle was also presented. The pressure-time curves of the left ventricle and thoracic aorta I were obtained for normal, MI, and inserted IABP conditions. Model verification was performed by comparing the simulation results with the clinical observations reported in the literature. IABP can be described by a theoretical model. Our model representing the cardiovascular system is capable of showing the effects of different pathologies such as MI and we have shown that MI effects can be reduced using IABP in accordance with the modelling results. The mathematical model should serve as a useful tool to simulate and better understand cardiovascular operation in normal and pathological conditions.

  3. Mathematical modeling of aeroelastic systems

    NASA Astrophysics Data System (ADS)

    Velmisov, Petr A.; Ankilov, Andrey V.; Semenova, Elizaveta P.

    2017-12-01

    In the paper, the stability of elastic elements of a class of designs that are in interaction with a gas or liquid flow is investigated. The definition of the stability of an elastic body corresponds to the concept of stability of dynamical systems by Lyapunov. As examples the mathematical models of flowing channels (models of vibration devices) at a subsonic flow and the mathematical models of protective surface at a supersonic flow are considered. Models are described by the related systems of the partial differential equations. An analytic investigation of stability is carried out on the basis of the construction of Lyapunov-type functionals, a numerical investigation is carried out on the basis of the Galerkin method. The various models of the gas-liquid environment (compressed, incompressible) and the various models of a deformable body (elastic linear and elastic nonlinear) are considered.

  4. Modelling and Optimizing Mathematics Learning in Children

    ERIC Educational Resources Information Center

    Käser, Tanja; Busetto, Alberto Giovanni; Solenthaler, Barbara; Baschera, Gian-Marco; Kohn, Juliane; Kucian, Karin; von Aster, Michael; Gross, Markus

    2013-01-01

    This study introduces a student model and control algorithm, optimizing mathematics learning in children. The adaptive system is integrated into a computer-based training system for enhancing numerical cognition aimed at children with developmental dyscalculia or difficulties in learning mathematics. The student model consists of a dynamic…

  5. A Review of Mathematical Models for Leukemia and Lymphoma

    PubMed Central

    Clapp, Geoffrey; Levy, Doron

    2014-01-01

    Recently, there has been significant activity in the mathematical community, aimed at developing quantitative tools for studying leukemia and lymphoma. Mathematical models have been applied to evaluate existing therapies and to suggest novel therapies. This article reviews the recent contributions of mathematical modeling to leukemia and lymphoma research. These developments suggest that mathematical modeling has great potential in this field. Collaboration between mathematicians, clinicians, and experimentalists can significantly improve leukemia and lymphoma therapy. PMID:26744598

  6. Mathematical modeling of a process the rolling delivery

    NASA Astrophysics Data System (ADS)

    Stepanov, Mikhail A.; Korolev, Andrey A.

    2018-03-01

    An adduced analysis of the scientific researches in a domain of the rolling equipments, also research of properties the working material. A one of perspective direction of scientific research this is mathematical modeling. That is broadly used in many scientific disciplines and especially at the technical, applied sciences. With the aid of mathematical modeling it can be study of physical properties of the researching objects and systems. A research of the rolling delivery and transporting devices realized with the aid of a construction of mathematical model of appropriate process. To be described the basic principles and conditions of a construction of mathematical models of the real objects. For example to be consider a construction of mathematical model the rolling delivery device. For a construction that is model used system of the equations, which consist of: Lagrange’s equation of a motion, describing of the law conservation of energy of a mechanical system, and the Navier - Stokes equations, which characterize of the flow of a continuous non-compressed fluid. A construction of mathematical model the rolling deliver to let determined of a total energy of device, and therefore to got the dependence upon the power of drive to a gap between of rolls. A corroborate the hypothesis about laminar the flow of a material into the rolling gap of deliver.

  7. Mathematical Modeling in the Secondary School Curriculum.

    ERIC Educational Resources Information Center

    Swetz, Frank, Ed.; Hartzler, J. S., Ed.

    Over the past 10 years, national conferences and committees investigating the state of American mathematics education have advocated an increased emphasis on problem solving and mathematical modeling situations in the secondary school curriculum. However, little effort has been made to prepare secondary school teachers to use mathematical modeling…

  8. Mathematical Problem Solving Ability of Junior High School Students through Ang’s Framework for Mathematical Modelling Instruction

    NASA Astrophysics Data System (ADS)

    Fasni, N.; Turmudi, T.; Kusnandi, K.

    2017-09-01

    This research background of this research is the importance of student problem solving abilities. The purpose of this study is to find out whether there are differences in the ability to solve mathematical problems between students who have learned mathematics using Ang’s Framework for Mathematical Modelling Instruction (AFFMMI) and students who have learned using scientific approach (SA). The method used in this research is a quasi-experimental method with pretest-postest control group design. Data analysis of mathematical problem solving ability using Indepent Sample Test. The results showed that there was a difference in the ability to solve mathematical problems between students who received learning with Ang’s Framework for Mathematical Modelling Instruction and students who received learning with a scientific approach. AFFMMI focuses on mathematical modeling. This modeling allows students to solve problems. The use of AFFMMI is able to improve the solving ability.

  9. A Two-Phase Space Resection Model for Accurate Topographic Reconstruction from Lunar Imagery with PushbroomScanners

    PubMed Central

    Xu, Xuemiao; Zhang, Huaidong; Han, Guoqiang; Kwan, Kin Chung; Pang, Wai-Man; Fang, Jiaming; Zhao, Gansen

    2016-01-01

    Exterior orientation parameters’ (EOP) estimation using space resection plays an important role in topographic reconstruction for push broom scanners. However, existing models of space resection are highly sensitive to errors in data. Unfortunately, for lunar imagery, the altitude data at the ground control points (GCPs) for space resection are error-prone. Thus, existing models fail to produce reliable EOPs. Motivated by a finding that for push broom scanners, angular rotations of EOPs can be estimated independent of the altitude data and only involving the geographic data at the GCPs, which are already provided, hence, we divide the modeling of space resection into two phases. Firstly, we estimate the angular rotations based on the reliable geographic data using our proposed mathematical model. Then, with the accurate angular rotations, the collinear equations for space resection are simplified into a linear problem, and the global optimal solution for the spatial position of EOPs can always be achieved. Moreover, a certainty term is integrated to penalize the unreliable altitude data for increasing the error tolerance. Experimental results evidence that our model can obtain more accurate EOPs and topographic maps not only for the simulated data, but also for the real data from Chang’E-1, compared to the existing space resection model. PMID:27077855

  10. A Two-Phase Space Resection Model for Accurate Topographic Reconstruction from Lunar Imagery with PushbroomScanners.

    PubMed

    Xu, Xuemiao; Zhang, Huaidong; Han, Guoqiang; Kwan, Kin Chung; Pang, Wai-Man; Fang, Jiaming; Zhao, Gansen

    2016-04-11

    Exterior orientation parameters' (EOP) estimation using space resection plays an important role in topographic reconstruction for push broom scanners. However, existing models of space resection are highly sensitive to errors in data. Unfortunately, for lunar imagery, the altitude data at the ground control points (GCPs) for space resection are error-prone. Thus, existing models fail to produce reliable EOPs. Motivated by a finding that for push broom scanners, angular rotations of EOPs can be estimated independent of the altitude data and only involving the geographic data at the GCPs, which are already provided, hence, we divide the modeling of space resection into two phases. Firstly, we estimate the angular rotations based on the reliable geographic data using our proposed mathematical model. Then, with the accurate angular rotations, the collinear equations for space resection are simplified into a linear problem, and the global optimal solution for the spatial position of EOPs can always be achieved. Moreover, a certainty term is integrated to penalize the unreliable altitude data for increasing the error tolerance. Experimental results evidence that our model can obtain more accurate EOPs and topographic maps not only for the simulated data, but also for the real data from Chang'E-1, compared to the existing space resection model.

  11. Modelling Mathematical Reasoning in Physics Education

    NASA Astrophysics Data System (ADS)

    Uhden, Olaf; Karam, Ricardo; Pietrocola, Maurício; Pospiech, Gesche

    2012-04-01

    Many findings from research as well as reports from teachers describe students' problem solving strategies as manipulation of formulas by rote. The resulting dissatisfaction with quantitative physical textbook problems seems to influence the attitude towards the role of mathematics in physics education in general. Mathematics is often seen as a tool for calculation which hinders a conceptual understanding of physical principles. However, the role of mathematics cannot be reduced to this technical aspect. Hence, instead of putting mathematics away we delve into the nature of physical science to reveal the strong conceptual relationship between mathematics and physics. Moreover, we suggest that, for both prospective teaching and further research, a focus on deeply exploring such interdependency can significantly improve the understanding of physics. To provide a suitable basis, we develop a new model which can be used for analysing different levels of mathematical reasoning within physics. It is also a guideline for shifting the attention from technical to structural mathematical skills while teaching physics. We demonstrate its applicability for analysing physical-mathematical reasoning processes with an example.

  12. Mental models accurately predict emotion transitions.

    PubMed

    Thornton, Mark A; Tamir, Diana I

    2017-06-06

    Successful social interactions depend on people's ability to predict others' future actions and emotions. People possess many mechanisms for perceiving others' current emotional states, but how might they use this information to predict others' future states? We hypothesized that people might capitalize on an overlooked aspect of affective experience: current emotions predict future emotions. By attending to regularities in emotion transitions, perceivers might develop accurate mental models of others' emotional dynamics. People could then use these mental models of emotion transitions to predict others' future emotions from currently observable emotions. To test this hypothesis, studies 1-3 used data from three extant experience-sampling datasets to establish the actual rates of emotional transitions. We then collected three parallel datasets in which participants rated the transition likelihoods between the same set of emotions. Participants' ratings of emotion transitions predicted others' experienced transitional likelihoods with high accuracy. Study 4 demonstrated that four conceptual dimensions of mental state representation-valence, social impact, rationality, and human mind-inform participants' mental models. Study 5 used 2 million emotion reports on the Experience Project to replicate both of these findings: again people reported accurate models of emotion transitions, and these models were informed by the same four conceptual dimensions. Importantly, neither these conceptual dimensions nor holistic similarity could fully explain participants' accuracy, suggesting that their mental models contain accurate information about emotion dynamics above and beyond what might be predicted by static emotion knowledge alone.

  13. Mental models accurately predict emotion transitions

    PubMed Central

    Thornton, Mark A.; Tamir, Diana I.

    2017-01-01

    Successful social interactions depend on people’s ability to predict others’ future actions and emotions. People possess many mechanisms for perceiving others’ current emotional states, but how might they use this information to predict others’ future states? We hypothesized that people might capitalize on an overlooked aspect of affective experience: current emotions predict future emotions. By attending to regularities in emotion transitions, perceivers might develop accurate mental models of others’ emotional dynamics. People could then use these mental models of emotion transitions to predict others’ future emotions from currently observable emotions. To test this hypothesis, studies 1–3 used data from three extant experience-sampling datasets to establish the actual rates of emotional transitions. We then collected three parallel datasets in which participants rated the transition likelihoods between the same set of emotions. Participants’ ratings of emotion transitions predicted others’ experienced transitional likelihoods with high accuracy. Study 4 demonstrated that four conceptual dimensions of mental state representation—valence, social impact, rationality, and human mind—inform participants’ mental models. Study 5 used 2 million emotion reports on the Experience Project to replicate both of these findings: again people reported accurate models of emotion transitions, and these models were informed by the same four conceptual dimensions. Importantly, neither these conceptual dimensions nor holistic similarity could fully explain participants’ accuracy, suggesting that their mental models contain accurate information about emotion dynamics above and beyond what might be predicted by static emotion knowledge alone. PMID:28533373

  14. Scaffolding Mathematical Modelling with a Solution Plan

    ERIC Educational Resources Information Center

    Schukajlow, Stanislaw; Kolter, Jana; Blum, Werner

    2015-01-01

    In the study presented in this paper, we examined the possibility to scaffold mathematical modelling with strategies. The strategies were prompted using an instrument called "solution plan" as a scaffold. The effects of this step by step instrument on mathematical modelling competency and on self-reported strategies were tested using…

  15. Leading Undergraduate Research Projects in Mathematical Modeling

    ERIC Educational Resources Information Center

    Seshaiyer, Padmanabhan

    2017-01-01

    In this article, we provide some useful perspectives and experiences in mentoring students in undergraduate research (UR) in mathematical modeling using differential equations. To engage students in this topic, we present a systematic approach to the creation of rich problems from real-world phenomena; present mathematical models that are derived…

  16. Mathematical modeling provides kinetic details of the human immune response to vaccination

    PubMed Central

    Le, Dustin; Miller, Joseph D.; Ganusov, Vitaly V.

    2015-01-01

    With major advances in experimental techniques to track antigen-specific immune responses many basic questions on the kinetics of virus-specific immunity in humans remain unanswered. To gain insights into kinetics of T and B cell responses in human volunteers we combined mathematical models and experimental data from recent studies employing vaccines against yellow fever and smallpox. Yellow fever virus-specific CD8 T cell population expanded slowly with the average doubling time of 2 days peaking 2.5 weeks post immunization. Interestingly, we found that the peak of the yellow fever-specific CD8 T cell response was determined by the rate of T cell proliferation and not by the precursor frequency of antigen-specific cells as has been suggested in several studies in mice. We also found that while the frequency of virus-specific T cells increased slowly, the slow increase could still accurately explain clearance of yellow fever virus in the blood. Our additional mathematical model described well the kinetics of virus-specific antibody-secreting cell and antibody response to vaccinia virus in vaccinated individuals suggesting that most of antibodies in 3 months post immunization were derived from the population of circulating antibody-secreting cells. Taken together, our analysis provided novel insights into mechanisms by which live vaccines induce immunity to viral infections and highlighted challenges of applying methods of mathematical modeling to the current, state-of-the-art yet limited immunological data. PMID:25621280

  17. Mathematical modeling provides kinetic details of the human immune response to vaccination.

    PubMed

    Le, Dustin; Miller, Joseph D; Ganusov, Vitaly V

    2014-01-01

    With major advances in experimental techniques to track antigen-specific immune responses many basic questions on the kinetics of virus-specific immunity in humans remain unanswered. To gain insights into kinetics of T and B cell responses in human volunteers we combined mathematical models and experimental data from recent studies employing vaccines against yellow fever and smallpox. Yellow fever virus-specific CD8 T cell population expanded slowly with the average doubling time of 2 days peaking 2.5 weeks post immunization. Interestingly, we found that the peak of the yellow fever-specific CD8 T cell response was determined by the rate of T cell proliferation and not by the precursor frequency of antigen-specific cells as has been suggested in several studies in mice. We also found that while the frequency of virus-specific T cells increased slowly, the slow increase could still accurately explain clearance of yellow fever virus in the blood. Our additional mathematical model described well the kinetics of virus-specific antibody-secreting cell and antibody response to vaccinia virus in vaccinated individuals suggesting that most of antibodies in 3 months post immunization were derived from the population of circulating antibody-secreting cells. Taken together, our analysis provided novel insights into mechanisms by which live vaccines induce immunity to viral infections and highlighted challenges of applying methods of mathematical modeling to the current, state-of-the-art yet limited immunological data.

  18. The Spectrum of Mathematical Models.

    ERIC Educational Resources Information Center

    Karplus, Walter J.

    1983-01-01

    Mathematical modeling problems encountered in many disciplines are discussed in terms of the modeling process and applications of models. The models are classified according to three types of abstraction: continuous-space-continuous-time, discrete-space-continuous-time, and discrete-space-discrete-time. Limitations in different kinds of modeling…

  19. Intensity level for exercise training in fibromyalgia by using mathematical models.

    PubMed

    Lemos, Maria Carolina D; Valim, Valéria; Zandonade, Eliana; Natour, Jamil

    2010-03-22

    It has not been assessed before whether mathematical models described in the literature for prescriptions of exercise can be used for fibromyalgia syndrome patients. The objective of this paper was to determine how age-predicted heart rate formulas can be used with fibromyalgia syndrome populations as well as to find out which mathematical models are more accurate to control exercise intensity. A total of 60 women aged 18-65 years with fibromyalgia syndrome were included; 32 were randomized to walking training at anaerobic threshold. Age-predicted formulas to maximum heart rate ("220 minus age" and "208 minus 0.7 x age") were correlated with achieved maximum heart rate (HRMax) obtained by spiroergometry. Subsequently, six mathematical models using heart rate reserve (HRR) and age-predicted HRMax formulas were studied to estimate the intensity level of exercise training corresponding to heart rate at anaerobic threshold (HRAT) obtained by spiroergometry. Linear and nonlinear regression models were used for correlations and residues analysis for the adequacy of the models. Age-predicted HRMax and HRAT formulas had a good correlation with achieved heart rate obtained in spiroergometry (r = 0.642; p < 0.05). For exercise prescription in the anaerobic threshold intensity, the percentages were 52.2-60.6% HRR and 75.5-80.9% HRMax. Formulas using HRR and the achieved HRMax showed better correlation. Furthermore, the percentages of HRMax and HRR were significantly higher for the trained individuals (p < 0.05). Age-predicted formulas can be used for estimating HRMax and for exercise prescriptions in women with fibromyalgia syndrome. Karnoven's formula using heart rate achieved in ergometric test showed a better correlation. For the prescription of exercises in the threshold intensity, 52% to 60% HRR or 75% to 80% HRMax must be used in sedentary women with fibromyalgia syndrome and these values are higher and must be corrected for trained patients.

  20. Development of a Multidisciplinary Middle School Mathematics Infusion Model

    ERIC Educational Resources Information Center

    Russo, Maria; Hecht, Deborah; Burghardt, M. David; Hacker, Michael; Saxman, Laura

    2011-01-01

    The National Science Foundation (NSF) funded project "Mathematics, Science, and Technology Partnership" (MSTP) developed a multidisciplinary instructional model for connecting mathematics to science, technology and engineering content areas at the middle school level. Specifically, the model infused mathematics into middle school curriculum…

  1. Ocular hemodynamics and glaucoma: the role of mathematical modeling.

    PubMed

    Harris, Alon; Guidoboni, Giovanna; Arciero, Julia C; Amireskandari, Annahita; Tobe, Leslie A; Siesky, Brent A

    2013-01-01

    To discuss the role of mathematical modeling in studying ocular hemodynamics, with a focus on glaucoma. We reviewed recent literature on glaucoma, ocular blood flow, autoregulation, the optic nerve head, and the use of mathematical modeling in ocular circulation. Many studies suggest that alterations in ocular hemodynamics play a significant role in the development, progression, and incidence of glaucoma. Although there is currently a limited number of studies involving mathematical modeling of ocular blood flow, regulation, and diseases (such as glaucoma), preliminary modeling work shows the potential of mathematical models to elucidate the mechanisms that contribute most significantly to glaucoma progression. Mathematical modeling is a useful tool when used synergistically with clinical and laboratory data in the study of ocular blood flow and glaucoma. The development of models to investigate the relationship between ocular hemodynamic alterations and glaucoma progression will provide a unique and useful method for studying the pathophysiology of glaucoma.

  2. Dealing with dissatisfaction in mathematical modelling to integrate QFD and Kano’s model

    NASA Astrophysics Data System (ADS)

    Retno Sari Dewi, Dian; Debora, Joana; Edy Sianto, Martinus

    2017-12-01

    The purpose of the study is to implement the integration of Quality Function Deployment (QFD) and Kano’s Model into mathematical model. Voice of customer data in QFD was collected using questionnaire and the questionnaire was developed based on Kano’s model. Then the operational research methodology was applied to build the objective function and constraints in the mathematical model. The relationship between voice of customer and engineering characteristics was modelled using linier regression model. Output of the mathematical model would be detail of engineering characteristics. The objective function of this model is to maximize satisfaction and minimize dissatisfaction as well. Result of this model is 62% .The major contribution of this research is to implement the existing mathematical model to integrate QFD and Kano’s Model in the case study of shoe cabinet.

  3. Mathematics, Modelling and Students in Transition

    ERIC Educational Resources Information Center

    Wake, Geoff

    2016-01-01

    This article is based on data from two major research projects that investigated students involved in mathematically demanding courses during their transition through college and into university. It explores the nature of modelling as a mathematical practice in this important transition phase for students. Theoretical considerations are informed…

  4. Nonlinear mathematical modeling and sensitivity analysis of hydraulic drive unit

    NASA Astrophysics Data System (ADS)

    Kong, Xiangdong; Yu, Bin; Quan, Lingxiao; Ba, Kaixian; Wu, Liujie

    2015-09-01

    The previous sensitivity analysis researches are not accurate enough and also have the limited reference value, because those mathematical models are relatively simple and the change of the load and the initial displacement changes of the piston are ignored, even experiment verification is not conducted. Therefore, in view of deficiencies above, a nonlinear mathematical model is established in this paper, including dynamic characteristics of servo valve, nonlinear characteristics of pressure-flow, initial displacement of servo cylinder piston and friction nonlinearity. The transfer function block diagram is built for the hydraulic drive unit closed loop position control, as well as the state equations. Through deriving the time-varying coefficient items matrix and time-varying free items matrix of sensitivity equations respectively, the expression of sensitivity equations based on the nonlinear mathematical model are obtained. According to structure parameters of hydraulic drive unit, working parameters, fluid transmission characteristics and measured friction-velocity curves, the simulation analysis of hydraulic drive unit is completed on the MATLAB/Simulink simulation platform with the displacement step 2 mm, 5 mm and 10 mm, respectively. The simulation results indicate that the developed nonlinear mathematical model is sufficient by comparing the characteristic curves of experimental step response and simulation step response under different constant load. Then, the sensitivity function time-history curves of seventeen parameters are obtained, basing on each state vector time-history curve of step response characteristic. The maximum value of displacement variation percentage and the sum of displacement variation absolute values in the sampling time are both taken as sensitivity indexes. The sensitivity indexes values above are calculated and shown visually in histograms under different working conditions, and change rules are analyzed. Then the sensitivity

  5. a Discrete Mathematical Model to Simulate Malware Spreading

    NASA Astrophysics Data System (ADS)

    Del Rey, A. Martin; Sánchez, G. Rodriguez

    2012-10-01

    With the advent and worldwide development of Internet, the study and control of malware spreading has become very important. In this sense, some mathematical models to simulate malware propagation have been proposed in the scientific literature, and usually they are based on differential equations exploiting the similarities with mathematical epidemiology. The great majority of these models study the behavior of a particular type of malware called computer worms; indeed, to the best of our knowledge, no model has been proposed to simulate the spreading of a computer virus (the traditional type of malware which differs from computer worms in several aspects). In this sense, the purpose of this work is to introduce a new mathematical model not based on continuous mathematics tools but on discrete ones, to analyze and study the epidemic behavior of computer virus. Specifically, cellular automata are used in order to design such model.

  6. Mathematical modeling of metabolism and hemodynamics.

    PubMed

    Costalat, R; Francoise, J-P; Menuel, C; Lahutte, M; Vallée, J-N; de Marco, G; Chiras, J; Guillevin, R

    2012-06-01

    We provide a mathematical study of a model of energy metabolism and hemodynamics of glioma allowing a better understanding of metabolic modifications leading to anaplastic transformation from low grade glioma. This mathematical analysis allows ultimately to unveil the solution to a viability problem which seems quite pertinent for applications to medecine.

  7. "Model Your Genes the Mathematical Way"--A Mathematical Biology Workshop for Secondary School Teachers

    ERIC Educational Resources Information Center

    Martins, Ana Margarida; Vera-Licona, Paola; Laubenbacher, Reinhard

    2008-01-01

    This article describes a mathematical biology workshop given to secondary school teachers of the Danville area in Virginia, USA. The goal of the workshop was to enable teams of teachers with biology and mathematics expertise to incorporate lesson plans in mathematical modelling into the curriculum. The biological focus of the activities is the…

  8. The Real and the Mathematical in Quantum Modeling: From Principles to Models and from Models to Principles

    NASA Astrophysics Data System (ADS)

    Plotnitsky, Arkady

    2017-06-01

    The history of mathematical modeling outside physics has been dominated by the use of classical mathematical models, C-models, primarily those of a probabilistic or statistical nature. More recently, however, quantum mathematical models, Q-models, based in the mathematical formalism of quantum theory have become more prominent in psychology, economics, and decision science. The use of Q-models in these fields remains controversial, in part because it is not entirely clear whether Q-models are necessary for dealing with the phenomena in question or whether C-models would still suffice. My aim, however, is not to assess the necessity of Q-models in these fields, but instead to reflect on what the possible applicability of Q-models may tell us about the corresponding phenomena there, vis-à-vis quantum phenomena in physics. In order to do so, I shall first discuss the key reasons for the use of Q-models in physics. In particular, I shall examine the fundamental principles that led to the development of quantum mechanics. Then I shall consider a possible role of similar principles in using Q-models outside physics. Psychology, economics, and decision science borrow already available Q-models from quantum theory, rather than derive them from their own internal principles, while quantum mechanics was derived from such principles, because there was no readily available mathematical model to handle quantum phenomena, although the mathematics ultimately used in quantum did in fact exist then. I shall argue, however, that the principle perspective on mathematical modeling outside physics might help us to understand better the role of Q-models in these fields and possibly to envision new models, conceptually analogous to but mathematically different from those of quantum theory, helpful or even necessary there or in physics itself. I shall suggest one possible type of such models, singularized probabilistic, SP, models, some of which are time-dependent, TDSP-models. The

  9. Some Reflections on the Teaching of Mathematical Modeling

    ERIC Educational Resources Information Center

    Warwick, Jon

    2007-01-01

    This paper offers some reflections on the difficulties of teaching mathematical modeling to students taking higher education courses in which modeling plays a significant role. In the author's experience, other aspects of the model development process often cause problems rather than the use of mathematics. Since these other aspects involve…

  10. Mathematical Manipulative Models: In Defense of “Beanbag Biology”

    PubMed Central

    Gaff, Holly; Weisstein, Anton E.

    2010-01-01

    Mathematical manipulative models have had a long history of influence in biological research and in secondary school education, but they are frequently neglected in undergraduate biology education. By linking mathematical manipulative models in a four-step process—1) use of physical manipulatives, 2) interactive exploration of computer simulations, 3) derivation of mathematical relationships from core principles, and 4) analysis of real data sets—we demonstrate a process that we have shared in biological faculty development workshops led by staff from the BioQUEST Curriculum Consortium over the past 24 yr. We built this approach based upon a broad survey of literature in mathematical educational research that has convincingly demonstrated the utility of multiple models that involve physical, kinesthetic learning to actual data and interactive simulations. Two projects that use this approach are introduced: The Biological Excel Simulations and Tools in Exploratory, Experiential Mathematics (ESTEEM) Project (http://bioquest.org/esteem) and Numerical Undergraduate Mathematical Biology Education (NUMB3R5 COUNT; http://bioquest.org/numberscount). Examples here emphasize genetics, ecology, population biology, photosynthesis, cancer, and epidemiology. Mathematical manipulative models help learners break through prior fears to develop an appreciation for how mathematical reasoning informs problem solving, inference, and precise communication in biology and enhance the diversity of quantitative biology education. PMID:20810952

  11. Accurately tracking single-cell movement trajectories in microfluidic cell sorting devices.

    PubMed

    Jeong, Jenny; Frohberg, Nicholas J; Zhou, Enlu; Sulchek, Todd; Qiu, Peng

    2018-01-01

    Microfluidics are routinely used to study cellular properties, including the efficient quantification of single-cell biomechanics and label-free cell sorting based on the biomechanical properties, such as elasticity, viscosity, stiffness, and adhesion. Both quantification and sorting applications require optimal design of the microfluidic devices and mathematical modeling of the interactions between cells, fluid, and the channel of the device. As a first step toward building such a mathematical model, we collected video recordings of cells moving through a ridged microfluidic channel designed to compress and redirect cells according to cell biomechanics. We developed an efficient algorithm that automatically and accurately tracked the cell trajectories in the recordings. We tested the algorithm on recordings of cells with different stiffness, and showed the correlation between cell stiffness and the tracked trajectories. Moreover, the tracking algorithm successfully picked up subtle differences of cell motion when passing through consecutive ridges. The algorithm for accurately tracking cell trajectories paves the way for future efforts of modeling the flow, forces, and dynamics of cell properties in microfluidics applications.

  12. To Assess Students' Attitudes, Skills and Competencies in Mathematical Modeling

    ERIC Educational Resources Information Center

    Lingefjard, Thomas; Holmquist, Mikael

    2005-01-01

    Peer-to-peer assessment, take-home exams and a mathematical modeling survey were used to monitor and assess students' attitudes, skills and competencies in mathematical modeling. The students were all in a secondary mathematics, teacher education program with a comprehensive amount of mathematics studies behind them. Findings indicate that…

  13. Methods to achieve accurate projection of regional and global raster databases

    USGS Publications Warehouse

    Usery, E. Lynn; Seong, Jeong Chang; Steinwand, Dan

    2002-01-01

    Modeling regional and global activities of climatic and human-induced change requires accurate geographic data from which we can develop mathematical and statistical tabulations of attributes and properties of the environment. Many of these models depend on data formatted as raster cells or matrices of pixel values. Recently, it has been demonstrated that regional and global raster datasets are subject to significant error from mathematical projection and that these errors are of such magnitude that model results may be jeopardized (Steinwand, et al., 1995; Yang, et al., 1996; Usery and Seong, 2001; Seong and Usery, 2001). There is a need to develop methods of projection that maintain the accuracy of these datasets to support regional and global analyses and modeling

  14. Mathematical model of rolling an elastic wheel over deformable support base

    NASA Astrophysics Data System (ADS)

    Volskaia, V. N.; Zhileykin, M. M.; Zakharov, A. Y.

    2018-02-01

    to provide the most accurate description of the interaction process of a wheeled propulsion devices and the ground, also this method allows to define tension in the ground, deformation of the ground and the tire and ground’s compression. However, the high laboriousness of computations is essential shortcoming of that method therefore it’s hard to use these models as part of the general motion model of multi-axis wheeled vehicles. The purpose of this research is the elaboration of mathematical model of elastic wheel rolling over deformable rough support base taking into account the contact patch deformation. The mathematical model of rectilinear rolling an elastic wheel over rough deformable support base, taking into account variation of contact patch area and variation in the direction of the radial and tangential reactions also load bearing capacity of the ground, is developed. The efficiency of developed mathematical model of rectilinear rolling an elastic wheel over rough deformable support base is proved by the simulation methods.

  15. Fuzzy logic, artificial neural network and mathematical model for prediction of white mulberry drying kinetics

    NASA Astrophysics Data System (ADS)

    Jahedi Rad, Shahpour; Kaveh, Mohammad; Sharabiani, Vali Rasooli; Taghinezhad, Ebrahim

    2018-05-01

    The thin-layer convective- infrared drying behavior of white mulberry was experimentally studied at infrared power levels of 500, 1000 and 1500 W, drying air temperatures of 40, 55 and 70 °C and inlet drying air speeds of 0.4, 1 and 1.6 m/s. Drying rate raised with the rise of infrared power levels at a distinct air temperature and velocity and thus decreased the drying time. Five mathematical models describing thin-layer drying have been fitted to the drying data. Midlli et al. model could satisfactorily describe the convective-infrared drying of white mulberry fruit with the values of the correlation coefficient (R 2=0.9986) and root mean square error of (RMSE= 0.04795). Artificial neural network (ANN) and fuzzy logic methods was desirably utilized for modeling output parameters (moisture ratio (MR)) regarding input parameters. Results showed that output parameters were more accurately predicted by fuzzy model than by the ANN and mathematical models. Correlation coefficient (R 2) and RMSE generated by the fuzzy model (respectively 0.9996 and 0.01095) were higher than referred values for the ANN model (0.9990 and 0.01988 respectively).

  16. Mathematical model of compact type evaporator

    NASA Astrophysics Data System (ADS)

    Borovička, Martin; Hyhlík, Tomáš

    2018-06-01

    In this paper, development of the mathematical model for evaporator used in heat pump circuits is covered, with focus on air dehumidification application. Main target of this ad-hoc numerical model is to simulate heat and mass transfer in evaporator for prescribed inlet conditions and different geometrical parameters. Simplified 2D mathematical model is developed in MATLAB SW. Solvers for multiple heat and mass transfer problems - plate surface temperature, condensate film temperature, local heat and mass transfer coefficients, refrigerant temperature distribution, humid air enthalpy change are included as subprocedures of this model. An automatic procedure of data transfer is developed in order to use results of MATLAB model in more complex simulation within commercial CFD code. In the end, Proper Orthogonal Decomposition (POD) method is introduced and implemented into MATLAB model.

  17. Optimal Cluster Mill Pass Scheduling With an Accurate and Rapid New Strip Crown Model

    NASA Astrophysics Data System (ADS)

    Malik, Arif S.; Grandhi, Ramana V.; Zipf, Mark E.

    2007-05-01

    Besides the requirement to roll coiled sheet at high levels of productivity, the optimal pass scheduling of cluster-type reversing cold mills presents the added challenge of assigning mill parameters that facilitate the best possible strip flatness. The pressures of intense global competition, and the requirements for increasingly thinner, higher quality specialty sheet products that are more difficult to roll, continue to force metal producers to commission innovative flatness-control technologies. This means that during the on-line computerized set-up of rolling mills, the mathematical model should not only determine the minimum total number of passes and maximum rolling speed, it should simultaneously optimize the pass-schedule so that desired flatness is assured, either by manual or automated means. In many cases today, however, on-line prediction of strip crown and corresponding flatness for the complex cluster-type rolling mills is typically addressed either by trial and error, by approximate deflection models for equivalent vertical roll-stacks, or by non-physical pattern recognition style models. The abundance of the aforementioned methods is largely due to the complexity of cluster-type mill configurations and the lack of deflection models with sufficient accuracy and speed for on-line use. Without adequate assignment of the pass-schedule set-up parameters, it may be difficult or impossible to achieve the required strip flatness. In this paper, we demonstrate optimization of cluster mill pass-schedules using a new accurate and rapid strip crown model. This pass-schedule optimization includes computations of the predicted strip thickness profile to validate mathematical constraints. In contrast to many of the existing methods for on-line prediction of strip crown and flatness on cluster mills, the demonstrated method requires minimal prior tuning and no extensive training with collected mill data. To rapidly and accurately solve the multi-contact problem

  18. Modellus: Learning Physics with Mathematical Modelling

    NASA Astrophysics Data System (ADS)

    Teodoro, Vitor

    Computers are now a major tool in research and development in almost all scientific and technological fields. Despite recent developments, this is far from true for learning environments in schools and most undergraduate studies. This thesis proposes a framework for designing curricula where computers, and computer modelling in particular, are a major tool for learning. The framework, based on research on learning science and mathematics and on computer user interface, assumes that: 1) learning is an active process of creating meaning from representations; 2) learning takes place in a community of practice where students learn both from their own effort and from external guidance; 3) learning is a process of becoming familiar with concepts, with links between concepts, and with representations; 4) direct manipulation user interfaces allow students to explore concrete-abstract objects such as those of physics and can be used by students with minimal computer knowledge. Physics is the science of constructing models and explanations about the physical world. And mathematical models are an important type of models that are difficult for many students. These difficulties can be rooted in the fact that most students do not have an environment where they can explore functions, differential equations and iterations as primary objects that model physical phenomena--as objects-to-think-with, reifying the formal objects of physics. The framework proposes that students should be introduced to modelling in a very early stage of learning physics and mathematics, two scientific areas that must be taught in very closely related way, as they were developed since Galileo and Newton until the beginning of our century, before the rise of overspecialisation in science. At an early stage, functions are the main type of objects used to model real phenomena, such as motions. At a later stage, rates of change and equations with rates of change play an important role. This type of equations

  19. Learning to teach mathematical modelling in secondary and tertiary education

    NASA Astrophysics Data System (ADS)

    Ferri, Rita Borromeo

    2017-07-01

    Since 2003 mathematical modelling in Germany is not only a topic for scientific disciplines in university mathematics courses, but also in school starting with primary school. This paper shows what mathematical modelling means in school and how it can be taught as a basis for complex modeling problems in tertiary education.

  20. Mathematical Manipulative Models: In Defense of "Beanbag Biology"

    ERIC Educational Resources Information Center

    Jungck, John R.; Gaff, Holly; Weisstein, Anton E.

    2010-01-01

    Mathematical manipulative models have had a long history of influence in biological research and in secondary school education, but they are frequently neglected in undergraduate biology education. By linking mathematical manipulative models in a four-step process--1) use of physical manipulatives, 2) interactive exploration of computer…

  1. Mathematical Modeling of Loop Heat Pipes

    NASA Technical Reports Server (NTRS)

    Kaya, Tarik; Ku, Jentung; Hoang, Triem T.; Cheung, Mark L.

    1998-01-01

    The primary focus of this study is to model steady-state performance of a Loop Heat Pipe (LHP). The mathematical model is based on the steady-state energy balance equations at each component of the LHP. The heat exchange between each LHP component and the surrounding is taken into account. Both convection and radiation environments are modeled. The loop operating temperature is calculated as a function of the applied power at a given loop condition. Experimental validation of the model is attempted by using two different LHP designs. The mathematical model is tested at different sink temperatures and at different elevations of the loop. Tbc comparison of the calculations and experimental results showed very good agreement (within 3%). This method proved to be a useful tool in studying steady-state LHP performance characteristics.

  2. Building Mathematical Models of Simple Harmonic and Damped Motion.

    ERIC Educational Resources Information Center

    Edwards, Thomas

    1995-01-01

    By developing a sequence of mathematical models of harmonic motion, shows that mathematical models are not right or wrong, but instead are better or poorer representations of the problem situation. (MKR)

  3. Mathematical modelling and quantitative methods.

    PubMed

    Edler, L; Poirier, K; Dourson, M; Kleiner, J; Mileson, B; Nordmann, H; Renwick, A; Slob, W; Walton, K; Würtzen, G

    2002-01-01

    The present review reports on the mathematical methods and statistical techniques presently available for hazard characterisation. The state of the art of mathematical modelling and quantitative methods used currently for regulatory decision-making in Europe and additional potential methods for risk assessment of chemicals in food and diet are described. Existing practices of JECFA, FDA, EPA, etc., are examined for their similarities and differences. A framework is established for the development of new and improved quantitative methodologies. Areas for refinement, improvement and increase of efficiency of each method are identified in a gap analysis. Based on this critical evaluation, needs for future research are defined. It is concluded from our work that mathematical modelling of the dose-response relationship would improve the risk assessment process. An adequate characterisation of the dose-response relationship by mathematical modelling clearly requires the use of a sufficient number of dose groups to achieve a range of different response levels. This need not necessarily lead to an increase in the total number of animals in the study if an appropriate design is used. Chemical-specific data relating to the mode or mechanism of action and/or the toxicokinetics of the chemical should be used for dose-response characterisation whenever possible. It is concluded that a single method of hazard characterisation would not be suitable for all kinds of risk assessments, and that a range of different approaches is necessary so that the method used is the most appropriate for the data available and for the risk characterisation issue. Future refinements to dose-response characterisation should incorporate more clearly the extent of uncertainty and variability in the resulting output.

  4. Studies on Mathematical Models of Wet Adhesion and Lifetime Prediction of Organic Coating/Steel by Grey System Theory.

    PubMed

    Meng, Fandi; Liu, Ying; Liu, Li; Li, Ying; Wang, Fuhui

    2017-06-28

    A rapid degradation of wet adhesion is the key factor controlling coating lifetime, for the organic coatings under marine hydrostatic pressure. The mathematical models of wet adhesion have been studied by Grey System Theory (GST). Grey models (GM) (1, 1) of epoxy varnish (EV) coating/steel and epoxy glass flake (EGF) coating/steel have been established, and a lifetime prediction formula has been proposed on the basis of these models. The precision assessments indicate that the established models are accurate, and the prediction formula is capable of making precise lifetime forecasting of the coatings.

  5. A Seminar in Mathematical Model-Building.

    ERIC Educational Resources Information Center

    Smith, David A.

    1979-01-01

    A course in mathematical model-building is described. Suggested modeling projects include: urban problems, biology and ecology, economics, psychology, games and gaming, cosmology, medicine, history, computer science, energy, and music. (MK)

  6. iSTEM: Promoting Fifth Graders' Mathematical Modeling

    ERIC Educational Resources Information Center

    Yanik, H. Bahadir; Karabas, Celil

    2014-01-01

    Modeling requires that people develop representations or procedures to address particular problem situations (Lesh et al. 2000). Mathematical modeling is used to describe essential characteristics of a phenomenon or a situation that one intends to study in the real world through building mathematical objects. This article describes how fifth-grade…

  7. Physical and mathematical cochlear models

    NASA Astrophysics Data System (ADS)

    Lim, Kian-Meng

    2000-10-01

    The cochlea is an intricate organ in the inner ear responsible for our hearing. Besides acting as a transducer to convert mechanical sound vibrations to electrical neural signals, the cochlea also amplifies and separates the sound signal into its spectral components for further processing in the brain. It operates over a broad-band of frequency and a huge dynamic range of input while maintaining a low power consumption. The present research takes the approach of building cochlear models to study and understand the underlying mechanics involved in the functioning of the cochlea. Both physical and mathematical models of the cochlea are constructed. The physical model is a first attempt to build a life- sized replica of the human cochlea using advanced micro- machining techniques. The model takes a modular design, with a removable silicon-wafer based partition membrane encapsulated in a plastic fluid chamber. Preliminary measurements in the model are obtained and they compare roughly with simulation results. Parametric studies on the design parameters of the model leads to an improved design of the model. The studies also revealed that the width and orthotropy of the basilar membrane in the cochlea have significant effects on the sharply tuned responses observed in the biological cochlea. The mathematical model is a physiologically based model that includes three-dimensional viscous fluid flow and a tapered partition with variable properties along its length. A hybrid asymptotic and numerical method provides a uniformly valid and efficient solution to the short and long wave regions in the model. Both linear and non- linear activity are included in the model to simulate the active cochlea. The mathematical model has successfully reproduced many features of the response in the biological cochlea, as observed in experiment measurements performed on animals. These features include sharply tuned frequency responses, significant amplification with inclusion of activity

  8. Mathematical models for principles of gyroscope theory

    NASA Astrophysics Data System (ADS)

    Usubamatov, Ryspek

    2017-01-01

    Gyroscope devices are primary units for navigation and control systems that have wide application in engineering. The main property of the gyroscope device is maintaining the axis of a spinning rotor. This gyroscope peculiarity is represented in terms of gyroscope effects in which known mathematical models have been formulated on the law of kinetic energy conservation and the change in the angular momentum. The gyroscope theory is represented by numerous publications, which mathematical models do not match the actual torques and motions in these devices.. The nature of gyroscope effects is more complex than represented in known publications. Recent investigations in this area have demonstrated that on a gyroscope can act until eleven internal torques simultaneously and interdependently around two axes. These gyroscope torques are generated by spinning rotor's mass-elements and by the gyroscope center-mass based on action of several inertial forces. The change in the angular momentum does not play first role for gyroscope motions. The external load generates several internal torques which directions may be distinguished. This situation leads changing of the angular velocities of gyroscope motions around two axes. Formulated mathematical models of gyroscope internal torques are representing the fundamental principle of gyroscope theory. In detail, the gyroscope is experienced the resistance torque generated by the centrifugal and Coriolis forces of the spinning rotor and the precession torque generated by the common inertial forces and the change in the angular momentum. The new mathematical models for the torques and motions of the gyroscope confirmed for most unsolvable problems. The mathematical models practically tested and the results are validated the theoretical approach.

  9. Mathematical model to estimate risk of calcium-containing renal stones

    NASA Technical Reports Server (NTRS)

    Pietrzyk, R. A.; Feiveson, A. H.; Whitson, P. A.

    1999-01-01

    BACKGROUND/AIMS: Astronauts exposed to microgravity during the course of spaceflight undergo physiologic changes that alter the urinary environment so as to increase the risk of renal stone formation. This study was undertaken to identify a simple method with which to evaluate the potential risk of renal stone development during spaceflight. METHOD: We used a large database of urinary risk factors obtained from 323 astronauts before and after spaceflight to generate a mathematical model with which to predict the urinary supersaturation of calcium stone forming salts. RESULT: This model, which involves the fewest possible analytical variables (urinary calcium, citrate, oxalate, phosphorus, and total volume), reliably and accurately predicted the urinary supersaturation of the calcium stone forming salts when compared to results obtained from a group of 6 astronauts who collected urine during flight. CONCLUSIONS: The use of this model will simplify both routine medical monitoring during spaceflight as well as the evaluation of countermeasures designed to minimize renal stone development. This model also can be used for Earth-based applications in which access to analytical resources is limited.

  10. The Relationship between Big Data and Mathematical Modeling: A Discussion in a Mathematical Education Scenario

    ERIC Educational Resources Information Center

    Dalla Vecchia, Rodrigo

    2015-01-01

    This study discusses aspects of the association between Mathematical Modeling (MM) and Big Data in the scope of mathematical education. We present an example of an activity to discuss two ontological factors that involve MM. The first is linked to the modeling stages. The second involves the idea of pedagogical objectives. The main findings…

  11. Intensity level for exercise training in fibromyalgia by using mathematical models

    PubMed Central

    2010-01-01

    Background It has not been assessed before whether mathematical models described in the literature for prescriptions of exercise can be used for fibromyalgia syndrome patients. The objective of this paper was to determine how age-predicted heart rate formulas can be used with fibromyalgia syndrome populations as well as to find out which mathematical models are more accurate to control exercise intensity. Methods A total of 60 women aged 18-65 years with fibromyalgia syndrome were included; 32 were randomized to walking training at anaerobic threshold. Age-predicted formulas to maximum heart rate ("220 minus age" and "208 minus 0.7 × age") were correlated with achieved maximum heart rate (HRMax) obtained by spiroergometry. Subsequently, six mathematical models using heart rate reserve (HRR) and age-predicted HRMax formulas were studied to estimate the intensity level of exercise training corresponding to heart rate at anaerobic threshold (HRAT) obtained by spiroergometry. Linear and nonlinear regression models were used for correlations and residues analysis for the adequacy of the models. Results Age-predicted HRMax and HRAT formulas had a good correlation with achieved heart rate obtained in spiroergometry (r = 0.642; p < 0.05). For exercise prescription in the anaerobic threshold intensity, the percentages were 52.2-60.6% HRR and 75.5-80.9% HRMax. Formulas using HRR and the achieved HRMax showed better correlation. Furthermore, the percentages of HRMax and HRR were significantly higher for the trained individuals (p < 0.05). Conclusion Age-predicted formulas can be used for estimating HRMax and for exercise prescriptions in women with fibromyalgia syndrome. Karnoven's formula using heart rate achieved in ergometric test showed a better correlation. For the prescription of exercises in the threshold intensity, 52% to 60% HRR or 75% to 80% HRMax must be used in sedentary women with fibromyalgia syndrome and these values are higher and must be corrected for

  12. The written mathematical communication profile of prospective math teacher in mathematical proving

    NASA Astrophysics Data System (ADS)

    Pantaleon, K. V.; Juniati, D.; Lukito, A.; Mandur, K.

    2018-01-01

    Written mathematical communication is the process of expressing mathematical ideas and understanding in writing. It is one of the important aspects that must be mastered by the prospective math teacher as tool of knowledge transfer. This research was a qualitative research that aimed to describe the mathematical communication profile of the prospective mathematics teacher in mathematical proving. This research involved 48 students of Mathematics Education Study Program; one of them with moderate math skills was chosen as the main subject. Data were collected through tests, assignments, and task-based interviews. The results of this study point out that in the proof of geometry, the subject explains what is understood, presents the idea in the form of drawing and symbols, and explains the content/meaning of a representation accurately and clearly, but the subject can not convey the argument systematically and logically. Whereas in the proof of algebra, the subject describes what is understood, explains the method used, and describes the content/meaning of a symbolic representation accurately, systematically, logically, but the argument presented is not clear because it is insufficient detailed and complete.

  13. Prospective Mathematics Teachers' Opinions about Mathematical Modeling Method and Applicability of This Method

    ERIC Educational Resources Information Center

    Akgün, Levent

    2015-01-01

    The aim of this study is to identify prospective secondary mathematics teachers' opinions about the mathematical modeling method and the applicability of this method in high schools. The case study design, which is among the qualitative research methods, was used in the study. The study was conducted with six prospective secondary mathematics…

  14. Developing Understanding of Mathematical Modeling in Secondary Teacher Preparation

    ERIC Educational Resources Information Center

    Anhalt, Cynthia Oropesa; Cortez, Ricardo

    2016-01-01

    This study examines the evolution of 11 prospective teachers' understanding of mathematical modeling through the implementation of a modeling module within a curriculum course in a secondary teacher preparation program. While the prospective teachers had not previously taken a course on mathematical modeling, they will be expected to include…

  15. Using a Functional Model to Develop a Mathematical Formula

    ERIC Educational Resources Information Center

    Otto, Charlotte A.; Everett, Susan A.; Luera, Gail R.

    2008-01-01

    The unifying theme of models was incorporated into a required Science Capstone course for pre-service elementary teachers based on national standards in science and mathematics. A model of a teeter-totter was selected for use as an example of a functional model for gathering data as well as a visual model of a mathematical equation for developing…

  16. Molecular modeling: An open invitation for applied mathematics

    NASA Astrophysics Data System (ADS)

    Mezey, Paul G.

    2013-10-01

    Molecular modeling methods provide a very wide range of challenges for innovative mathematical and computational techniques, where often high dimensionality, large sets of data, and complicated interrelations imply a multitude of iterative approximations. The physical and chemical basis of these methodologies involves quantum mechanics with several non-intuitive aspects, where classical interpretation and classical analogies are often misleading or outright wrong. Hence, instead of the everyday, common sense approaches which work so well in engineering, in molecular modeling one often needs to rely on rather abstract mathematical constraints and conditions, again emphasizing the high level of reliance on applied mathematics. Yet, the interdisciplinary aspects of the field of molecular modeling also generates some inertia and perhaps too conservative reliance on tried and tested methodologies, that is at least partially caused by the less than up-to-date involvement in the newest developments in applied mathematics. It is expected that as more applied mathematicians take up the challenge of employing the latest advances of their field in molecular modeling, important breakthroughs may follow. In this presentation some of the current challenges of molecular modeling are discussed.

  17. Application of mathematical modeling in sustained release delivery systems.

    PubMed

    Grassi, Mario; Grassi, Gabriele

    2014-08-01

    This review, presenting as starting point the concept of the mathematical modeling, is aimed at the physical and mathematical description of the most important mechanisms regulating drug delivery from matrix systems. The precise knowledge of the delivery mechanisms allows us to set up powerful mathematical models which, in turn, are essential for the design and optimization of appropriate drug delivery systems. The fundamental mechanisms for drug delivery from matrices are represented by drug diffusion, matrix swelling, matrix erosion, drug dissolution with possible recrystallization (e.g., as in the case of amorphous and nanocrystalline drugs), initial drug distribution inside the matrix, matrix geometry, matrix size distribution (in the case of spherical matrices of different diameter) and osmotic pressure. Depending on matrix characteristics, the above-reported variables may play a different role in drug delivery; thus the mathematical model needs to be built solely on the most relevant mechanisms of the particular matrix considered. Despite the somewhat diffident behavior of the industrial world, in the light of the most recent findings, we believe that mathematical modeling may have a tremendous potential impact in the pharmaceutical field. We do believe that mathematical modeling will be more and more important in the future especially in the light of the rapid advent of personalized medicine, a novel therapeutic approach intended to treat each single patient instead of the 'average' patient.

  18. The Mathematical Modeling and Computer Simulation of Electrochemical Micromachining Using Ultrashort Pulses

    NASA Astrophysics Data System (ADS)

    Kozak, J.; Gulbinowicz, D.; Gulbinowicz, Z.

    2009-05-01

    The need for complex and accurate three dimensional (3-D) microcomponents is increasing rapidly for many industrial and consumer products. Electrochemical machining process (ECM) has the potential of generating desired crack-free and stress-free surfaces of microcomponents. This paper reports a study of pulse electrochemical micromachining (PECMM) using ultrashort (nanoseconds) pulses for generating complex 3-D microstructures of high accuracy. A mathematical model of the microshaping process with taking into consideration unsteady phenomena in electrical double layer has been developed. The software for computer simulation of PECM has been developed and the effects of machining parameters on anodic localization and final shape of machined surface are presented.

  19. Mathematical modeling for novel cancer drug discovery and development.

    PubMed

    Zhang, Ping; Brusic, Vladimir

    2014-10-01

    Mathematical modeling enables: the in silico classification of cancers, the prediction of disease outcomes, optimization of therapy, identification of promising drug targets and prediction of resistance to anticancer drugs. In silico pre-screened drug targets can be validated by a small number of carefully selected experiments. This review discusses the basics of mathematical modeling in cancer drug discovery and development. The topics include in silico discovery of novel molecular drug targets, optimization of immunotherapies, personalized medicine and guiding preclinical and clinical trials. Breast cancer has been used to demonstrate the applications of mathematical modeling in cancer diagnostics, the identification of high-risk population, cancer screening strategies, prediction of tumor growth and guiding cancer treatment. Mathematical models are the key components of the toolkit used in the fight against cancer. The combinatorial complexity of new drugs discovery is enormous, making systematic drug discovery, by experimentation, alone difficult if not impossible. The biggest challenges include seamless integration of growing data, information and knowledge, and making them available for a multiplicity of analyses. Mathematical models are essential for bringing cancer drug discovery into the era of Omics, Big Data and personalized medicine.

  20. The use of mathematical models in teaching wastewater treatment engineering.

    PubMed

    Morgenroth, E; Arvin, E; Vanrolleghem, P

    2002-01-01

    Mathematical modeling of wastewater treatment processes has become increasingly popular in recent years. To prepare students for their future careers, environmental engineering education should provide students with sufficient background and experiences to understand and apply mathematical models efficiently and responsibly. Approaches for introducing mathematical modeling into courses on wastewater treatment engineering are discussed depending on the learning objectives, level of the course and the time available.

  1. Mathematical modeling of swirled flows in industrial applications

    NASA Astrophysics Data System (ADS)

    Dekterev, A. A.; Gavrilov, A. A.; Sentyabov, A. V.

    2018-03-01

    Swirled flows are widely used in technological devices. Swirling flows are characterized by a wide range of flow regimes. 3D mathematical modeling of flows is widely used in research and design. For correct mathematical modeling of such a flow, it is necessary to use turbulence models, which take into account important features of the flow. Based on the experience of computational modeling of a wide class of problems with swirling flows, recommendations on the use of turbulence models for calculating the applied problems are proposed.

  2. A Mathematical Evaluation of the Core Conductor Model

    PubMed Central

    Clark, John; Plonsey, Robert

    1966-01-01

    This paper is a mathematical evaluation of the core conductor model where its three dimensionality is taken into account. The problem considered is that of a single, active, unmyelinated nerve fiber situated in an extensive, homogeneous, conducting medium. Expressions for the various core conductor parameters have been derived in a mathematically rigorous manner according to the principles of electromagnetic theory. The purpose of employing mathematical rigor in this study is to bring to light the inherent assumptions of the one dimensional core conductor model, providing a method of evaluating the accuracy of this linear model. Based on the use of synthetic squid axon data, the conclusion of this study is that the linear core conductor model is a good approximation for internal but not external parameters. PMID:5903155

  3. Mathematical modeling relevant to closed artificial ecosystems

    USGS Publications Warehouse

    DeAngelis, D.L.

    2003-01-01

    The mathematical modeling of ecosystems has contributed much to the understanding of the dynamics of such systems. Ecosystems can include not only the natural variety, but also artificial systems designed and controlled by humans. These can range from agricultural systems and activated sludge plants, down to mesocosms, microcosms, and aquaria, which may have practical or research applications. Some purposes may require the design of systems that are completely closed, as far as material cycling is concerned. In all cases, mathematical modeling can help not only to understand the dynamics of the system, but also to design methods of control to keep the system operating in desired ranges. This paper reviews mathematical modeling relevant to the simulation and control of closed or semi-closed artificial ecosystems designed for biological production and recycling in applications in space. Published by Elsevier Science Ltd on behalf of COSPAR.

  4. Mathematical modelling of clostridial acetone-butanol-ethanol fermentation.

    PubMed

    Millat, Thomas; Winzer, Klaus

    2017-03-01

    Clostridial acetone-butanol-ethanol (ABE) fermentation features a remarkable shift in the cellular metabolic activity from acid formation, acidogenesis, to the production of industrial-relevant solvents, solventogensis. In recent decades, mathematical models have been employed to elucidate the complex interlinked regulation and conditions that determine these two distinct metabolic states and govern the transition between them. In this review, we discuss these models with a focus on the mechanisms controlling intra- and extracellular changes between acidogenesis and solventogenesis. In particular, we critically evaluate underlying model assumptions and predictions in the light of current experimental knowledge. Towards this end, we briefly introduce key ideas and assumptions applied in the discussed modelling approaches, but waive a comprehensive mathematical presentation. We distinguish between structural and dynamical models, which will be discussed in their chronological order to illustrate how new biological information facilitates the 'evolution' of mathematical models. Mathematical models and their analysis have significantly contributed to our knowledge of ABE fermentation and the underlying regulatory network which spans all levels of biological organization. However, the ties between the different levels of cellular regulation are not well understood. Furthermore, contradictory experimental and theoretical results challenge our current notion of ABE metabolic network structure. Thus, clostridial ABE fermentation still poses theoretical as well as experimental challenges which are best approached in close collaboration between modellers and experimentalists.

  5. Longitudinal mathematics development of students with learning disabilities and students without disabilities: a comparison of linear, quadratic, and piecewise linear mixed effects models.

    PubMed

    Kohli, Nidhi; Sullivan, Amanda L; Sadeh, Shanna; Zopluoglu, Cengiz

    2015-04-01

    Effective instructional planning and intervening rely heavily on accurate understanding of students' growth, but relatively few researchers have examined mathematics achievement trajectories, particularly for students with special needs. We applied linear, quadratic, and piecewise linear mixed-effects models to identify the best-fitting model for mathematics development over elementary and middle school and to ascertain differences in growth trajectories of children with learning disabilities relative to their typically developing peers. The analytic sample of 2150 students was drawn from the Early Childhood Longitudinal Study - Kindergarten Cohort, a nationally representative sample of United States children who entered kindergarten in 1998. We first modeled students' mathematics growth via multiple mixed-effects models to determine the best fitting model of 9-year growth and then compared the trajectories of students with and without learning disabilities. Results indicate that the piecewise linear mixed-effects model captured best the functional form of students' mathematics trajectories. In addition, there were substantial achievement gaps between students with learning disabilities and students with no disabilities, and their trajectories differed such that students without disabilities progressed at a higher rate than their peers who had learning disabilities. The results underscore the need for further research to understand how to appropriately model students' mathematics trajectories and the need for attention to mathematics achievement gaps in policy. Copyright © 2015 Society for the Study of School Psychology. Published by Elsevier Ltd. All rights reserved.

  6. The impact of mathematical models of teaching materials on square and rectangle concepts to improve students' mathematical connection ability and mathematical disposition in middle school

    NASA Astrophysics Data System (ADS)

    Afrizal, Irfan Mufti; Dachlan, Jarnawi Afghani

    2017-05-01

    The aim of this study was to determine design of mathematical models of teaching materials to improve students' mathematical connection ability and mathematical disposition in middle school through experimental studies. The design in this study was quasi-experimental with non-equivalent control group type. This study consisted of two phases, the first phase was identify students' learning obstacle on square and rectangle concepts to obtain the appropriate design of teaching materials, beside that there were internalization of the values or characters expected to appear on students through the teaching materials. Second phase was experiments on the effectiveness and efficiency of mathematical models of teaching materials to improve students' mathematical connection ability and mathematical disposition. The result of this study are 1) Students' learning obstacle that have identified was categorized as an epistemological obstacle. 2) The improvement of students' mathematical connection ability and mathematical disposition who used mathematical teaching materials is better than the students who used conventional learning.

  7. Mathematical Modelling in the Early School Years

    ERIC Educational Resources Information Center

    English, Lyn D.; Watters, James J.

    2005-01-01

    In this article we explore young children's development of mathematical knowledge and reasoning processes as they worked two modelling problems (the "Butter Beans Problem" and the "Airplane Problem"). The problems involve authentic situations that need to be interpreted and described in mathematical ways. Both problems include tables of data,…

  8. Mathematics Models in Chemistry--An Innovation for Non-Mathematics and Non-Science Majors

    ERIC Educational Resources Information Center

    Rash, Agnes M.; Zurbach, E. Peter

    2004-01-01

    The intention of this article is to present a year-long interdisciplinary course, Mathematical Models in Chemistry. The course is comprised of eleven units, each of which has both a mathematical and a chemical component. A syllabus of the course is given and the format of the class is explained. The interaction of the professors and the content is…

  9. Mathematical models for predicting human mobility in the context of infectious disease spread: introducing the impedance model.

    PubMed

    Sallah, Kankoé; Giorgi, Roch; Bengtsson, Linus; Lu, Xin; Wetter, Erik; Adrien, Paul; Rebaudet, Stanislas; Piarroux, Renaud; Gaudart, Jean

    2017-11-22

    Mathematical models of human mobility have demonstrated a great potential for infectious disease epidemiology in contexts of data scarcity. While the commonly used gravity model involves parameter tuning and is thus difficult to implement without reference data, the more recent radiation model based on population densities is parameter-free, but biased. In this study we introduce the new impedance model, by analogy with electricity. Previous research has compared models on the basis of a few specific available spatial patterns. In this study, we use a systematic simulation-based approach to assess the performances. Five hundred spatial patterns were generated using various area sizes and location coordinates. Model performances were evaluated based on these patterns. For simulated data, comparison measures were average root mean square error (aRMSE) and bias criteria. Modeling of the 2010 Haiti cholera epidemic with a basic susceptible-infected-recovered (SIR) framework allowed an empirical evaluation through assessing the goodness-of-fit of the observed epidemic curve. The new, parameter-free impedance model outperformed previous models on simulated data according to average aRMSE and bias criteria. The impedance model achieved better performances with heterogeneous population densities and small destination populations. As a proof of concept, the basic compartmental SIR framework was used to confirm the results obtained with the impedance model in predicting the spread of cholera in Haiti in 2010. The proposed new impedance model provides accurate estimations of human mobility, especially when the population distribution is highly heterogeneous. This model can therefore help to achieve more accurate predictions of disease spread in the context of an epidemic.

  10. Achilles and the tortoise: Some caveats to mathematical modeling in biology.

    PubMed

    Gilbert, Scott F

    2018-01-31

    Mathematical modeling has recently become a much-lauded enterprise, and many funding agencies seek to prioritize this endeavor. However, there are certain dangers associated with mathematical modeling, and knowledge of these pitfalls should also be part of a biologist's training in this set of techniques. (1) Mathematical models are limited by known science; (2) Mathematical models can tell what can happen, but not what did happen; (3) A model does not have to conform to reality, even if it is logically consistent; (4) Models abstract from reality, and sometimes what they eliminate is critically important; (5) Mathematics can present a Platonic ideal to which biologically organized matter strives, rather than a trial-and-error bumbling through evolutionary processes. This "Unity of Science" approach, which sees biology as the lowest physical science and mathematics as the highest science, is part of a Western belief system, often called the Great Chain of Being (or Scala Natura), that sees knowledge emerge as one passes from biology to chemistry to physics to mathematics, in an ascending progression of reason being purification from matter. This is also an informal model for the emergence of new life. There are now other informal models for integrating development and evolution, but each has its limitations. Copyright © 2018 Elsevier Ltd. All rights reserved.

  11. Mathematical model of whole-process calculation for bottom-blowing copper smelting

    NASA Astrophysics Data System (ADS)

    Li, Ming-zhou; Zhou, Jie-min; Tong, Chang-ren; Zhang, Wen-hai; Li, He-song

    2017-11-01

    The distribution law of materials in smelting products is key to cost accounting and contaminant control. Regardless, the distribution law is difficult to determine quickly and accurately by mere sampling and analysis. Mathematical models for material and heat balance in bottom-blowing smelting, converting, anode furnace refining, and electrolytic refining were established based on the principles of material (element) conservation, energy conservation, and control index constraint in copper bottom-blowing smelting. Simulation of the entire process of bottom-blowing copper smelting was established using a self-developed MetCal software platform. A whole-process simulation for an enterprise in China was then conducted. Results indicated that the quantity and composition information of unknown materials, as well as heat balance information, can be quickly calculated using the model. Comparison of production data revealed that the model can basically reflect the distribution law of the materials in bottom-blowing copper smelting. This finding provides theoretical guidance for mastering the performance of the entire process.

  12. Mathematical Modeling Is Also Physics--Interdisciplinary Teaching between Mathematics and Physics in Danish Upper Secondary Education

    ERIC Educational Resources Information Center

    Michelsen, Claus

    2015-01-01

    Mathematics plays a crucial role in physics. This role is brought about predominantly through the building, employment, and assessment of mathematical models, and teachers and educators should capture this relationship in the classroom in an effort to improve students' achievement and attitude in both physics and mathematics. But although there…

  13. The effect of Missouri mathematics project learning model on students’ mathematical problem solving ability

    NASA Astrophysics Data System (ADS)

    Handayani, I.; Januar, R. L.; Purwanto, S. E.

    2018-01-01

    This research aims to know the influence of Missouri Mathematics Project Learning Model to Mathematical Problem-solving Ability of Students at Junior High School. This research is a quantitative research and uses experimental research method of Quasi Experimental Design. The research population includes all student of grade VII of Junior High School who are enrolled in the even semester of the academic year 2016/2017. The Sample studied are 76 students from experimental and control groups. The sampling technique being used is cluster sampling method. The instrument is consisted of 7 essay questions whose validity, reliability, difficulty level and discriminating power have been tested. Before analyzing the data by using t-test, the data has fulfilled the requirement for normality and homogeneity. The result of data shows that there is the influence of Missouri mathematics project learning model to mathematical problem-solving ability of students at junior high school with medium effect.

  14. Automatic mathematical modeling for real time simulation program (AI application)

    NASA Technical Reports Server (NTRS)

    Wang, Caroline; Purinton, Steve

    1989-01-01

    A methodology is described for automatic mathematical modeling and generating simulation models. The major objective was to create a user friendly environment for engineers to design, maintain, and verify their models; to automatically convert the mathematical models into conventional code for computation; and finally, to document the model automatically.

  15. A Mathematical Model for the Middle Ear Ventilation

    NASA Astrophysics Data System (ADS)

    Molnárka, G.; Miletics, E. M.; Fücsek, M.

    2008-09-01

    The otitis media is one of the mostly existing illness for the children, therefore investigation of the human middle ear ventilation is an actual problem. In earlier investigations both experimental and theoretical approach one can find in ([l]-[3]). Here we give a new mathematical and computer model to simulate this ventilation process. This model able to describe the diffusion and flow processes simultaneously, therefore it gives more precise results than earlier models did. The article contains the mathematical model and some results of the simulation.

  16. Developing Teachers' Models for Assessing Students' Competence in Mathematical Modelling through Lesson Study

    ERIC Educational Resources Information Center

    Aydogan Yenmez, Arzu; Erbas, Ayhan Kursat; Cakiroglu, Erdinc; Alacaci, Cengiz; Cetinkaya, Bulent

    2017-01-01

    Applications and modelling have gained a prominent role in mathematics education reform documents and curricula. Thus, there is a growing need for studies focusing on the effective use of mathematical modelling in classrooms. Assessment is an integral part of using modelling activities in classrooms, since it allows teachers to identify and manage…

  17. Mathematical modeling of inhalation exposure

    NASA Technical Reports Server (NTRS)

    Fiserova-Bergerova, V.

    1976-01-01

    The paper presents a mathematical model of inhalation exposure in which uptake, distribution and excretion are described by exponential functions, while rate constants are determined by tissue volumes, blood perfusion and by the solubility of vapors (partition coefficients). In the model, tissues are grouped into four pharmokinetic compartments. The model is used to study continuous and interrupted chronic exposures and is applied to the inhalation of Forane and methylene chloride.

  18. A Case Study of Teachers' Development of Well-Structured Mathematical Modelling Activities

    ERIC Educational Resources Information Center

    Stohlmann, Micah; Maiorca, Cathrine; Allen, Charlie

    2017-01-01

    This case study investigated how three teachers developed mathematical modelling activities integrated with content standards through participation in a course on mathematical modelling. The class activities involved experiencing a mathematical modelling activity, reading and rating example mathematical modelling activities, reading articles about…

  19. Changing Pre-Service Mathematics Teachers' Beliefs about Using Computers for Teaching and Learning Mathematics: The Effect of Three Different Models

    ERIC Educational Resources Information Center

    Karatas, Ilhan

    2014-01-01

    This study examines the effect of three different computer integration models on pre-service mathematics teachers' beliefs about using computers in mathematics education. Participants included 104 pre-service mathematics teachers (36 second-year students in the Computer Oriented Model group, 35 fourth-year students in the Integrated Model (IM)…

  20. Studies on Mathematical Models of Wet Adhesion and Lifetime Prediction of Organic Coating/Steel by Grey System Theory

    PubMed Central

    Meng, Fandi; Liu, Ying; Liu, Li; Li, Ying; Wang, Fuhui

    2017-01-01

    A rapid degradation of wet adhesion is the key factor controlling coating lifetime, for the organic coatings under marine hydrostatic pressure. The mathematical models of wet adhesion have been studied by Grey System Theory (GST). Grey models (GM) (1, 1) of epoxy varnish (EV) coating/steel and epoxy glass flake (EGF) coating/steel have been established, and a lifetime prediction formula has been proposed on the basis of these models. The precision assessments indicate that the established models are accurate, and the prediction formula is capable of making precise lifetime forecasting of the coatings. PMID:28773073

  1. Authenticity of Mathematical Modeling

    ERIC Educational Resources Information Center

    Tran, Dung; Dougherty, Barbara J.

    2014-01-01

    Some students leave high school never quite sure of the relevancy of the mathematics they have learned. They fail to see links between school mathematics and the mathematics of everyday life that requires thoughtful decision making and often complex problem solving. Is it possible to bridge the gap between school mathematics and the mathematics in…

  2. Mathematical modeling of a Ti:sapphire solid-state laser

    NASA Technical Reports Server (NTRS)

    Swetits, John J.

    1987-01-01

    The project initiated a study of a mathematical model of a tunable Ti:sapphire solid-state laser. A general mathematical model was developed for the purpose of identifying design parameters which will optimize the system, and serve as a useful predictor of the system's behavior.

  3. Elementary Preservice Teachers' and Elementary Inservice Teachers' Knowledge of Mathematical Modeling

    ERIC Educational Resources Information Center

    Schwerdtfeger, Sara

    2017-01-01

    This study examined the differences in knowledge of mathematical modeling between a group of elementary preservice teachers and a group of elementary inservice teachers. Mathematical modeling has recently come to the forefront of elementary mathematics classrooms because of the call to add mathematical modeling tasks in mathematics classes through…

  4. Investigating and Developing Engineering Students' Mathematical Modelling and Problem-Solving Skills

    ERIC Educational Resources Information Center

    Wedelin, Dag; Adawi, Tom; Jahan, Tabassum; Andersson, Sven

    2015-01-01

    How do engineering students approach mathematical modelling problems and how can they learn to deal with such problems? In the context of a course in mathematical modelling and problem solving, and using a qualitative case study approach, we found that the students had little prior experience of mathematical modelling. They were also inexperienced…

  5. A discrete mathematical model applied to genetic regulation and metabolic networks.

    PubMed

    Asenjo, A J; Ramirez, P; Rapaport, I; Aracena, J; Goles, E; Andrews, B A

    2007-03-01

    This paper describes the use of a discrete mathematical model to represent the basic mechanisms of regulation of the bacteria E. coli in batch fermentation. The specific phenomena studied were the changes in metabolism and genetic regulation when the bacteria use three different carbon substrates (glucose, glycerol, and acetate). The model correctly predicts the behavior of E. coli vis-à-vis substrate mixtures. In a mixture of glucose, glycerol, and acetate, it prefers glucose, then glycerol, and finally acetate. The model included 67 nodes; 28 were genes, 20 enzymes, and 19 regulators/biochemical compounds. The model represents both the genetic regulation and metabolic networks in an inrtegrated form, which is how they function biologically. This is one of the first attempts to include both of these networks in one model. Previously, discrete mathematical models were used only to describe genetic regulation networks. The study of the network dynamics generated 8 (2(3)) fixed points, one for each nutrient configuration (substrate mixture) in the medium. The fixed points of the discrete model reflect the phenotypes described. Gene expression and the patterns of the metabolic fluxes generated are described accurately. The activation of the gene regulation network depends basically on the presence of glucose and glycerol. The model predicts the behavior when mixed carbon sources are utilized as well as when there is no carbon source present. Fictitious jokers (Joker1, Joker2, and Repressor SdhC) had to be created to control 12 genes whose regulation mechanism is unknown, since glycerol and glucose do not act directly on the genes. The approach presented in this paper is particularly useful to investigate potential unknown gene regulation mechanisms; such a novel approach can also be used to describe other gene regulation situations such as the comparison between non-recombinant and recombinant yeast strain, producing recombinant proteins, presently under

  6. Mathematical models of ABE fermentation: review and analysis.

    PubMed

    Mayank, Rahul; Ranjan, Amrita; Moholkar, Vijayanand S

    2013-12-01

    Among different liquid biofuels that have emerged in the recent past, biobutanol produced via fermentation processes is of special interest due to very similar properties to that of gasoline. For an effective design, scale-up, and optimization of the acetone-butanol-ethanol (ABE) fermentation process, it is necessary to have insight into the micro- and macro-mechanisms of the process. The mathematical models for ABE fermentation are efficient tools for this purpose, which have evolved from simple stoichiometric fermentation equations in the 1980s to the recent sophisticated and elaborate kinetic models based on metabolic pathways. In this article, we have reviewed the literature published in the area of mathematical modeling of the ABE fermentation. We have tried to present an analysis of these models in terms of their potency in describing the overall physiology of the process, design features, mode of operation along with comparison and validation with experimental results. In addition, we have also highlighted important facets of these models such as metabolic pathways, basic kinetics of different metabolites, biomass growth, inhibition modeling and other additional features such as cell retention and immobilized cultures. Our review also covers the mathematical modeling of the downstream processing of ABE fermentation, i.e. recovery and purification of solvents through flash distillation, liquid-liquid extraction, and pervaporation. We believe that this review will be a useful source of information and analysis on mathematical models for ABE fermentation for both the appropriate scientific and engineering communities.

  7. Accurate lithography simulation model based on convolutional neural networks

    NASA Astrophysics Data System (ADS)

    Watanabe, Yuki; Kimura, Taiki; Matsunawa, Tetsuaki; Nojima, Shigeki

    2017-07-01

    Lithography simulation is an essential technique for today's semiconductor manufacturing process. In order to calculate an entire chip in realistic time, compact resist model is commonly used. The model is established for faster calculation. To have accurate compact resist model, it is necessary to fix a complicated non-linear model function. However, it is difficult to decide an appropriate function manually because there are many options. This paper proposes a new compact resist model using CNN (Convolutional Neural Networks) which is one of deep learning techniques. CNN model makes it possible to determine an appropriate model function and achieve accurate simulation. Experimental results show CNN model can reduce CD prediction errors by 70% compared with the conventional model.

  8. The mathematical and computer modeling of the worm tool shaping

    NASA Astrophysics Data System (ADS)

    Panchuk, K. L.; Lyashkov, A. A.; Ayusheev, T. V.

    2017-06-01

    Traditionally mathematical profiling of the worm tool is carried out on the first T. Olivier method, known in the theory of gear gearings, with receiving an intermediate surface of the making lath. It complicates process of profiling and its realization by means of computer 3D-modeling. The purpose of the work is the improvement of mathematical model of profiling and its realization based on the methods of 3D-modeling. Research problems are: receiving of the mathematical model of profiling which excludes the presence of the making lath in it; realization of the received model by means of frame and superficial modeling; development and approbation of technology of solid-state modeling for the solution of the problem of profiling. As the basic, the kinematic method of research of the mutually envelope surfaces is accepted. Computer research is executed by means of CAD based on the methods of 3D-modeling. We have developed mathematical model of profiling of the worm tool; frame, superficial and solid-state models of shaping of the mutually enveloping surfaces of the detail and the tool are received. The offered mathematical models and the technologies of 3D-modeling of shaping represent tools for theoretical and experimental profiling of the worm tool. The results of researches can be used at design of metal-cutting tools.

  9. A Mathematical Model Development for the Lateral Collapse of Octagonal Tubes

    NASA Astrophysics Data System (ADS)

    Ghazali Kamardan, M.; Sufahani, Suliadi; Othman, M. Z. M.; Che-Him, Norziha; Khalid, Kamil; Roslan, Rozaini; Ali, Maselan; Zaidi, A. M. A.

    2018-04-01

    Many researches has been done on the lateral collapse of tube. However, the previous researches only focus on cylindrical and square tubes. Then a research has been done discovering the collapse behaviour of hexagonal tube and the mathematic model of the deformation behaviour had been developed [8]. The purpose of this research is to study the lateral collapse behaviour of symmetric octagonal tubes and hence to develop a mathematical model of the collapse behaviour of these tubes. For that, a predictive mathematical model was developed and a finite element analysis procedure was conducted for the lateral collapse behaviour of symmetric octagonal tubes. Lastly, the mathematical model was verified by using the finite element analysis simulation results. It was discovered that these tubes performed different deformation behaviour than the cylindrical tube. Symmetric octagonal tubes perform 2 phases of elastic - plastic deformation behaviour patterns. The mathematical model had managed to show the fundamental of the deformation behaviour of octagonal tubes. However, further studies need to be conducted in order to further improve on the proposed mathematical model.

  10. Validation and upgrading of physically based mathematical models

    NASA Technical Reports Server (NTRS)

    Duval, Ronald

    1992-01-01

    The validation of the results of physically-based mathematical models against experimental results was discussed. Systematic techniques are used for: (1) isolating subsets of the simulator mathematical model and comparing the response of each subset to its experimental response for the same input conditions; (2) evaluating the response error to determine whether it is the result of incorrect parameter values, incorrect structure of the model subset, or unmodeled external effects of cross coupling; and (3) modifying and upgrading the model and its parameter values to determine the most physically appropriate combination of changes.

  11. Components of Mathematics Anxiety: Factor Modeling of the MARS30-Brief.

    PubMed

    Pletzer, Belinda; Wood, Guilherme; Scherndl, Thomas; Kerschbaum, Hubert H; Nuerk, Hans-Christoph

    2016-01-01

    Mathematics anxiety involves feelings of tension, discomfort, high arousal, and physiological reactivity interfering with number manipulation and mathematical problem solving. Several factor analytic models indicate that mathematics anxiety is rather a multidimensional than unique construct. However, the factor structure of mathematics anxiety has not been fully clarified by now. This issue shall be addressed in the current study. The Mathematics Anxiety Rating Scale (MARS) is a reliable measure of mathematics anxiety (Richardson and Suinn, 1972), for which several reduced forms have been developed. Most recently, a shortened version of the MARS (MARS30-brief) with comparable reliability was published. Different studies suggest that mathematics anxiety involves up to seven different factors. Here we examined the factor structure of the MARS30-brief by means of confirmatory factor analysis. The best model fit was obtained by a six-factor model, dismembering the known two general factors "Mathematical Test Anxiety" (MTA) and "Numerical Anxiety" (NA) in three factors each. However, a more parsimonious 5-factor model with two sub-factors for MTA and three for NA fitted the data comparably well. Factors were differentially susceptible to sex differences and differences between majors. Measurement invariance for sex was established.

  12. An Integrated Approach to Mathematical Modeling: A Classroom Study.

    ERIC Educational Resources Information Center

    Doerr, Helen M.

    Modeling, simulation, and discrete mathematics have all been identified by professional mathematics education organizations as important areas for secondary school study. This classroom study focused on the components and tools for modeling and how students use these tools to construct their understanding of contextual problems in the content area…

  13. Evaluation of Limb Load Asymmetry Using Two New Mathematical Models

    PubMed Central

    Kumar, Senthil NS; Omar, Baharudin; Joseph, Leonard H.; Htwe, Ohnmar; Jagannathan, K.; Hamdan, Nor M Y; Rajalakshmi, D.

    2015-01-01

    Quantitative measurement of limb loading is important in orthopedic and neurological rehabilitation. In current practice, mathematical models such as Symmetry index (SI), Symmetry ratio (SR), and Symmetry angle (SA) are used to quantify limb loading asymmetry. Literatures have identified certain limitations with the above mathematical models. Hence this study presents two new mathematical models Modified symmetry index (MSI) and Limb loading error (LLE) that would address these limitations. Furthermore, the current mathematical models were compared against the new model with the goal of achieving a better model. This study uses hypothetical data to simulate an algorithmic preliminary computational measure to perform with all numerical possibilities of even and uneven limb loading that can occur in human legs. Descriptive statistics are used to interpret the limb loading patterns: symmetry, asymmetry and maximum asymmetry. The five mathematical models were similar in analyzing symmetry between limbs. However, for asymmetry and maximum asymmetry data, the SA and SR values do not give any meaningful interpretation, and SI gives an inflated value. The MSI and LLE are direct, easy to interpret and identify the loading patterns with the side of asymmetry. The new models are notable as they quantify the amount and side of asymmetry under different loading patterns. PMID:25716372

  14. Mathematical modeling of molecular diffusion through mucus

    PubMed Central

    Cu, Yen; Saltzman, W. Mark

    2008-01-01

    The rate of molecular transport through the mucus gel can be an important determinant of efficacy for therapeutic agents delivered by oral, intranasal, intravaginal/rectal, and intraocular routes. Transport through mucus can be described by mathematical models based on principles of physical chemistry and known characteristics of the mucus gel, its constituents, and of the drug itself. In this paper, we review mathematical models of molecular diffusion in mucus, as well as the techniques commonly used to measure diffusion of solutes in the mucus gel, mucus gel mimics, and mucosal epithelia. PMID:19135488

  15. Mathematical modeling of physiological systems: an essential tool for discovery.

    PubMed

    Glynn, Patric; Unudurthi, Sathya D; Hund, Thomas J

    2014-08-28

    Mathematical models are invaluable tools for understanding the relationships between components of a complex system. In the biological context, mathematical models help us understand the complex web of interrelations between various components (DNA, proteins, enzymes, signaling molecules etc.) in a biological system, gain better understanding of the system as a whole, and in turn predict its behavior in an altered state (e.g. disease). Mathematical modeling has enhanced our understanding of multiple complex biological processes like enzyme kinetics, metabolic networks, signal transduction pathways, gene regulatory networks, and electrophysiology. With recent advances in high throughput data generation methods, computational techniques and mathematical modeling have become even more central to the study of biological systems. In this review, we provide a brief history and highlight some of the important applications of modeling in biological systems with an emphasis on the study of excitable cells. We conclude with a discussion about opportunities and challenges for mathematical modeling going forward. In a larger sense, the review is designed to help answer a simple but important question that theoreticians frequently face from interested but skeptical colleagues on the experimental side: "What is the value of a model?" Copyright © 2014 Elsevier Inc. All rights reserved.

  16. Mathematical Models of Breast and Ovarian Cancers

    PubMed Central

    Botesteanu, Dana-Adriana; Lipkowitz, Stanley; Lee, Jung-Min; Levy, Doron

    2016-01-01

    Women constitute the majority of the aging United States (US) population, and this has substantial implications on cancer population patterns and management practices. Breast cancer is the most common women's malignancy, while ovarian cancer is the most fatal gynecological malignancy in the US. In this review we focus on these subsets of women's cancers, seen more commonly in postmenopausal and elderly women. In order to systematically investigate the complexity of cancer progression and response to treatment in breast and ovarian malignancies, we assert that integrated mathematical modeling frameworks viewed from a systems biology perspective are needed. Such integrated frameworks could offer innovative contributions to the clinical women's cancers community, since answers to clinical questions cannot always be reached with contemporary clinical and experimental tools. Here, we recapitulate clinically known data regarding the progression and treatment of the breast and ovarian cancers. We compare and contrast the two malignancies whenever possible, in order to emphasize areas where substantial contributions could be made by clinically inspired and validated mathematical modeling. We show how current paradigms in the mathematical oncology community focusing on the two malignancies do not make comprehensive use of, nor substantially reflect existing clinical data, and we highlight the modeling areas in most critical need of clinical data integration. We emphasize that the primary goal of any mathematical study of women's cancers should be to address clinically relevant questions. PMID:27259061

  17. Mathematical Modelling Research in Turkey: A Content Analysis Study

    ERIC Educational Resources Information Center

    Çelik, H. Coskun

    2017-01-01

    The aim of the present study was to examine the mathematical modelling studies done between 2004 and 2015 in Turkey and to reveal their tendencies. Forty-nine studies were selected using purposeful sampling based on the term, "mathematical modelling" with Higher Education Academic Search Engine. They were analyzed with content analysis.…

  18. Research Methods in Healthcare Epidemiology and Antimicrobial Stewardship-Mathematical Modeling.

    PubMed

    Barnes, Sean L; Kasaie, Parastu; Anderson, Deverick J; Rubin, Michael

    2016-11-01

    Mathematical modeling is a valuable methodology used to study healthcare epidemiology and antimicrobial stewardship, particularly when more traditional study approaches are infeasible, unethical, costly, or time consuming. We focus on 2 of the most common types of mathematical modeling, namely compartmental modeling and agent-based modeling, which provide important advantages-such as shorter developmental timelines and opportunities for extensive experimentation-over observational and experimental approaches. We summarize these advantages and disadvantages via specific examples and highlight recent advances in the methodology. A checklist is provided to serve as a guideline in the development of mathematical models in healthcare epidemiology and antimicrobial stewardship. Infect Control Hosp Epidemiol 2016;1-7.

  19. Helicopter flight dynamics simulation with a time-accurate free-vortex wake model

    NASA Astrophysics Data System (ADS)

    Ribera, Maria

    This dissertation describes the implementation and validation of a coupled rotor-fuselage simulation model with a time-accurate free-vortex wake model capable of capturing the response to maneuvers of arbitrary amplitude. The resulting model has been used to analyze different flight conditions, including both steady and transient maneuvers. The flight dynamics model is based on a system of coupled nonlinear rotor-fuselage differential equations in first-order, state-space form. The rotor model includes flexible blades, with coupled flap-lag-torsion dynamics and swept tips; the rigid body dynamics are modeled with the non-linear Euler equations. The free wake models the rotor flow field by tracking the vortices released at the blade tips. Their behavior is described by the equations of vorticity transport, which is approximated using finite differences, and solved using a time-accurate numerical scheme. The flight dynamics model can be solved as a system of non-linear algebraic trim equations to determine the steady state solution, or integrated in time in response to pilot-applied controls. This study also implements new approaches to reduce the prohibitive computational costs associated with such complex models without losing accuracy. The mathematical model was validated for trim conditions in level flight, turns, climbs and descents. The results obtained correlate well with flight test data, both in level flight as well as turning and climbing and descending flight. The swept tip model was also found to improve the trim predictions, particularly at high speed. The behavior of the rigid body and the rotor blade dynamics were also studied and related to the aerodynamic load distributions obtained with the free wake induced velocities. The model was also validated in a lateral maneuver from hover. The results show improvements in the on-axis prediction, and indicate a possible relation between the off-axis prediction and the lack of rotor-body interaction

  20. Mathematics as a Conduit for Translational Research in Post-Traumatic Osteoarthritis

    PubMed Central

    Ayati, Bruce P.; Kapitanov, Georgi I.; Coleman, Mitchell C.; Anderson, Donald D.; Martin, James A.

    2016-01-01

    Biomathematical models offer a powerful method of clarifying complex temporal interactions and the relationships among multiple variables in a system. We present a coupled in silico biomathematical model of articular cartilage degeneration in response to impact and/or aberrant loading such as would be associated with injury to an articular joint. The model incorporates fundamental biological and mechanical information obtained from explant and small animal studies to predict post-traumatic osteoarthritis (PTOA) progression, with an eye toward eventual application in human patients. In this sense, we refer to the mathematics as a “conduit of translation”. The new in silico framework presented in this paper involves a biomathematical model for the cellular and biochemical response to strains computed using finite element analysis. The model predicts qualitative responses presently, utilizing system parameter values largely taken from the literature. To contribute to accurate predictions, models need to be accurately parameterized with values that are based on solid science. We discuss a parameter identification protocol that will enable us to make increasingly accurate predictions of PTOA progression using additional data from smaller scale explant and small animal assays as they become available. By distilling the data from the explant and animal assays into parameters for biomathematical models, mathematics can translate experimental data to clinically relevant knowledge. PMID:27653021

  1. Components of Mathematics Anxiety: Factor Modeling of the MARS30-Brief

    PubMed Central

    Pletzer, Belinda; Wood, Guilherme; Scherndl, Thomas; Kerschbaum, Hubert H.; Nuerk, Hans-Christoph

    2016-01-01

    Mathematics anxiety involves feelings of tension, discomfort, high arousal, and physiological reactivity interfering with number manipulation and mathematical problem solving. Several factor analytic models indicate that mathematics anxiety is rather a multidimensional than unique construct. However, the factor structure of mathematics anxiety has not been fully clarified by now. This issue shall be addressed in the current study. The Mathematics Anxiety Rating Scale (MARS) is a reliable measure of mathematics anxiety (Richardson and Suinn, 1972), for which several reduced forms have been developed. Most recently, a shortened version of the MARS (MARS30-brief) with comparable reliability was published. Different studies suggest that mathematics anxiety involves up to seven different factors. Here we examined the factor structure of the MARS30-brief by means of confirmatory factor analysis. The best model fit was obtained by a six-factor model, dismembering the known two general factors “Mathematical Test Anxiety” (MTA) and “Numerical Anxiety” (NA) in three factors each. However, a more parsimonious 5-factor model with two sub-factors for MTA and three for NA fitted the data comparably well. Factors were differentially susceptible to sex differences and differences between majors. Measurement invariance for sex was established. PMID:26924996

  2. RF tumour ablation: computer simulation and mathematical modelling of the effects of electrical and thermal conductivity.

    PubMed

    Lobo, S M; Liu, Z-J; Yu, N C; Humphries, S; Ahmed, M; Cosman, E R; Lenkinski, R E; Goldberg, W; Goldberg, S N

    2005-05-01

    This study determined the effects of thermal conductivity on RF ablation tissue heating using mathematical modelling and computer simulations of RF heating coupled to thermal transport. Computer simulation of the Bio-Heat equation coupled with temperature-dependent solutions for RF electric fields (ETherm) was used to generate temperature profiles 2 cm away from a 3 cm internally-cooled electrode. Multiple conditions of clinically relevant electrical conductivities (0.07-12 S m-1) and 'tumour' radius (5-30 mm) at a given background electrical conductivity (0.12 S m-1) were studied. Temperature response surfaces were plotted for six thermal conductivities, ranging from 0.3-2 W m-1 degrees C (the range of anticipated clinical and experimental systems). A temperature response surface was obtained for each thermal conductivity at 25 electrical conductivities and 17 radii (n=425 temperature data points). The simulated temperature response was fit to a mathematical model derived from prior phantom data. This mathematical model is of the form (T=a+bRc exp(dR) s(f) exp(g)(s)) for RF generator-energy dependent situations and (T=h+k exp(mR)+n?exp(p)(s)) for RF generator-current limited situations, where T is the temperature (degrees C) 2 cm from the electrode and a, b, c, d, f, g, h, k, m, n and p are fitting parameters. For each of the thermal conductivity temperature profiles generated, the mathematical model fit the response surface to an r2 of 0.97-0.99. Parameters a, b, c, d, f, k and m were highly correlated to thermal conductivity (r2=0.96-0.99). The monotonic progression of fitting parameters permitted their mathematical expression using simple functions. Additionally, the effect of thermal conductivity simplified the above equation to the extent that g, h, n and p were found to be invariant. Thus, representation of the temperature response surface could be accurately expressed as a function of electrical conductivity, radius and thermal conductivity. As a result

  3. PREFACE: Physics-Based Mathematical Models for Nanotechnology

    NASA Astrophysics Data System (ADS)

    Voon, Lok C. Lew Yan; Melnik, Roderick; Willatzen, Morten

    2008-03-01

    in the cross-disciplinary research area: low-dimensional semiconductor nanostructures. Since the main properties of two-dimensional heterostructures (such as quantum wells) are now quite well understood, there has been a consistently growing interest in the mathematical physics community to further dimensionality reduction of semiconductor structures. Experimental achievements in realizing one-dimensional and quasi-zero-dimensional heterostructures have opened new opportunities for theory and applications of such low-dimensional semiconductor nanostructures. One of the most important implications of this process has been a critical re-examining of assumptions under which traditional quantum mechanical models have been derived in this field. Indeed, the formation of LDSNs, in particular quantum dots, is a competition between the surface energy in the structure and strain energy. However, current models for bandstructure calculations use quite a simplified analysis of strain relaxation effects, although such effects are in the heart of nanostructure formation. By now, it has been understood that traditional models in this field may not be adequate for modeling realistic objects based on LDSNs due to neglecting many effects that may profoundly influence optoelectronic properties of the nanostructures. Among such effects are electromechanical effects, including strain relaxation, piezoelectric effect, spontaneous polarization, and higher order nonlinear effects. Up to date, major efforts have been concentrated on the analysis of idealized, isolated quantum dots, while a typical self-assembled semiconductor quantum dot nanostructure is an array (or a molecule) of many individual quantum dots sitting on the same `substrate' known as the wetting layer. Each such dot contains several hundred thousand atoms. In order to account for quantum effects accurately in a situation like that, attempts can be made to apply ab initio or atomistic methodologies, but then one would face a

  4. Low-dimensional, morphologically accurate models of subthreshold membrane potential

    PubMed Central

    Kellems, Anthony R.; Roos, Derrick; Xiao, Nan; Cox, Steven J.

    2009-01-01

    The accurate simulation of a neuron’s ability to integrate distributed synaptic input typically requires the simultaneous solution of tens of thousands of ordinary differential equations. For, in order to understand how a cell distinguishes between input patterns we apparently need a model that is biophysically accurate down to the space scale of a single spine, i.e., 1 μm. We argue here that one can retain this highly detailed input structure while dramatically reducing the overall system dimension if one is content to accurately reproduce the associated membrane potential at a small number of places, e.g., at the site of action potential initiation, under subthreshold stimulation. The latter hypothesis permits us to approximate the active cell model with an associated quasi-active model, which in turn we reduce by both time-domain (Balanced Truncation) and frequency-domain (ℋ2 approximation of the transfer function) methods. We apply and contrast these methods on a suite of typical cells, achieving up to four orders of magnitude in dimension reduction and an associated speed-up in the simulation of dendritic democratization and resonance. We also append a threshold mechanism and indicate that this reduction has the potential to deliver an accurate quasi-integrate and fire model. PMID:19172386

  5. Mathematical modeling of cancer metabolism.

    PubMed

    Medina, Miguel Ángel

    2018-04-01

    Systemic approaches are needed and useful for the study of the very complex issue of cancer. Modeling has a central position in these systemic approaches. Metabolic reprogramming is nowadays acknowledged as an essential hallmark of cancer. Mathematical modeling could contribute to a better understanding of cancer metabolic reprogramming and to identify new potential ways of therapeutic intervention. Herein, I review several alternative approaches to metabolic modeling and their current and future impact in oncology. Copyright © 2018 Elsevier B.V. All rights reserved.

  6. Mathematical model of polyethylene pipe bending stress state

    NASA Astrophysics Data System (ADS)

    Serebrennikov, Anatoly; Serebrennikov, Daniil

    2018-03-01

    Introduction of new machines and new technologies of polyethylene pipeline installation is usually based on the polyethylene pipe flexibility. It is necessary that existing bending stresses do not lead to an irreversible polyethylene pipe deformation and to violation of its strength characteristics. Derivation of the mathematical model which allows calculating analytically the bending stress level of polyethylene pipes with consideration of nonlinear characteristics is presented below. All analytical calculations made with the mathematical model are experimentally proved and confirmed.

  7. Mathematical models to characterize early epidemic growth: A Review

    PubMed Central

    Chowell, Gerardo; Sattenspiel, Lisa; Bansal, Shweta; Viboud, Cécile

    2016-01-01

    There is a long tradition of using mathematical models to generate insights into the transmission dynamics of infectious diseases and assess the potential impact of different intervention strategies. The increasing use of mathematical models for epidemic forecasting has highlighted the importance of designing reliable models that capture the baseline transmission characteristics of specific pathogens and social contexts. More refined models are needed however, in particular to account for variation in the early growth dynamics of real epidemics and to gain a better understanding of the mechanisms at play. Here, we review recent progress on modeling and characterizing early epidemic growth patterns from infectious disease outbreak data, and survey the types of mathematical formulations that are most useful for capturing a diversity of early epidemic growth profiles, ranging from sub-exponential to exponential growth dynamics. Specifically, we review mathematical models that incorporate spatial details or realistic population mixing structures, including meta-population models, individual-based network models, and simple SIR-type models that incorporate the effects of reactive behavior changes or inhomogeneous mixing. In this process, we also analyze simulation data stemming from detailed large-scale agent-based models previously designed and calibrated to study how realistic social networks and disease transmission characteristics shape early epidemic growth patterns, general transmission dynamics, and control of international disease emergencies such as the 2009 A/H1N1 influenza pandemic and the 2014-15 Ebola epidemic in West Africa. PMID:27451336

  8. Mathematical models to characterize early epidemic growth: A review

    NASA Astrophysics Data System (ADS)

    Chowell, Gerardo; Sattenspiel, Lisa; Bansal, Shweta; Viboud, Cécile

    2016-09-01

    There is a long tradition of using mathematical models to generate insights into the transmission dynamics of infectious diseases and assess the potential impact of different intervention strategies. The increasing use of mathematical models for epidemic forecasting has highlighted the importance of designing reliable models that capture the baseline transmission characteristics of specific pathogens and social contexts. More refined models are needed however, in particular to account for variation in the early growth dynamics of real epidemics and to gain a better understanding of the mechanisms at play. Here, we review recent progress on modeling and characterizing early epidemic growth patterns from infectious disease outbreak data, and survey the types of mathematical formulations that are most useful for capturing a diversity of early epidemic growth profiles, ranging from sub-exponential to exponential growth dynamics. Specifically, we review mathematical models that incorporate spatial details or realistic population mixing structures, including meta-population models, individual-based network models, and simple SIR-type models that incorporate the effects of reactive behavior changes or inhomogeneous mixing. In this process, we also analyze simulation data stemming from detailed large-scale agent-based models previously designed and calibrated to study how realistic social networks and disease transmission characteristics shape early epidemic growth patterns, general transmission dynamics, and control of international disease emergencies such as the 2009 A/H1N1 influenza pandemic and the 2014-2015 Ebola epidemic in West Africa.

  9. Mathematical model comparing of the multi-level economics systems

    NASA Astrophysics Data System (ADS)

    Brykalov, S. M.; Kryanev, A. V.

    2017-12-01

    The mathematical model (scheme) of a multi-level comparison of the economic system, characterized by the system of indices, is worked out. In the mathematical model of the multi-level comparison of the economic systems, the indicators of peer review and forecasting of the economic system under consideration can be used. The model can take into account the uncertainty in the estimated values of the parameters or expert estimations. The model uses the multi-criteria approach based on the Pareto solutions.

  10. Evolution of Mathematics Teachers' Pedagogical Knowledge When They Are Teaching through Modeling

    ERIC Educational Resources Information Center

    Aydogan Yenmez, Arzu; Erbas, Ayhan Kursat; Alacaci, Cengiz; Cakiroglu, Erdinc; Cetinkaya, Bulent

    2017-01-01

    Use of mathematical modeling in mathematics education has been receiving significant attention as a way to develop students' mathematical knowledge and skills. As effective use of modeling in classes depends on the competencies of teachers we need to know more about the nature of teachers' knowledge to use modeling in mathematics education and how…

  11. Mathematical Modelling for Patient Selection in Proton Therapy.

    PubMed

    Mee, T; Kirkby, N F; Kirkby, K J

    2018-05-01

    Proton beam therapy (PBT) is still relatively new in cancer treatment and the clinical evidence base is relatively sparse. Mathematical modelling offers assistance when selecting patients for PBT and predicting the demand for service. Discrete event simulation, normal tissue complication probability, quality-adjusted life-years and Markov Chain models are all mathematical and statistical modelling techniques currently used but none is dominant. As new evidence and outcome data become available from PBT, comprehensive models will emerge that are less dependent on the specific technologies of radiotherapy planning and delivery. Copyright © 2018 The Royal College of Radiologists. Published by Elsevier Ltd. All rights reserved.

  12. An Accurate and Dynamic Computer Graphics Muscle Model

    NASA Technical Reports Server (NTRS)

    Levine, David Asher

    1997-01-01

    A computer based musculo-skeletal model was developed at the University in the departments of Mechanical and Biomedical Engineering. This model accurately represents human shoulder kinematics. The result of this model is the graphical display of bones moving through an appropriate range of motion based on inputs of EMGs and external forces. The need existed to incorporate a geometric muscle model in the larger musculo-skeletal model. Previous muscle models did not accurately represent muscle geometries, nor did they account for the kinematics of tendons. This thesis covers the creation of a new muscle model for use in the above musculo-skeletal model. This muscle model was based on anatomical data from the Visible Human Project (VHP) cadaver study. Two-dimensional digital images from the VHP were analyzed and reconstructed to recreate the three-dimensional muscle geometries. The recreated geometries were smoothed, reduced, and sliced to form data files defining the surfaces of each muscle. The muscle modeling function opened these files during run-time and recreated the muscle surface. The modeling function applied constant volume limitations to the muscle and constant geometry limitations to the tendons.

  13. League tables and school effectiveness: a mathematical model.

    PubMed Central

    Hoyle, Rebecca B; Robinson, James C

    2003-01-01

    'School performance tables', an alphabetical list of secondary schools along with aggregates of their pupils' performances in national tests, have been published in the UK since 1992. Inevitably, the media have responded by publishing ranked 'league tables'. Despite concern over the potentially divisive effect of such tables, the current government has continued to publish this information in the same form. The effect of this information on standards and on the social make-up of the community has been keenly debated. Since there is no control group available that would allow us to investigate this issue directly, we present here a simple mathematical model. Our results indicate that, while random fluctuations from year to year can cause large distortions in the league-table positions, some schools still establish themselves as 'desirable'. To our surprise, we found that 'value-added' tables were no more accurate than tables based on raw exam scores, while a different method of drawing up the tables, in which exam results are averaged over a period of time, appears to give a much more reliable measure of school performance. PMID:12590748

  14. Mathematical Model Development and Simulation Support

    NASA Technical Reports Server (NTRS)

    Francis, Ronald C.; Tobbe, Patrick A.

    2000-01-01

    This report summarizes the work performed in support of the Contact Dynamics 6DOF Facility and the Flight Robotics Lab at NASA/ MSFC in the areas of Mathematical Model Development and Simulation Support.

  15. On a Mathematical Model with Noncompact Boundary Conditions Describing Bacterial Population

    NASA Astrophysics Data System (ADS)

    Boulanouar, Mohamed

    2013-04-01

    In this work, we are concerned with the well-posedness of a mathematical model describing a maturation-velocity structured bacterial population. Each bacterium is distinguished by its degree of maturity and its maturation velocity. The bacterial mitosis is mathematically described by noncompact boundary conditions. We show that the mathematical model is governed by a positive strongly continuous semigroup.

  16. Mathematical Modeling: Are Prior Experiences Important?

    ERIC Educational Resources Information Center

    Czocher, Jennifer A.; Moss, Diana L.

    2017-01-01

    Why are math modeling problems the source of such frustration for students and teachers? The conceptual understanding that students have when engaging with a math modeling problem varies greatly. They need opportunities to make their own assumptions and design the mathematics to fit these assumptions (CCSSI 2010). Making these assumptions is part…

  17. A mathematical approach for evaluating Markov models in continuous time without discrete-event simulation.

    PubMed

    van Rosmalen, Joost; Toy, Mehlika; O'Mahony, James F

    2013-08-01

    Markov models are a simple and powerful tool for analyzing the health and economic effects of health care interventions. These models are usually evaluated in discrete time using cohort analysis. The use of discrete time assumes that changes in health states occur only at the end of a cycle period. Discrete-time Markov models only approximate the process of disease progression, as clinical events typically occur in continuous time. The approximation can yield biased cost-effectiveness estimates for Markov models with long cycle periods and if no half-cycle correction is made. The purpose of this article is to present an overview of methods for evaluating Markov models in continuous time. These methods use mathematical results from stochastic process theory and control theory. The methods are illustrated using an applied example on the cost-effectiveness of antiviral therapy for chronic hepatitis B. The main result is a mathematical solution for the expected time spent in each state in a continuous-time Markov model. It is shown how this solution can account for age-dependent transition rates and discounting of costs and health effects, and how the concept of tunnel states can be used to account for transition rates that depend on the time spent in a state. The applied example shows that the continuous-time model yields more accurate results than the discrete-time model but does not require much computation time and is easily implemented. In conclusion, continuous-time Markov models are a feasible alternative to cohort analysis and can offer several theoretical and practical advantages.

  18. Mathematical Modelling at Secondary School: The MACSI-Clongowes Wood College Experience

    ERIC Educational Resources Information Center

    Charpin, J. P. F.; O'Hara, S.; Mackey, D.

    2013-01-01

    In Ireland, to encourage the study of STEM (science, technology, engineering and mathematics) subjects and particularly mathematics, the Mathematics Applications Consortium for Science and Industry (MACSI) and Clongowes Wood College (County Kildare, Ireland) organized a mathematical modelling workshop for senior cycle secondary school students.…

  19. Study on the Mathematical Model of Dielectric Recovery Characteristics in High Voltage SF6 Circuit Breaker

    NASA Astrophysics Data System (ADS)

    Lin, Xin; Wang, Feiming; Xu, Jianyuan; Xia, Yalong; Liu, Weidong

    2016-03-01

    According to the stream theory, this paper proposes a mathematical model of the dielectric recovery characteristic based on the two-temperature ionization equilibrium equation. Taking the dynamic variation of charged particle's ionization and attachment into account, this model can be used in collaboration with the Coulomb collision model, which gives the relationship of the heavy particle temperature and electron temperature to calculate the electron density and temperature under different pressure and electric field conditions, so as to deliver the breakdown electric field strength under different pressure conditions. Meanwhile an experiment loop of the circuit breaker has been built to measure the breakdown voltage. It is shown that calculated results are in conformity with experiment results on the whole while results based on the stream criterion are larger than experiment results. This indicates that the mathematical model proposed here is more accurate for calculating the dielectric recovery characteristic, it is derived from the stream model with some improvement and refinement and has great significance for increasing the simulation accuracy of circuit breaker's interruption characteristic. supported by Science and Technology Project of State Grid Corporation of China (No. GY17201200063), National Natural Science Foundation of China (No. 51277123), Basic Research Project of Liaoning Key Laboratory of Education Department (LZ2015055)

  20. Mathematical modelling of skeletal repair.

    PubMed

    MacArthur, B D; Please, C P; Taylor, M; Oreffo, R O C

    2004-01-23

    Tissue engineering offers significant promise as a viable alternative to current clinical strategies for replacement of damaged tissue as a consequence of disease or trauma. Since mathematical modelling is a valuable tool in the analysis of complex systems, appropriate use of mathematical models has tremendous potential for advancing the understanding of the physical processes involved in such tissue reconstruction. In this review, the potential benefits, and limitations, of theoretical modelling in tissue engineering applications are examined with specific emphasis on tissue engineering of bone. A central tissue engineering approach is the in vivo implantation of a biomimetic scaffold seeded with an appropriate population of stem or progenitor cells. This review will therefore consider the theory behind a number of key factors affecting the success of such a strategy including: stem cell or progenitor population expansion and differentiation ex vivo; cell adhesion and migration, and the effective design of scaffolds; and delivery of nutrient to avascular structures. The focus will be on current work in this area, as well as on highlighting limitations and suggesting possible directions for future work to advance health-care for all.

  1. Comparison of learning models based on mathematics logical intelligence in affective domain

    NASA Astrophysics Data System (ADS)

    Widayanto, Arif; Pratiwi, Hasih; Mardiyana

    2018-04-01

    The purpose of this study was to examine the presence or absence of different effects of multiple treatments (used learning models and logical-mathematical intelligence) on the dependent variable (affective domain of mathematics). This research was quasi experimental using 3x3 of factorial design. The population of this research was VIII grade students of junior high school in Karanganyar under the academic year 2017/2018. Data collected in this research was analyzed by two ways analysis of variance with unequal cells using 5% of significance level. The result of the research were as follows: (1) Teaching and learning with model TS lead to better achievement in affective domain than QSH, teaching and learning with model QSH lead to better achievement in affective domain than using DI; (2) Students with high mathematics logical intelligence have better achievement in affective domain than students with low mathematics logical intelligence have; (3) In teaching and learning mathematics using learning model TS, students with moderate mathematics logical intelligence have better achievement in affective domain than using DI; and (4) In teaching and learning mathematics using learning model TS, students with low mathematics logical intelligence have better achievement in affective domain than using QSH and DI.

  2. Automatic mathematical modeling for real time simulation system

    NASA Technical Reports Server (NTRS)

    Wang, Caroline; Purinton, Steve

    1988-01-01

    A methodology for automatic mathematical modeling and generating simulation models is described. The models will be verified by running in a test environment using standard profiles with the results compared against known results. The major objective is to create a user friendly environment for engineers to design, maintain, and verify their model and also automatically convert the mathematical model into conventional code for conventional computation. A demonstration program was designed for modeling the Space Shuttle Main Engine Simulation. It is written in LISP and MACSYMA and runs on a Symbolic 3670 Lisp Machine. The program provides a very friendly and well organized environment for engineers to build a knowledge base for base equations and general information. It contains an initial set of component process elements for the Space Shuttle Main Engine Simulation and a questionnaire that allows the engineer to answer a set of questions to specify a particular model. The system is then able to automatically generate the model and FORTRAN code. The future goal which is under construction is to download the FORTRAN code to VAX/VMS system for conventional computation. The SSME mathematical model will be verified in a test environment and the solution compared with the real data profile. The use of artificial intelligence techniques has shown that the process of the simulation modeling can be simplified.

  3. Review and verification of CARE 3 mathematical model and code

    NASA Technical Reports Server (NTRS)

    Rose, D. M.; Altschul, R. E.; Manke, J. W.; Nelson, D. L.

    1983-01-01

    The CARE-III mathematical model and code verification performed by Boeing Computer Services were documented. The mathematical model was verified for permanent and intermittent faults. The transient fault model was not addressed. The code verification was performed on CARE-III, Version 3. A CARE III Version 4, which corrects deficiencies identified in Version 3, is being developed.

  4. Mathematical models of continuous flow electrophoresis: Electrophoresis technology

    NASA Technical Reports Server (NTRS)

    Saville, Dudley A.

    1986-01-01

    Two aspects of continuous flow electrophoresis were studied: (1) the structure of the flow field in continuous flow devices; and (2) the electrokinetic properties of suspended particles relevant to electrophoretic separations. Mathematical models were developed to describe flow structure and stability, with particular emphasis on effects due to buoyancy. To describe the fractionation of an arbitrary particulate sample by continuous flow electrophoresis, a general mathematical model was constructed. In this model, chamber dimensions, field strength, buffer composition, and other design variables can be altered at will to study their effects on resolution and throughput. All these mathematical models were implemented on a digital computer and the codes are available for general use. Experimental and theoretical work with particulate samples probed how particle mobility is related to buffer composition. It was found that ions on the surface of small particles are mobile, contrary to the widely accepted view. This influences particle mobility and suspension conductivity. A novel technique was used to measure the mobility of particles in concentrated suspensions.

  5. A study of structural properties of gene network graphs for mathematical modeling of integrated mosaic gene networks.

    PubMed

    Petrovskaya, Olga V; Petrovskiy, Evgeny D; Lavrik, Inna N; Ivanisenko, Vladimir A

    2017-04-01

    Gene network modeling is one of the widely used approaches in systems biology. It allows for the study of complex genetic systems function, including so-called mosaic gene networks, which consist of functionally interacting subnetworks. We conducted a study of a mosaic gene networks modeling method based on integration of models of gene subnetworks by linear control functionals. An automatic modeling of 10,000 synthetic mosaic gene regulatory networks was carried out using computer experiments on gene knockdowns/knockouts. Structural analysis of graphs of generated mosaic gene regulatory networks has revealed that the most important factor for building accurate integrated mathematical models, among those analyzed in the study, is data on expression of genes corresponding to the vertices with high properties of centrality.

  6. Mathematical modeling of infectious disease dynamics

    PubMed Central

    Siettos, Constantinos I.; Russo, Lucia

    2013-01-01

    Over the last years, an intensive worldwide effort is speeding up the developments in the establishment of a global surveillance network for combating pandemics of emergent and re-emergent infectious diseases. Scientists from different fields extending from medicine and molecular biology to computer science and applied mathematics have teamed up for rapid assessment of potentially urgent situations. Toward this aim mathematical modeling plays an important role in efforts that focus on predicting, assessing, and controlling potential outbreaks. To better understand and model the contagious dynamics the impact of numerous variables ranging from the micro host–pathogen level to host-to-host interactions, as well as prevailing ecological, social, economic, and demographic factors across the globe have to be analyzed and thoroughly studied. Here, we present and discuss the main approaches that are used for the surveillance and modeling of infectious disease dynamics. We present the basic concepts underpinning their implementation and practice and for each category we give an annotated list of representative works. PMID:23552814

  7. Mathematical model of glucose-insulin homeostasis in healthy rats.

    PubMed

    Lombarte, Mercedes; Lupo, Maela; Campetelli, German; Basualdo, Marta; Rigalli, Alfredo

    2013-10-01

    According to the World Health Organization there are over 220 million people in the world with diabetes and 3.4 million people died in 2004 as a consequence of this pathology. Development of an artificial pancreas would allow to restore control of blood glucose by coupling an infusion pump to a continuous glucose sensor in the blood. The design of such a device requires the development and application of mathematical models which represent the gluco-regulatory system. Models developed by other research groups describe very well the gluco-regulatory system but have a large number of mathematical equations and require complex methodologies for the estimation of its parameters. In this work we propose a mathematical model to study the homeostasis of glucose and insulin in healthy rats. The proposed model consists of three differential equations and 8 parameters that describe the variation of: blood glucose concentration, blood insulin concentration and amount of glucose in the intestine. All parameters were obtained by setting functions to the values of glucose and insulin in blood obtained after oral glucose administration. In vivo and in silico validations were performed. Additionally, a qualitative analysis has been done to verify the aforementioned model. We have shown that this model has a single, biologically consistent equilibrium point. This model is a first step in the development of a mathematical model for the type I diabetic rat. Copyright © 2013 Elsevier Inc. All rights reserved.

  8. Modeling eBook acceptance: A study on mathematics teachers

    NASA Astrophysics Data System (ADS)

    Jalal, Azlin Abd; Ayub, Ahmad Fauzi Mohd; Tarmizi, Rohani Ahmad

    2014-12-01

    The integration and effectiveness of eBook utilization in Mathematics teaching and learning greatly relied upon the teachers, hence the need to understand their perceptions and beliefs. The eBook, an individual laptop completed with digitized textbook sofwares, were provided for each students in line with the concept of 1 student:1 laptop. This study focuses on predicting a model on the acceptance of the eBook among Mathematics teachers. Data was collected from 304 mathematics teachers in selected schools using a survey questionnaire. The selection were based on the proportionate stratified sampling. Structural Equation Modeling (SEM) were employed where the model was tested and evaluated and was found to have a good fit. The variance explained for the teachers' attitude towards eBook is approximately 69.1% where perceived usefulness appeared to be a stronger determinant compared to perceived ease of use. This study concluded that the attitude of mathematics teachers towards eBook depends largely on the perception of how useful the eBook is on improving their teaching performance, implying that teachers should be kept updated with the latest mathematical application and sofwares to use with the eBook to ensure positive attitude towards using it in class.

  9. Mathematical supply-chain modelling: Product analysis of cost and time

    NASA Astrophysics Data System (ADS)

    Easters, D. J.

    2014-03-01

    Establishing a mathematical supply-chain model is a proposition that has received attention due to its inherent benefits of evolving global supply-chain efficiencies. This paper discusses the prevailing relationships found within apparel supply-chain environments, and contemplates the complex issues indicated for constituting a mathematical model. Principal results identified within the data suggest, that the multifarious nature of global supply-chain activities require a degree of simplification in order to fully dilate the necessary factors which affect, each sub-section of the chain. Subsequently, the research findings allowed the division of supply-chain components into sub-sections, which amassed a coherent method of product development activity. Concurrently, the supply-chain model was found to allow systematic mathematical formulae analysis, of cost and time, within the multiple contexts of each subsection encountered. The paper indicates the supply-chain model structure, the mathematics, and considers how product analysis of cost and time can improve the comprehension of product lifecycle management.

  10. Illustrations of mathematical modeling in biology: epigenetics, meiosis, and an outlook.

    PubMed

    Richards, D; Berry, S; Howard, M

    2012-01-01

    In the past few years, mathematical modeling approaches in biology have begun to fulfill their promise by assisting in the dissection of complex biological systems. Here, we review two recent examples of predictive mathematical modeling in plant biology. The first involves the quantitative epigenetic silencing of the floral repressor gene FLC in Arabidopsis, mediated by a Polycomb-based system. The second involves the spatiotemporal dynamics of telomere bouquet formation in wheat-rye meiosis. Although both the biology and the modeling framework of the two systems are different, both exemplify how mathematical modeling can help to accelerate discovery of the underlying mechanisms in complex biological systems. In both cases, the models that developed were relatively minimal, including only essential features, but both nevertheless yielded fundamental insights. We also briefly review the current state of mathematical modeling in biology, difficulties inherent in its application, and its potential future development.

  11. The prediction of epidemics through mathematical modeling.

    PubMed

    Schaus, Catherine

    2014-01-01

    Mathematical models may be resorted to in an endeavor to predict the development of epidemics. The SIR model is one of the applications. Still too approximate, the use of statistics awaits more data in order to come closer to reality.

  12. Mathematical modeling to predict residential solid waste generation.

    PubMed

    Benítez, Sara Ojeda; Lozano-Olvera, Gabriela; Morelos, Raúl Adalberto; Vega, Carolina Armijo de

    2008-01-01

    One of the challenges faced by waste management authorities is determining the amount of waste generated by households in order to establish waste management systems, as well as trying to charge rates compatible with the principle applied worldwide, and design a fair payment system for households according to the amount of residential solid waste (RSW) they generate. The goal of this research work was to establish mathematical models that correlate the generation of RSW per capita to the following variables: education, income per household, and number of residents. This work was based on data from a study on generation, quantification and composition of residential waste in a Mexican city in three stages. In order to define prediction models, five variables were identified and included in the model. For each waste sampling stage a different mathematical model was developed, in order to find the model that showed the best linear relation to predict residential solid waste generation. Later on, models to explore the combination of included variables and select those which showed a higher R(2) were established. The tests applied were normality, multicolinearity and heteroskedasticity. Another model, formulated with four variables, was generated and the Durban-Watson test was applied to it. Finally, a general mathematical model is proposed to predict residential waste generation, which accounts for 51% of the total.

  13. Two Mathematical Models of Nonlinear Vibrations

    NASA Technical Reports Server (NTRS)

    Brugarolas, Paul; Bayard, David; Spanos, John; Breckenridge, William

    2007-01-01

    Two innovative mathematical models of nonlinear vibrations, and methods of applying them, have been conceived as byproducts of an effort to develop a Kalman filter for highly precise estimation of bending motions of a large truss structure deployed in outer space from a space-shuttle payload bay. These models are also applicable to modeling and analysis of vibrations in other engineering disciplines, on Earth as well as in outer space.

  14. Effectiveness of discovery learning model on mathematical problem solving

    NASA Astrophysics Data System (ADS)

    Herdiana, Yunita; Wahyudin, Sispiyati, Ririn

    2017-08-01

    This research is aimed to describe the effectiveness of discovery learning model on mathematical problem solving. This research investigate the students' problem solving competency before and after learned by using discovery learning model. The population used in this research was student in grade VII in one of junior high school in West Bandung Regency. From nine classes, class VII B were randomly selected as the sample of experiment class, and class VII C as control class, which consist of 35 students every class. The method in this research was quasi experiment. The instrument in this research is pre-test, worksheet and post-test about problem solving of mathematics. Based on the research, it can be conclude that the qualification of problem solving competency of students who gets discovery learning model on level 80%, including in medium category and it show that discovery learning model effective to improve mathematical problem solving.

  15. Parental modelling of mathematical affect: self-efficacy and emotional arousal

    NASA Astrophysics Data System (ADS)

    Bartley, Sarah R.; Ingram, Naomi

    2017-12-01

    This study explored the relationship between parents' mathematics self-efficacy and emotional arousal to mathematics and their 12- and 13-year-old children's mathematics self-efficacy and emotional arousal to mathematics. Parental modelling of affective relationships during homework was a focus. Eighty-four parent and child pairings from seven schools in New Zealand were examined using embedded design methodology. No significant correlations were found when the parents' mathematics self-efficacy and emotional arousal to mathematics were compared with the children's mathematics self-efficacy and emotional arousal to mathematics. However, the parents' level of emotional arousal to mathematics was found to have affected their willingness to assist with mathematics homework. For those parents who assisted, a significant positive correlation was found between their mathematics self-efficacy and their children's emotional arousal to mathematics. Parents who did assist were generally reported as being calm, and used techniques associated with positive engagement. Fathers were calmer and more likely to express readiness to assist with mathematics homework than mothers. A further significant positive correlation was found between fathers' emotional arousal to mathematics and children's mathematics self-efficacy. Implications from the study suggest directions for future research.

  16. Mathematical modeling of hydromechanical extrusion

    NASA Astrophysics Data System (ADS)

    Agapitova, O. Yu.; Byvaltsev, S. V.; Zalazinsky, A. G.

    2017-12-01

    The mathematical modeling of the hydromechanical extrusion of metals through two sequentially installed cone dies is carried out. The optimum parameters of extrusion tools are determined to minimize the extrusion force. A software system has been developed to solve problems of plastic deformation of metals and to provide an optimum design of extrusion tools.

  17. Developing teachers' models for assessing students' competence in mathematical modelling through lesson study

    NASA Astrophysics Data System (ADS)

    Aydogan Yenmez, Arzu; Erbas, Ayhan Kursat; Cakiroglu, Erdinc; Alacaci, Cengiz; Cetinkaya, Bulent

    2017-08-01

    Applications and modelling have gained a prominent role in mathematics education reform documents and curricula. Thus, there is a growing need for studies focusing on the effective use of mathematical modelling in classrooms. Assessment is an integral part of using modelling activities in classrooms, since it allows teachers to identify and manage problems that arise in various stages of the modelling process. However, teachers' difficulties in assessing student modelling work are a challenge to be considered when implementing modelling in the classroom. Thus, the purpose of this study was to investigate how teachers' knowledge on generating assessment criteria for assessing student competence in mathematical modelling evolved through a professional development programme, which is based on a lesson study approach and modelling perspective. The data was collected with four teachers from two public high schools over a five-month period. The professional development programme included a cyclical process, with each cycle consisting of an introductory meeting, the implementation of a model-eliciting activity with students, and a follow-up meeting. The results showed that the professional development programme contributed to teachers' knowledge for generating assessment criteria on the products, and the observable actions that affect the modelling cycle.

  18. Striking a Balance: Students' Tendencies to Oversimplify or Overcomplicate in Mathematical Modeling

    ERIC Educational Resources Information Center

    Gould, Heather; Wasserman, Nicholas H.

    2014-01-01

    With the adoption of the "Common Core State Standards for Mathematics" (CCSSM), the process of mathematical modeling has been given increased attention in mathematics education. This article reports on a study intended to inform the implementation of modeling in classroom contexts by examining students' interactions with the process of…

  19. Attitudes of Pre-Service Mathematics Teachers towards Modelling: A South African Inquiry

    ERIC Educational Resources Information Center

    Jacobs, Gerrie J.; Durandt, Rina

    2017-01-01

    This study explores the attitudes of mathematics pre-service teachers, based on their initial exposure to a model-eliciting challenge. The new Curriculum and Assessment Policy Statement determines that mathematics students should be able to identify, investigate and solve problems via modelling. The unpreparedness of mathematics teachers in…

  20. Cooking Potatoes: Experimentation and Mathematical Modeling.

    ERIC Educational Resources Information Center

    Chen, Xiao Dong

    2002-01-01

    Describes a laboratory activity involving a mathematical model of cooking potatoes that can be solved analytically. Highlights the microstructure aspects of the experiment. Provides the key aspects of the results, detailed background readings, laboratory procedures and data analyses. (MM)

  1. Mathematical modeling of forest fire initiation in three dimensional setting

    Treesearch

    Valeriy Perminov

    2007-01-01

    In this study, the assignment and theoretical investigations of the problems of forest fire initiation were carried out, including development of a mathematical model for description of heat and mass transfer processes in overterrestrial layer of atmosphere at crown forest fire initiation, taking into account their mutual influence. Mathematical model of forest fire...

  2. About a mathematical model of market

    NASA Astrophysics Data System (ADS)

    Kulikov, D. A.

    2017-01-01

    In the paper a famous mathematical model of macroeconomics, which is called “market model” was considered. Traditional versions of this model have no periodic solutions and, therefore, they cannot describe a cyclic recurrence of the market economy. In the paper for the corresponding equation a delay was added. It allows obtaining sufficient conditions for existence of the stable cycles.

  3. Uncertainty and Complexity in Mathematical Modeling

    ERIC Educational Resources Information Center

    Cannon, Susan O.; Sanders, Mark

    2017-01-01

    Modeling is an effective tool to help students access mathematical concepts. Finding a math teacher who has not drawn a fraction bar or pie chart on the board would be difficult, as would finding students who have not been asked to draw models and represent numbers in different ways. In this article, the authors will discuss: (1) the properties of…

  4. [Mathematical models and epidemiological analysis].

    PubMed

    Gerasimov, A N

    2010-01-01

    The limited use of mathematical simulation in epidemiology is due not only to the difficulty of monitoring the epidemic process and identifying its parameters but also to the application of oversimplified models. It is shown that realistic reproduction of actual morbidity dynamics requires taking into account heterogeneity and finiteness of the population and seasonal character of pathogen transmission mechanism.

  5. Mathematics Student Teachers' Modelling Approaches While Solving the Designed Esme Rug Problem

    ERIC Educational Resources Information Center

    Hidiroglu, Çaglar Naci; Dede, Ayse Tekin; Ünver, Semiha Kula; Güzel, Esra Bukova

    2017-01-01

    The purpose of the study is to analyze the mathematics student teachers' solutions on the Esme Rug Problem through 7-stage mathematical modelling process. This problem was designed by the researchers by considering the modelling problems' main properties. The study was conducted with twenty one secondary mathematics student teachers. The data were…

  6. Examining of Model Eliciting Activities Developed by Mathematics Student Teachers

    ERIC Educational Resources Information Center

    Dede, Ayse Tekin; Hidiroglu, Çaglar Naci; Güzel, Esra Bukova

    2017-01-01

    The purpose of this study is to examine the model eliciting activities developed by the mathematics student teachers in the context of the principles of the model eliciting activities. The participants of the study conducted as a case study design were twenty one mathematics student teachers working on seven groups. The data collection tools were…

  7. Visual Modeling as a Motivation for Studying Mathematics and Art

    ERIC Educational Resources Information Center

    Sendova, Evgenia; Grkovska, Slavica

    2005-01-01

    The paper deals with the possibility of enriching the curriculum in mathematics, informatics and art by means of visual modeling of abstract paintings. The authors share their belief that in building a computer model of a construct, one gains deeper insight into the construct, and is motivated to elaborate one's knowledge in mathematics and…

  8. Accurate modelling of unsteady flows in collapsible tubes.

    PubMed

    Marchandise, Emilie; Flaud, Patrice

    2010-01-01

    The context of this paper is the development of a general and efficient numerical haemodynamic tool to help clinicians and researchers in understanding of physiological flow phenomena. We propose an accurate one-dimensional Runge-Kutta discontinuous Galerkin (RK-DG) method coupled with lumped parameter models for the boundary conditions. The suggested model has already been successfully applied to haemodynamics in arteries and is now extended for the flow in collapsible tubes such as veins. The main difference with cardiovascular simulations is that the flow may become supercritical and elastic jumps may appear with the numerical consequence that scheme may not remain monotone if no limiting procedure is introduced. We show that our second-order RK-DG method equipped with an approximate Roe's Riemann solver and a slope-limiting procedure allows us to capture elastic jumps accurately. Moreover, this paper demonstrates that the complex physics associated with such flows is more accurately modelled than with traditional methods such as finite difference methods or finite volumes. We present various benchmark problems that show the flexibility and applicability of the numerical method. Our solutions are compared with analytical solutions when they are available and with solutions obtained using other numerical methods. Finally, to illustrate the clinical interest, we study the emptying process in a calf vein squeezed by contracting skeletal muscle in a normal and pathological subject. We compare our results with experimental simulations and discuss the sensitivity to parameters of our model.

  9. The stability of colorectal cancer mathematical models

    NASA Astrophysics Data System (ADS)

    Khairudin, Nur Izzati; Abdullah, Farah Aini

    2013-04-01

    Colorectal cancer is one of the most common types of cancer. To better understand about the kinetics of cancer growth, mathematical models are used to provide insight into the progression of this natural process which enables physicians and oncologists to determine optimal radiation and chemotherapy schedules and develop a prognosis, both of which are indispensable for treating cancer. This thesis investigates the stability of colorectal cancer mathematical models. We found that continuous saturating feedback is the best available model of colorectal cancer growth. We also performed stability analysis. The result shows that cancer progress in sequence of genetic mutations or epigenetic which lead to a very large number of cells population until become unbounded. The cell population growth initiate and its saturating feedback is overcome when mutation changes causing the net per-capita growth rate of stem or transit cells exceed critical threshold.

  10. Focus group discussion in mathematical physics learning

    NASA Astrophysics Data System (ADS)

    Ellianawati; Rudiana, D.; Sabandar, J.; Subali, B.

    2018-03-01

    The Focus Group Discussion (FGD) activity in Mathematical Physics learning has helped students perform the stages of problem solving reflectively. The FGD implementation was conducted to explore the problems and find the right strategy to improve the students' ability to solve the problem accurately which is one of reflective thinking component that has been difficult to improve. The research method used is descriptive qualitative by using single subject response in Physics student. During the FGD process, one student was observed of her reflective thinking development in solving the physics problem. The strategy chosen in the discussion activity was the Cognitive Apprenticeship-Instruction (CA-I) syntax. Based on the results of this study, it is obtained the information that after going through a series of stages of discussion, the students' reflective thinking skills is increased significantly. The scaffolding stage in the CA-I model plays an important role in the process of solving physics problems accurately. Students are able to recognize and formulate problems by describing problem sketches, identifying the variables involved, applying mathematical equations that accord to physics concepts, executing accurately, and applying evaluation by explaining the solution to various contexts.

  11. Mathematical modeling of moving boundary problems in thermal energy storage

    NASA Technical Reports Server (NTRS)

    Solomon, A. D.

    1980-01-01

    The capability for predicting the performance of thermal energy storage (RES) subsystems and components using PCM's based on mathematical and physical models is developed. Mathematical models of the dynamic thermal behavior of (TES) subsystems using PCM's based on solutions of the moving boundary thermal conduction problem and on heat and mass transfer engineering correlations are also discussed.

  12. Program Helps Generate Boundary-Element Mathematical Models

    NASA Technical Reports Server (NTRS)

    Goldberg, R. K.

    1995-01-01

    Composite Model Generation-Boundary Element Method (COM-GEN-BEM) computer program significantly reduces time and effort needed to construct boundary-element mathematical models of continuous-fiber composite materials at micro-mechanical (constituent) scale. Generates boundary-element models compatible with BEST-CMS boundary-element code for anlaysis of micromechanics of composite material. Written in PATRAN Command Language (PCL).

  13. Mathematical modelling and numerical simulation of forces in milling process

    NASA Astrophysics Data System (ADS)

    Turai, Bhanu Murthy; Satish, Cherukuvada; Prakash Marimuthu, K.

    2018-04-01

    Machining of the material by milling induces forces, which act on the work piece material, tool and which in turn act on the machining tool. The forces involved in milling process can be quantified, mathematical models help to predict these forces. A lot of research has been carried out in this area in the past few decades. The current research aims at developing a mathematical model to predict forces at different levels which arise machining of Aluminium6061 alloy. Finite element analysis was used to develop a FE model to predict the cutting forces. Simulation was done for varying cutting conditions. Different experiments was designed using Taguchi method. A L9 orthogonal array was designed and the output was measure for the different experiments. The same was used to develop the mathematical model.

  14. Mathematical properties and parameter estimation for transit compartment pharmacodynamic models.

    PubMed

    Yates, James W T

    2008-07-03

    One feature of recent research in pharmacodynamic modelling has been the move towards more mechanistically based model structures. However, in all of these models there are common sub-systems, such as feedback loops and time-delays, whose properties and contribution to the model behaviour merit some mathematical analysis. In this paper a common pharmacodynamic model sub-structure is considered: the linear transit compartment. These models have a number of interesting properties as the length of the cascade chain is increased. In the limiting case a pure time-delay is achieved [Milsum, J.H., 1966. Biological Control Systems Analysis. McGraw-Hill Book Company, New York] and the initial behaviour becoming increasingly sensitive to parameter value perturbation. It is also shown that the modelled drug effect is attenuated, though the duration of action is longer. Through this analysis the range of behaviours that such models are capable of reproducing are characterised. The properties of these models and the experimental requirements are discussed in order to highlight how mathematical analysis prior to experimentation can enhance the utility of mathematical modelling.

  15. Mathematical Modeling of an Oscillating Droplet

    NASA Technical Reports Server (NTRS)

    Berry, S.; Hyers, R. W.; Racz, L. M.; Abedian, B.; Rose, M. Franklin (Technical Monitor)

    2000-01-01

    Oscillating droplets are of interest in a number of disciplines. A practical application is the oscillating drop method, which is a technique for measuring surface tension and viscosity of liquid metals. It is especially suited to undercooled and highly reactive metals, because it is performed by electromagnetic levitation. The natural oscillation frequency of the droplets is related to the surface tension of the material, and the decay of oscillations is related to its viscosity. The fluid flow inside the droplet must be laminar in order for this technique to yield good results. Because no experimental method has yet been developed to visualize flow in electromagnetically-levitated oscillating metal droplets, mathematical modeling is required to determine whether or not turbulence occurs. Three mathematical models of the flow: (1) assuming laminar conditions, (2) using the k-epsilon turbulence model, and (3) using the RNG turbulence model, respectively, are compared and contrasted to determine the physical characteristics of the flow. It is concluded that the RNG model is the best suited for describing this problem. The goal of the presented work was to characterize internal flow in an oscillating droplet of liquid metal, and to verify the accuracy of the characterization by comparing calculated surface tension and viscosity.

  16. Leading a New Pedagogical Approach to Australian Curriculum Mathematics: Using the Dual Mathematical Modelling Cycle Framework

    ERIC Educational Resources Information Center

    Lamb, Janeen; Kawakami, Takashi; Saeki, Akihiko; Matsuzaki, Akio

    2014-01-01

    The aim of this study was to investigate the use of the "dual mathematical modelling cycle framework" as one way to meet the espoused goals of the Australian Curriculum Mathematics. This study involved 23 Year 6 students from one Australian primary school who engaged in an "Oil Tank Task" that required them to develop two…

  17. Mathematical Methods of Subjective Modeling in Scientific Research: I. The Mathematical and Empirical Basis

    NASA Astrophysics Data System (ADS)

    Pyt'ev, Yu. P.

    2018-01-01

    mathematical formalism for subjective modeling, based on modelling of uncertainty, reflecting unreliability of subjective information and fuzziness that is common for its content. The model of subjective judgments on values of an unknown parameter x ∈ X of the model M( x) of a research object is defined by the researcher-modeler as a space1 ( X, p( X), P{I^{\\bar x}}, Be{l^{\\bar x}}) with plausibility P{I^{\\bar x}} and believability Be{l^{\\bar x}} measures, where x is an uncertain element taking values in X that models researcher—modeler's uncertain propositions about an unknown x ∈ X, measures P{I^{\\bar x}}, Be{l^{\\bar x}} model modalities of a researcher-modeler's subjective judgments on the validity of each x ∈ X: the value of P{I^{\\bar x}}(\\tilde x = x) determines how relatively plausible, in his opinion, the equality (\\tilde x = x) is, while the value of Be{l^{\\bar x}}(\\tilde x = x) determines how the inequality (\\tilde x = x) should be relatively believed in. Versions of plausibility Pl and believability Bel measures and pl- and bel-integrals that inherit some traits of probabilities, psychophysics and take into account interests of researcher-modeler groups are considered. It is shown that the mathematical formalism of subjective modeling, unlike "standard" mathematical modeling, •enables a researcher-modeler to model both precise formalized knowledge and non-formalized unreliable knowledge, from complete ignorance to precise knowledge of the model of a research object, to calculate relative plausibilities and believabilities of any features of a research object that are specified by its subjective model M(\\tilde x), and if the data on observations of a research object is available, then it: •enables him to estimate the adequacy of subjective model to the research objective, to correct it by combining subjective ideas and the observation data after testing their consistency, and, finally, to empirically recover the model of a research

  18. Development of mathematical models of environmental physiology

    NASA Technical Reports Server (NTRS)

    Stolwijk, J. A. J.; Mitchell, J. W.; Nadel, E. R.

    1971-01-01

    Selected articles concerned with mathematical or simulation models of human thermoregulation are presented. The articles presented include: (1) development and use of simulation models in medicine, (2) model of cardio-vascular adjustments during exercise, (3) effective temperature scale based on simple model of human physiological regulatory response, (4) behavioral approach to thermoregulatory set point during exercise, and (5) importance of skin temperature in sweat regulation.

  19. Can Mathematical Models Predict the Outcomes of Prostate Cancer Patients Undergoing Intermittent Androgen Deprivation Therapy?

    NASA Astrophysics Data System (ADS)

    Everett, R. A.; Packer, A. M.; Kuang, Y.

    Androgen deprivation therapy is a common treatment for advanced or metastatic prostate cancer. Like the normal prostate, most tumors depend on androgens for proliferation and survival but often develop treatment resistance. Hormonal treatment causes many undesirable side effects which significantly decrease the quality of life for patients. Intermittently applying androgen deprivation in cycles reduces the total duration with these negative effects and may reduce selective pressure for resistance. We extend an existing model which used measurements of patient testosterone levels to accurately fit measured serum prostate specific antigen (PSA) levels. We test the model's predictive accuracy, using only a subset of the data to find parameter values. The results are compared with those of an existing piecewise linear model which does not use testosterone as an input. Since actual treatment protocol is to re-apply therapy when PSA levels recover beyond some threshold value, we develop a second method for predicting the PSA levels. Based on a small set of data from seven patients, our results showed that the piecewise linear model produced slightly more accurate results while the two predictive methods are comparable. This suggests that a simpler model may be more beneficial for a predictive use compared to a more biologically insightful model, although further research is needed in this field prior to implementing mathematical models as a predictive method in a clinical setting. Nevertheless, both models are an important step in this direction.

  20. Can Mathematical Models Predict the Outcomes of Prostate Cancer Patients Undergoing Intermittent Androgen Deprivation Therapy?

    NASA Astrophysics Data System (ADS)

    Everett, R. A.; Packer, A. M.; Kuang, Y.

    2014-04-01

    Androgen deprivation therapy is a common treatment for advanced or metastatic prostate cancer. Like the normal prostate, most tumors depend on androgens for proliferation and survival but often develop treatment resistance. Hormonal treatment causes many undesirable side effects which significantly decrease the quality of life for patients. Intermittently applying androgen deprivation in cycles reduces the total duration with these negative effects and may reduce selective pressure for resistance. We extend an existing model which used measurements of patient testosterone levels to accurately fit measured serum prostate specific antigen (PSA) levels. We test the model's predictive accuracy, using only a subset of the data to find parameter values. The results are compared with those of an existing piecewise linear model which does not use testosterone as an input. Since actual treatment protocol is to re-apply therapy when PSA levels recover beyond some threshold value, we develop a second method for predicting the PSA levels. Based on a small set of data from seven patients, our results showed that the piecewise linear model produced slightly more accurate results while the two predictive methods are comparable. This suggests that a simpler model may be more beneficial for a predictive use compared to a more biologically insightful model, although further research is needed in this field prior to implementing mathematical models as a predictive method in a clinical setting. Nevertheless, both models are an important step in this direction.

  1. Mathematical model for predicting human vertebral fracture

    NASA Technical Reports Server (NTRS)

    Benedict, J. V.

    1973-01-01

    Mathematical model has been constructed to predict dynamic response of tapered, curved beam columns in as much as human spine closely resembles this form. Model takes into consideration effects of impact force, mass distribution, and material properties. Solutions were verified by dynamic tests on curved, tapered, elastic polyethylene beam.

  2. Mathematical model of an air-filled alpha stirling refrigerator

    NASA Astrophysics Data System (ADS)

    McFarlane, Patrick; Semperlotti, Fabio; Sen, Mihir

    2013-10-01

    This work develops a mathematical model for an alpha Stirling refrigerator with air as the working fluid and will be useful in optimizing the mechanical design of these machines. Two pistons cyclically compress and expand air while moving sinusoidally in separate chambers connected by a regenerator, thus creating a temperature difference across the system. A complete non-linear mathematical model of the machine, including air thermodynamics, and heat transfer from the walls, as well as heat transfer and fluid resistance in the regenerator, is developed. Non-dimensional groups are derived, and the mathematical model is numerically solved. The heat transfer and work are found for both chambers, and the coefficient of performance of each chamber is calculated. Important design parameters are varied and their effect on refrigerator performance determined. This sensitivity analysis, which shows what the significant parameters are, is a useful tool for the design of practical Stirling refrigeration systems.

  3. Frequencies as Proportions: Using a Teaching Model Based on Pirie and Kieren's Model of Mathematical Understanding

    ERIC Educational Resources Information Center

    Wright, Vince

    2014-01-01

    Pirie and Kieren (1989 "For the learning of mathematics", 9(3)7-11, 1992 "Journal of Mathematical Behavior", 11, 243-257, 1994a "Educational Studies in Mathematics", 26, 61-86, 1994b "For the Learning of Mathematics":, 14(1)39-43) created a model (P-K) that describes a dynamic and recursive process by which…

  4. Analysis of creative mathematical thinking ability by using model eliciting activities (MEAs)

    NASA Astrophysics Data System (ADS)

    Winda, A.; Sufyani, P.; Elah, N.

    2018-05-01

    Lack of creative mathematical thinking ability can lead to not accustomed with open ended problem. Students’ creative mathematical thinking ability in the first grade at one of junior high school in Tangerang City is not fully developed. The reason of students’ creative mathematical thinking ability is not optimally developed is so related with learning process which has done by the mathematics teacher, maybe the learning design that teacher use is unsuitable for increasing students’ activity in the learning process. This research objective is to see the differences in students’ ways of answering the problems in terms of students’ creative mathematical thinking ability during the implementation of Model Eliciting Activities (MEAs). This research use post-test experimental class design. The indicators for creative mathematical thinking ability in this research arranged in three parts, as follow: (1) Fluency to answer the problems; (2) Flexibility to solve the problems; (3) Originality of answers. The result of this research found that by using the same learning model and same instrument from Model Eliciting Activities (MEAs) there are some differences in the way students answer the problems and Model Eliciting Activities (MEAs) can be one of approach used to increase students’ creative mathematical thinking ability.

  5. Modelling Mathematics Problem Solving Item Responses Using a Multidimensional IRT Model

    ERIC Educational Resources Information Center

    Wu, Margaret; Adams, Raymond

    2006-01-01

    This research examined students' responses to mathematics problem-solving tasks and applied a general multidimensional IRT model at the response category level. In doing so, cognitive processes were identified and modelled through item response modelling to extract more information than would be provided using conventional practices in scoring…

  6. A Conceptual Model of Mathematical Reasoning for School Mathematics

    ERIC Educational Resources Information Center

    Jeannotte, Doris; Kieran, Carolyn

    2017-01-01

    The development of students' mathematical reasoning (MR) is a goal of several curricula and an essential element of the culture of the mathematics education research community. But what mathematical reasoning consists of is not always clear; it is generally assumed that everyone has a sense of what it is. Wanting to clarify the elements of MR,…

  7. Mathematical Modelling in Engineering: A Proposal to Introduce Linear Algebra Concepts

    ERIC Educational Resources Information Center

    Cárcamo Bahamonde, Andrea; Gómez Urgelles, Joan; Fortuny Aymemí, Josep

    2016-01-01

    The modern dynamic world requires that basic science courses for engineering, including linear algebra, emphasise the development of mathematical abilities primarily associated with modelling and interpreting, which are not exclusively calculus abilities. Considering this, an instructional design was created based on mathematical modelling and…

  8. Mathematical modelling of tissue formation in chondrocyte filter cultures.

    PubMed

    Catt, C J; Schuurman, W; Sengers, B G; van Weeren, P R; Dhert, W J A; Please, C P; Malda, J

    2011-12-17

    In the field of cartilage tissue engineering, filter cultures are a frequently used three-dimensional differentiation model. However, understanding of the governing processes of in vitro growth and development of tissue in these models is limited. Therefore, this study aimed to further characterise these processes by means of an approach combining both experimental and applied mathematical methods. A mathematical model was constructed, consisting of partial differential equations predicting the distribution of cells and glycosaminoglycans (GAGs), as well as the overall thickness of the tissue. Experimental data was collected to allow comparison with the predictions of the simulation and refinement of the initial models. Healthy mature equine chondrocytes were expanded and subsequently seeded on collagen-coated filters and cultured for up to 7 weeks. Resulting samples were characterised biochemically, as well as histologically. The simulations showed a good representation of the experimentally obtained cell and matrix distribution within the cultures. The mathematical results indicate that the experimental GAG and cell distribution is critically dependent on the rate at which the cell differentiation process takes place, which has important implications for interpreting experimental results. This study demonstrates that large regions of the tissue are inactive in terms of proliferation and growth of the layer. In particular, this would imply that higher seeding densities will not significantly affect the growth rate. A simple mathematical model was developed to predict the observed experimental data and enable interpretation of the principal underlying mechanisms controlling growth-related changes in tissue composition.

  9. Teaching Writing and Communication in a Mathematical Modeling Course

    ERIC Educational Resources Information Center

    Linhart, Jean Marie

    2014-01-01

    Writing and communication are essential skills for success in the workplace or in graduate school, yet writing and communication are often the last thing that instructors think about incorporating into a mathematics course. A mathematical modeling course provides a natural environment for writing assignments. This article is an analysis of the…

  10. Neutral model analysis of landscape patterns from mathematical morphology

    Treesearch

    Kurt H. Riitters; Peter Vogt; Pierre Soille; Jacek Kozak; Christine Estreguil

    2007-01-01

    Mathematical morphology encompasses methods for characterizing land-cover patterns in ecological research and biodiversity assessments. This paper reports a neutral model analysis of patterns in the absence of a structuring ecological process, to help set standards for comparing and interpreting patterns identified by mathematical morphology on real land-cover maps. We...

  11. The Effect of Teacher Beliefs on Student Competence in Mathematical Modeling--An Intervention Study

    ERIC Educational Resources Information Center

    Mischo, Christoph; Maaß, Katja

    2013-01-01

    This paper presents an intervention study whose aim was to promote teacher beliefs about mathematics and learning mathematics and student competences in mathematical modeling. In the intervention, teachers received written curriculum materials about mathematical modeling. The concept underlying the materials was based on constructivist ideas and…

  12. Application of the Refined Integral Method in the mathematical modeling of drug delivery from one-layer torus-shaped devices.

    PubMed

    Helbling, Ignacio M; Ibarra, Juan C D; Luna, Julio A

    2012-02-28

    A mathematical modeling of controlled release of drug from one-layer torus-shaped devices is presented. Analytical solutions based on Refined Integral Method (RIM) are derived. The validity and utility of the model are ascertained by comparison of the simulation results with matrix-type vaginal rings experimental release data reported in the literature. For the comparisons, the pair-wise procedure is used to measure quantitatively the fit of the theoretical predictions to the experimental data. A good agreement between the model prediction and the experimental data is observed. A comparison with a previously reported model is also presented. More accurate results are achieved for small A/C(s) ratios. Copyright © 2011 Elsevier B.V. All rights reserved.

  13. Mathematical modelling of an electromagnetics automobile suspension

    NASA Astrophysics Data System (ADS)

    Amin, Ahmad Zaki Mohamad; Ahmad, Shamsuddin; Hoe, Yeak Su

    2017-04-01

    The mathematical modelling of the electromagnetic automobile suspension (EAS) is presented. The solution of the model is found using Runge-Kutta Method via MAPLE. The graphs of the vertical displacement, different vertical displacement and road profiles and acceleration of car body against time are investigated and validated using certain criteria.

  14. Predicting Relationships between Mathematics Anxiety, Mathematics Teaching Anxiety, Self-Efficacy Beliefs towards Mathematics and Mathematics Teaching

    ERIC Educational Resources Information Center

    Unlu, Melihan; Ertekin, Erhan; Dilmac, Bulent

    2017-01-01

    The purpose of the research is to investigate the relationships between self-efficacy beliefs toward mathematics, mathematics anxiety and self-efficacy beliefs toward mathematics teaching, mathematics teaching anxiety variables and testing the relationships between these variables with structural equation model. The sample of the research, which…

  15. Mathematical Model Of Nerve/Muscle Interaction

    NASA Technical Reports Server (NTRS)

    Hannaford, Blake

    1990-01-01

    Phasic Excitation/Activation (PEA) mathematical model simulates short-term nonlinear dynamics of activation and control of muscle by nerve. Includes electronic and mechanical elements. Is homeomorphic at level of its three major building blocks, which represent motoneuron, dynamics of activation of muscle, and mechanics of muscle.

  16. An Interdisciplinary Approach to Designing Online Learning: Fostering Pre-Service Mathematics Teachers' Capabilities in Mathematical Modelling

    ERIC Educational Resources Information Center

    Geiger, Vince; Mulligan, Joanne; Date-Huxtable, Liz; Ahlip, Rehez; Jones, D. Heath; May, E. Julian; Rylands, Leanne; Wright, Ian

    2018-01-01

    In this article we describe and evaluate processes utilized to develop an online learning module on mathematical modelling for pre-service teachers. The module development process involved a range of professionals working within the STEM disciplines including mathematics and science educators, mathematicians, scientists, in-service and pre-service…

  17. Two Project-Based Strategies in an Interdisciplinary Mathematical Modeling in Biology Course

    ERIC Educational Resources Information Center

    Ludwig, Patrice; Tongen, Anthony; Walton, Brian

    2018-01-01

    James Madison University faculty team-teach an interdisciplinary mathematical modeling course for mathematics and biology students. We have used two different project-based approaches to emphasize the mathematical concepts taught in class, while also exposing students to new areas of mathematics not formally covered in class. The first method…

  18. Mathematical Modeling of Renal Hemodynamics in Physiology and Pathophysiology

    PubMed Central

    Sgouralis, Ioannis; Layton, Anita T.

    2015-01-01

    In addition to the excretion of metabolic waste and toxin, the kidney plays an indispensable role in regulating the balance of water, electrolyte, acid-base, and blood pressure. For the kidney to maintain proper functions, hemodynamic control is crucial. In this review, we describe representative mathematical models that have been developed to better understand the kidney's autoregulatory processes. We consider mathematical models that simulate glomerular filtration, and renal blood flow regulation by means of the myogenic response and tubuloglomerular feedback. We discuss the extent to which these modeling efforts have expanded the understanding of renal functions in health and disease. PMID:25765886

  19. Mathematical modeling of the aerodynamics of high-angle-of-attack maneuvers

    NASA Technical Reports Server (NTRS)

    Schiff, L. B.; Tobak, M.; Malcolm, G. N.

    1980-01-01

    This paper is a review of the current state of aerodynamic mathematical modeling for aircraft motions at high angles of attack. The mathematical model serves to define a set of characteristic motions from whose known aerodynamic responses the aerodynamic response to an arbitrary high angle-of-attack flight maneuver can be predicted. Means are explored of obtaining stability parameter information in terms of the characteristic motions, whether by wind-tunnel experiments, computational methods, or by parameter-identification methods applied to flight-test data. A rationale is presented for selecting and verifying the aerodynamic mathematical model at the lowest necessary level of complexity. Experimental results describing the wing-rock phenomenon are shown to be accommodated within the most recent mathematical model by admitting the existence of aerodynamic hysteresis in the steady-state variation of the rolling moment with roll angle. Interpretation of the experimental results in terms of bifurcation theory reveals the general conditions under which aerodynamic hysteresis must exist.

  20. Mathematics as a conduit for translational research in post-traumatic osteoarthritis.

    PubMed

    Ayati, Bruce P; Kapitanov, Georgi I; Coleman, Mitchell C; Anderson, Donald D; Martin, James A

    2017-03-01

    Biomathematical models offer a powerful method of clarifying complex temporal interactions and the relationships among multiple variables in a system. We present a coupled in silico biomathematical model of articular cartilage degeneration in response to impact and/or aberrant loading such as would be associated with injury to an articular joint. The model incorporates fundamental biological and mechanical information obtained from explant and small animal studies to predict post-traumatic osteoarthritis (PTOA) progression, with an eye toward eventual application in human patients. In this sense, we refer to the mathematics as a "conduit of translation." The new in silico framework presented in this paper involves a biomathematical model for the cellular and biochemical response to strains computed using finite element analysis. The model predicts qualitative responses presently, utilizing system parameter values largely taken from the literature. To contribute to accurate predictions, models need to be accurately parameterized with values that are based on solid science. We discuss a parameter identification protocol that will enable us to make increasingly accurate predictions of PTOA progression using additional data from smaller scale explant and small animal assays as they become available. By distilling the data from the explant and animal assays into parameters for biomathematical models, mathematics can translate experimental data to clinically relevant knowledge. © 2016 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 35:566-572, 2017. © 2016 Orthopaedic Research Society. Published by Wiley Periodicals, Inc.

  1. Explorations in the Modeling of the Learning of Mathematics.

    ERIC Educational Resources Information Center

    Fuson, Karen C., Ed.; And Others

    Eleven research reports in the area of models of learning mathematics are presented in this publication of the Mathematics Education Reports series. The papers represent a mixture of theories, viewpoints, and references to other areas. Content areas addressed range from preschool to college levels. All the papers are concerned with the learning of…

  2. Understanding the Difficulties Faced by Engineering Undergraduates in Learning Mathematical Modelling

    ERIC Educational Resources Information Center

    Soon, Wanmei; Lioe, Luis Tirtasanjaya; McInnes, Brett

    2011-01-01

    The teaching of mathematics in Singapore continues, in most cases, to follow a traditional model. While this traditional approach has many advantages, it does not always adequately prepare students for University-level mathematics, especially applied mathematics. In particular, it does not cultivate the ability to deal with "non-routine…

  3. Aspects of Mathematical Modelling of Pressure Retarded Osmosis

    PubMed Central

    Anissimov, Yuri G.

    2016-01-01

    In power generating terms, a pressure retarded osmosis (PRO) energy generating plant, on a river entering a sea or ocean, is equivalent to a hydroelectric dam with a height of about 60 meters. Therefore, PRO can add significantly to existing renewable power generation capacity if economical constrains of the method are resolved. PRO energy generation relies on a semipermeable membrane that is permeable to water and impermeable to salt. Mathematical modelling plays an important part in understanding flows of water and salt near and across semipermeable membranes and helps to optimize PRO energy generation. Therefore, the modelling can help realizing PRO energy generation potential. In this work, a few aspects of mathematical modelling of the PRO process are reviewed and discussed. PMID:26848696

  4. Mathematical models of human paralyzed muscle after long-term training.

    PubMed

    Law, L A Frey; Shields, R K

    2007-01-01

    Spinal cord injury (SCI) results in major musculoskeletal adaptations, including muscle atrophy, faster contractile properties, increased fatigability, and bone loss. The use of functional electrical stimulation (FES) provides a method to prevent paralyzed muscle adaptations in order to sustain force-generating capacity. Mathematical muscle models may be able to predict optimal activation strategies during FES, however muscle properties further adapt with long-term training. The purpose of this study was to compare the accuracy of three muscle models, one linear and two nonlinear, for predicting paralyzed soleus muscle force after exposure to long-term FES training. Further, we contrasted the findings between the trained and untrained limbs. The three models' parameters were best fit to a single force train in the trained soleus muscle (N=4). Nine additional force trains (test trains) were predicted for each subject using the developed models. Model errors between predicted and experimental force trains were determined, including specific muscle force properties. The mean overall error was greatest for the linear model (15.8%) and least for the nonlinear Hill Huxley type model (7.8%). No significant error differences were observed between the trained versus untrained limbs, although model parameter values were significantly altered with training. This study confirmed that nonlinear models most accurately predict both trained and untrained paralyzed muscle force properties. Moreover, the optimized model parameter values were responsive to the relative physiological state of the paralyzed muscle (trained versus untrained). These findings are relevant for the design and control of neuro-prosthetic devices for those with SCI.

  5. Mathematical Modelling as a Tool to Understand Cell Self-renewal and Differentiation.

    PubMed

    Getto, Philipp; Marciniak-Czochra, Anna

    2015-01-01

    Mathematical modeling is a powerful technique to address key questions and paradigms in a variety of complex biological systems and can provide quantitative insights into cell kinetics, fate determination and development of cell populations. The chapter is devoted to a review of modeling of the dynamics of stem cell-initiated systems using mathematical methods of ordinary differential equations. Some basic concepts and tools for cell population dynamics are summarized and presented as a gentle introduction to non-mathematicians. The models take into account different plausible mechanisms regulating homeostasis. Two mathematical frameworks are proposed reflecting, respectively, a discrete (punctuated by division events) and a continuous character of transitions between differentiation stages. Advantages and constraints of the mathematical approaches are presented on examples of models of blood systems and compared to patients data on healthy hematopoiesis.

  6. A Structural Equation Model Explaining 8th Grade Students' Mathematics Achievements

    ERIC Educational Resources Information Center

    Yurt, Eyüp; Sünbül, Ali Murat

    2014-01-01

    The purpose of this study is to investigate, via a model, the explanatory and predictive relationships among the following variables: Mathematical Problem Solving and Reasoning Skills, Sources of Mathematics Self-Efficacy, Spatial Ability, and Mathematics Achievements of Secondary School 8th Grade Students. The sample group of the study, itself…

  7. Accurate Modeling Method for Cu Interconnect

    NASA Astrophysics Data System (ADS)

    Yamada, Kenta; Kitahara, Hiroshi; Asai, Yoshihiko; Sakamoto, Hideo; Okada, Norio; Yasuda, Makoto; Oda, Noriaki; Sakurai, Michio; Hiroi, Masayuki; Takewaki, Toshiyuki; Ohnishi, Sadayuki; Iguchi, Manabu; Minda, Hiroyasu; Suzuki, Mieko

    This paper proposes an accurate modeling method of the copper interconnect cross-section in which the width and thickness dependence on layout patterns and density caused by processes (CMP, etching, sputtering, lithography, and so on) are fully, incorporated and universally expressed. In addition, we have developed specific test patterns for the model parameters extraction, and an efficient extraction flow. We have extracted the model parameters for 0.15μm CMOS using this method and confirmed that 10%τpd error normally observed with conventional LPE (Layout Parameters Extraction) was completely dissolved. Moreover, it is verified that the model can be applied to more advanced technologies (90nm, 65nm and 55nm CMOS). Since the interconnect delay variations due to the processes constitute a significant part of what have conventionally been treated as random variations, use of the proposed model could enable one to greatly narrow the guardbands required to guarantee a desired yield, thereby facilitating design closure.

  8. Comparison of actual oxygen delivery kinetics to those predicted by mathematical modeling following stage 1 palliation just prior to superior cavopulmonary anastomosis.

    PubMed

    Yuki, Koichi; DiNardo, James A

    2015-02-01

    Optimizing systemic oxygen delivery (DO2) and hemodynamics in children with hypoplastic left heart syndrome (HLHS) is a clinical challenge. Mathematical modeling of the HLHS circulation has been used to determine the relationship between oxygen kinetic parameters and DO2 and to determine how DO2 might be optimized. The model demonstrates that neither arterial oxygen saturation (SaO2) nor mixed venous oxygen saturation (SvO2) alone accurately predicts DO2. Oxygen delivery kinetics predicted by previously described mathematical modeling were compared with actual patients' hemodynamic data. We sought to determine which patient derived parameters correlated best with DO2. Patients with HLHS who underwent cardiac catheterization prior to surgery to create a superior cavopulmonary anastomosis from 2007 to 2011 were identified. Hemodynamic data obtained were compared with the data derived from the mathematical model. Correlations between SaO2, SvO2, SaO2-SvO2, SaO2/(SaO2-SvO2), pulmonary-to-systemic blood flow ratio (Qp/Qs), and DO2 were evaluated using both linear and nonlinear analyses, and R(2) was calculated. Patients' data fit most aspects of the mathematical model. DO2 had the best correlation with SaO2/(SaO2-SvO2; R(2) = 0.8755) followed by SaO2 -SvO2 (R(2) = 0.8063), while SaO2 or SvO2 alone did not demonstrate a significant correlation as predicated by the mathematical model (R(2) = 0.09564 and 0.4831, respectively). SaO2/(SaO2 -SvO2) would be useful clinically to track changes in DO2 that occur with changes in patient condition or with interventions. © 2014 John Wiley & Sons Ltd.

  9. Mathematical models of thermoregulation and heat transfer in mammals. A compendium of research

    NASA Technical Reports Server (NTRS)

    Shitzer, A.

    1972-01-01

    An annotated compendium on mathematical modeling of mammal thermoregulation systems is presented. Author abstracts, tables containing the more used mathematical models, solutions to these models, and each thermoregulation mechanism considered are included.

  10. Editorial: Mathematical Methods and Modeling in Machine Fault Diagnosis

    DOE PAGES

    Yan, Ruqiang; Chen, Xuefeng; Li, Weihua; ...

    2014-12-18

    Modern mathematics has commonly been utilized as an effective tool to model mechanical equipment so that their dynamic characteristics can be studied analytically. This will help identify potential failures of mechanical equipment by observing change in the equipment’s dynamic parameters. On the other hand, dynamic signals are also important and provide reliable information about the equipment’s working status. Modern mathematics has also provided us with a systematic way to design and implement various signal processing methods, which are used to analyze these dynamic signals, and to enhance intrinsic signal components that are directly related to machine failures. This special issuemore » is aimed at stimulating not only new insights on mathematical methods for modeling but also recently developed signal processing methods, such as sparse decomposition with potential applications in machine fault diagnosis. Finally, the papers included in this special issue provide a glimpse into some of the research and applications in the field of machine fault diagnosis through applications of the modern mathematical methods.« less

  11. Experimental evaluation of a mathematical model for predicting transfer efficiency of a high volume-low pressure air spray gun.

    PubMed

    Tan, Y M; Flynn, M R

    2000-10-01

    The transfer efficiency of a spray-painting gun is defined as the amount of coating applied to the workpiece divided by the amount sprayed. Characterizing this transfer process allows for accurate estimation of the overspray generation rate, which is important for determining a spray painter's exposure to airborne contaminants. This study presents an experimental evaluation of a mathematical model for predicting the transfer efficiency of a high volume-low pressure spray gun. The effects of gun-to-surface distance and nozzle pressure on the agreement between the transfer efficiency measurement and prediction were examined. Wind tunnel studies and non-volatile vacuum pump oil in place of commercial paint were used to determine transfer efficiency at nine gun-to-surface distances and four nozzle pressure levels. The mathematical model successfully predicts transfer efficiency within the uncertainty limits. The least squares regression between measured and predicted transfer efficiency has a slope of 0.83 and an intercept of 0.12 (R2 = 0.98). Two correction factors were determined to improve the mathematical model. At higher nozzle pressure settings, 6.5 psig and 5.5 psig, the correction factor is a function of both gun-to-surface distance and nozzle pressure level. At lower nozzle pressures, 4 psig and 2.75 psig, gun-to-surface distance slightly influences the correction factor, while nozzle pressure has no discernible effect.

  12. Taking the mystery out of mathematical model applications to karst aquifers—A primer

    USGS Publications Warehouse

    Kuniansky, Eve L.

    2014-01-01

    Advances in mathematical model applications toward the understanding of the complex flow, characterization, and water-supply management issues for karst aquifers have occurred in recent years. Different types of mathematical models can be applied successfully if appropriate information is available and the problems are adequately identified. The mathematical approaches discussed in this paper are divided into three major categories: 1) distributed parameter models, 2) lumped parameter models, and 3) fitting models. The modeling approaches are described conceptually with examples (but without equations) to help non-mathematicians understand the applications.

  13. Strong Inference in Mathematical Modeling: A Method for Robust Science in the Twenty-First Century.

    PubMed

    Ganusov, Vitaly V

    2016-01-01

    While there are many opinions on what mathematical modeling in biology is, in essence, modeling is a mathematical tool, like a microscope, which allows consequences to logically follow from a set of assumptions. Only when this tool is applied appropriately, as microscope is used to look at small items, it may allow to understand importance of specific mechanisms/assumptions in biological processes. Mathematical modeling can be less useful or even misleading if used inappropriately, for example, when a microscope is used to study stars. According to some philosophers (Oreskes et al., 1994), the best use of mathematical models is not when a model is used to confirm a hypothesis but rather when a model shows inconsistency of the model (defined by a specific set of assumptions) and data. Following the principle of strong inference for experimental sciences proposed by Platt (1964), I suggest "strong inference in mathematical modeling" as an effective and robust way of using mathematical modeling to understand mechanisms driving dynamics of biological systems. The major steps of strong inference in mathematical modeling are (1) to develop multiple alternative models for the phenomenon in question; (2) to compare the models with available experimental data and to determine which of the models are not consistent with the data; (3) to determine reasons why rejected models failed to explain the data, and (4) to suggest experiments which would allow to discriminate between remaining alternative models. The use of strong inference is likely to provide better robustness of predictions of mathematical models and it should be strongly encouraged in mathematical modeling-based publications in the Twenty-First century.

  14. Mathematical Model of Armed Helicopter vs Tank Duel

    DTIC Science & Technology

    The purpose of this thesis is to mathematically model a duel between the armed helicopter and the tank. In addition to providing a parametric...analysis of B. O. Koopman’s classical Detection-Destruction Duel , two additional models were constructed and analyzed. All three models stem from stochastic

  15. Some Aspects of Mathematical Model of Collaborative Learning

    ERIC Educational Resources Information Center

    Nakamura, Yasuyuki; Yasutake, Koichi; Yamakawa, Osamu

    2012-01-01

    There are some mathematical learning models of collaborative learning, with which we can learn how students obtain knowledge and we expect to design effective education. We put together those models and classify into three categories; model by differential equations, so-called Ising spin and a stochastic process equation. Some of the models do not…

  16. Strong Inference in Mathematical Modeling: A Method for Robust Science in the Twenty-First Century

    PubMed Central

    Ganusov, Vitaly V.

    2016-01-01

    While there are many opinions on what mathematical modeling in biology is, in essence, modeling is a mathematical tool, like a microscope, which allows consequences to logically follow from a set of assumptions. Only when this tool is applied appropriately, as microscope is used to look at small items, it may allow to understand importance of specific mechanisms/assumptions in biological processes. Mathematical modeling can be less useful or even misleading if used inappropriately, for example, when a microscope is used to study stars. According to some philosophers (Oreskes et al., 1994), the best use of mathematical models is not when a model is used to confirm a hypothesis but rather when a model shows inconsistency of the model (defined by a specific set of assumptions) and data. Following the principle of strong inference for experimental sciences proposed by Platt (1964), I suggest “strong inference in mathematical modeling” as an effective and robust way of using mathematical modeling to understand mechanisms driving dynamics of biological systems. The major steps of strong inference in mathematical modeling are (1) to develop multiple alternative models for the phenomenon in question; (2) to compare the models with available experimental data and to determine which of the models are not consistent with the data; (3) to determine reasons why rejected models failed to explain the data, and (4) to suggest experiments which would allow to discriminate between remaining alternative models. The use of strong inference is likely to provide better robustness of predictions of mathematical models and it should be strongly encouraged in mathematical modeling-based publications in the Twenty-First century. PMID:27499750

  17. Modeling Achievement in Mathematics: The Role of Learner and Learning Environment Characteristics

    ERIC Educational Resources Information Center

    Nasser-Abu Alhija, Fadia; Amasha, Marcel

    2012-01-01

    This study examined a structural model of mathematics achievement among Druze 8th graders in Israel. The model integrates 2 psychosocial theories: goal theory and social learning theory. Variables in the model included gender, father's and mother's education, classroom mastery and performance goal orientation, mathematics self-efficacy and…

  18. "When Mathematical Activity Moves You": An Exploration of the Design and Use of Purposefully Embodied Mathematical Activities, Models, Contexts, and Environments

    ERIC Educational Resources Information Center

    Campbell, William James

    2017-01-01

    This dissertation describes a mathematics curriculum and instruction design experiment involving a series of embodied mathematical activities conducted in two Colorado elementary schools Activities designed for this experiment include multi-scalar number line models focused on supporting students' understanding of elementary mathematics. Realistic…

  19. Mathematical models of bipolar disorder

    NASA Astrophysics Data System (ADS)

    Daugherty, Darryl; Roque-Urrea, Tairi; Urrea-Roque, John; Troyer, Jessica; Wirkus, Stephen; Porter, Mason A.

    2009-07-01

    We use limit cycle oscillators to model bipolar II disorder, which is characterized by alternating hypomanic and depressive episodes and afflicts about 1% of the United States adult population. We consider two non-linear oscillator models of a single bipolar patient. In both frameworks, we begin with an untreated individual and examine the mathematical effects and resulting biological consequences of treatment. We also briefly consider the dynamics of interacting bipolar II individuals using weakly-coupled, weakly-damped harmonic oscillators. We discuss how the proposed models can be used as a framework for refined models that incorporate additional biological data. We conclude with a discussion of possible generalizations of our work, as there are several biologically-motivated extensions that can be readily incorporated into the series of models presented here.

  20. Investigating and developing engineering students' mathematical modelling and problem-solving skills

    NASA Astrophysics Data System (ADS)

    Wedelin, Dag; Adawi, Tom; Jahan, Tabassum; Andersson, Sven

    2015-09-01

    How do engineering students approach mathematical modelling problems and how can they learn to deal with such problems? In the context of a course in mathematical modelling and problem solving, and using a qualitative case study approach, we found that the students had little prior experience of mathematical modelling. They were also inexperienced problem solvers, unaware of the importance of understanding the problem and exploring alternatives, and impeded by inappropriate beliefs, attitudes and expectations. Important impacts of the course belong to the metacognitive domain. The nature of the problems, the supervision and the follow-up lectures were emphasised as contributing to the impacts of the course, where students show major development. We discuss these empirical results in relation to a framework for mathematical thinking and the notion of cognitive apprenticeship. Based on the results, we argue that this kind of teaching should be considered in the education of all engineers.

  1. The Conceptualization of the Mathematical Modelling Process in Technology-Aided Environment

    ERIC Educational Resources Information Center

    Hidiroglu, Çaglar Naci; Güzel, Esra Bukova

    2017-01-01

    The aim of the study is to conceptualize the technology-aided mathematical modelling process in the frame of cognitive modelling perspective. The grounded theory approach was adopted in the study. The research was conducted with seven groups consisting of nineteen prospective mathematics teachers. The data were collected from the video records of…

  2. Beauty as Fit: A Metaphor in Mathematics?

    ERIC Educational Resources Information Center

    Raman, Manya; Öhman, Lars-Daniel

    2013-01-01

    Beauty, which plays a central role in the practice of mathematics (Sinclair 2002), is almost absent in discussions of school mathematics (Dreyfus and Eisenberg 1986). This is problematic, because students will decide whether or not to continue their studies in mathematics without having an accurate picture of what the subject is about. In order to…

  3. The use of mathematical models to inform influenza pandemic preparedness and response

    PubMed Central

    Wu, Joseph T; Cowling, Benjamin J

    2011-01-01

    Summary Influenza pandemics have occurred throughout history and were associated with substantial excess mortality and morbidity. Mathematical models of infectious diseases permit quantitative description of epidemic processes based on the underlying biological mechanisms. Mathematical models have been widely used in the past decade to aid pandemic planning by allowing detailed predictions of the speed of spread of an influenza pandemic and the likely effectiveness of alternative control strategies. During the initial waves of the 2009 influenza pandemic, mathematical models were used to track the spread of the virus, predict the time course of the pandemic and assess the likely impact of large-scale vaccination. While mathematical modeling has made substantial contributions to influenza pandemic preparedness, its use as a real-time tool for pandemic control is currently limited by the lack of essential surveillance information such as serologic data. Mathematical modeling provided a useful framework for analyzing and interpreting surveillance data during the 2009 influenza pandemic, for highlighting limitations in existing pandemic surveillance systems, and for guiding how these systems should be strengthened in order to cope with future epidemics of influenza or other emerging infectious diseases. PMID:21727183

  4. Redundancy management of electrohydraulic servoactuators by mathematical model referencing

    NASA Technical Reports Server (NTRS)

    Campbell, R. A.

    1971-01-01

    A description of a mathematical model reference system is presented which provides redundancy management for an electrohydraulic servoactuator. The mathematical model includes a compensation network that calculates reference parameter perturbations induced by external disturbance forces. This is accomplished by using the measured pressure differential data taken from the physical system. This technique was experimentally verified by tests performed using the H-1 engine thrust vector control system for Saturn IB. The results of these tests are included in this report. It was concluded that this technique improves the tracking accuracy of the model reference system to the extent that redundancy management of electrohydraulic servosystems may be performed using this method.

  5. Mathematical modeling of renal hemodynamics in physiology and pathophysiology.

    PubMed

    Sgouralis, Ioannis; Layton, Anita T

    2015-06-01

    In addition to the excretion of metabolic waste and toxin, the kidney plays an indispensable role in regulating the balance of water, electrolyte, acid-base, and blood pressure. For the kidney to maintain proper functions, hemodynamic control is crucial. In this review, we describe representative mathematical models that have been developed to better understand the kidney's autoregulatory processes. We consider mathematical models that simulate glomerular filtration, and renal blood flow regulation by means of the myogenic response and tubuloglomerular feedback. We discuss the extent to which these modeling efforts have expanded the understanding of renal functions in health and disease. Copyright © 2015 Elsevier Inc. All rights reserved.

  6. The development of a combined mathematical model to forecast the incidence of hepatitis E in Shanghai, China.

    PubMed

    Ren, Hong; Li, Jian; Yuan, Zheng-An; Hu, Jia-Yu; Yu, Yan; Lu, Yi-Han

    2013-09-08

    Sporadic hepatitis E has become an important public health concern in China. Accurate forecasting of the incidence of hepatitis E is needed to better plan future medical needs. Few mathematical models can be used because hepatitis E morbidity data has both linear and nonlinear patterns. We developed a combined mathematical model using an autoregressive integrated moving average model (ARIMA) and a back propagation neural network (BPNN) to forecast the incidence of hepatitis E. The morbidity data of hepatitis E in Shanghai from 2000 to 2012 were retrieved from the China Information System for Disease Control and Prevention. The ARIMA-BPNN combined model was trained with 144 months of morbidity data from January 2000 to December 2011, validated with 12 months of data January 2012 to December 2012, and then employed to forecast hepatitis E incidence January 2013 to December 2013 in Shanghai. Residual analysis, Root Mean Square Error (RMSE), normalized Bayesian Information Criterion (BIC), and stationary R square methods were used to compare the goodness-of-fit among ARIMA models. The Bayesian regularization back-propagation algorithm was used to train the network. The mean error rate (MER) was used to assess the validity of the combined model. A total of 7,489 hepatitis E cases was reported in Shanghai from 2000 to 2012. Goodness-of-fit (stationary R2=0.531, BIC= -4.768, Ljung-Box Q statistics=15.59, P=0.482) and parameter estimates were used to determine the best-fitting model as ARIMA (0,1,1)×(0,1,1)12. Predicted morbidity values in 2012 from best-fitting ARIMA model and actual morbidity data from 2000 to 2011 were used to further construct the combined model. The MER of the ARIMA model and the ARIMA-BPNN combined model were 0.250 and 0.176, respectively. The forecasted incidence of hepatitis E in 2013 was 0.095 to 0.372 per 100,000 population. There was a seasonal variation with a peak during January-March and a nadir during August-October. Time series analysis

  7. Mathematical Modeling Of A Nuclear/Thermionic Power Source

    NASA Technical Reports Server (NTRS)

    Vandersande, Jan W.; Ewell, Richard C.

    1992-01-01

    Report discusses mathematical modeling to predict performance and lifetime of spacecraft power source that is integrated combination of nuclear-fission reactor and thermionic converters. Details of nuclear reaction, thermal conditions in core, and thermionic performance combined with model of swelling of fuel.

  8. Mathematical model of a smoldering log.

    Treesearch

    Fernando de Souza Costa; David Sandberg

    2004-01-01

    A mathematical model is developed describing the natural smoldering of logs. It is considered the steady one dimensional propagation of infinitesimally thin fronts of drying, pyrolysis, and char oxidation in a horizontal semi-infinite log. Expressions for the burn rates, distribution profiles of temperature, and positions of the drying, pyrolysis, and smoldering fronts...

  9. Mathematical and Computational Modeling in Complex Biological Systems

    PubMed Central

    Li, Wenyang; Zhu, Xiaoliang

    2017-01-01

    The biological process and molecular functions involved in the cancer progression remain difficult to understand for biologists and clinical doctors. Recent developments in high-throughput technologies urge the systems biology to achieve more precise models for complex diseases. Computational and mathematical models are gradually being used to help us understand the omics data produced by high-throughput experimental techniques. The use of computational models in systems biology allows us to explore the pathogenesis of complex diseases, improve our understanding of the latent molecular mechanisms, and promote treatment strategy optimization and new drug discovery. Currently, it is urgent to bridge the gap between the developments of high-throughput technologies and systemic modeling of the biological process in cancer research. In this review, we firstly studied several typical mathematical modeling approaches of biological systems in different scales and deeply analyzed their characteristics, advantages, applications, and limitations. Next, three potential research directions in systems modeling were summarized. To conclude, this review provides an update of important solutions using computational modeling approaches in systems biology. PMID:28386558

  10. Mathematical and Computational Modeling in Complex Biological Systems.

    PubMed

    Ji, Zhiwei; Yan, Ke; Li, Wenyang; Hu, Haigen; Zhu, Xiaoliang

    2017-01-01

    The biological process and molecular functions involved in the cancer progression remain difficult to understand for biologists and clinical doctors. Recent developments in high-throughput technologies urge the systems biology to achieve more precise models for complex diseases. Computational and mathematical models are gradually being used to help us understand the omics data produced by high-throughput experimental techniques. The use of computational models in systems biology allows us to explore the pathogenesis of complex diseases, improve our understanding of the latent molecular mechanisms, and promote treatment strategy optimization and new drug discovery. Currently, it is urgent to bridge the gap between the developments of high-throughput technologies and systemic modeling of the biological process in cancer research. In this review, we firstly studied several typical mathematical modeling approaches of biological systems in different scales and deeply analyzed their characteristics, advantages, applications, and limitations. Next, three potential research directions in systems modeling were summarized. To conclude, this review provides an update of important solutions using computational modeling approaches in systems biology.

  11. Mathematical Modeling in the People's Republic of China--Indicators of Participation and Performance on COMAP's Modeling Contest

    ERIC Educational Resources Information Center

    Tian, Xiaoxi

    2014-01-01

    In recent years, Mainland Chinese teams have been the dominant participants in the two COMAP-sponsored mathematical modeling competitions: the Mathematical Contest in Modeling (MCM) and the Interdisciplinary Contest in Modeling (ICM). This study examines five factors that lead to the Chinese teams' dramatic increase in participation rate and…

  12. 3ARM: A Fast, Accurate Radiative Transfer Model for Use in Climate Models

    NASA Technical Reports Server (NTRS)

    Bergstrom, R. W.; Kinne, S.; Sokolik, I. N.; Toon, O. B.; Mlawer, E. J.; Clough, S. A.; Ackerman, T. P.; Mather, J.

    1996-01-01

    A new radiative transfer model combining the efforts of three groups of researchers is discussed. The model accurately computes radiative transfer in a inhomogeneous absorbing, scattering and emitting atmospheres. As an illustration of the model, results are shown for the effects of dust on the thermal radiation.

  13. 3ARM: A Fast, Accurate Radiative Transfer Model for use in Climate Models

    NASA Technical Reports Server (NTRS)

    Bergstrom, R. W.; Kinne, S.; Sokolik, I. N.; Toon, O. B.; Mlawer, E. J.; Clough, S. A.; Ackerman, T. P.; Mather, J.

    1996-01-01

    A new radiative transfer model combining the efforts of three groups of researchers is discussed. The model accurately computes radiative transfer in a inhomogeneous absorbing, scattering and emitting atmospheres. As an illustration of the model, results are shown for the effects of dust on the thermal radiation.

  14. 3ARM: A Fast, Accurate Radiative Transfer Model For Use in Climate Models

    NASA Technical Reports Server (NTRS)

    Bergstrom, R. W.; Kinne, S.; Sokolik, I. N.; Toon, O. B.; Mlawer, E. J.; Clough, S. A.; Ackerman, T. P.; Mather, J.

    1996-01-01

    A new radiative transfer model combining the efforts of three groups of researchers is discussed. The model accurately computes radiative transfer in a inhomogeneous absorbing, scattering and emitting atmospheres. As an illustration of the model, results are shown for the effects of dust on the thermal radiation.

  15. A Mathematical Model of Marine Diesel Engine Speed Control System

    NASA Astrophysics Data System (ADS)

    Sinha, Rajendra Prasad; Balaji, Rajoo

    2018-02-01

    Diesel engine is inherently an unstable machine and requires a reliable control system to regulate its speed for safe and efficient operation. Also, the diesel engine may operate at fixed or variable speeds depending upon user's needs and accordingly the speed control system should have essential features to fulfil these requirements. This paper proposes a mathematical model of a marine diesel engine speed control system with droop governing function. The mathematical model includes static and dynamic characteristics of the control loop components. Model of static characteristic of the rotating fly weights speed sensing element provides an insight into the speed droop features of the speed controller. Because of big size and large time delay, the turbo charged diesel engine is represented as a first order system or sometimes even simplified to a pure integrator with constant gain which is considered acceptable in control literature. The proposed model is mathematically less complex and quick to use for preliminary analysis of the diesel engine speed controller performance.

  16. Mathematical Models for Immunology: Current State of the Art and Future Research Directions.

    PubMed

    Eftimie, Raluca; Gillard, Joseph J; Cantrell, Doreen A

    2016-10-01

    The advances in genetics and biochemistry that have taken place over the last 10 years led to significant advances in experimental and clinical immunology. In turn, this has led to the development of new mathematical models to investigate qualitatively and quantitatively various open questions in immunology. In this study we present a review of some research areas in mathematical immunology that evolved over the last 10 years. To this end, we take a step-by-step approach in discussing a range of models derived to study the dynamics of both the innate and immune responses at the molecular, cellular and tissue scales. To emphasise the use of mathematics in modelling in this area, we also review some of the mathematical tools used to investigate these models. Finally, we discuss some future trends in both experimental immunology and mathematical immunology for the upcoming years.

  17. Research Area 3: Mathematics (3.1 Modeling of Complex Systems)

    DTIC Science & Technology

    2017-10-31

    RESEARCH AREA 3: MATHEMATICS (3.1 Modeling of Complex Systems). Proposal should be directed to Dr. John Lavery The views, opinions and/or findings...so designated by other documentation. 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS (ES) U.S. Army Research Office P.O. Box 12211 Research ...Title: RESEARCH AREA 3: MATHEMATICS (3.1 Modeling of Complex Systems). Proposal should be directed to Dr. John Lavery Report Term: 0-Other Email

  18. Some aspects of mathematical and chemical modeling of complex chemical processes

    NASA Technical Reports Server (NTRS)

    Nemes, I.; Botar, L.; Danoczy, E.; Vidoczy, T.; Gal, D.

    1983-01-01

    Some theoretical questions involved in the mathematical modeling of the kinetics of complex chemical process are discussed. The analysis is carried out for the homogeneous oxidation of ethylbenzene in the liquid phase. Particular attention is given to the determination of the general characteristics of chemical systems from an analysis of mathematical models developed on the basis of linear algebra.

  19. Fun with maths: exploring implications of mathematical models for malaria eradication.

    PubMed

    Eckhoff, Philip A; Bever, Caitlin A; Gerardin, Jaline; Wenger, Edward A

    2014-12-11

    Mathematical analyses and modelling have an important role informing malaria eradication strategies. Simple mathematical approaches can answer many questions, but it is important to investigate their assumptions and to test whether simple assumptions affect the results. In this note, four examples demonstrate both the effects of model structures and assumptions and also the benefits of using a diversity of model approaches. These examples include the time to eradication, the impact of vaccine efficacy and coverage, drug programs and the effects of duration of infections and delays to treatment, and the influence of seasonality and migration coupling on disease fadeout. An excessively simple structure can miss key results, but simple mathematical approaches can still achieve key results for eradication strategy and define areas for investigation by more complex models.

  20. Development of syntax of intuition-based learning model in solving mathematics problems

    NASA Astrophysics Data System (ADS)

    Yeni Heryaningsih, Nok; Khusna, Hikmatul

    2018-01-01

    The aim of the research was to produce syntax of Intuition Based Learning (IBL) model in solving mathematics problem for improving mathematics students’ achievement that valid, practical and effective. The subject of the research were 2 classes in grade XI students of SMAN 2 Sragen, Central Java. The type of the research was a Research and Development (R&D). Development process adopted Plomp and Borg & Gall development model, they were preliminary investigation step, design step, realization step, evaluation and revision step. Development steps were as follow: (1) Collected the information and studied of theories in Preliminary Investigation step, studied about intuition, learning model development, students condition, and topic analysis, (2) Designed syntax that could bring up intuition in solving mathematics problem and then designed research instruments. They were several phases that could bring up intuition, Preparation phase, Incubation phase, Illumination phase and Verification phase, (3) Realized syntax of Intuition Based Learning model that has been designed to be the first draft, (4) Did validation of the first draft to the validator, (5) Tested the syntax of Intuition Based Learning model in the classrooms to know the effectiveness of the syntax, (6) Conducted Focus Group Discussion (FGD) to evaluate the result of syntax model testing in the classrooms, and then did the revision on syntax IBL model. The results of the research were produced syntax of IBL model in solving mathematics problems that valid, practical and effective. The syntax of IBL model in the classroom were, (1) Opening with apperception, motivations and build students’ positive perceptions, (2) Teacher explains the material generally, (3) Group discussion about the material, (4) Teacher gives students mathematics problems, (5) Doing exercises individually to solve mathematics problems with steps that could bring up students’ intuition: Preparations, Incubation, Illumination, and

  1. A theory of drug tolerance and dependence II: the mathematical model.

    PubMed

    Peper, Abraham

    2004-08-21

    The preceding paper presented a model of drug tolerance and dependence. The model assumes the development of tolerance to a repeatedly administered drug to be the result of a regulated adaptive process. The oral detection and analysis of exogenous substances is proposed to be the primary stimulus for the mechanism of drug tolerance. Anticipation and environmental cues are in the model considered secondary stimuli, becoming primary in dependence and addiction or when the drug administration bypasses the natural-oral-route, as is the case when drugs are administered intravenously. The model considers adaptation to the effect of a drug and adaptation to the interval between drug taking autonomous tolerance processes. Simulations with the mathematical model demonstrate the model's behaviour to be consistent with important characteristics of the development of tolerance to repeatedly administered drugs: the gradual decrease in drug effect when tolerance develops, the high sensitivity to small changes in drug dose, the rebound phenomenon and the large reactions following withdrawal in dependence. The present paper discusses the mathematical model in terms of its design. The model is a nonlinear, learning feedback system, fully satisfying control theoretical principles. It accepts any form of the stimulus-the drug intake-and describes how the physiological processes involved affect the distribution of the drug through the body and the stability of the regulation loop. The mathematical model verifies the proposed theory and provides a basis for the implementation of mathematical models of specific physiological processes.

  2. What Is Mathematical Modelling? Exploring Prospective Teachers' Use of Experiments to Connect Mathematics to the Study of Motion

    ERIC Educational Resources Information Center

    Carrejo, David J.; Marshall, Jill

    2007-01-01

    This paper focuses on the construction, development, and use of mathematical models by prospective science and mathematics teachers enrolled in a university physics course. By studying their involvement in an inquiry-based, experimental approach to learning kinematics, we address a fundamental question about the meaning and role of abstraction in…

  3. Can phenological models predict tree phenology accurately under climate change conditions?

    NASA Astrophysics Data System (ADS)

    Chuine, Isabelle; Bonhomme, Marc; Legave, Jean Michel; García de Cortázar-Atauri, Inaki; Charrier, Guillaume; Lacointe, André; Améglio, Thierry

    2014-05-01

    The onset of the growing season of trees has been globally earlier by 2.3 days/decade during the last 50 years because of global warming and this trend is predicted to continue according to climate forecast. The effect of temperature on plant phenology is however not linear because temperature has a dual effect on bud development. On one hand, low temperatures are necessary to break bud dormancy, and on the other hand higher temperatures are necessary to promote bud cells growth afterwards. Increasing phenological changes in temperate woody species have strong impacts on forest trees distribution and productivity, as well as crops cultivation areas. Accurate predictions of trees phenology are therefore a prerequisite to understand and foresee the impacts of climate change on forests and agrosystems. Different process-based models have been developed in the last two decades to predict the date of budburst or flowering of woody species. They are two main families: (1) one-phase models which consider only the ecodormancy phase and make the assumption that endodormancy is always broken before adequate climatic conditions for cell growth occur; and (2) two-phase models which consider both the endodormancy and ecodormancy phases and predict a date of dormancy break which varies from year to year. So far, one-phase models have been able to predict accurately tree bud break and flowering under historical climate. However, because they do not consider what happens prior to ecodormancy, and especially the possible negative effect of winter temperature warming on dormancy break, it seems unlikely that they can provide accurate predictions in future climate conditions. It is indeed well known that a lack of low temperature results in abnormal pattern of bud break and development in temperate fruit trees. An accurate modelling of the dormancy break date has thus become a major issue in phenology modelling. Two-phases phenological models predict that global warming should delay

  4. Quantum dots as contrast agents for endoscopy: mathematical modeling and experimental validation of the optimal excitation wavelength

    NASA Astrophysics Data System (ADS)

    Roy, Mathieu; DaCosta, Ralph S.; Weersink, Robert; Netchev, George; Davidson, Sean R. H.; Chan, Warren; Wilson, Brian C.

    2007-02-01

    Our group is investigating the use of ZnS-capped CdSe quantum dot (QD) bioconjugates combined with fluorescence endoscopy for improved early cancer detection in the esophagus, colon and lung. A major challenge in using fluorescent contrast agents in vivo is to extract the relevant signal from the tissue autofluorescence (AF). Our studies are aimed at maximizing the QD signal to AF background ratio (SBR) to facilitate detection. This work quantitatively evaluates the effect of the excitation wavelength on the SBR, using both experimental measurements and mathematical modeling. Experimental SBR measurements were done by imaging QD solutions placed onto (surface) or embedded in (sub-surface) ex vivo murine tissue samples (brain, kidney, liver, lung), using a polymethylmethacrylate (PMMA) microchannel phantom. The results suggest that the maximum contrast is reached when the excitation wavelength is set at 400+/-20 μm for the surface configuration. For the sub-surface configuration, the optimal excitation wavelength varies with the tissue type and QD emission wavelengths. Our mathematical model, based on an approximation to the diffusion equation, successfully predicts the optimal excitation wavelength for the surface configuration, but needs further modifications to be accurate in the sub-surface configuration.

  5. Systems oncology: towards patient-specific treatment regimes informed by multiscale mathematical modelling.

    PubMed

    Powathil, Gibin G; Swat, Maciej; Chaplain, Mark A J

    2015-02-01

    The multiscale complexity of cancer as a disease necessitates a corresponding multiscale modelling approach to produce truly predictive mathematical models capable of improving existing treatment protocols. To capture all the dynamics of solid tumour growth and its progression, mathematical modellers need to couple biological processes occurring at various spatial and temporal scales (from genes to tissues). Because effectiveness of cancer therapy is considerably affected by intracellular and extracellular heterogeneities as well as by the dynamical changes in the tissue microenvironment, any model attempt to optimise existing protocols must consider these factors ultimately leading to improved multimodal treatment regimes. By improving existing and building new mathematical models of cancer, modellers can play important role in preventing the use of potentially sub-optimal treatment combinations. In this paper, we analyse a multiscale computational mathematical model for cancer growth and spread, incorporating the multiple effects of radiation therapy and chemotherapy in the patient survival probability and implement the model using two different cell based modelling techniques. We show that the insights provided by such multiscale modelling approaches can ultimately help in designing optimal patient-specific multi-modality treatment protocols that may increase patients quality of life. Copyright © 2014 Elsevier Ltd. All rights reserved.

  6. Learning and Teaching Mathematics through Real Life Models

    ERIC Educational Resources Information Center

    Takaci, Djurdjica; Budinski, Natalija

    2011-01-01

    This paper proposes modelling based learning as a tool for learning and teaching mathematics in high school. We report on an example of modelling real world problems in two high schools in Serbia where students were introduced for the first time to the basic concepts of modelling. Student use of computers and educational software, GeoGebra, was…

  7. Physical and mathematical modeling of antimicrobial photodynamic therapy

    NASA Astrophysics Data System (ADS)

    Bürgermeister, Lisa; López, Fernando Romero; Schulz, Wolfgang

    2014-07-01

    Antimicrobial photodynamic therapy (aPDT) is a promising method to treat local bacterial infections. The therapy is painless and does not cause bacterial resistances. However, there are gaps in understanding the dynamics of the processes, especially in periodontal treatment. This work describes the advances in fundamental physical and mathematical modeling of aPDT used for interpretation of experimental evidence. The result is a two-dimensional model of aPDT in a dental pocket phantom model. In this model, the propagation of laser light and the kinetics of the chemical reactions are described as coupled processes. The laser light induces the chemical processes depending on its intensity. As a consequence of the chemical processes, the local optical properties and distribution of laser light change as well as the reaction rates. The mathematical description of these coupled processes will help to develop treatment protocols and is the first step toward an inline feedback system for aPDT users.

  8. An Accurate Temperature Correction Model for Thermocouple Hygrometers 1

    PubMed Central

    Savage, Michael J.; Cass, Alfred; de Jager, James M.

    1982-01-01

    Numerous water relation studies have used thermocouple hygrometers routinely. However, the accurate temperature correction of hygrometer calibration curve slopes seems to have been largely neglected in both psychrometric and dewpoint techniques. In the case of thermocouple psychrometers, two temperature correction models are proposed, each based on measurement of the thermojunction radius and calculation of the theoretical voltage sensitivity to changes in water potential. The first model relies on calibration at a single temperature and the second at two temperatures. Both these models were more accurate than the temperature correction models currently in use for four psychrometers calibrated over a range of temperatures (15-38°C). The model based on calibration at two temperatures is superior to that based on only one calibration. The model proposed for dewpoint hygrometers is similar to that for psychrometers. It is based on the theoretical voltage sensitivity to changes in water potential. Comparison with empirical data from three dewpoint hygrometers calibrated at four different temperatures indicates that these instruments need only be calibrated at, e.g. 25°C, if the calibration slopes are corrected for temperature. PMID:16662241

  9. Multiscale mathematical modeling of the hypothalamo-pituitary-gonadal axis.

    PubMed

    Clément, Frédérique

    2016-07-01

    Although the fields of systems and integrative biology are in full expansion, few teams are involved worldwide into the study of reproductive function from the mathematical modeling viewpoint. This may be due to the fact that the reproductive function is not compulsory for individual organism survival, even if it is for species survival. Alternatively, the complexity of reproductive physiology may be discouraging. Indeed, the hypothalamo-pituitary-gonadal (HPG) axis involves not only several organs and tissues but also intricate time (from the neuronal millisecond timescale to circannual rhythmicity) and space (from molecules to organs) scales. Yet, mathematical modeling, and especially multiscale modeling, can renew our approaches of the molecular, cellular, and physiological processes underlying the control of reproductive functions. In turn, the remarkable dynamic features exhibited by the HPG axis raise intriguing and challenging questions to modelers and applied mathematicians. In this article, we draw a panoramic review of some mathematical models designed in the framework of the female HPG, with a special focus on the gonadal and central control of follicular development. On the gonadal side, the modeling of follicular development calls to the generic formalism of structured cell populations, that allows one to make mechanistic links between the control of cell fate (proliferation, differentiation, or apoptosis) and that of the follicle fate (ovulation or degeneration) or to investigate how the functional interactions between the oocyte and its surrounding cells shape the follicle morphogenesis. On the central, mainly hypothalamic side, models based on dynamical systems with multiple timescales allow one to represent within a single framework both the pulsatile and surge patterns of the neurohormone GnRH. Beyond their interest in basic research investigations, mathematical models can also be at the source of useful tools to study the encoding and decoding of

  10. Computing Linear Mathematical Models Of Aircraft

    NASA Technical Reports Server (NTRS)

    Duke, Eugene L.; Antoniewicz, Robert F.; Krambeer, Keith D.

    1991-01-01

    Derivation and Definition of Linear Aircraft Model (LINEAR) computer program provides user with powerful, and flexible, standard, documented, and verified software tool for linearization of mathematical models of aerodynamics of aircraft. Intended for use in software tool to drive linear analysis of stability and design of control laws for aircraft. Capable of both extracting such linearized engine effects as net thrust, torque, and gyroscopic effects, and including these effects in linear model of system. Designed to provide easy selection of state, control, and observation variables used in particular model. Also provides flexibility of allowing alternate formulations of both state and observation equations. Written in FORTRAN.

  11. Mathematical modeling of human brain physiological data

    NASA Astrophysics Data System (ADS)

    Böhm, Matthias; Faltermeier, Rupert; Brawanski, Alexander; Lang, Elmar W.

    2013-12-01

    Recently, a mathematical model of the basic physiological processes regulating the cerebral perfusion and oxygen supply was introduced [Jung , J. Math. Biol.JMBLAJ0303-681210.1007/s00285-005-0343-5 51, 491 (2005)]. Although this model correctly describes the interdependence of arterial blood pressure (ABP) and intracranial pressure (ICP), it fails badly when it comes to explaining certain abnormal correlations seen in about 80% of the recordings of ABP together with ICP and the partial oxygen pressure (TiPO2) of the neuronal tissue, taken at an intensive care unit during neuromonitoring of patients with a severe brain trauma. Such recordings occasionally show segments, where the mean arterial blood pressure is correlated with the partial oxygen pressure in tissue but anticorrelated with the intracranial pressure. The origin of such abnormal correlations has not been fully understood yet. Here, two extensions to the previous approach are proposed which can reproduce such abnormal correlations in simulations quantitatively. Furthermore, as the simulations are based on a mathematical model, additional insight into the physiological mechanisms from which such abnormal correlations originate can be gained.

  12. Mathematical modeling and simulation of aquatic and aerial animal locomotion

    NASA Astrophysics Data System (ADS)

    Hou, T. Y.; Stredie, V. G.; Wu, T. Y.

    2007-08-01

    In this paper, we investigate the locomotion of fish and birds by applying a new unsteady, flexible wing theory that takes into account the strong nonlinear dynamics semi-analytically. We also make extensive comparative study between the new approach and the modified vortex blob method inspired from Chorin's and Krasny's work. We first implement the modified vortex blob method for two examples and then discuss the numerical implementation of the nonlinear analytical mathematical model of Wu. We will demonstrate that Wu's method can capture the nonlinear effects very well by applying it to some specific cases and by comparing with the experiments available. In particular, we apply Wu's method to analyze Wagner's result for a wing abruptly undergoing an increase in incidence angle. Moreover, we study the vorticity generated by a wing in heaving, pitching and bending motion. In both cases, we show that the new method can accurately represent the vortex structure behind a flying wing and its influence on the bound vortex sheet on the wing.

  13. Using Spreadsheets to Teach Aspects of Biology Involving Mathematical Models

    ERIC Educational Resources Information Center

    Carlton, Kevin; Nicholls, Mike; Ponsonby, David

    2004-01-01

    Some aspects of biology, for example the Hardy-Weinberg simulation of population genetics or modelling heat flow in lizards, have an undeniable mathematical basis. Students can find the level of mathematical skill required to deal with such concepts to be an insurmountable hurdle to understanding. If not used effectively, spreadsheet models…

  14. Mathematical modeling of kidney transport.

    PubMed

    Layton, Anita T

    2013-01-01

    In addition to metabolic waste and toxin excretion, the kidney also plays an indispensable role in regulating the balance of water, electrolytes, nitrogen, and acid-base. In this review, we describe representative mathematical models that have been developed to better understand kidney physiology and pathophysiology, including the regulation of glomerular filtration, the regulation of renal blood flow by means of the tubuloglomerular feedback mechanisms and of the myogenic mechanism, the urine concentrating mechanism, epithelial transport, and regulation of renal oxygen transport. We discuss the extent to which these modeling efforts have expanded our understanding of renal function in both health and disease. Copyright © 2013 Wiley Periodicals, Inc.

  15. Science Modelling in Pre-Calculus: How to Make Mathematics Problems Contextually Meaningful

    ERIC Educational Resources Information Center

    Sokolowski, Andrzej; Yalvac, Bugrahan; Loving, Cathleen

    2011-01-01

    "Use of mathematical representations to model and interpret physical phenomena and solve problems is one of the major teaching objectives in high school math curriculum" [National Council of Teachers of Mathematics (NCTM), "Principles and Standards for School Mathematics", NCTM, Reston, VA, 2000]. Commonly used pre-calculus textbooks provide a…

  16. A Mathematical Model of a Simple Amplifier Using a Ferroelectric Transistor

    NASA Technical Reports Server (NTRS)

    Sayyah, Rana; Hunt, Mitchell; MacLeod, Todd C.; Ho, Fat D.

    2009-01-01

    This paper presents a mathematical model characterizing the behavior of a simple amplifier using a FeFET. The model is based on empirical data and incorporates several variables that affect the output, including frequency, load resistance, and gate-to-source voltage. Since the amplifier is the basis of many circuit configurations, a mathematical model that describes the behavior of a FeFET-based amplifier will help in the integration of FeFETs into many other circuits.

  17. Perturbing the Hypothalamic Pituitary Adrenal Axis:A Mathematical Model for Interpreting PTSDAssessment Tests

    DTIC Science & Technology

    2017-08-15

    RESEARCH Perturbing the Hypothalamic–Pituitary–Adrenal Axis: A Mathematical Model for Interpreting PTSD Assessment Tests Lae Un Kim1, Maria R...D’Orsogna2, and Tom Chou1 1Department of Biomathematics, University of California, Los Angeles, USA 2Department of Mathematics , California State University...observed features and experimental responses can arise from a bistable mathematical model containing two steady-states, rather than relying on specific

  18. Improving Primary School Prospective Teachers' Understanding of the Mathematics Modeling Process

    ERIC Educational Resources Information Center

    Bal, Aytgen Pinar; Doganay, Ahmet

    2014-01-01

    The development of mathematical thinking plays an important role on the solution of problems faced in daily life. Determining the relevant variables and necessary procedural steps in order to solve problems constitutes the essence of mathematical thinking. Mathematical modeling provides an opportunity for explaining thoughts in real life by making…

  19. An accurate model for predicting high frequency noise of nanoscale NMOS SOI transistors

    NASA Astrophysics Data System (ADS)

    Shen, Yanfei; Cui, Jie; Mohammadi, Saeed

    2017-05-01

    A nonlinear and scalable model suitable for predicting high frequency noise of N-type Metal Oxide Semiconductor (NMOS) transistors is presented. The model is developed for a commercial 45 nm CMOS SOI technology and its accuracy is validated through comparison with measured performance of a microwave low noise amplifier. The model employs the virtual source nonlinear core and adds parasitic elements to accurately simulate the RF behavior of multi-finger NMOS transistors up to 40 GHz. For the first time, the traditional long-channel thermal noise model is supplemented with an injection noise model to accurately represent the noise behavior of these short-channel transistors up to 26 GHz. The developed model is simple and easy to extract, yet very accurate.

  20. Envisioning migration: Mathematics in both experimental analysis and modeling of cell behavior

    PubMed Central

    Zhang, Elizabeth R.; Wu, Lani F.; Altschuler, Steven J.

    2013-01-01

    The complex nature of cell migration highlights the power and challenges of applying mathematics to biological studies. Mathematics may be used to create model equations that recapitulate migration, which can predict phenomena not easily uncovered by experiments or intuition alone. Alternatively, mathematics may be applied to interpreting complex data sets with better resolution—potentially empowering scientists to discern subtle patterns amid the noise and heterogeneity typical of migrating cells. Iteration between these two methods is necessary in order to reveal connections within the cell migration signaling network, as well as to understand the behavior that arises from those connections. Here, we review recent quantitative analysis and mathematical modeling approaches to the cell migration problem. PMID:23660413

  1. Friction-Stir Welding and Mathematical Modeling

    NASA Technical Reports Server (NTRS)

    Rostant, Victor D.

    1999-01-01

    The friction-stir welding process is a remarkable way for making butt and lap joints in aluminum alloys. This process operates by passing a rotating tool between two closely butted plates. Through this process it generates a lot of heat and heated material is stirred from both sides of the plates in which the outcome will one high quality weld. My research has been done to study the FSW through mathematical modeling, and using modeling to better understand what take place during the friction-stir weld.

  2. Does the cognitive reflection test measure cognitive reflection? A mathematical modeling approach.

    PubMed

    Campitelli, Guillermo; Gerrans, Paul

    2014-04-01

    We used a mathematical modeling approach, based on a sample of 2,019 participants, to better understand what the cognitive reflection test (CRT; Frederick In Journal of Economic Perspectives, 19, 25-42, 2005) measures. This test, which is typically completed in less than 10 min, contains three problems and aims to measure the ability or disposition to resist reporting the response that first comes to mind. However, since the test contains three mathematically based problems, it is possible that the test only measures mathematical abilities, and not cognitive reflection. We found that the models that included an inhibition parameter (i.e., the probability of inhibiting an intuitive response), as well as a mathematical parameter (i.e., the probability of using an adequate mathematical procedure), fitted the data better than a model that only included a mathematical parameter. We also found that the inhibition parameter in males is best explained by both rational thinking ability and the disposition toward actively open-minded thinking, whereas in females this parameter was better explained by rational thinking only. With these findings, this study contributes to the understanding of the processes involved in solving the CRT, and will be particularly useful for researchers who are considering using this test in their research.

  3. Authentic Integration: A Model for Integrating Mathematics and Science in the Classroom

    ERIC Educational Resources Information Center

    Treacy, Páraic; O'Donoghue, John

    2014-01-01

    Attempts at integrating mathematics and science have been made previously but no definitive, widely adopted teaching model has been developed to date. Research suggests that hands-on, practical, student-centred tasks should form a central element when designing an effective model for the integration of mathematics and science. Aided by this…

  4. Reality-Theoretical Models-Mathematics: A Ternary Perspective on Physics Lessons in Upper-Secondary School

    ERIC Educational Resources Information Center

    Hansson, Lena; Hansson, Örjan; Juter, Kristina; Redfors, Andreas

    2015-01-01

    This article discusses the role of mathematics during physics lessons in upper-secondary school. Mathematics is an inherent part of theoretical models in physics and makes powerful predictions of natural phenomena possible. Ability to use both theoretical models and mathematics is central in physics. This paper takes as a starting point that the…

  5. Promoting students’ mathematical problem-solving skills through 7e learning cycle and hypnoteaching model

    NASA Astrophysics Data System (ADS)

    Saleh, H.; Suryadi, D.; Dahlan, J. A.

    2018-01-01

    The aim of this research was to find out whether 7E learning cycle under hypnoteaching model can enhance students’ mathematical problem-solving skill. This research was quasi-experimental study. The design of this study was pretest-posttest control group design. There were two groups of sample used in the study. The experimental group was given 7E learning cycle under hypnoteaching model, while the control group was given conventional model. The population of this study was the student of mathematics education program at one university in Tangerang. The statistical analysis used to test the hypothesis of this study were t-test and Mann-Whitney U. The result of this study show that: (1) The students’ achievement of mathematical problem solving skill who obtained 7E learning cycle under hypnoteaching model are higher than the students who obtained conventional model; (2) There are differences in the students’ enhancement of mathematical problem-solving skill based on students’ prior mathematical knowledge (PMK) category (high, middle, and low).

  6. Mathematical Modeling, Sense Making, and the Common Core State Standards

    ERIC Educational Resources Information Center

    Schoenfeld, Alan H.

    2013-01-01

    On October 14, 2013 the Mathematics Education Department at Teachers College hosted a full-day conference focused on the Common Core Standards Mathematical Modeling requirements to be implemented in September 2014 and in honor of Professor Henry Pollak's 25 years of service to the school. This article is adapted from my talk at this conference…

  7. Mathematical model of the SH-3G helicopter

    NASA Technical Reports Server (NTRS)

    Phillips, J. D.

    1982-01-01

    A mathematical model of the Sikorsky SH-3G helicopter based on classical nonlinear, quasi-steady rotor theory was developed. The model was validated statically and dynamically by comparison with Navy flight-test data. The model incorporates ad hoc revisions which address the ideal assumptions of classical rotor theory and improve the static trim characteristics to provide a more realistic simulation, while retaining the simplicity of the classical model.

  8. Correlation of spacecraft thermal mathematical models to reference data

    NASA Astrophysics Data System (ADS)

    Torralbo, Ignacio; Perez-Grande, Isabel; Sanz-Andres, Angel; Piqueras, Javier

    2018-03-01

    Model-to-test correlation is a frequent problem in spacecraft-thermal control design. The idea is to determine the values of the parameters of the thermal mathematical model (TMM) that allows reaching a good fit between the TMM results and test data, in order to reduce the uncertainty of the mathematical model. Quite often, this task is performed manually, mainly because a good engineering knowledge and experience is needed to reach a successful compromise, but the use of a mathematical tool could facilitate this work. The correlation process can be considered as the minimization of the error of the model results with regard to the reference data. In this paper, a simple method is presented suitable to solve the TMM-to-test correlation problem, using Jacobian matrix formulation and Moore-Penrose pseudo-inverse, generalized to include several load cases. Aside, in simple cases, this method also allows for analytical solutions to be obtained, which helps to analyze some problems that appear when the Jacobian matrix is singular. To show the implementation of the method, two problems have been considered, one more academic, and the other one the TMM of an electronic box of PHI instrument of ESA Solar Orbiter mission, to be flown in 2019. The use of singular value decomposition of the Jacobian matrix to analyze and reduce these models is also shown. The error in parameter space is used to assess the quality of the correlation results in both models.

  9. A mathematical model for describing the mechanical behaviour of root canal instruments.

    PubMed

    Zhang, E W; Cheung, G S P; Zheng, Y F

    2011-01-01

    The purpose of this study was to establish a general mathematical model for describing the mechanical behaviour of root canal instruments by combining a theoretical analytical approach with a numerical finite-element method. Mathematical formulas representing the longitudinal (taper, helical angle and pitch) and cross-sectional configurations and area, the bending and torsional inertia, the curvature of the boundary point and the (geometry of) loading condition were derived. Torsional and bending stresses and the resultant deformation were expressed mathematically as a function of these geometric parameters, modulus of elasticity of the material and the applied load. As illustrations, three brands of NiTi endodontic files of different cross-sectional configurations (ProTaper, Hero 642, and Mani NRT) were analysed under pure torsion and pure bending situation by entering the model into a finite-element analysis package (ANSYS). Numerical results confirmed that mathematical models were a feasible method to analyse the mechanical properties and predict the stress and deformation for root canal instruments during root canal preparation. Mathematical and numerical model can be a suitable way to examine mechanical behaviours as a criterion of the instrument design and to predict the stress and strain experienced by the endodontic instruments during root canal preparation. © 2010 International Endodontic Journal.

  10. UAH mathematical model of the variable polarity plasma ARC welding system calculation

    NASA Technical Reports Server (NTRS)

    Hung, R. J.

    1994-01-01

    Significant advantages of Variable Polarity Plasma Arc (VPPA) welding process include faster welding, fewer repairs, less joint preparation, reduced weldment distortion, and absence of porosity. A mathematical model is presented to analyze the VPPA welding process. Results of the mathematical model were compared with the experimental observation accomplished by the GDI team.

  11. Correlation Educational Model in Primary Education Curriculum of Mathematics and Computer Science

    ERIC Educational Resources Information Center

    Macinko Kovac, Maja; Eret, Lidija

    2012-01-01

    This article gives insight into methodical correlation model of teaching mathematics and computer science. The model shows the way in which the related areas of computer science and mathematics can be supplemented, if it transforms the way of teaching and creates a "joint" lessons. Various didactic materials are designed, in which all…

  12. The Singing Wineglass: An Exercise in Mathematical Modelling

    ERIC Educational Resources Information Center

    Voges, E. L.; Joubert, S. V.

    2008-01-01

    Lecturers in mathematical modelling courses are always on the lookout for new examples to illustrate the modelling process. A physical phenomenon, documented as early as the nineteenth century, was recalled: when a wineglass "sings", waves are visible on the surface of the wine. These surface waves are used as an exercise in mathematical…

  13. Unlocking the black box: teaching mathematical modeling with popular culture.

    PubMed

    Lofgren, Eric T

    2016-10-01

    Mathematical modeling is an important tool in biological research, allowing for the synthesis of results from many studies into an understanding of a system. Despite this, the need for extensive subject matter knowledge and complex mathematics often leaves modeling as an esoteric subspecialty. A 2-fold approach can be used to make modeling more approachable for students and those interested in obtaining a functional knowledge of modeling. The first is the use of a popular culture disease system-a zombie epidemic-to allow for exploration of the concepts of modeling using a flexible framework. The second is the use of available interactive and non-calculus-based tools to allow students to work with and implement models to cement their understanding. © FEMS 2016. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

  14. Mathematical modelling of the growth of human fetus anatomical structures.

    PubMed

    Dudek, Krzysztof; Kędzia, Wojciech; Kędzia, Emilia; Kędzia, Alicja; Derkowski, Wojciech

    2017-09-01

    The goal of this study was to present a procedure that would enable mathematical analysis of the increase of linear sizes of human anatomical structures, estimate mathematical model parameters and evaluate their adequacy. Section material consisted of 67 foetuses-rectus abdominis muscle and 75 foetuses- biceps femoris muscle. The following methods were incorporated to the study: preparation and anthropologic methods, image digital acquisition, Image J computer system measurements and statistical analysis method. We used an anthropologic method based on age determination with the use of crown-rump length-CRL (V-TUB) by Scammon and Calkins. The choice of mathematical function should be based on a real course of the curve presenting growth of anatomical structure linear size Ύ in subsequent weeks t of pregnancy. Size changes can be described with a segmental-linear model or one-function model with accuracy adequate enough for clinical purposes. The interdependence of size-age is described with many functions. However, the following functions are most often considered: linear, polynomial, spline, logarithmic, power, exponential, power-exponential, log-logistic I and II, Gompertz's I and II and von Bertalanffy's function. With the use of the procedures described above, mathematical models parameters were assessed for V-PL (the total length of body) and CRL body length increases, rectus abdominis total length h, its segments hI, hII, hIII, hIV, as well as biceps femoris length and width of long head (LHL and LHW) and of short head (SHL and SHW). The best adjustments to measurement results were observed in the exponential and Gompertz's models.

  15. Cognitive Predictors of Achievement Growth in Mathematics: A Five Year Longitudinal Study

    PubMed Central

    Geary, David C.

    2011-01-01

    The study's goal was to identify the beginning of first grade quantitative competencies that predict mathematics achievement start point and growth through fifth grade. Measures of number, counting, and arithmetic competencies were administered in early first grade and used to predict mathematics achievement through fifth (n = 177), while controlling for intelligence, working memory, and processing speed. Multilevel models revealed intelligence, processing speed, and the central executive component of working memory predicted achievement or achievement growth in mathematics and, as a contrast domain, word reading. The phonological loop was uniquely predictive of word reading and the visuospatial sketch pad of mathematics. Early fluency in processing and manipulating numerical set size and Arabic numerals, accurate use of sophisticated counting procedures for solving addition problems, and accuracy in making placements on a mathematical number line were uniquely predictive of mathematics achievement. Use of memory-based processes to solve addition problems predicted mathematics and reading achievement but in different ways. The results identify the early quantitative competencies that uniquely contribute to mathematics learning. PMID:21942667

  16. Envisioning migration: mathematics in both experimental analysis and modeling of cell behavior.

    PubMed

    Zhang, Elizabeth R; Wu, Lani F; Altschuler, Steven J

    2013-10-01

    The complex nature of cell migration highlights the power and challenges of applying mathematics to biological studies. Mathematics may be used to create model equations that recapitulate migration, which can predict phenomena not easily uncovered by experiments or intuition alone. Alternatively, mathematics may be applied to interpreting complex data sets with better resolution--potentially empowering scientists to discern subtle patterns amid the noise and heterogeneity typical of migrating cells. Iteration between these two methods is necessary in order to reveal connections within the cell migration signaling network, as well as to understand the behavior that arises from those connections. Here, we review recent quantitative analysis and mathematical modeling approaches to the cell migration problem. Copyright © 2013 Elsevier Ltd. All rights reserved.

  17. Mathematical modeling of efficacy and safety for anticancer drugs clinical development.

    PubMed

    Lavezzi, Silvia Maria; Borella, Elisa; Carrara, Letizia; De Nicolao, Giuseppe; Magni, Paolo; Poggesi, Italo

    2018-01-01

    Drug attrition in oncology clinical development is higher than in other therapeutic areas. In this context, pharmacometric modeling represents a useful tool to explore drug efficacy in earlier phases of clinical development, anticipating overall survival using quantitative model-based metrics. Furthermore, modeling approaches can be used to characterize earlier the safety and tolerability profile of drug candidates, and, thus, the risk-benefit ratio and the therapeutic index, supporting the design of optimal treatment regimens and accelerating the whole process of clinical drug development. Areas covered: Herein, the most relevant mathematical models used in clinical anticancer drug development during the last decade are described. Less recent models were considered in the review if they represent a standard for the analysis of certain types of efficacy or safety measures. Expert opinion: Several mathematical models have been proposed to predict overall survival from earlier endpoints and validate their surrogacy in demonstrating drug efficacy in place of overall survival. An increasing number of mathematical models have also been developed to describe the safety findings. Modeling has been extensively used in anticancer drug development to individualize dosing strategies based on patient characteristics, and design optimal dosing regimens balancing efficacy and safety.

  18. Mathematical model of salt cavern leaching for gas storage in high-insoluble salt formations.

    PubMed

    Li, Jinlong; Shi, Xilin; Yang, Chunhe; Li, Yinping; Wang, Tongtao; Ma, Hongling

    2018-01-10

    A mathematical model is established to predict the salt cavern development during leaching in high-insoluble salt formations. The salt-brine mass transfer rate is introduced, and the effects of the insoluble sediments on the development of the cavern are included. Considering the salt mass conservation in the cavern, the couple equations of the cavern shape, brine concentration and brine velocity are derived. According to the falling and accumulating rules of the insoluble particles, the governing equations of the insoluble sediments are deduced. A computer program using VC++ language is developed to obtain the numerical solution of these equations. To verify the proposed model, the leaching processes of two salt caverns of Jintan underground gas storage are simulated by the program, using the actual geological and technological parameters. The same simulation is performed by the current mainstream leaching software in China. The simulation results of the two programs are compared with the available field data. It shows that the proposed software is more accurate on the shape prediction of the cavern bottom and roof, which demonstrates the reliability and applicability of the model.

  19. Using the Scientific Method to Engage Mathematical Modeling: An Investigation of pi

    ERIC Educational Resources Information Center

    Archer, Lester A. C.; Ng, Karen E.

    2016-01-01

    The purpose of this paper is to explain how to use the scientific method as the framework to introduce mathematical model. Two interdisciplinary activities, targeted for students in grade 6 or grade 7, are explained to show the application of the scientific method while building a mathematical model to investigate the relationship between the…

  20. How Long is my Toilet Roll?--A Simple Exercise in Mathematical Modelling

    ERIC Educational Resources Information Center

    Johnston, Peter R.

    2013-01-01

    The simple question of how much paper is left on my toilet roll is studied from a mathematical modelling perspective. As is typical with applied mathematics, models of increasing complexity are introduced and solved. Solutions produced at each step are compared with the solution from the previous step. This process exposes students to the typical…

  1. Pedagogical Content Knowledge in Mathematical Modelling Instruction

    ERIC Educational Resources Information Center

    Tan, Liang Soon; Ang, Keng Cheng

    2012-01-01

    This paper posits that teachers' pedagogical content knowledge in mathematical modelling instruction can be demonstrated in the crafting of action plans and expected teaching and learning moves via their lesson images (Schoenfeld, 1998). It can also be developed when teachers shape appropriate teaching moves in response to students' learning…

  2. Mathematics Underground

    ERIC Educational Resources Information Center

    Luther, Kenneth H.

    2012-01-01

    Mathematical modeling of groundwater flow is a topic at the intersection of mathematics and geohydrology and is rarely encountered in undergraduate mathematics. However, this subject is full of interesting and meaningful examples of truly "applied" mathematics accessible to undergraduates, from the pre-calculus to advanced mathematics levels. This…

  3. Mathematical model to predict drivers' reaction speeds.

    PubMed

    Long, Benjamin L; Gillespie, A Isabella; Tanaka, Martin L

    2012-02-01

    Mental distractions and physical impairments can increase the risk of accidents by affecting a driver's ability to control the vehicle. In this article, we developed a linear mathematical model that can be used to quantitatively predict drivers' performance over a variety of possible driving conditions. Predictions were not limited only to conditions tested, but also included linear combinations of these tests conditions. Two groups of 12 participants were evaluated using a custom drivers' reaction speed testing device to evaluate the effect of cell phone talking, texting, and a fixed knee brace on the components of drivers' reaction speed. Cognitive reaction time was found to increase by 24% for cell phone talking and 74% for texting. The fixed knee brace increased musculoskeletal reaction time by 24%. These experimental data were used to develop a mathematical model to predict reaction speed for an untested condition, talking on a cell phone with a fixed knee brace. The model was verified by comparing the predicted reaction speed to measured experimental values from an independent test. The model predicted full braking time within 3% of the measured value. Although only a few influential conditions were evaluated, we present a general approach that can be expanded to include other types of distractions, impairments, and environmental conditions.

  4. Mathematical models for optimization of the centrifugal stage of a refrigerating compressor

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Nuzhdin, A.S.

    1987-09-01

    The authors describe a general approach to the creating of mathematical models of energy and head losses in the flow part of the centrifugal compressor. The mathematical model of the pressure head and efficiency of a two-section stage proposed in this paper is meant for determining its characteristics for the assigned geometric dimensions and for optimizing by variance calculations. Characteristic points on the plot of velocity distribution over the margin of the vanes of the impeller and the diffuser of the centrifugal stage with a combined diffuser are presented. To assess the reliability of the mathematical model the authors comparedmore » some calculated data with the experimental ones.« less

  5. Nonconvex Model of Material Growth: Mathematical Theory

    NASA Astrophysics Data System (ADS)

    Ganghoffer, J. F.; Plotnikov, P. I.; Sokolowski, J.

    2018-06-01

    The model of volumetric material growth is introduced in the framework of finite elasticity. The new results obtained for the model are presented with complete proofs. The state variables include the deformations, temperature and the growth factor matrix function. The existence of global in time solutions for the quasistatic deformations boundary value problem coupled with the energy balance and the evolution of the growth factor is shown. The mathematical results can be applied to a wide class of growth models in mechanics and biology.

  6. UH-60A Black Hawk engineering simulation program. Volume 1: Mathematical model

    NASA Technical Reports Server (NTRS)

    Howlett, J. J.

    1981-01-01

    A nonlinear mathematical model of the UR-60A Black Hawk helicopter was developed. This mathematical model, which was based on the Sikorsky General Helicopter (Gen Hel) Flight Dynamics Simulation, provides NASA with an engineering simulation for performance and handling qualities evaluations. This mathematical model is total systems definition of the Black Hawk helicopter represented at a uniform level of sophistication considered necessary for handling qualities evaluations. The model is a total force, large angle representation in six rigid body degrees of freedom. Rotor blade flapping, lagging, and hub rotational degrees of freedom are also represented. In addition to the basic helicopter modules, supportive modules were defined for the landing interface, power unit, ground effects, and gust penetration. Information defining the cockpit environment relevant to pilot in the loop simulation is presented.

  7. A mathematical model of aortic aneurysm formation

    PubMed Central

    Hao, Wenrui; Gong, Shihua; Wu, Shuonan; Xu, Jinchao; Go, Michael R.; Friedman, Avner; Zhu, Dai

    2017-01-01

    Abdominal aortic aneurysm (AAA) is a localized enlargement of the abdominal aorta, such that the diameter exceeds 3 cm. The natural history of AAA is progressive growth leading to rupture, an event that carries up to 90% risk of mortality. Hence there is a need to predict the growth of the diameter of the aorta based on the diameter of a patient’s aneurysm at initial screening and aided by non-invasive biomarkers. IL-6 is overexpressed in AAA and was suggested as a prognostic marker for the risk in AAA. The present paper develops a mathematical model which relates the growth of the abdominal aorta to the serum concentration of IL-6. Given the initial diameter of the aorta and the serum concentration of IL-6, the model predicts the growth of the diameter at subsequent times. Such a prediction can provide guidance to how closely the patient’s abdominal aorta should be monitored. The mathematical model is represented by a system of partial differential equations taking place in the aortic wall, where the media is assumed to have the constituency of an hyperelastic material. PMID:28212412

  8. Use of mathematical modelling to assess the impact of vaccines on antibiotic resistance.

    PubMed

    Atkins, Katherine E; Lafferty, Erin I; Deeny, Sarah R; Davies, Nicholas G; Robotham, Julie V; Jit, Mark

    2018-06-01

    Antibiotic resistance is a major global threat to the provision of safe and effective health care. To control antibiotic resistance, vaccines have been proposed as an essential intervention, complementing improvements in diagnostic testing, antibiotic stewardship, and drug pipelines. The decision to introduce or amend vaccination programmes is routinely based on mathematical modelling. However, few mathematical models address the impact of vaccination on antibiotic resistance. We reviewed the literature using PubMed to identify all studies that used an original mathematical model to quantify the impact of a vaccine on antibiotic resistance transmission within a human population. We reviewed the models from the resulting studies in the context of a new framework to elucidate the pathways through which vaccination might impact antibiotic resistance. We identified eight mathematical modelling studies; the state of the literature highlighted important gaps in our understanding. Notably, studies are limited in the range of pathways represented, their geographical scope, and the vaccine-pathogen combinations assessed. Furthermore, to translate model predictions into public health decision making, more work is needed to understand how model structure and parameterisation affects model predictions and how to embed these predictions within economic frameworks. Copyright © 2018 Elsevier Ltd. All rights reserved.

  9. Mathematical modeling in chronobiology.

    PubMed

    Bordyugov, G; Westermark, P O; Korenčič, A; Bernard, S; Herzel, H

    2013-01-01

    Circadian clocks are autonomous oscillators entrained by external Zeitgebers such as light-dark and temperature cycles. On the cellular level, rhythms are generated by negative transcriptional feedback loops. In mammals, the suprachiasmatic nucleus (SCN) in the anterior part of the hypothalamus plays the role of the central circadian pacemaker. Coupling between individual neurons in the SCN leads to precise self-sustained oscillations even in the absence of external signals. These neuronal rhythms orchestrate the phasing of circadian oscillations in peripheral organs. Altogether, the mammalian circadian system can be regarded as a network of coupled oscillators. In order to understand the dynamic complexity of these rhythms, mathematical models successfully complement experimental investigations. Here we discuss basic ideas of modeling on three different levels (1) rhythm generation in single cells by delayed negative feedbacks, (2) synchronization of cells via external stimuli or cell-cell coupling, and (3) optimization of chronotherapy.

  10. Exploring Differential Effects of Mathematics Courses on Mathematics Achievement

    ERIC Educational Resources Information Center

    Ma, Xin; McIntyre, Laureen J.

    2005-01-01

    Using data from the Longitudinal Study of Mathematics Participation (N = 1,518 students from 34 schools), we investigated the effects of pure and applied mathematics courses on mathematics achievement, controlling for prior mathematics achievement. Results of multilevel modelling showed that the effects of pure mathematics were significant after…

  11. Establishing an Explanatory Model for Mathematics Identity

    ERIC Educational Resources Information Center

    Cribbs, Jennifer D.; Hazari, Zahra; Sonnert, Gerhard; Sadler, Philip M.

    2015-01-01

    This article empirically tests a previously developed theoretical framework for mathematics identity based on students' beliefs. The study employs data from more than 9,000 college calculus students across the United States to build a robust structural equation model. While it is generally thought that students' beliefs about their own competence…

  12. Mathematical Modeling Projects: Success for All Students

    ERIC Educational Resources Information Center

    Shelton, Therese

    2018-01-01

    Mathematical modeling allows flexibility for a project-based experience. We share details of our regular capstone course, successful for virtually 100% of our math majors for almost two decades. Our research-like approach in this course accommodates a variety of student backgrounds and interests, and has produced some award-winning student…

  13. Mathematical models used in segmentation and fractal methods of 2-D ultrasound images

    NASA Astrophysics Data System (ADS)

    Moldovanu, Simona; Moraru, Luminita; Bibicu, Dorin

    2012-11-01

    Mathematical models are widely used in biomedical computing. The extracted data from images using the mathematical techniques are the "pillar" achieving scientific progress in experimental, clinical, biomedical, and behavioural researches. This article deals with the representation of 2-D images and highlights the mathematical support for the segmentation operation and fractal analysis in ultrasound images. A large number of mathematical techniques are suitable to be applied during the image processing stage. The addressed topics cover the edge-based segmentation, more precisely the gradient-based edge detection and active contour model, and the region-based segmentation namely Otsu method. Another interesting mathematical approach consists of analyzing the images using the Box Counting Method (BCM) to compute the fractal dimension. The results of the paper provide explicit samples performed by various combination of methods.

  14. Mathematical modeling of gene expression: a guide for the perplexed biologist

    PubMed Central

    Ay, Ahmet; Arnosti, David N.

    2011-01-01

    The detailed analysis of transcriptional networks holds a key for understanding central biological processes, and interest in this field has exploded due to new large-scale data acquisition techniques. Mathematical modeling can provide essential insights, but the diversity of modeling approaches can be a daunting prospect to investigators new to this area. For those interested in beginning a transcriptional mathematical modeling project we provide here an overview of major types of models and their applications to transcriptional networks. In this discussion of recent literature on thermodynamic, Boolean and differential equation models we focus on considerations critical for choosing and validating a modeling approach that will be useful for quantitative understanding of biological systems. PMID:21417596

  15. Complexity analysis and mathematical tools towards the modelling of living systems.

    PubMed

    Bellomo, N; Bianca, C; Delitala, M

    2009-09-01

    This paper is a review and critical analysis of the mathematical kinetic theory of active particles applied to the modelling of large living systems made up of interacting entities. The first part of the paper is focused on a general presentation of the mathematical tools of the kinetic theory of active particles. The second part provides a review of a variety of mathematical models in life sciences, namely complex social systems, opinion formation, evolution of epidemics with virus mutations, and vehicular traffic, crowds and swarms. All the applications are technically related to the mathematical structures reviewed in the first part of the paper. The overall contents are based on the concept that living systems, unlike the inert matter, have the ability to develop behaviour geared towards their survival, or simply to improve the quality of their life. In some cases, the behaviour evolves in time and generates destructive and/or proliferative events.

  16. Improving science and mathematics education with computational modelling in interactive engagement environments

    NASA Astrophysics Data System (ADS)

    Neves, Rui Gomes; Teodoro, Vítor Duarte

    2012-09-01

    A teaching approach aiming at an epistemologically balanced integration of computational modelling in science and mathematics education is presented. The approach is based on interactive engagement learning activities built around computational modelling experiments that span the range of different kinds of modelling from explorative to expressive modelling. The activities are designed to make a progressive introduction to scientific computation without requiring prior development of a working knowledge of programming, generate and foster the resolution of cognitive conflicts in the understanding of scientific and mathematical concepts and promote performative competency in the manipulation of different and complementary representations of mathematical models. The activities are supported by interactive PDF documents which explain the fundamental concepts, methods and reasoning processes using text, images and embedded movies, and include free space for multimedia enriched student modelling reports and teacher feedback. To illustrate, an example from physics implemented in the Modellus environment and tested in undergraduate university general physics and biophysics courses is discussed.

  17. Modeling Simple Telescope Optics in Secondary Mathematics Classrooms

    NASA Astrophysics Data System (ADS)

    Siegel, Lauren; Dickinson, G.; Hooper, E. J.; Daniels, M.

    2007-12-01

    This presentation describes the results of collaboration between instructors in the UTeach teacher preparation program at the University of Texas at Austin, and an astronomer teaching at the university as part of a National Science Foundation Astronomy and Astrophysics Postdoctoral Fellowship. The astronomer provided training to give pre-service teachers an authentic understanding of the principles of telescope optics. This made it possible for the preservice teachers to include real design constraints and optical properties into lessons developed as part of a collaborative field experience to teach astronomical telescope design and construction to high school Algebra II students. One result is a sequence of investigations designed to explore how and why the physical and mathematical properties of parabolic mirrors both enable and constrain our ability to build and use telescopes to focus light from distant objects. Various approaches, including generating and exploring computer models, traditional proofs, even making paper models, are all woven together into a coherent set of eleven investigations for use in mathematics and science classrooms. The presentation will include a description of the suite of investigations, as well as a discussion of the collaborative process which generated the work and resulted in an article submission to a preeminent teaching journal. Teaching Algebra and Geometry Concepts by Modeling Telescope Optics, 2008, Mathematics Teacher is currently in press. Many thanks to the University of Texas UTeach Program for sponsorship of this submission.

  18. A mathematical model for the virus medical imaging technique

    NASA Astrophysics Data System (ADS)

    Fioranelli, Massimo; Sepehri, Alireza

    In this paper, we introduce a mathematical model for the virus medical imaging (VMI). In this method, first, by proposing a mathematical model, we show that there are two types of viruses that each of them produce one type of signal. Some of these signals can be received by males and others by females. Then, we will show that in the VMI technique, viruses can communicate with cells, interior to human’s body via two ways. (1) Viruses can form a wire that passes the skin and reaches to a special cell. (2) Viruses can communicate with viruses interior to body in the wireless form and send some signals for controlling evolutions of cells interior to human’s body.

  19. A New Model for the Integration of Science and Mathematics: The Balance Model

    ERIC Educational Resources Information Center

    Kiray, S. Ahmet

    2012-01-01

    The aim of this study is to develop an integrated scientific and mathematical model that is suited to the background of Turkish teachers. The dimensions of the model are given and compared to the models which have been previously developed and the findings of earlier studies on the topic. The model is called the balance, reflecting the…

  20. Secondary Teachers' Conceptions and Practices of Assessment Models: The Case for Mathematics Teachers in Jordan

    ERIC Educational Resources Information Center

    Al Duwairi, Ahmed

    2013-01-01

    This study aimed at investigating the extent to which secondary schools mathematics teachers practice to assessment models in their mathematics teaching and learning. Definitely, the study aimed at answering the following questions: (1) To what extent do secondary schools mathematics teachers practice each of the assessment models in their…

  1. Fast and Accurate Circuit Design Automation through Hierarchical Model Switching.

    PubMed

    Huynh, Linh; Tagkopoulos, Ilias

    2015-08-21

    In computer-aided biological design, the trifecta of characterized part libraries, accurate models and optimal design parameters is crucial for producing reliable designs. As the number of parts and model complexity increase, however, it becomes exponentially more difficult for any optimization method to search the solution space, hence creating a trade-off that hampers efficient design. To address this issue, we present a hierarchical computer-aided design architecture that uses a two-step approach for biological design. First, a simple model of low computational complexity is used to predict circuit behavior and assess candidate circuit branches through branch-and-bound methods. Then, a complex, nonlinear circuit model is used for a fine-grained search of the reduced solution space, thus achieving more accurate results. Evaluation with a benchmark of 11 circuits and a library of 102 experimental designs with known characterization parameters demonstrates a speed-up of 3 orders of magnitude when compared to other design methods that provide optimality guarantees.

  2. Structural Equation Model to Validate: Mathematics-Computer Interaction, Computer Confidence, Mathematics Commitment, Mathematics Motivation and Mathematics Confidence

    ERIC Educational Resources Information Center

    Garcia-Santillán, Arturo; Moreno-Garcia, Elena; Escalera-Chávez, Milka E.; Rojas-Kramer, Carlos A.; Pozos-Texon, Felipe

    2016-01-01

    Most mathematics students show a definite tendency toward an attitudinal deficiency, which can be primarily understood as intolerance to the matter, affecting their scholar performance adversely. In addition, information and communication technologies have been gradually included within the process of teaching mathematics. Such adoption of…

  3. The role of mathematical models in understanding pattern formation in developmental biology.

    PubMed

    Umulis, David M; Othmer, Hans G

    2015-05-01

    In a Wall Street Journal article published on April 5, 2013, E. O. Wilson attempted to make the case that biologists do not really need to learn any mathematics-whenever they run into difficulty with numerical issues, they can find a technician (aka mathematician) to help them out of their difficulty. He formalizes this in Wilsons Principle No. 1: "It is far easier for scientists to acquire needed collaboration from mathematicians and statisticians than it is for mathematicians and statisticians to find scientists able to make use of their equations." This reflects a complete misunderstanding of the role of mathematics in all sciences throughout history. To Wilson, mathematics is mere number crunching, but as Galileo said long ago, "The laws of Nature are written in the language of mathematics[Formula: see text] the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word." Mathematics has moved beyond the geometry-based model of Galileo's time, and in a rebuttal to Wilson, E. Frenkel has pointed out the role of mathematics in synthesizing the general principles in science (Both point and counter-point are available in Wilson and Frenkel in Notices Am Math Soc 60(7):837-838, 2013). We will take this a step further and show how mathematics has been used to make new and experimentally verified discoveries in developmental biology and how mathematics is essential for understanding a problem that has puzzled experimentalists for decades-that of how organisms can scale in size. Mathematical analysis alone cannot "solve" these problems since the validation lies at the molecular level, but conversely, a growing number of questions in biology cannot be solved without mathematical analysis and modeling. Herein, we discuss a few examples of the productive intercourse between mathematics and biology.

  4. MATHEMATICAL MODELING OF PESTICIDES IN THE ENVIRONMENT: CURRENT AND FUTURE DEVELOPMENTS

    EPA Science Inventory

    Transport models, total ecosystem models with aggregated linear approximations, evaluative models, hierarchical models, and influence analysis methods are mathematical techniques that are particularly applicable to the problems encountered when characterizing pesticide chemicals ...

  5. A Simple and Accurate Rate-Driven Infiltration Model

    NASA Astrophysics Data System (ADS)

    Cui, G.; Zhu, J.

    2017-12-01

    In this study, we develop a novel Rate-Driven Infiltration Model (RDIMOD) for simulating infiltration into soils. Unlike traditional methods, RDIMOD avoids numerically solving the highly non-linear Richards equation or simply modeling with empirical parameters. RDIMOD employs infiltration rate as model input to simulate one-dimensional infiltration process by solving an ordinary differential equation. The model can simulate the evolutions of wetting front, infiltration rate, and cumulative infiltration on any surface slope including vertical and horizontal directions. Comparing to the results from the Richards equation for both vertical infiltration and horizontal infiltration, RDIMOD simply and accurately predicts infiltration processes for any type of soils and soil hydraulic models without numerical difficulty. Taking into account the accuracy, capability, and computational effectiveness and stability, RDIMOD can be used in large-scale hydrologic and land-atmosphere modeling.

  6. Mathematical modeling and hydrodynamics of Electrochemical deburring process

    NASA Astrophysics Data System (ADS)

    Prabhu, Satisha; Abhishek Kumar, K., Dr

    2018-04-01

    The electrochemical deburring (ECD) is a variation of electrochemical machining is considered as one of the efficient methods for deburring of intersecting features and internal parts. Since manual deburring costs are comparatively high one can potentially use this method in both batch production and flow production. The other advantage of this process is that time of deburring as is on the order of seconds as compared to other methods. In this paper, the mathematical modeling of Electrochemical deburring is analysed from its deburring time and base metal removal point of view. Simultaneously material removal rate is affected by electrolyte temperature and bubble formation. The mathematical model and hydrodynamics of the process throw limelight upon optimum velocity calculations which can be theoretically determined. The analysis can be the powerful tool for prediction of the above-mentioned parameters by experimentation.

  7. Accurate electromagnetic modeling of terahertz detectors

    NASA Technical Reports Server (NTRS)

    Focardi, Paolo; McGrath, William R.

    2004-01-01

    Twin slot antennas coupled to superconducting devices have been developed over the years as single pixel detectors in the terahertz (THz) frequency range for space-based and astronomy applications. Used either for mixing or direct detection, they have been object of several investigations, and are currently being developed for several missions funded or co-funded by NASA. Although they have shown promising performance in terms of noise and sensitivity, so far they have usually also shown a considerable disagreement in terms of performance between calculations and measurements, especially when considering center frequency and bandwidth. In this paper we present a thorough and accurate electromagnetic model of complete detector and we compare the results of calculations with measurements. Starting from a model of the embedding circuit, the effect of all the other elements in the detector in the coupled power have been analyzed. An extensive variety of measured and calculated data, as presented in this paper, demonstrates the effectiveness and reliability of the electromagnetic model at frequencies between 600 GHz and 2.5THz.

  8. A novel individual-cell-based mathematical model based on multicellular tumour spheroids for evaluating doxorubicin-related delivery in avascular regions.

    PubMed

    Liu, Jiali; Yan, Fangrong; Chen, Hongzhu; Wang, Wenjie; Liu, Wenyue; Hao, Kun; Wang, Guangji; Zhou, Fang; Zhang, Jingwei

    2017-09-01

    Effective drug delivery in the avascular regions of tumours, which is crucial for the promising antitumour activity of doxorubicin-related therapy, is governed by two inseparable processes: intercellular diffusion and intracellular retention. To accurately evaluate doxorubicin-related delivery in the avascular regions, these two processes should be assessed together. Here we describe a new approach to such an assessment. An individual-cell-based mathematical model based on multicellular tumour spheroids was developed that describes the different intercellular diffusion and intracellular retention kinetics of doxorubicin in each cell layer. The different effects of a P-glycoprotein inhibitor (LY335979) and a hypoxia inhibitor (YC-1) were quantitatively evaluated and compared, in vitro (tumour spheroids) and in vivo (HepG2 tumours in mice). This approach was further tested by evaluating in these models, an experimental doxorubicin derivative, INNO 206, which is in Phase II clinical trials. Inhomogeneous, hypoxia-induced, P-glycoprotein expression compromised active transport of doxorubicin in the central area, that is, far from the vasculature. LY335979 inhibited efflux due to P-glycoprotein but limited levels of doxorubicin outside the inner cells, whereas YC-1 co-administration specifically increased doxorubicin accumulation in the inner cells without affecting the extracellular levels. INNO 206 exhibited a more effective distribution profile than doxorubicin. The individual-cell-based mathematical model accurately evaluated and predicted doxorubicin-related delivery and regulation in the avascular regions of tumours. The described framework provides a mechanistic basis for the proper development of doxorubicin-related drug co-administration profiles and nanoparticle development and could avoid unnecessary clinical trials. © 2017 The British Pharmacological Society.

  9. Mathematical Models of Blast-Induced TBI: Current Status, Challenges, and Prospects

    PubMed Central

    Gupta, Raj K.; Przekwas, Andrzej

    2013-01-01

    Blast-induced traumatic brain injury (TBI) has become a signature wound of recent military activities and is the leading cause of death and long-term disability among U.S. soldiers. The current limited understanding of brain injury mechanisms impedes the development of protection, diagnostic, and treatment strategies. We believe mathematical models of blast wave brain injury biomechanics and neurobiology, complemented with in vitro and in vivo experimental studies, will enable a better understanding of injury mechanisms and accelerate the development of both protective and treatment strategies. The goal of this paper is to review the current state of the art in mathematical and computational modeling of blast-induced TBI, identify research gaps, and recommend future developments. A brief overview of blast wave physics, injury biomechanics, and the neurobiology of brain injury is used as a foundation for a more detailed discussion of multiscale mathematical models of primary biomechanics and secondary injury and repair mechanisms. The paper also presents a discussion of model development strategies, experimental approaches to generate benchmark data for model validation, and potential applications of the model for prevention and protection against blast wave TBI. PMID:23755039

  10. How to build a course in mathematical-biological modeling: content and processes for knowledge and skill.

    PubMed

    Hoskinson, Anne-Marie

    2010-01-01

    Biological problems in the twenty-first century are complex and require mathematical insight, often resulting in mathematical models of biological systems. Building mathematical-biological models requires cooperation among biologists and mathematicians, and mastery of building models. A new course in mathematical modeling presented the opportunity to build both content and process learning of mathematical models, the modeling process, and the cooperative process. There was little guidance from the literature on how to build such a course. Here, I describe the iterative process of developing such a course, beginning with objectives and choosing content and process competencies to fulfill the objectives. I include some inductive heuristics for instructors seeking guidance in planning and developing their own courses, and I illustrate with a description of one instructional model cycle. Students completing this class reported gains in learning of modeling content, the modeling process, and cooperative skills. Student content and process mastery increased, as assessed on several objective-driven metrics in many types of assessments.

  11. Mathematical models for Isoptera (Insecta) mound growth.

    PubMed

    Buschini, M L T; Abuabara, M A P; Petrere, Miguel

    2008-08-01

    In this research we proposed two mathematical models for Isoptera mound growth derived from the Von Bertalanffy growth curve, one appropriated for Nasutitermes coxipoensis, and a more general formulation. The mean height and the mean diameter of ten small colonies were measured each month for twelve months, from April, 1995 to April, 1996. Through these data, the monthly volumes were calculated for each of them. Then the growth in height and in volume was estimated and the models proposed.

  12. Experimental Analysis and Mathematical Modeling on Mg-Li Alloy Sheets with Three Crystal Structures during Cold Rolling and Heat Treatment.

    PubMed

    Tang, Yan; Le, Qichi; Wang, Tong; Chen, Xingrui

    2017-10-12

    The microstructural evolution, mechanical properties, and mathematical relationship of an α, α + β, and β phase Mg-Li alloy during the cold rolling and annealing process were investigated. The results showed that the increased Li element gradually transformed the Mg matrix structure from hcp to bcc. Simultaneously, the alloy plasticity was improved remarkably during cold rolling. In the annealing process, a sort of abnormal grain growth was found in Mg-11Li-3Al-2Zn-0.2Y, but was not detected in Mg-5Li-3Al-2Zn-0.2Y and Mg-8Li-3Al-2Zn-0.2Y. Moreover, the mechanical properties of alloy were evidently improved through a kind of solid solution in the β matrix. To accurately quantify this strengthening effect, the method of mathematical modeling was used to determine the relationship between strength and multiple factors.

  13. Conceptualization of Approaches and Thought Processes Emerging in Validating of Model in Mathematical Modeling in Technology Aided Environment

    ERIC Educational Resources Information Center

    Hidiroglu, Çaglar Naci; Bukova Güzel, Esra

    2013-01-01

    The aim of the present study is to conceptualize the approaches displayed for validation of model and thought processes provided in mathematical modeling process performed in technology-aided learning environment. The participants of this grounded theory study were nineteen secondary school mathematics student teachers. The data gathered from the…

  14. Modelling a Simple Mechanical System.

    ERIC Educational Resources Information Center

    Morland, Tim

    1999-01-01

    Provides an example of the modeling power of Mathematics, demonstrated in a piece of A-Level student coursework which was undertaken as part of the MEI Structured Mathematics scheme. A system of two masses and two springs oscillating in one dimension is found to be accurately modeled by a system of linear differential equations. (Author/ASK)

  15. Accurate Modeling of Ionospheric Electromagnetic Fields Generated by a Low Altitude VLF Transmitter

    DTIC Science & Technology

    2009-03-31

    AFRL-RV-HA-TR-2009-1055 Accurate Modeling of Ionospheric Electromagnetic Fields Generated by a Low Altitude VLF Transmitter ...m (or even 500 m) at mid to high latitudes . At low latitudes , the FDTD model exhibits variations that make it difficult to determine a reliable...Scientific, Final 3. DATES COVERED (From - To) 02-08-2006 – 31-12-2008 4. TITLE AND SUBTITLE Accurate Modeling of Ionospheric Electromagnetic Fields

  16. Predicting data saturation in qualitative surveys with mathematical models from ecological research.

    PubMed

    Tran, Viet-Thi; Porcher, Raphael; Tran, Viet-Chi; Ravaud, Philippe

    2017-02-01

    Sample size in surveys with open-ended questions relies on the principle of data saturation. Determining the point of data saturation is complex because researchers have information on only what they have found. The decision to stop data collection is solely dictated by the judgment and experience of researchers. In this article, we present how mathematical modeling may be used to describe and extrapolate the accumulation of themes during a study to help researchers determine the point of data saturation. The model considers a latent distribution of the probability of elicitation of all themes and infers the accumulation of themes as arising from a mixture of zero-truncated binomial distributions. We illustrate how the model could be used with data from a survey with open-ended questions on the burden of treatment involving 1,053 participants from 34 different countries and with various conditions. The performance of the model in predicting the number of themes to be found with the inclusion of new participants was investigated by Monte Carlo simulations. Then, we tested how the slope of the expected theme accumulation curve could be used as a stopping criterion for data collection in surveys with open-ended questions. By doubling the sample size after the inclusion of initial samples of 25 to 200 participants, the model reliably predicted the number of themes to be found. Mean estimation error ranged from 3% to 1% with simulated data and was <2% with data from the study of the burden of treatment. Sequentially calculating the slope of the expected theme accumulation curve for every five new participants included was a feasible approach to balance the benefits of including these new participants in the study. In our simulations, a stopping criterion based on a value of 0.05 for this slope allowed for identifying 97.5% of the themes while limiting the inclusion of participants eliciting nothing new in the study. Mathematical models adapted from ecological research

  17. A systematic approach for the accurate non-invasive estimation of blood glucose utilizing a novel light-tissue interaction adaptive modelling scheme

    NASA Astrophysics Data System (ADS)

    Rybynok, V. O.; Kyriacou, P. A.

    2007-10-01

    Diabetes is one of the biggest health challenges of the 21st century. The obesity epidemic, sedentary lifestyles and an ageing population mean prevalence of the condition is currently doubling every generation. Diabetes is associated with serious chronic ill health, disability and premature mortality. Long-term complications including heart disease, stroke, blindness, kidney disease and amputations, make the greatest contribution to the costs of diabetes care. Many of these long-term effects could be avoided with earlier, more effective monitoring and treatment. Currently, blood glucose can only be monitored through the use of invasive techniques. To date there is no widely accepted and readily available non-invasive monitoring technique to measure blood glucose despite the many attempts. This paper challenges one of the most difficult non-invasive monitoring techniques, that of blood glucose, and proposes a new novel approach that will enable the accurate, and calibration free estimation of glucose concentration in blood. This approach is based on spectroscopic techniques and a new adaptive modelling scheme. The theoretical implementation and the effectiveness of the adaptive modelling scheme for this application has been described and a detailed mathematical evaluation has been employed to prove that such a scheme has the capability of extracting accurately the concentration of glucose from a complex biological media.

  18. Mathematical and computational modeling simulation of solar drying Systems

    USDA-ARS?s Scientific Manuscript database

    Mathematical modeling of solar drying systems has the primary aim of predicting the required drying time for a given commodity, dryer type, and environment. Both fundamental (Fickian diffusion) and semi-empirical drying models have been applied to the solar drying of a variety of agricultural commo...

  19. Methodology and Results of Mathematical Modelling of Complex Technological Processes

    NASA Astrophysics Data System (ADS)

    Mokrova, Nataliya V.

    2018-03-01

    The methodology of system analysis allows us to draw a mathematical model of the complex technological process. The mathematical description of the plasma-chemical process was proposed. The importance the quenching rate and initial temperature decrease time was confirmed for producing the maximum amount of the target product. The results of numerical integration of the system of differential equations can be used to describe reagent concentrations, plasma jet rate and temperature in order to achieve optimal mode of hardening. Such models are applicable both for solving control problems and predicting future states of sophisticated technological systems.

  20. Mathematical models and photogrammetric exploitation of image sensing

    NASA Astrophysics Data System (ADS)

    Puatanachokchai, Chokchai

    Mathematical models of image sensing are generally categorized into physical/geometrical sensor models and replacement sensor models. While the former is determined from image sensing geometry, the latter is based on knowledge of the physical/geometric sensor models and on using such models for its implementation. The main thrust of this research is in replacement sensor models which have three important characteristics: (1) Highly accurate ground-to-image functions; (2) Rigorous error propagation that is essentially of the same accuracy as the physical model; and, (3) Adjustability, or the ability to upgrade the replacement sensor model parameters when additional control information becomes available after the replacement sensor model has replaced the physical model. In this research, such replacement sensor models are considered as True Replacement Models or TRMs. TRMs provide a significant advantage of universality, particularly for image exploitation functions. There have been several writings about replacement sensor models, and except for the so called RSM (Replacement Sensor Model as a product described in the Manual of Photogrammetry), almost all of them pay very little or no attention to errors and their propagation. This is because, it is suspected, the few physical sensor parameters are usually replaced by many more parameters, thus presenting a potential error estimation difficulty. The third characteristic, adjustability, is perhaps the most demanding. It provides an equivalent flexibility to that of triangulation using the physical model. Primary contributions of this thesis include not only "the eigen-approach", a novel means of replacing the original sensor parameter covariance matrices at the time of estimating the TRM, but also the implementation of the hybrid approach that combines the eigen-approach with the added parameters approach used in the RSM. Using either the eigen-approach or the hybrid approach, rigorous error propagation can be

  1. Mathematical model of highways network optimization

    NASA Astrophysics Data System (ADS)

    Sakhapov, R. L.; Nikolaeva, R. V.; Gatiyatullin, M. H.; Makhmutov, M. M.

    2017-12-01

    The article deals with the issue of highways network design. Studies show that the main requirement from road transport for the road network is to ensure the realization of all the transport links served by it, with the least possible cost. The goal of optimizing the network of highways is to increase the efficiency of transport. It is necessary to take into account a large number of factors that make it difficult to quantify and qualify their impact on the road network. In this paper, we propose building an optimal variant for locating the road network on the basis of a mathematical model. The article defines the criteria for optimality and objective functions that reflect the requirements for the road network. The most fully satisfying condition for optimality is the minimization of road and transport costs. We adopted this indicator as a criterion of optimality in the economic-mathematical model of a network of highways. Studies have shown that each offset point in the optimal binding road network is associated with all other corresponding points in the directions providing the least financial costs necessary to move passengers and cargo from this point to the other corresponding points. The article presents general principles for constructing an optimal network of roads.

  2. Humanize Your Classroom with the History of Mathematics.

    ERIC Educational Resources Information Center

    Bidwell, James K.

    1993-01-01

    History humanizes mathematics and explains the "whys" by showing its logical development. Communicating, connecting, and valuing of mathematics can be effected by interjecting historical moments, reading biographies, creating displays for the classroom, and tracing historically accurate developments of topics in class. (Contains 26…

  3. A model of professional competences in mathematics to update mathematical and didactic knowledge of teachers

    NASA Astrophysics Data System (ADS)

    Díaz, Verónica; Poblete, Alvaro

    2017-07-01

    This paper describes part of a research and development project carried out in public elementary schools. Its objective was to update the mathematical and didactic knowledge of teachers in two consecutive levels in urban and rural public schools of Region de Los Lagos and Region de Los Rios of southern Chile. To that effect, and by means of an advanced training project based on a professional competences model, didactic interventions based on types of problems and types of mathematical competences with analysis of contents and learning assessment were designed. The teachers' competence regarding the didactic strategy used and its results, as well as the students' learning achievements are specified. The project made possible to validate a strategy of lifelong improvement in mathematics, based on the professional competences of teachers and their didactic transposition in the classroom, as an alternative to consolidate learning in areas considered vulnerable in two regions of the country.

  4. Investigating the Representational Fluency of Pre-Service Mathematics Teachers in a Modelling Process

    ERIC Educational Resources Information Center

    Delice, Ali; Kertil, Mahmut

    2015-01-01

    This article reports the results of a study that investigated pre-service mathematics teachers' modelling processes in terms of representational fluency in a modelling activity related to a cassette player. A qualitative approach was used in the data collection process. Students' individual and group written responses to the mathematical modelling…

  5. [Three dimensional mathematical model of tooth for finite element analysis].

    PubMed

    Puskar, Tatjana; Vasiljević, Darko; Marković, Dubravka; Jevremović, Danimir; Pantelić, Dejan; Savić-Sević, Svetlana; Murić, Branka

    2010-01-01

    The mathematical model of the abutment tooth is the starting point of the finite element analysis of stress and deformation of dental structures. The simplest and easiest way is to form a model according to the literature data of dimensions and morphological characteristics of teeth. Our method is based on forming 3D models using standard geometrical forms (objects) in programmes for solid modeling. Forming the mathematical model of abutment of the second upper premolar for finite element analysis of stress and deformation of dental structures. The abutment tooth has a form of a complex geometric object. It is suitable for modeling in programs for solid modeling SolidWorks. After analysing the literature data about the morphological characteristics of teeth, we started the modeling dividing the tooth (complex geometric body) into simple geometric bodies (cylinder, cone, pyramid,...). Connecting simple geometric bodies together or substricting bodies from the basic body, we formed complex geometric body, tooth. The model is then transferred into Abaqus, a computational programme for finite element analysis. Transferring the data was done by standard file format for transferring 3D models ACIS SAT. Using the programme for solid modeling SolidWorks, we developed three models of abutment of the second maxillary premolar: the model of the intact abutment, the model of the endodontically treated tooth with two remaining cavity walls and the model of the endodontically treated tooth with two remaining walls and inserted post. Mathematical models of the abutment made according to the literature data are very similar with the real abutment and the simplifications are minimal. These models enable calculations of stress and deformation of the dental structures. The finite element analysis provides useful information in understanding biomechanical problems and gives guidance for clinical research.

  6. Analysis mathematical literacy skills in terms of the students’ metacognition on PISA-CPS model

    NASA Astrophysics Data System (ADS)

    Ovan; Waluya, S. B.; Nugroho, S. E.

    2018-03-01

    This research was aimed to know the effectiveness of PISA-CPS model and desceibe the mathematical literacy skills (KLM) in terms of the students’ metacognition. This study used Mixed Methods approaches with the concurrent embedded desaign. The technique of data analysis on quantitative research done analysis of lesson plan, prerequisite test, test hypotesis 1 and hypotesis test. While qualitative research done data reduction, data presentation, and drawing conclution and data verification. The subject of this study was the students of Grade Eight (VIII) of SMP Islam Sultan Agung 4 Semarang, Central Java. The writer analyzed the data with quantitative and qualitative approaches based on the metacognition of the students in low, medium and high groups. Subsequently, taken the mathematical literacy skills (KLM) from students’ metacognition in low, medium, and high . The results of the study showed that the PISA-CPS model was complete and the students’ mathematical literacy skills in terms of the students’ metacognition taught by the PISA-CPS model was higher than the expository learning. metacognitions’ students classified low hadmathematical literacy skills (KLM) less good, metacognitions’ students classified medium had mathematical literacy skills (KLM) good enough, metacognitions’ students classified high had mathematical literacy skills (KLM) very good. Based onresult analysis got conclusion that the PISA-CPS model was effective toward the students’ mathematical literacy skills (KLM). To increase the students’ mathematical literacy skills (KLM), the teachers need to provide reinforcements in the form of the exercises so that the student’s mathematical literacy was achieved at level 5 and level 6.

  7. An accurate halo model for fitting non-linear cosmological power spectra and baryonic feedback models

    NASA Astrophysics Data System (ADS)

    Mead, A. J.; Peacock, J. A.; Heymans, C.; Joudaki, S.; Heavens, A. F.

    2015-12-01

    We present an optimized variant of the halo model, designed to produce accurate matter power spectra well into the non-linear regime for a wide range of cosmological models. To do this, we introduce physically motivated free parameters into the halo-model formalism and fit these to data from high-resolution N-body simulations. For a variety of Λ cold dark matter (ΛCDM) and wCDM models, the halo-model power is accurate to ≃ 5 per cent for k ≤ 10h Mpc-1 and z ≤ 2. An advantage of our new halo model is that it can be adapted to account for the effects of baryonic feedback on the power spectrum. We demonstrate this by fitting the halo model to power spectra from the OWLS (OverWhelmingly Large Simulations) hydrodynamical simulation suite via parameters that govern halo internal structure. We are able to fit all feedback models investigated at the 5 per cent level using only two free parameters, and we place limits on the range of these halo parameters for feedback models investigated by the OWLS simulations. Accurate predictions to high k are vital for weak-lensing surveys, and these halo parameters could be considered nuisance parameters to marginalize over in future analyses to mitigate uncertainty regarding the details of feedback. Finally, we investigate how lensing observables predicted by our model compare to those from simulations and from HALOFIT for a range of k-cuts and feedback models and quantify the angular scales at which these effects become important. Code to calculate power spectra from the model presented in this paper can be found at https://github.com/alexander-mead/hmcode.

  8. An Examination of Preservice Teachers' Capacity to Create Mathematical Modeling Problems for Children

    ERIC Educational Resources Information Center

    Paolucci, Catherine; Wessels, Helena

    2017-01-01

    This study examined preservice teachers' (PSTs) capacity to create mathematical modeling problems (MMPs) for grades 1 to 3. PSTs created MMPs for their choice of grade level and aligned the mathematical content of their MMPs with the relevant mathematics curriculum. PSTs were given criteria adapted from Galbraith's MMP design principles to guide…

  9. V/STOL tilt rotor study. Volume 5: A mathematical model for real time flight simulation of the Bell model 301 tilt rotor research aircraft

    NASA Technical Reports Server (NTRS)

    Harendra, P. B.; Joglekar, M. J.; Gaffey, T. M.; Marr, R. L.

    1973-01-01

    A mathematical model for real-time flight simulation of a tilt rotor research aircraft was developed. The mathematical model was used to support the aircraft design, pilot training, and proof-of-concept aspects of the development program. The structure of the mathematical model is indicated by a block diagram. The mathematical model differs from that for a conventional fixed wing aircraft principally in the added requirement to represent the dynamics and aerodynamics of the rotors, the interaction of the rotor wake with the airframe, and the rotor control and drive systems. The constraints imposed on the mathematical model are defined.

  10. Mathematical Analysis of an SIQR Influenza Model with Imperfect Quarantine.

    PubMed

    Erdem, Mustafa; Safan, Muntaser; Castillo-Chavez, Carlos

    2017-07-01

    The identification of mechanisms responsible for recurrent epidemic outbreaks, such as age structure, cross-immunity and variable delays in the infective classes, has challenged and fascinated epidemiologists and mathematicians alike. This paper addresses, motivated by mathematical work on influenza models, the impact of imperfect quarantine on the dynamics of SIR-type models. A susceptible-infectious-quarantine-recovered (SIQR) model is formulated with quarantined individuals altering the transmission dynamics process through their possibly reduced ability to generate secondary cases of infection. Mathematical and numerical analyses of the model of the equilibria and their stability have been carried out. Uniform persistence of the model has been established. Numerical simulations show that the model supports Hopf bifurcation as a function of the values of the quarantine effectiveness and other parameters. The upshot of this work is somewhat surprising since it is shown that SIQR model oscillatory behavior, as shown by multiple researchers, is in fact not robust to perturbations in the quarantine regime.

  11. Generalized mathematical model of red muds’ thickener of alumina production

    NASA Astrophysics Data System (ADS)

    Fedorova, E. R.; Vinogradova, A. A.

    2018-03-01

    The article describes the principle of a generalized mathematical model of the red mud’s thickener construction. The model of the red muds’ thickener of alumina production consists of sub-models of flocculation zones containing solid fraction feed slurry, free-fall and cramped sedimentation zones or effective sedimentation zones, bleaching zones. The generalized mathematical model of thickener allows predicting the content of solid fraction in the condensed product and in the upper discharge. The sub-model of solid phase aggregation allows one to count up average size of floccules, which is created during the flocculation process in feedwell. The sub-model of the free-fall and cramped sedimentation zone allows one to count up the concentration profile taking into account the variable cross-sectional area of the thickener. The sub-model of the bleaching zone is constructed on the basis of the theory of the precipitation of Kinc, supplemented by correction factors.

  12. Mathematical modeling and design of a novel 2-DOF micro attraction actuator for a micro optical switch

    NASA Astrophysics Data System (ADS)

    Kamiya, Daiki; Bagheri, Saeed; Horie, Mikio

    2004-08-01

    Many studies on optical switches have been performed in an attempt to develop optical information networks to speed information technology. In reality, however, mirror manipulators cannot be applied to multiple input and output systems due to both insufficient output displacements by the mirror parts inside the manipulator, and the difficulty of designing structures and mechanisms suitable for multi-dimensional manipulation. The principal reasons for insufficient displacement are the high rigidity of the elastic parts compared to the available driving forces and the pull-in effect. Therefore, in order to develop optical switches capable of multiple input and output switching, we suggest a novel 2-DOF(degree of freedom) electrostatic microactuator. The actuator is composed of one mirror with four beams laid about it in a corkscrew pattern, with four corkscrew electrodes on the substrate below and one mirror support pyramid situated under the mirror. Using electrostatic force, one or more of the beams are attracted from their outer ends toward the substrate. The mirror is then tilted by an angle proportional to the attracted length along the beam. The inclination and direction of the mirror are determined by the combined attracted length of the four beams. In this work we derive the mathematical model for the corkscrew beam microactuator for optical switches and show that this mathematical model accurately simulates the device by comparison with finite element analysis results. We use this mathematical model for design of the microactuator. Further we show that the designed optical switch microactuator is capable of rotating the mirror from +32 to -32 degrees about two axes with a maximum operating voltage of 163 volts. Finally, stress analysis of the actuator shows that the generated stress in the structure is at most 369 MPa.

  13. Mathematical model of design loading vessel

    NASA Astrophysics Data System (ADS)

    Budnik, V. Yu

    2017-10-01

    Transport by ferry is very important in our time. The paper shows the factors that affect the operation of the ferry. The constraints of the designed system were identified. The indicators of quality were articulated. It can be done by means of improving the decision-making process and the choice of the optimum loading options to ensure efficient functioning of Kerch strait ferry line. The algorithm and a mathematical model were developed.

  14. The Effects of Mathematical Modeling on Creative Production Ability and Self-Directed Learning Attitude

    ERIC Educational Resources Information Center

    Kim, Sun Hee; Kim, Soojin

    2010-01-01

    What should we do to educate the mathematically gifted and how should we do it? In this research, to satisfy diverse mathematical and cognitive demands of the gifted who have excellent learning ability and task tenacity in mathematics, we sought to apply mathematical modeling. One of the objectives of the gifted education in Korea is cultivating…

  15. Mathematical modeling of drug dissolution.

    PubMed

    Siepmann, J; Siepmann, F

    2013-08-30

    The dissolution of a drug administered in the solid state is a pre-requisite for efficient subsequent transport within the human body. This is because only dissolved drug molecules/ions/atoms are able to diffuse, e.g. through living tissue. Thus, generally major barriers, including the mucosa of the gastro intestinal tract, can only be crossed after dissolution. Consequently, the process of dissolution is of fundamental importance for the bioavailability and, hence, therapeutic efficacy of various pharmaco-treatments. Poor aqueous solubility and/or very low dissolution rates potentially lead to insufficient availability at the site of action and, hence, failure of the treatment in vivo, despite a potentially ideal chemical structure of the drug to interact with its target site. Different physical phenomena are involved in the process of drug dissolution in an aqueous body fluid, namely the wetting of the particle's surface, breakdown of solid state bonds, solvation, diffusion through the liquid unstirred boundary layer surrounding the particle as well as convection in the surrounding bulk fluid. Appropriate mathematical equations can be used to quantify these mass transport steps, and more or less complex theories can be developed to describe the resulting drug dissolution kinetics. This article gives an overview on the current state of the art of modeling drug dissolution and points out the assumptions the different theories are based on. Various practical examples are given in order to illustrate the benefits of such models. This review is not restricted to mathematical theories considering drugs exhibiting poor aqueous solubility and/or low dissolution rates, but also addresses models quantifying drug release from controlled release dosage forms, in which the process of drug dissolution plays a major role. Copyright © 2013 Elsevier B.V. All rights reserved.

  16. Performance analysis on free-piston Stirling cryocooler based on an idealized mathematical model

    NASA Astrophysics Data System (ADS)

    Guo, Y. X.; Chao, Y. J.; Gan, Z. H.; Li, S. Z.; Wang, B.

    2017-12-01

    Free-piston Stirling cryocoolers have extensive applications for its simplicity in structure and decrease in mass. However, the elimination of the motor and the crankshaft has made its thermodynamic characteristic different from that of Stirling cryocoolers with displacer driving mechanism. Therefore, an idealized mathematical model has been established, and with this model, an attempt has been made to analyse the thermodynamic characteristic and the performance of free-piston Stirling cryocooler. To certify this mathematical model, a comparison has been made between the model and a numerical model. This study reveals that due to the displacer damping force necessary for the production of cooling capacity, the free-piston Stirling cryocooler is inherently less efficient than Stirling cryocooler with displacer driving mechanism. Viscous flow resistance and incomplete heat transfer in the regenerator are the two major causes of the discrepancy between the results of the idealized mathematical model and the numerical model.

  17. On accurate determination of contact angle

    NASA Technical Reports Server (NTRS)

    Concus, P.; Finn, R.

    1992-01-01

    Methods are proposed that exploit a microgravity environment to obtain highly accurate measurement of contact angle. These methods, which are based on our earlier mathematical results, do not require detailed measurement of a liquid free-surface, as they incorporate discontinuous or nearly-discontinuous behavior of the liquid bulk in certain container geometries. Physical testing is planned in the forthcoming IML-2 space flight and in related preparatory ground-based experiments.

  18. A structural equation modeling analysis of students' understanding in basic mathematics

    NASA Astrophysics Data System (ADS)

    Oktavia, Rini; Arif, Salmawaty; Ferdhiana, Ridha; Yuni, Syarifah Meurah; Ihsan, Mahyus

    2017-11-01

    This research, in general, aims to identify incoming students' understanding and misconceptions of several basic concepts in mathematics. The participants of this study are the 2015 incoming students of Faculty of Mathematics and Natural Science of Syiah Kuala University, Indonesia. Using an instrument that were developed based on some anecdotal and empirical evidences on students' misconceptions, a survey involving 325 participants was administered and several quantitative and qualitative analysis of the survey data were conducted. In this article, we discuss the confirmatory factor analysis using Structural Equation Modeling (SEM) on factors that determine the new students' overall understanding of basic mathematics. The results showed that students' understanding on algebra, arithmetic, and geometry were significant predictors for their overall understanding of basic mathematics. This result supported that arithmetic and algebra are not the only predictors of students' understanding of basic mathematics.

  19. Zoonotic Transmission of Waterborne Disease: A Mathematical Model.

    PubMed

    Waters, Edward K; Hamilton, Andrew J; Sidhu, Harvinder S; Sidhu, Leesa A; Dunbar, Michelle

    2016-01-01

    Waterborne parasites that infect both humans and animals are common causes of diarrhoeal illness, but the relative importance of transmission between humans and animals and vice versa remains poorly understood. Transmission of infection from animals to humans via environmental reservoirs, such as water sources, has attracted attention as a potential source of endemic and epidemic infections, but existing mathematical models of waterborne disease transmission have limitations for studying this phenomenon, as they only consider contamination of environmental reservoirs by humans. This paper develops a mathematical model that represents the transmission of waterborne parasites within and between both animal and human populations. It also improves upon existing models by including animal contamination of water sources explicitly. Linear stability analysis and simulation results, using realistic parameter values to describe Giardia transmission in rural Australia, show that endemic infection of an animal host with zoonotic protozoa can result in endemic infection in human hosts, even in the absence of person-to-person transmission. These results imply that zoonotic transmission via environmental reservoirs is important.

  20. Mathematical Modelling of Bacterial Populations in Bio-remediation Processes

    NASA Astrophysics Data System (ADS)

    Vasiliadou, Ioanna A.; Vayenas, Dimitris V.; Chrysikopoulos, Constantinos V.

    2011-09-01

    An understanding of bacterial behaviour concerns many field applications, such as the enhancement of water, wastewater and subsurface bio-remediation, the prevention of environmental pollution and the protection of human health. Numerous microorganisms have been identified to be able to degrade chemical pollutants, thus, a variety of bacteria are known that can be used in bio-remediation processes. In this study the development of mathematical models capable of describing bacterial behaviour considered in bio-augmentation plans, such as bacterial growth, consumption of nutrients, removal of pollutants, bacterial transport and attachment in porous media, is presented. The mathematical models may be used as a guide in designing and assessing the conditions under which areas contaminated with pollutants can be better remediated.

  1. Technology Modeling by Mathematics Professors in Required Courses for Secondary Mathematics Pre-Service Teachers: A Case Study in Two Universities

    ERIC Educational Resources Information Center

    Asing-Cashman, Joyce G.

    2011-01-01

    The purpose of this qualitative case study was to examine the modeling of technology by mathematics professors in two universities in teaching required courses for secondary level pre-service mathematics teachers. Six professors participated in this case study. Their responses were documented in pre- and post-interviews and data were gathered from…

  2. Mathematical interpretation of Brownian motor model: Limit cycles and directed transport phenomena

    NASA Astrophysics Data System (ADS)

    Yang, Jianqiang; Ma, Hong; Zhong, Suchuang

    2018-03-01

    In this article, we first suggest that the attractor of Brownian motor model is one of the reasons for the directed transport phenomenon of Brownian particle. We take the classical Smoluchowski-Feynman (SF) ratchet model as an example to investigate the relationship between limit cycles and directed transport phenomenon of the Brownian particle. We study the existence and variation rule of limit cycles of SF ratchet model at changing parameters through mathematical methods. The influences of these parameters on the directed transport phenomenon of a Brownian particle are then analyzed through numerical simulations. Reasonable mathematical explanations for the directed transport phenomenon of Brownian particle in SF ratchet model are also formulated on the basis of the existence and variation rule of the limit cycles and numerical simulations. These mathematical explanations provide a theoretical basis for applying these theories in physics, biology, chemistry, and engineering.

  3. Authentic Integration: a model for integrating mathematics and science in the classroom

    NASA Astrophysics Data System (ADS)

    Treacy, Páraic; O'Donoghue, John

    2014-07-01

    Attempts at integrating mathematics and science have been made previously but no definitive, widely adopted teaching model has been developed to date. Research suggests that hands-on, practical, student-centred tasks should form a central element when designing an effective model for the integration of mathematics and science. Aided by this research, the author created a new model entitled 'Authentic Integration' which caters for the specific needs of integration of mathematics and science. This model requires that each lesson be based around a rich task which relates to the real world and ensures that hands-on group work, inquiry, and discussion are central to the lesson. It was found that Authentic Integration, when applied in four Irish post-primary schools, positively affected pupil understanding. The teachers who completed the intervention displayed a very positive attitude towards the approach, intimating that they would continue to implement the practice in their classrooms.

  4. 2016 KIVA-hpFE Development: A Robust and Accurate Engine Modeling Software

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Carrington, David Bradley; Waters, Jiajia

    Los Alamos National Laboratory and its collaborators are facilitating engine modeling by improving accuracy and robustness of the modeling, and improving the robustness of software. We also continue to improve the physical modeling methods. We are developing and implementing new mathematical algorithms, those that represent the physics within an engine. We provide software that others may use directly or that they may alter with various models e.g., sophisticated chemical kinetics, different turbulent closure methods or other fuel injection and spray systems.

  5. Secondary School Students' Construction and Use of Mathematical Models in Solving Word Problems

    ERIC Educational Resources Information Center

    Llinares, Salvador; Roig, Ana Isabel

    2008-01-01

    This study focussed on how secondary school students construct and use mathematical models as conceptual tools when solving word problems. The participants were 511 secondary-school students who were in the final year of compulsory education (15-16 years old). Four levels of the development of constructing and using mathematical models were…

  6. A mathematical model for late term cancer chemotherapy

    NASA Astrophysics Data System (ADS)

    Izard, Zac; Hirschbeck, Sarah; Volk, Christian; Shojania Feizabadi, Mitra

    2006-03-01

    A mathematical model for cancer treated with the ``on-off'' type where the drug is either active or inactive and when the chemotherapeutic treatment only affects the cycling cells is presented. This model is considered for late term chemotherapy when the total population of cells doesn't show a significant change. The size of the cycling cells as a function of time has been investigated.

  7. Allele-sharing models: LOD scores and accurate linkage tests.

    PubMed

    Kong, A; Cox, N J

    1997-11-01

    Starting with a test statistic for linkage analysis based on allele sharing, we propose an associated one-parameter model. Under general missing-data patterns, this model allows exact calculation of likelihood ratios and LOD scores and has been implemented by a simple modification of existing software. Most important, accurate linkage tests can be performed. Using an example, we show that some previously suggested approaches to handling less than perfectly informative data can be unacceptably conservative. Situations in which this model may not perform well are discussed, and an alternative model that requires additional computations is suggested.

  8. Allele-sharing models: LOD scores and accurate linkage tests.

    PubMed Central

    Kong, A; Cox, N J

    1997-01-01

    Starting with a test statistic for linkage analysis based on allele sharing, we propose an associated one-parameter model. Under general missing-data patterns, this model allows exact calculation of likelihood ratios and LOD scores and has been implemented by a simple modification of existing software. Most important, accurate linkage tests can be performed. Using an example, we show that some previously suggested approaches to handling less than perfectly informative data can be unacceptably conservative. Situations in which this model may not perform well are discussed, and an alternative model that requires additional computations is suggested. PMID:9345087

  9. Bell's Inequality: Revolution in Quantum Physics or Just AN Inadequate Mathematical Model?

    NASA Astrophysics Data System (ADS)

    Khrennikov, Andrei

    The main aim of this review is to stress the role of mathematical models in physics. The Bell inequality (BI) is often called the "most famous inequality of the 20th century." It is commonly accepted that its violation in corresponding experiments induced a revolution in quantum physics. Unlike "old quantum mechanics" (of Einstein, Schrodinger Bohr, Heisenberg, Pauli, Landau, Fock), "modern quantum mechanics" (of Bell, Aspect, Zeilinger, Shimony, Green-berger, Gisin, Mermin) takes seriously so called quantum non-locality. We will show that the conclusion that one has to give up the realism (i.e., a possibility to assign results of measurements to physical systems) or the locality (i.e., to assume action at a distance) is heavily based on one special mathematical model. This model was invented by A. N. Kolmogorov in 1933. One should pay serious attention to the role of mathematical models in physics. The problems of the realism and locality induced by Bell's argument can be solved by using non-Kolmogorovian probabilistic models. We compare this situation with non-Euclidean geometric models in relativity theory.

  10. Mathematical modeling of human cardiovascular system for simulation of orthostatic response

    NASA Technical Reports Server (NTRS)

    Melchior, F. M.; Srinivasan, R. S.; Charles, J. B.

    1992-01-01

    This paper deals with the short-term response of the human cardiovascular system to orthostatic stresses in the context of developing a mathematical model of the overall system. It discusses the physiological issues involved and how these issues have been handled in published cardiovascular models for simulation of orthostatic response. Most of the models are stimulus specific with no demonstrated capability for simulating the responses to orthostatic stimuli of different types. A comprehensive model incorporating all known phenomena related to cardiovascular regulation would greatly help to interpret the various orthostatic responses of the system in a consistent manner and to understand the interactions among its elements. This paper provides a framework for future efforts in mathematical modeling of the entire cardiovascular system.

  11. Missing the Promise of Mathematical Modeling

    ERIC Educational Resources Information Center

    Meyer, Dan

    2015-01-01

    The Common Core State Standards for Mathematics (CCSSM) have exerted enormous pressure on every participant in a child's education. Students are struggling to meet new standards for mathematics learning, and parents are struggling to understand how to help them. Teachers are growing in their capacity to develop new mathematical competencies, and…

  12. Fast and accurate calculation of dilute quantum gas using Uehling–Uhlenbeck model equation

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Yano, Ryosuke, E-mail: ryosuke.yano@tokiorisk.co.jp

    The Uehling–Uhlenbeck (U–U) model equation is studied for the fast and accurate calculation of a dilute quantum gas. In particular, the direct simulation Monte Carlo (DSMC) method is used to solve the U–U model equation. DSMC analysis based on the U–U model equation is expected to enable the thermalization to be accurately obtained using a small number of sample particles and the dilute quantum gas dynamics to be calculated in a practical time. Finally, the applicability of DSMC analysis based on the U–U model equation to the fast and accurate calculation of a dilute quantum gas is confirmed by calculatingmore » the viscosity coefficient of a Bose gas on the basis of the Green–Kubo expression and the shock layer of a dilute Bose gas around a cylinder.« less

  13. Mathematical modeling analysis of intratumoral disposition of anticancer agents and drug delivery systems.

    PubMed

    Popilski, Hen; Stepensky, David

    2015-05-01

    Solid tumors are characterized by complex morphology. Numerous factors relating to the composition of the cells and tumor stroma, vascularization and drainage of fluids affect the local microenvironment within a specific location inside the tumor. As a result, the intratumoral drug/drug delivery system (DDS) disposition following systemic or local administration is non-homogeneous and its complexity reflects the differences in the local microenvironment. Mathematical models can be used to analyze the intratumoral drug/DDS disposition and pharmacological effects and to assist in choice of optimal anticancer treatment strategies. The mathematical models that have been applied by different research groups to describe the intratumoral disposition of anticancer drugs/DDSs are summarized in this article. The properties of these models and of their suitability for prediction of the drug/DDS intratumoral disposition and pharmacological effects are reviewed. Currently available mathematical models appear to neglect some of the major factors that govern the drug/DDS intratumoral disposition, and apparently possess limited prediction capabilities. More sophisticated and detailed mathematical models and their extensive validation are needed for reliable prediction of different treatment scenarios and for optimization of drug treatment in the individual cancer patients.

  14. Aerodynamic mathematical modeling - basic concepts

    NASA Technical Reports Server (NTRS)

    Tobak, M.; Schiff, L. B.

    1981-01-01

    The mathematical modeling of the aerodynamic response of an aircraft to arbitrary maneuvers is reviewed. Bryan's original formulation, linear aerodynamic indicial functions, and superposition are considered. These concepts are extended into the nonlinear regime. The nonlinear generalization yields a form for the aerodynamic response that can be built up from the responses to a limited number of well defined characteristic motions, reproducible in principle either in wind tunnel experiments or flow field computations. A further generalization leads to a form accommodating the discontinuous and double valued behavior characteristics of hysteresis in the steady state aerodynamic response.

  15. Biological-Mathematical Modeling of Chronic Toxicity.

    DTIC Science & Technology

    1981-07-22

    34Mathematical Model of Uptake and Distribution," Uptake and Distribution of Anesthetic Agents, E. M. Papper and R. J. Kitz (Editors, McGraw-Hill Book Co., Inc...distribution, In: Papper , E.M. and Kltz, R.J.(eds.) Uptake and distribution of anesthetic agents, McGraw- Hill, New York, p. 72 3. Plpleson, W.W...1963) Quantitative prediction of anesthetic concentrations. In: Papper , E.M. and Kitz, R.J. (eds.) Uptake and distribution of anesthetic agents, McGraw

  16. Mathematical Modeling of Ultraporous Nonmetallic Reticulated Materials

    NASA Astrophysics Data System (ADS)

    Alifanov, O. M.; Cherepanov, V. V.; Morzhukhina, A. V.

    2015-01-01

    We have developed an imitation statistical mathematical model reflecting the structure and the thermal, electrophysical, and optical properties of nonmetallic ultraporous reticulated materials. This model, in combination with a nonstationary thermal experiment and methods of the theory of inverse heat transfer problems, permits determining the little-studied characteristics of the above materials such as the radiative and conductive heat conductivities, the spectral scattering and absorption coefficients, the scattering indicatrix, and the dielectric constants, which are of great practical interest but are difficult to investigate.

  17. Mathematical models in simulation process in rehabilitation of persons with disabilities

    NASA Astrophysics Data System (ADS)

    Gorie, Nina; Dolga, Valer; Mondoc, Alina

    2012-11-01

    The problems of people with disability are varied. A disability may be physical, cognitive, mental, sensory, emotional, developmental or some combination of these. The major disabilities which can appear in people's lives are: the blindness, the deafness, the limb-girdle muscular dystrophy, the orthopedic impairment, the visual impairment. A disability is an umbrella term, covering impairments, activity limitations and participation restrictions. A disability may occur during a person's lifetime or may be present from birth. The authors conclude that some of these disabilities like physical, cognitive, mental, sensory, emotional, developmental can be rehabilitated. Starting from this state of affairs the authors present briefly the possibility of using certain mechatronic systems for rehabilitation of persons with different disabilities. The authors focus their presentation on alternative calling the Stewart platform in order to achieve the proposed goal. The authors present a mathematical model of systems theory approach under the parallel system and described its contents can. The authors analyze in a meaningful mathematical model describing the procedure of rehabilitation process. From the affected function biomechanics and taking into account medical recommendations the authors illustrate the mathematical models of rehabilitation work. The authors assemble a whole mathematical model of parallel structure and the rehabilitation process and making simulation and highlighting the results estimated. The authors present in the end work the results envisaged in the end analysis work, conclusions and steps for future work program..

  18. Mathematical model of a DIC position sensing system within an optical trap

    NASA Astrophysics Data System (ADS)

    Wulff, Kurt D.; Cole, Daniel G.; Clark, Robert L.

    2005-08-01

    The quantitative study of displacements and forces of motor proteins and processes that occur at the microscopic level and below require a high level of sensitivity. For optical traps, two techniques for position sensing have been accepted and used quite extensively: quadrant photodiodes and an interferometric position sensing technique based on DIC imaging. While quadrant photodiodes have been studied in depth and mathematically characterized, a mathematical characterization of the interferometric position sensor has not been presented to the authors' knowledge. The interferometric position sensing method works off of the DIC imaging capabilities of a microscope. Circularly polarized light is sent into the microscope and the Wollaston prism used for DIC imaging splits the beam into its orthogonal components, displacing them by a set distance determined by the user. The distance between the axes of the beams is set so the beams overlap at the specimen plane and effectively share the trapped microsphere. A second prism then recombines the light beams and the exiting laser light's polarization is measured and related to position. In this paper we outline the mathematical characterization of a microsphere suspended in an optical trap using a DIC position sensing method. The sensitivity of this mathematical model is then compared to the QPD model. The mathematical model of a microsphere in an optical trap can serve as a calibration curve for an experimental setup.

  19. Improving students’ mathematical critical thinking through rigorous teaching and learning model with informal argument

    NASA Astrophysics Data System (ADS)

    Hamid, H.

    2018-01-01

    The purpose of this study is to analyze an improvement of students’ mathematical critical thinking (CT) ability in Real Analysis course by using Rigorous Teaching and Learning (RTL) model with informal argument. In addition, this research also attempted to understand students’ CT on their initial mathematical ability (IMA). This study was conducted at a private university in academic year 2015/2016. The study employed the quasi-experimental method with pretest-posttest control group design. The participants of the study were 83 students in which 43 students were in the experimental group and 40 students were in the control group. The finding of the study showed that students in experimental group outperformed students in control group on mathematical CT ability based on their IMA (high, medium, low) in learning Real Analysis. In addition, based on medium IMA the improvement of mathematical CT ability of students who were exposed to RTL model with informal argument was greater than that of students who were exposed to CI (conventional instruction). There was also no effect of interaction between RTL model and CI model with both (high, medium, and low) IMA increased mathematical CT ability. Finally, based on (high, medium, and low) IMA there was a significant improvement in the achievement of all indicators of mathematical CT ability of students who were exposed to RTL model with informal argument than that of students who were exposed to CI.

  20. Preservice Secondary Teachers' Conceptions from a Mathematical Modeling Activity and Connections to the Common Core State Standards

    ERIC Educational Resources Information Center

    Stohlmann, Micah; Maiorca, Cathrine; Olson, Travis A.

    2015-01-01

    Mathematical modeling is an essential integrated piece of the Common Core State Standards. However, researchers have shown that mathematical modeling activities can be difficult for teachers to implement. Teachers are more likely to implement mathematical modeling activities if they have their own successful experiences with such activities. This…

  1. Applying Mathematical Optimization Methods to an ACT-R Instance-Based Learning Model.

    PubMed

    Said, Nadia; Engelhart, Michael; Kirches, Christian; Körkel, Stefan; Holt, Daniel V

    2016-01-01

    Computational models of cognition provide an interface to connect advanced mathematical tools and methods to empirically supported theories of behavior in psychology, cognitive science, and neuroscience. In this article, we consider a computational model of instance-based learning, implemented in the ACT-R cognitive architecture. We propose an approach for obtaining mathematical reformulations of such cognitive models that improve their computational tractability. For the well-established Sugar Factory dynamic decision making task, we conduct a simulation study to analyze central model parameters. We show how mathematical optimization techniques can be applied to efficiently identify optimal parameter values with respect to different optimization goals. Beyond these methodological contributions, our analysis reveals the sensitivity of this particular task with respect to initial settings and yields new insights into how average human performance deviates from potential optimal performance. We conclude by discussing possible extensions of our approach as well as future steps towards applying more powerful derivative-based optimization methods.

  2. Existence and characterization of optimal control in mathematics model of diabetics population

    NASA Astrophysics Data System (ADS)

    Permatasari, A. H.; Tjahjana, R. H.; Udjiani, T.

    2018-03-01

    Diabetes is a chronic disease with a huge burden affecting individuals and the whole society. In this paper, we constructed the optimal control mathematical model by applying a strategy to control the development of diabetic population. The constructed mathematical model considers the dynamics of disabled people due to diabetes. Moreover, an optimal control approach is proposed in order to reduce the burden of pre-diabetes. Implementation of control is done by preventing the pre-diabetes develop into diabetics with and without complications. The existence of optimal control and characterization of optimal control is discussed in this paper. Optimal control is characterized by applying the Pontryagin minimum principle. The results indicate that there is an optimal control in optimization problem in mathematics model of diabetic population. The effect of the optimal control variable (prevention) is strongly affected by the number of healthy people.

  3. Mathematical modeling of ignition of woodlands resulted from accident on the pipeline

    NASA Astrophysics Data System (ADS)

    Perminov, V. A.; Loboda, E. L.; Reyno, V. V.

    2014-11-01

    Accidents occurring at the sites of pipelines, accompanied by environmental damage, economic loss, and sometimes loss of life. In this paper we calculated the sizes of the possible ignition zones in emergency situations on pipelines located close to the forest, accompanied by the appearance of fireballs. In this paper, using the method of mathematical modeling calculates the maximum size of the ignition zones of vegetation as a result of accidental releases of flammable substances. The paper suggested in the context of the general mathematical model of forest fires give a new mathematical setting and method of numerical solution of a problem of a forest fire modeling. The boundary-value problem is solved numerically using the method of splitting according to physical processes. The dependences of the size of the forest fuel for different amounts of leaked flammable substances and moisture content of vegetation.

  4. Models of Intervention in Mathematics: Reweaving the Tapestry

    ERIC Educational Resources Information Center

    Fosnot, Catherine

    2010-01-01

    Explore successful models of intervention. No Child Left Behind has set the high expectation that every child meet grade level expectations. This publication synthesizes the research on intervention programs and best practices related to mathematical instructional pedagogy and differentiation to assist teachers, schools, and school districts in…

  5. A Mathematical Model of the Thermo-Anemometric Flowmeter

    PubMed Central

    Korobiichuk, Igor; Bezvesilna, Olena; Ilchenko, Andriі; Shadura, Valentina; Nowicki, Michał; Szewczyk, Roman

    2015-01-01

    A thermo-anemometric flowmeter design and the principles of its work are presented in the article. A mathematical model of the temperature field in a stream of biofuel is proposed. This model allows one to determine the fuel consumption with high accuracy. Numerical modeling of the heater heat balance in the fuel flow of a thermo-anemometric flowmeter is conducted and the results are analyzed. Methods for increasing the measurement speed and accuracy of a thermo-anemometric flowmeter are proposed. PMID:26378535

  6. A Mathematical Model of the Thermo-Anemometric Flowmeter.

    PubMed

    Korobiichuk, Igor; Bezvesilna, Olena; Ilchenko, Andriі; Shadura, Valentina; Nowicki, Michał; Szewczyk, Roman

    2015-09-11

    A thermo-anemometric flowmeter design and the principles of its work are presented in the article. A mathematical model of the temperature field in a stream of biofuel is proposed. This model allows one to determine the fuel consumption with high accuracy. Numerical modeling of the heater heat balance in the fuel flow of a thermo-anemometric flowmeter is conducted and the results are analyzed. Methods for increasing the measurement speed and accuracy of a thermo-anemometric flowmeter are proposed.

  7. Mathematical modeling of heat treatment processes conserving biological activity of plant bioresources

    NASA Astrophysics Data System (ADS)

    Rodionova, N. S.; Popov, E. S.; Pozhidaeva, E. A.; Pynzar, S. S.; Ryaskina, L. O.

    2018-05-01

    The aim of this study is to develop a mathematical model of the heat exchange process of LT-processing to estimate the dynamics of temperature field changes and optimize the regime parameters, due to the non-stationarity process, the physicochemical and thermophysical properties of food systems. The application of LT-processing, based on the use of low-temperature modes in thermal culinary processing of raw materials with preliminary vacuum packaging in a polymer heat- resistant film is a promising trend in the development of technics and technology in the catering field. LT-processing application of food raw materials guarantees the preservation of biologically active substances in food environments, which are characterized by a certain thermolability, as well as extend the shelf life and high consumer characteristics of food systems that are capillary-porous bodies. When performing the mathematical modeling of the LT-processing process, the packet of symbolic mathematics “Maple” was used, as well as the mathematical packet flexPDE that uses the finite element method for modeling objects with distributed parameters. The processing of experimental results was evaluated with the help of the developed software in the programming language Python 3.4. To calculate and optimize the parameters of the LT processing process of polycomponent food systems, the differential equation of non-stationary thermal conductivity was used, the solution of which makes it possible to identify the temperature change at any point of the solid at different moments. The present study specifies data on the thermophysical characteristics of the polycomponent food system based on plant raw materials, with the help of which the physico-mathematical model of the LT- processing process has been developed. The obtained mathematical model allows defining of the dynamics of the temperature field in different sections of the LT-processed polycomponent food systems on the basis of calculating the

  8. The Role of Mathematical Models in Understanding Pattern Formation in Developmental Biology

    PubMed Central

    Umulis, David M.

    2016-01-01

    In a Wall Street Journal article published on April 5, 2013, E. O. Wilson attempted to make the case that biologists do not really need to learn any mathematics—whenever they run into difficulty with numerical issues, they can find a technician (aka mathematician) to help them out of their difficulty. He formalizes this in Wilsons Principle No. 1: “It is far easier for scientists to acquire needed collaboration from mathematicians and statisticians than it is for mathematicians and statisticians to find scientists able to make use of their equations.” This reflects a complete misunderstanding of the role of mathematics in all sciences throughout history. To Wilson, mathematics is mere number crunching, but as Galileo said long ago, “The laws of Nature are written in the language of mathematics…the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word.” Mathematics has moved beyond the geometry-based model of Galileo’s time, and in a rebuttal to Wilson, E. Frenkel has pointed out the role of mathematics in synthesizing the general principles in science (Both point and counter-point are available in Wilson and Frenkel in Notices Am Math Soc 60(7):837–838, 2013). We will take this a step further and show how mathematics has been used to make new and experimentally verified discoveries in developmental biology and how mathematics is essential for understanding a problem that has puzzled experimentalists for decades—that of how organisms can scale in size. Mathematical analysis alone cannot “solve” these problems since the validation lies at the molecular level, but conversely, a growing number of questions in biology cannot be solved without mathematical analysis and modeling. Herein, we discuss a few examples of the productive intercourse between mathematics and biology. PMID:25280665

  9. Mathematical psychology.

    PubMed

    Batchelder, William H

    2010-09-01

    Mathematical psychology is a sub-field of psychology that started in the 1950s and has continued to grow as an important contributor to formal psychological theory, especially in the cognitive areas of psychology such as learning, memory, classification, choice response time, decision making, attention, and problem solving. In addition, there are several scientific sub-areas that were originated by mathematical psychologists such as the foundations of measurement, stochastic memory models, and psychologically motivated reformulations of expected utility theory. Mathematical psychology does not include all uses of mathematics and statistics in psychology, and indeed there is a long history of such uses especially in the areas of perception and psychometrics. What is most unique about mathematical psychology is its approach to theory construction. While accepting the behaviorist dictum that the data in psychology must be observable and replicable, mathematical models are specified in terms of unobservable formal constructs that can predict detailed aspects of data across multiple experimental and natural settings. By now almost all the substantive areas of cognitive and experimental psychology have formal mathematical models and theories, and many of these are due to researchers that identify with mathematical psychology. Copyright © 2010 John Wiley & Sons, Ltd. For further resources related to this article, please visit the WIREs website. Copyright © 2010 John Wiley & Sons, Ltd.

  10. On the mathematical modeling of the Reynolds stress's equations

    NASA Technical Reports Server (NTRS)

    Lin, Avi

    1990-01-01

    By considering the Reynolds stress equations as a possible descriptor of complex turbulent fields, pressure-velocity interaction and turbulence dissipation are studied as two of the main physical contributions to Reynolds stress balancing in turbulent flow fields. It is proven that the pressure interaction term contains turbulence generation elements. However, the usual 'return to isotropy' element appears more weakly than in the standard models. In addition, convection-like elements are discovered mathematically, but there is no mathematical evidence that the pressure fluctuations contribute to the turbulent transport mechanism. Calculations of some simple one-dimensional fields indicate that this extra convection, rather than the turbulent transport, is needed mathematically. Similarly, an expression for the turbulence dissipation is developed. The end result is a dynamic equation for the dissipation tensor which is based on the tensorial length scales.

  11. RealSurf - A Tool for the Interactive Visualization of Mathematical Models

    NASA Astrophysics Data System (ADS)

    Stussak, Christian; Schenzel, Peter

    For applications in fine art, architecture and engineering it is often important to visualize and to explore complex mathematical models. In former times there were static models of them collected in museums respectively in mathematical institutes. In order to check their properties for esthetical reasons it could be helpful to explore them interactively in 3D in real time. For the class of implicitly given algebraic surfaces we developed the tool RealSurf. Here we give an introduction to the program and some hints for the design of interesting surfaces.

  12. Mathematical modeling and simulation of a thermal system

    NASA Astrophysics Data System (ADS)

    Toropoc, Mirela; Gavrila, Camelia; Frunzulica, Rodica; Toma, Petrica D.

    2016-12-01

    The aim of the present paper is the conception of a mathematical model and simulation of a system formed by a heatexchanger for domestic hot water preparation, a storage tank for hot water and a radiator, starting from the mathematical equations describing this system and developed using Scilab-Xcos program. The model helps to determine the evolution in time for the hot water temperature, for the return temperature in the primary circuit of the heat exchanger, for the supply temperature in the secondary circuit, the thermal power for heating and for hot water preparation to the consumer respectively. In heating systems, heat-exchangers have an important role and their performances influence the energy efficiency of the systems. In the meantime, it is very important to follow the behavior of such systems in dynamic regimes. Scilab-Xcos program can be utilized to follow the important parameters of the systems in different functioning scenarios.

  13. Pest control through viral disease: mathematical modeling and analysis.

    PubMed

    Bhattacharyya, S; Bhattacharya, D K

    2006-01-07

    This paper deals with the mathematical modeling of pest management under viral infection (i.e. using viral pesticide) and analysis of its essential mathematical features. As the viral infection induces host lysis which releases more virus into the environment, on the average 'kappa' viruses per host, kappain(1,infinity), the 'virus replication parameter' is chosen as the main parameter on which the dynamics of the infection depends. We prove that there exists a threshold value kappa(0) beyond which the endemic equilibrium bifurcates from the free disease one. Still for increasing kappa values, the endemic equilibrium bifurcates towards a periodic solution. We further analyse the orbital stability of the periodic orbits arising from bifurcation by applying Poor's condition. A concluding discussion with numerical simulation of the model is then presented.

  14. The effect of mathematical model development on the instruction of acceleration to introductory physics students

    NASA Astrophysics Data System (ADS)

    Sauer, Tim Allen

    The purpose of this study was to evaluate the effectiveness of utilizing student constructed theoretical math models when teaching acceleration to high school introductory physics students. The goal of the study was for the students to be able to utilize mathematical modeling strategies to improve their problem solving skills, as well as their standardized scientific and conceptual understanding. This study was based on mathematical modeling research, conceptual change research and constructivist theory of learning, all of which suggest that mathematical modeling is an effective way to influence students' conceptual connectiveness and sense making of formulaic equations and problem solving. A total of 48 students in two sections of high school introductory physics classes received constructivist, inquiry-based, cooperative learning, and conceptual change-oriented instruction. The difference in the instruction for the 24 students in the mathematical modeling treatment group was that they constructed every formula they needed to solve problems from data they collected. In contrast, the instructional design for the control group of 24 students allowed the same instruction with assigned problems solved with formulas given to them without explanation. The results indicated that the mathematical modeling students were able to solve less familiar and more complicated problems with greater confidence and mental flexibility than the control group students. The mathematical modeling group maintained fewer alternative conceptions consistently in the interviews than did the control group. The implications for acceleration instruction from these results were discussed.

  15. Mathematical modelling of radiotherapy strategies for early breast cancer.

    PubMed

    Enderling, Heiko; Anderson, Alexander R A; Chaplain, Mark A J; Munro, Alastair J; Vaidya, Jayant S

    2006-07-07

    Targeted intraoperative radiotherapy (Targit) is a new concept of partial breast irradiation where single fraction radiotherapy is delivered directly to the tumour bed. Apart from logistic advantages, this strategy minimizes the risk of missing the tumour bed and avoids delay between surgery and radiotherapy. It is presently being compared with the standard fractionated external beam radiotherapy (EBRT) in randomized trials. In this paper we present a mathematical model for the growth and invasion of a solid tumour into a domain of tissue (in this case breast tissue), and then a model for surgery and radiation treatment of this tumour. We use the established linear-quadratic (LQ) model to compute the survival probabilities for both tumour cells and irradiated breast tissue and then simulate the effects of conventional EBRT and Targit. True local recurrence of the tumour could arise either from stray tumour cells, or the tumour bed that harbours morphologically normal cells having a predisposition to genetic changes, such as a loss of heterozygosity (LOH) in genes that are crucial for tumourigenesis, e.g. tumour suppressor genes (TSGs). Our mathematical model predicts that the single high dose of radiotherapy delivered by Targit would result in eliminating all these sources of recurrence, whereas the fractionated EBRT would eliminate stray tumour cells, but allow (by virtue of its very schedule) the cells with LOH in TSGs or cell-cycle checkpoint genes to pass on low-dose radiation-induced DNA damage and consequently mutations that may favour the development of a new tumour. The mathematical model presented here is an initial attempt to model a biologically complex phenomenon that has until now received little attention in the literature and provides a 'proof of principle' that it is possible to produce clinically testable hypotheses on the effects of different approaches of radiotherapy for breast cancer.

  16. The mathematical cell model reconstructed from interference microscopy data

    NASA Astrophysics Data System (ADS)

    Rogotnev, A. A.; Nikitiuk, A. S.; Naimark, O. B.; Nebogatikov, V. O.; Grishko, V. V.

    2017-09-01

    The mathematical model of cell dynamics is developed to link the dynamics of the phase cell thickness with the signs of the oncological pathology. The measurements of irregular oscillations of cancer cells phase thickness were made with laser interference microscope MIM-340 in order to substantiate this model. These data related to the dynamics of phase thickness for different cross-sections of cells (nuclei, nucleolus, and cytoplasm) allow the reconstruction of the attractor of dynamic system. The attractor can be associated with specific types of collective modes of phase thickness responsible for the normal and cancerous cell dynamics. Specific type of evolution operator was determined using an algorithm of designing of the mathematical cell model and temporal phase thickness data for cancerous and normal cells. Qualitative correspondence of attractor types to the cell states was analyzed in terms of morphological signs associated with maximum value of mean square irregular oscillations of phase thickness dynamics.

  17. Mathematical Modeling of Microbial Community Dynamics: A Methodological Review

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Song, Hyun-Seob; Cannon, William R.; Beliaev, Alex S.

    Microorganisms in nature form diverse communities that dynamically change in structure and function in response to environmental variations. As a complex adaptive system, microbial communities show higher-order properties that are not present in individual microbes, but arise from their interactions. Predictive mathematical models not only help to understand the underlying principles of the dynamics and emergent properties of natural and synthetic microbial communities, but also provide key knowledge required for engineering them. In this article, we provide an overview of mathematical tools that include not only current mainstream approaches, but also less traditional approaches that, in our opinion, can bemore » potentially useful. We discuss a broad range of methods ranging from low-resolution supra-organismal to high-resolution individual-based modeling. Particularly, we highlight the integrative approaches that synergistically combine disparate methods. In conclusion, we provide our outlook for the key aspects that should be further developed to move microbial community modeling towards greater predictive power.« less

  18. Nitric oxide bioavailability in the microcirculation: insights from mathematical models.

    PubMed

    Tsoukias, Nikolaos M

    2008-11-01

    Over the last 30 years nitric oxide (NO) has emerged as a key signaling molecule involved in a number of physiological functions, including in the regulation of microcirculatory tone. Despite significant scientific contributions, fundamental questions about NO's role in the microcirculation remain unanswered. Mathematical modeling can assist in investigations of microcirculatory NO physiology and address experimental limitations in quantifying vascular NO concentrations. The number of mathematical models investigating the fate of NO in the vasculature has increased over the last few years, and new models are continuously emerging, incorporating an increasing level of complexity and detail. Models investigate mechanisms that affect NO availability in health and disease. They examine the significance of NO release from nonendothelial sources, the effect of transient release, and the complex interaction of NO with other substances, such as heme-containing proteins and reactive oxygen species. Models are utilized to test and generate hypotheses for the mechanisms that regulate NO-dependent signaling in the microcirculation.

  19. Accurate Modeling of Galaxy Clustering on Small Scales: Testing the Standard ΛCDM + Halo Model

    NASA Astrophysics Data System (ADS)

    Sinha, Manodeep; Berlind, Andreas A.; McBride, Cameron; Scoccimarro, Roman

    2015-01-01

    The large-scale distribution of galaxies can be explained fairly simply by assuming (i) a cosmological model, which determines the dark matter halo distribution, and (ii) a simple connection between galaxies and the halos they inhabit. This conceptually simple framework, called the halo model, has been remarkably successful at reproducing the clustering of galaxies on all scales, as observed in various galaxy redshift surveys. However, none of these previous studies have carefully modeled the systematics and thus truly tested the halo model in a statistically rigorous sense. We present a new accurate and fully numerical halo model framework and test it against clustering measurements from two luminosity samples of galaxies drawn from the SDSS DR7. We show that the simple ΛCDM cosmology + halo model is not able to simultaneously reproduce the galaxy projected correlation function and the group multiplicity function. In particular, the more luminous sample shows significant tension with theory. We discuss the implications of our findings and how this work paves the way for constraining galaxy formation by accurate simultaneous modeling of multiple galaxy clustering statistics.

  20. Developing calculus textbook model that supported with GeoGebra to enhancing students’ mathematical problem solving and mathematical representation

    NASA Astrophysics Data System (ADS)

    Dewi, N. R.; Arini, F. Y.

    2018-03-01

    The main purpose of this research is developing and produces a Calculus textbook model that supported with GeoGebra. This book was designed to enhancing students’ mathematical problem solving and mathematical representation. There were three stages in this research i.e. define, design, and develop. The textbooks consisted of 6 chapters which each chapter contains introduction, core materials and include examples and exercises. The textbook developed phase begins with the early stages of designed the book (draft 1) which then validated by experts. Revision of draft 1 produced draft 2. The data were analyzed with descriptive statistics. The analysis showed that the Calculus textbook model that supported with GeoGebra, valid and fill up the criteria of practicality.

  1. Accurate path integration in continuous attractor network models of grid cells.

    PubMed

    Burak, Yoram; Fiete, Ila R

    2009-02-01

    Grid cells in the rat entorhinal cortex display strikingly regular firing responses to the animal's position in 2-D space and have been hypothesized to form the neural substrate for dead-reckoning. However, errors accumulate rapidly when velocity inputs are integrated in existing models of grid cell activity. To produce grid-cell-like responses, these models would require frequent resets triggered by external sensory cues. Such inadequacies, shared by various models, cast doubt on the dead-reckoning potential of the grid cell system. Here we focus on the question of accurate path integration, specifically in continuous attractor models of grid cell activity. We show, in contrast to previous models, that continuous attractor models can generate regular triangular grid responses, based on inputs that encode only the rat's velocity and heading direction. We consider the role of the network boundary in the integration performance of the network and show that both periodic and aperiodic networks are capable of accurate path integration, despite important differences in their attractor manifolds. We quantify the rate at which errors in the velocity integration accumulate as a function of network size and intrinsic noise within the network. With a plausible range of parameters and the inclusion of spike variability, our model networks can accurately integrate velocity inputs over a maximum of approximately 10-100 meters and approximately 1-10 minutes. These findings form a proof-of-concept that continuous attractor dynamics may underlie velocity integration in the dorsolateral medial entorhinal cortex. The simulations also generate pertinent upper bounds on the accuracy of integration that may be achieved by continuous attractor dynamics in the grid cell network. We suggest experiments to test the continuous attractor model and differentiate it from models in which single cells establish their responses independently of each other.

  2. Chancroid transmission dynamics: a mathematical modeling approach.

    PubMed

    Bhunu, C P; Mushayabasa, S

    2011-12-01

    Mathematical models have long been used to better understand disease transmission dynamics and how to effectively control them. Here, a chancroid infection model is presented and analyzed. The disease-free equilibrium is shown to be globally asymptotically stable when the reproduction number is less than unity. High levels of treatment are shown to reduce the reproduction number suggesting that treatment has the potential to control chancroid infections in any given community. This result is also supported by numerical simulations which show a decline in chancroid cases whenever the reproduction number is less than unity.

  3. A mathematical model of 'Pride and Prejudice'.

    PubMed

    Rinaldi, Sergio; Rossa, Fabio Della; Landi, Pietro

    2014-04-01

    A mathematical model is proposed for interpreting the love story between Elizabeth and Darcy portrayed by Jane Austen in the popular novel Pride and Prejudice. The analysis shows that the story is characterized by a sudden explosion of sentimental involvements, revealed by the existence of a saddle-node bifurcation in the model. The paper is interesting not only because it deals for the first time with catastrophic bifurcations in romantic relation-ships, but also because it enriches the list of examples in which love stories are described through ordinary differential equations.

  4. On mathematical modelling of flameless combustion

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Mancini, Marco; Schwoeppe, Patrick; Weber, Roman

    2007-07-15

    A further analysis of the IFRF semi-industrial-scale experiments on flameless (mild) combustion of natural gas is carried out. The experimental burner features a strong oxidizer jet and two weak natural gas jets. Numerous publications have shown the inability of various RANS-based mathematical models to predict the structure of the weak jet. We have proven that the failure is in error predictions of the entrainment and therefore is not related to any chemistry submodels, as has been postulated. (author)

  5. Nonlinear-programming mathematical modeling of coal blending for power plant

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Tang Longhua; Zhou Junhu; Yao Qiang

    At present most of the blending works are guided by experience or linear-programming (LP) which can not reflect the coal complicated characteristics properly. Experimental and theoretical research work shows that most of the coal blend properties can not always be measured as a linear function of the properties of the individual coals in the blend. The authors introduced nonlinear functions or processes (including neural network and fuzzy mathematics), established on the experiments directed by the authors and other researchers, to quantitatively describe the complex coal blend parameters. Finally nonlinear-programming (NLP) mathematical modeling of coal blend is introduced and utilized inmore » the Hangzhou Coal Blending Center. Predictions based on the new method resulted in different results from the ones based on LP modeling. The authors concludes that it is very important to introduce NLP modeling, instead of NL modeling, into the work of coal blending.« less

  6. Creation of Anatomically Accurate Computer-Aided Design (CAD) Solid Models from Medical Images

    NASA Technical Reports Server (NTRS)

    Stewart, John E.; Graham, R. Scott; Samareh, Jamshid A.; Oberlander, Eric J.; Broaddus, William C.

    1999-01-01

    Most surgical instrumentation and implants used in the world today are designed with sophisticated Computer-Aided Design (CAD)/Computer-Aided Manufacturing (CAM) software. This software automates the mechanical development of a product from its conceptual design through manufacturing. CAD software also provides a means of manipulating solid models prior to Finite Element Modeling (FEM). Few surgical products are designed in conjunction with accurate CAD models of human anatomy because of the difficulty with which these models are created. We have developed a novel technique that creates anatomically accurate, patient specific CAD solids from medical images in a matter of minutes.

  7. A Professional Experience Model for Primary Pre-Service Teachers Specialising in Mathematics

    ERIC Educational Resources Information Center

    McMaster, Heather; Cavanagh, Michael

    2016-01-01

    Many primary pre-service teachers (PSTs) who are enthused by tertiary courses that espouse and model a socio-constructivist approach to teaching mathematics, revert to a traditional approach when they encounter mathematics teaching during professional experience. An intervention was designed to translate the initial pedagogical intent of four…

  8. Mathematical modeling of acid-base physiology

    PubMed Central

    Occhipinti, Rossana; Boron, Walter F.

    2015-01-01

    pH is one of the most important parameters in life, influencing virtually every biological process at the cellular, tissue, and whole-body level. Thus, for cells, it is critical to regulate intracellular pH (pHi) and, for multicellular organisms, to regulate extracellular pH (pHo). pHi regulation depends on the opposing actions of plasma-membrane transporters that tend to increase pHi, and others that tend to decrease pHi. In addition, passive fluxes of uncharged species (e.g., CO2, NH3) and charged species (e.g., HCO3− , NH4+) perturb pHi. These movements not only influence one another, but also perturb the equilibria of a multitude of intracellular and extracellular buffers. Thus, even at the level of a single cell, perturbations in acid-base reactions, diffusion, and transport are so complex that it is impossible to understand them without a quantitative model. Here we summarize some mathematical models developed to shed light onto the complex interconnected events triggered by acids-base movements. We then describe a mathematical model of a spherical cell–which to our knowledge is the first one capable of handling a multitude of buffer reaction–that our team has recently developed to simulate changes in pHi and pHo caused by movements of acid-base equivalents across the plasma membrane of a Xenopus oocyte. Finally, we extend our work to a consideration of the effects of simultaneous CO2 and HCO3− influx into a cell, and envision how future models might extend to other cell types (e.g., erythrocytes) or tissues (e.g., renal proximal-tubule epithelium) important for whole-body pH homeostasis. PMID:25617697

  9. The mathematical research for the Kuramoto model of the describing neuronal synchrony in the brain

    NASA Astrophysics Data System (ADS)

    Lin, Chang; Lin, Mai-mai

    2009-08-01

    The Kuramoto model of the describing neuronal synchrony is mathematically investigated in the brain. A general analytical solutions (the most sententious description) for the Kuramoto model, incorporating the inclusion of a Ki,j (t) term to represent time-varying coupling strengths, have been obtained by using the precise mathematical approach. We derive an exact analytical expression, opening out the connotative and latent linear relation, for the mathematical character of the phase configurations in the Kuramoto model of the describing neuronal synchrony in the brain.

  10. Applicability of mathematical modeling to problems of environmental physiology

    NASA Technical Reports Server (NTRS)

    White, Ronald J.; Lujan, Barbara F.; Leonard, Joel I.; Srinivasan, R. Srini

    1988-01-01

    The paper traces the evolution of mathematical modeling and systems analysis from terrestrial research to research related to space biomedicine and back again to terrestrial research. Topics covered include: power spectral analysis of physiological signals; pattern recognition models for detection of disease processes; and, computer-aided diagnosis programs used in conjunction with a special on-line biomedical computer library.

  11. A mathematical model of microalgae growth in cylindrical photobioreactor

    NASA Astrophysics Data System (ADS)

    Bakeri, Noorhadila Mohd; Jamaian, Siti Suhana

    2017-08-01

    Microalgae are unicellular organisms, which exist individually or in chains or groups but can be utilized in many applications. Researchers have done various efforts in order to increase the growth rate of microalgae. Microalgae have a potential as an effective tool for wastewater treatment, besides as a replacement for natural fuel such as coal and biodiesel. The growth of microalgae can be estimated by using Geider model, which this model is based on photosynthesis irradiance curve (PI-curve) and focused on flat panel photobioreactor. Therefore, in this study a mathematical model for microalgae growth in cylindrical photobioreactor is proposed based on the Geider model. The light irradiance is the crucial part that affects the growth rate of microalgae. The absorbed photon flux will be determined by calculating the average light irradiance in a cylindrical system illuminated by unidirectional parallel flux and considering the cylinder as a collection of differential parallelepipeds. Results from this study showed that the specific growth rate of microalgae increases until the constant level is achieved. Therefore, the proposed mathematical model can be used to estimate the rate of microalgae growth in cylindrical photobioreactor.

  12. Local Debonding and Fiber Breakage in Composite Materials Modeled Accurately

    NASA Technical Reports Server (NTRS)

    Bednarcyk, Brett A.; Arnold, Steven M.

    2001-01-01

    A prerequisite for full utilization of composite materials in aerospace components is accurate design and life prediction tools that enable the assessment of component performance and reliability. Such tools assist both structural analysts, who design and optimize structures composed of composite materials, and materials scientists who design and optimize the composite materials themselves. NASA Glenn Research Center's Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC) software package (http://www.grc.nasa.gov/WWW/LPB/mac) addresses this need for composite design and life prediction tools by providing a widely applicable and accurate approach to modeling composite materials. Furthermore, MAC/GMC serves as a platform for incorporating new local models and capabilities that are under development at NASA, thus enabling these new capabilities to progress rapidly to a stage in which they can be employed by the code's end users.

  13. Mathematical Model of Cytomegalovirus (CMV) Disease

    NASA Astrophysics Data System (ADS)

    Sriningsih, R.; Subhan, M.; Nasution, M. L.

    2018-04-01

    The article formed the mathematical model of cytomegalovirus (CMV) disease. Cytomegalovirus (CMV) is a type of herpes virus. This virus is actually not dangerous, but if the body's immune weakens the virus can cause serious problems for health and even can cause death. This virus is also susceptible to infect pregnant women. In addition, the baby may also be infected through the placenta. If this is experienced early in pregnancy, it will increase the risk of miscarriage. If the baby is born, it can cause disability in the baby. The model is formed by determining its variables and parameters based on assumptions. The goal is to analyze the dynamics of cytomegalovirus (CMV) disease spread.

  14. Mathematical modeling of tomographic scanning of cylindrically shaped test objects

    NASA Astrophysics Data System (ADS)

    Kapranov, B. I.; Vavilova, G. V.; Volchkova, A. V.; Kuznetsova, I. S.

    2018-05-01

    The paper formulates mathematical relationships that describe the length of the radiation absorption band in the test object for the first generation tomographic scan scheme. A cylindrically shaped test object containing an arbitrary number of standard circular irregularities is used to perform mathematical modeling. The obtained mathematical relationships are corrected with respect to chemical composition and density of the test object material. The equations are derived to calculate the resulting attenuation radiation from cobalt-60 isotope when passing through the test object. An algorithm to calculate the radiation flux intensity is provided. The presented graphs describe the dependence of the change in the γ-quantum flux intensity on the change in the radiation source position and the scanning angle of the test object.

  15. Mathematical modeling the radiation effects on humoral immunity

    NASA Astrophysics Data System (ADS)

    Smirnova, O. A.

    A mathematical model of humoral immune response in nonirradiated and irradiated mammals is developed. It is based on conventional theories and experimental facts in this field. The model is a system of nonlinear differential equations which describe the dynamics of concentrations of antibody and antigen molecules, immunocompetent B lymphocytes, and the rest blood lymphocytes, as well as the bone-marrow lymphocyte precursors. The interaction of antigen molecules with antibodies and with antibody-like receptors on immunocompetent cells is also incorporated. The model quantitatively reproduces the dynamics of the humoral immune response to the T-independent antigen (capsular antigen of plague microbe) in nonirradiated mammals (CBA mice). It describes the peculiarities of the humoral immune response in CBA mice exposed to acute radiation before or after introducing antigen. The model predicts an adaptation of humoral immune system to low dose rate chronic irradiation in the result of which the intensity of immune response relaxes to a new, lower than normal, stable level. The mechanisms of this phenomenon are revealed. The results obtained show that the developed model, after the appropriate identification, can be used to predict the effects of acute and low-level long-term irradiation on the system of humoral immunity in humans. Employment of the mathematical model identified in the proper way should be important in estimating the radiation risk for cosmonauts and astronauts on long space missions such as a voyage to Mars or a lunar colony.

  16. Mathematical models frame environmental dispute [Review of the article Useless arithmetic: Ten points to ponder when using mathematical models in environmental decision making

    USGS Publications Warehouse

    Lamb, Berton Lee; Burkardt, Nina

    2008-01-01

    When Linda Pilkey- Jarvis and Orrin Pilkey state in their article, "Useless Arithmetic," that "mathematical models are simplified, generalized representations of a process or system," they probably do not mean to imply that these models are simple. Rather, the models are simpler than nature and that is the heart of the problem with predictive models. We have had a long professional association with the developers and users of one of these simplifications of nature in the form of a mathematical model known as Physical Habitat Simulation (PHABSIM), which is part of the Instream Flow Incremental Methodology (IFIM). The IFIM is a suite of techniques, including PHABSIM, that allows the analyst to incorporate hydrology , hydraulics, habitat, water quality, stream temperature, and other variables into a tradeoff analysis that decision makers can use to design a flow regime to meet management objectives (Stalnaker et al. 1995). Although we are not the developers of the IFIM, we have worked with those who did design it, and we have tried to understand how the IFIM and PHABSIM are actually used in decision making (King, Burkardt, and Clark 2006; Lamb 1989).

  17. Accuracy of Cycling Power Meters against a Mathematical Model of Treadmill Cycling.

    PubMed

    Maier, Thomas; Schmid, Lucas; Müller, Beat; Steiner, Thomas; Wehrlin, Jon Peter

    2017-06-01

    The aim of this study was to compare the accuracy among a high number of current mobile cycling power meters used by elite and recreational cyclists against a first principle-based mathematical model of treadmill cycling. 54 power meters from 9 manufacturers used by 32 cyclists were calibrated. While the cyclist coasted downhill on a motorised treadmill, a back-pulling system was adjusted to counter the downhill force. The system was then loaded 3 times with 4 different masses while the cyclist pedalled to keep his position. The mean deviation (trueness) to the model and coefficient of variation (precision) were analysed. The mean deviations of the power meters were -0.9±3.2% (mean±SD) with 6 power meters deviating by more than±5%. The coefficients of variation of the power meters were 1.2±0.9% (mean±SD), with Stages varying more than SRM (p<0.001) and PowerTap (p<0.001). In conclusion, current power meters used by elite and recreational cyclists vary considerably in their trueness; precision is generally high but differs between manufacturers. Calibrating and adjusting the trueness of every power meter against a first principle-based reference is advised for accurate measurements. © Georg Thieme Verlag KG Stuttgart · New York.

  18. A Primer on Mathematical Modeling in the Study of Organisms and Their Parts.

    PubMed

    Montévil, Maël

    2018-01-01

    Mathematical modeling is a very powerful tool for understanding natural phenomena. Such a tool carries its own assumptions and should always be used critically. In this chapter, we highlight the key ingredients and steps of modeling and focus on their biological interpretation. In particular, we discuss the role of theoretical principles in writing models. We also highlight the meaning and interpretation of equations. The main aim of this chapter is to facilitate the interaction between biologists and mathematical modelers. We focus on the case of cell proliferation and motility in the context of multicellular organisms.

  19. Critical Thinking Skills of Students through Mathematics Learning with ASSURE Model Assisted by Software Autograph

    NASA Astrophysics Data System (ADS)

    Kristianti, Y.; Prabawanto, S.; Suhendra, S.

    2017-09-01

    This study aims to examine the ability of critical thinking and students who attain learning mathematics with learning model ASSURE assisted Autograph software. The design of this study was experimental group with pre-test and post-test control group. The experimental group obtained a mathematics learning with ASSURE-assisted model Autograph software and the control group acquired the mathematics learning with the conventional model. The data are obtained from the research results through critical thinking skills tests. This research was conducted at junior high school level with research population in one of junior high school student in Subang Regency of Lesson Year 2016/2017 and research sample of class VIII student in one of junior high school in Subang Regency for 2 classes. Analysis of research data is administered quantitatively. Quantitative data analysis was performed on the normalized gain level between the two sample groups using a one-way anova test. The results show that mathematics learning with ASSURE assisted model Autograph software can improve the critical thinking ability of junior high school students. Mathematical learning using ASSURE-assisted model Autograph software is significantly better in improving the critical thinking skills of junior high school students compared with conventional models.

  20. Invasion emerges from cancer cell adaptation to competitive microenvironments: Quantitative predictions from multiscale mathematical models

    PubMed Central

    Rejniak, Katarzyna A.; Gerlee, Philip

    2013-01-01

    Summary In this review we summarize our recent efforts using mathematical modeling and computation to simulate cancer invasion, with a special emphasis on the tumor microenvironment. We consider cancer progression as a complex multiscale process and approach it with three single-cell based mathematical models that examine the interactions between tumor microenvironment and cancer cells at several scales. The models exploit distinct mathematical and computational techniques, yet they share core elements and can be compared and/or related to each other. The overall aim of using mathematical models is to uncover the fundamental mechanisms that lend cancer progression its direction towards invasion and metastasis. The models effectively simulate various modes of cancer cell adaptation to the microenvironment in a growing tumor. All three point to a general mechanism underlying cancer invasion: competition for adaptation between distinct cancer cell phenotypes, driven by a tumor microenvironment with scarce resources. These theoretical predictions pose an intriguing experimental challenge: test the hypothesis that invasion is an emergent property of cancer cell populations adapting to selective microenvironment pressure, rather than culmination of cancer progression producing cells with the “invasive phenotype”. In broader terms, we propose that fundamental insights into cancer can be achieved by experimentation interacting with theoretical frameworks provided by computational and mathematical modeling. PMID:18524624

  1. A Novel Physiology-Based Mathematical Model to Estimate Red Blood Cell Lifespan in Different Human Age Groups.

    PubMed

    An, Guohua; Widness, John A; Mock, Donald M; Veng-Pedersen, Peter

    2016-09-01

    Direct measurement of red blood cell (RBC) survival in humans has improved from the original accurate but limited differential agglutination technique to the current reliable, safe, and accurate biotin method. Despite this, all of these methods are time consuming and require blood sampling over several months to determine the RBC lifespan. For situations in which RBC survival information must be obtained quickly, these methods are not suitable. With the exception of adults and infants, RBC survival has not been extensively investigated in other age groups. To address this need, we developed a novel, physiology-based mathematical model that quickly estimates RBC lifespan in healthy individuals at any age. The model is based on the assumption that the total number of RBC recirculations during the lifespan of each RBC (denoted by N max) is relatively constant for all age groups. The model was initially validated using the data from our prior infant and adult biotin-labeled red blood cell studies and then extended to the other age groups. The model generated the following estimated RBC lifespans in 2-year-old, 5-year-old, 8-year-old, and 10-year-old children: 62, 74, 82, and 86 days, respectively. We speculate that this model has useful clinical applications. For example, HbA1c testing is not reliable in identifying children with diabetes because HbA1c is directly affected by RBC lifespan. Because our model can estimate RBC lifespan in children at any age, corrections to HbA1c values based on the model-generated RBC lifespan could improve diabetes diagnosis as well as therapy in children.

  2. Not just a theory--the utility of mathematical models in evolutionary biology.

    PubMed

    Servedio, Maria R; Brandvain, Yaniv; Dhole, Sumit; Fitzpatrick, Courtney L; Goldberg, Emma E; Stern, Caitlin A; Van Cleve, Jeremy; Yeh, D Justin

    2014-12-01

    Progress in science often begins with verbal hypotheses meant to explain why certain biological phenomena exist. An important purpose of mathematical models in evolutionary research, as in many other fields, is to act as “proof-of-concept” tests of the logic in verbal explanations, paralleling the way in which empirical data are used to test hypotheses. Because not all subfields of biology use mathematics for this purpose, misunderstandings of the function of proof-of-concept modeling are common. In the hope of facilitating communication, we discuss the role of proof-of-concept modeling in evolutionary biology.

  3. Studies in Mathematics, Volume XVI. Some Uses of Mathematics: A Source Book for Teachers and Students of School Mathematics.

    ERIC Educational Resources Information Center

    Bell, Max S., Ed.

    This is a collection of articles dealing with mathematical applications for use by high school teachers and students. The articles are intended to illustrate several themes: (1) how mathematics is applied via construction of mathematical models; (2) the various types of activities in applied mathematics; (3) the role of pure mathematics in applied…

  4. Accurate protein structure modeling using sparse NMR data and homologous structure information.

    PubMed

    Thompson, James M; Sgourakis, Nikolaos G; Liu, Gaohua; Rossi, Paolo; Tang, Yuefeng; Mills, Jeffrey L; Szyperski, Thomas; Montelione, Gaetano T; Baker, David

    2012-06-19

    While information from homologous structures plays a central role in X-ray structure determination by molecular replacement, such information is rarely used in NMR structure determination because it can be incorrect, both locally and globally, when evolutionary relationships are inferred incorrectly or there has been considerable evolutionary structural divergence. Here we describe a method that allows robust modeling of protein structures of up to 225 residues by combining (1)H(N), (13)C, and (15)N backbone and (13)Cβ chemical shift data, distance restraints derived from homologous structures, and a physically realistic all-atom energy function. Accurate models are distinguished from inaccurate models generated using incorrect sequence alignments by requiring that (i) the all-atom energies of models generated using the restraints are lower than models generated in unrestrained calculations and (ii) the low-energy structures converge to within 2.0 Å backbone rmsd over 75% of the protein. Benchmark calculations on known structures and blind targets show that the method can accurately model protein structures, even with very remote homology information, to a backbone rmsd of 1.2-1.9 Å relative to the conventional determined NMR ensembles and of 0.9-1.6 Å relative to X-ray structures for well-defined regions of the protein structures. This approach facilitates the accurate modeling of protein structures using backbone chemical shift data without need for side-chain resonance assignments and extensive analysis of NOESY cross-peak assignments.

  5. The enhancement of mathematical analogical reasoning ability of university students through concept attainment model

    NASA Astrophysics Data System (ADS)

    Angraini, L. M.; Kusumah, Y. S.; Dahlan, J. A.

    2018-05-01

    This study aims to see the enhancement of mathematical analogical reasoning ability of the university students through concept attainment model learning based on overall and Prior Mathematical Knowledge (PMK) and interaction of both. Quasi experiments with the design of this experimental-controlled equivalent group involved 54 of second semester students at the one of State Islamic University. The instrument used is pretest-postest. Kolmogorov-Smirnov test, Levene test, t test, two-way ANOVA test were used to analyse the data. The result of this study includes: (1) The enhancement of the mathematical analogical reasoning ability of the students who gets the learning of concept attainment model is better than the enhancement of the mathematical analogical reasoning ability of the students who gets the conventional learning as a whole and based on PMK; (2) There is no interaction between the learning that is used and PMK on enhancing mathematical analogical reasoning ability.

  6. Terrestrial implications of mathematical modeling developed for space biomedical research

    NASA Technical Reports Server (NTRS)

    Lujan, Barbara F.; White, Ronald J.; Leonard, Joel I.; Srinivasan, R. Srini

    1988-01-01

    This paper summarizes several related research projects supported by NASA which seek to apply computer models to space medicine and physiology. These efforts span a wide range of activities, including mathematical models used for computer simulations of physiological control systems; power spectral analysis of physiological signals; pattern recognition models for detection of disease processes; and computer-aided diagnosis programs.

  7. Application of mathematical models to metronomic chemotherapy: What can be inferred from minimal parameterized models?

    PubMed

    Ledzewicz, Urszula; Schättler, Heinz

    2017-08-10

    Metronomic chemotherapy refers to the frequent administration of chemotherapy at relatively low, minimally toxic doses without prolonged treatment interruptions. Different from conventional or maximum-tolerated-dose chemotherapy which aims at an eradication of all malignant cells, in a metronomic dosing the goal often lies in the long-term management of the disease when eradication proves elusive. Mathematical modeling and subsequent analysis (theoretical as well as numerical) have become an increasingly more valuable tool (in silico) both for determining conditions under which specific treatment strategies should be preferred and for numerically optimizing treatment regimens. While elaborate, computationally-driven patient specific schemes that would optimize the timing and drug dose levels are still a part of the future, such procedures may become instrumental in making chemotherapy effective in situations where it currently fails. Ideally, mathematical modeling and analysis will develop into an additional decision making tool in the complicated process that is the determination of efficient chemotherapy regimens. In this article, we review some of the results that have been obtained about metronomic chemotherapy from mathematical models and what they infer about the structure of optimal treatment regimens. Copyright © 2017 Elsevier B.V. All rights reserved.

  8. Mathematical modeling of a nickel-cadmium battery

    NASA Technical Reports Server (NTRS)

    Fan, Deyuan; White, Ralph E.

    1991-01-01

    Extensions are presented for a mathematical model of an Ni-CD cell (Fan and White, 1991). These extensions consist of intercalation thermodynamics for the nickel electrode and oxygen generation and reduction reactions during charge and overcharge. The simulated results indicate that intercalation may be important in the nickel electrode and that including the oxygen reactions provides a means of predicting the efficiency of the cell on charge and discharge.

  9. Discovery learning model with geogebra assisted for improvement mathematical visual thinking ability

    NASA Astrophysics Data System (ADS)

    Juandi, D.; Priatna, N.

    2018-05-01

    The main goal of this study is to improve the mathematical visual thinking ability of high school student through implementation the Discovery Learning Model with Geogebra Assisted. This objective can be achieved through study used quasi-experimental method, with non-random pretest-posttest control design. The sample subject of this research consist of 62 senior school student grade XI in one of school in Bandung district. The required data will be collected through documentation, observation, written tests, interviews, daily journals, and student worksheets. The results of this study are: 1) Improvement students Mathematical Visual Thinking Ability who obtain learning with applied the Discovery Learning Model with Geogebra assisted is significantly higher than students who obtain conventional learning; 2) There is a difference in the improvement of students’ Mathematical Visual Thinking ability between groups based on prior knowledge mathematical abilities (high, medium, and low) who obtained the treatment. 3) The Mathematical Visual Thinking Ability improvement of the high group is significantly higher than in the medium and low groups. 4) The quality of improvement ability of high and low prior knowledge is moderate category, in while the quality of improvement ability in the high category achieved by student with medium prior knowledge.

  10. Dynamics of Zika virus outbreaks: an overview of mathematical modeling approaches.

    PubMed

    Wiratsudakul, Anuwat; Suparit, Parinya; Modchang, Charin

    2018-01-01

    The Zika virus was first discovered in 1947. It was neglected until a major outbreak occurred on Yap Island, Micronesia, in 2007. Teratogenic effects resulting in microcephaly in newborn infants is the greatest public health threat. In 2016, the Zika virus epidemic was declared as a Public Health Emergency of International Concern (PHEIC). Consequently, mathematical models were constructed to explicitly elucidate related transmission dynamics. In this review article, two steps of journal article searching were performed. First, we attempted to identify mathematical models previously applied to the study of vector-borne diseases using the search terms "dynamics," "mathematical model," "modeling," and "vector-borne" together with the names of vector-borne diseases including chikungunya, dengue, malaria, West Nile, and Zika. Then the identified types of model were further investigated. Second, we narrowed down our survey to focus on only Zika virus research. The terms we searched for were "compartmental," "spatial," "metapopulation," "network," "individual-based," "agent-based" AND "Zika." All relevant studies were included regardless of the year of publication. We have collected research articles that were published before August 2017 based on our search criteria. In this publication survey, we explored the Google Scholar and PubMed databases. We found five basic model architectures previously applied to vector-borne virus studies, particularly in Zika virus simulations. These include compartmental, spatial, metapopulation, network, and individual-based models. We found that Zika models carried out for early epidemics were mostly fit into compartmental structures and were less complicated compared to the more recent ones. Simple models are still commonly used for the timely assessment of epidemics. Nevertheless, due to the availability of large-scale real-world data and computational power, recently there has been growing interest in more complex modeling frameworks

  11. Mathematical models of tumor heterogeneity and drug resistance

    NASA Astrophysics Data System (ADS)

    Greene, James

    In this dissertation we develop mathematical models of tumor heterogeneity and drug resistance in cancer chemotherapy. Resistance to chemotherapy is one of the major causes of the failure of cancer treatment. Furthermore, recent experimental evidence suggests that drug resistance is a complex biological phenomena, with many influences that interact nonlinearly. Here we study the influence of such heterogeneity on treatment outcomes, both in general frameworks and under specific mechanisms. We begin by developing a mathematical framework for describing multi-drug resistance to cancer. Heterogeneity is reflected by a continuous parameter, which can either describe a single resistance mechanism (such as the expression of P-gp in the cellular membrane) or can account for the cumulative effect of several mechanisms and factors. The model is written as a system of integro-differential equations, structured by the continuous "trait," and includes density effects as well as mutations. We study the limiting behavior of the model, both analytically and numerically, and apply it to study treatment protocols. We next study a specific mechanism of tumor heterogeneity and its influence on cell growth: the cell-cycle. We derive two novel mathematical models, a stochastic agent-based model and an integro-differential equation model, each of which describes the growth of cancer cells as a dynamic transition between proliferative and quiescent states. By examining the role all parameters play in the evolution of intrinsic tumor heterogeneity, and the sensitivity of the population growth to parameter values, we show that the cell-cycle length has the most significant effect on the growth dynamics. In addition, we demonstrate that the agent-based model can be approximated well by the more computationally efficient integro-differential equations, when the number of cells is large. The model is closely tied to experimental data of cell growth, and includes a novel implementation of

  12. Developing Student-Centered Learning Model to Improve High Order Mathematical Thinking Ability

    ERIC Educational Resources Information Center

    Saragih, Sahat; Napitupulu, Elvis

    2015-01-01

    The purpose of this research was to develop student-centered learning model aiming to improve high order mathematical thinking ability of junior high school students of based on curriculum 2013 in North Sumatera, Indonesia. The special purpose of this research was to analyze and to formulate the purpose of mathematics lesson in high order…

  13. The limitations of mathematical modeling in high school physics education

    NASA Astrophysics Data System (ADS)

    Forjan, Matej

    The theme of the doctoral dissertation falls within the scope of didactics of physics. Theoretical analysis of the key constraints that occur in the transmission of mathematical modeling of dynamical systems into field of physics education in secondary schools is presented. In an effort to explore the extent to which current physics education promotes understanding of models and modeling, we analyze the curriculum and the three most commonly used textbooks for high school physics. We focus primarily on the representation of the various stages of modeling in the solved tasks in textbooks and on the presentation of certain simplifications and idealizations, which are in high school physics frequently used. We show that one of the textbooks in most cases fairly and reasonably presents the simplifications, while the other two half of the analyzed simplifications do not explain. It also turns out that the vast majority of solved tasks in all the textbooks do not explicitly represent model assumptions based on what we can conclude that in high school physics the students do not develop sufficiently a sense of simplification and idealizations, which is a key part of the conceptual phase of modeling. For the introduction of modeling of dynamical systems the knowledge of students is also important, therefore we performed an empirical study on the extent to which high school students are able to understand the time evolution of some dynamical systems in the field of physics. The research results show the students have a very weak understanding of the dynamics of systems in which the feedbacks are present. This is independent of the year or final grade in physics and mathematics. When modeling dynamical systems in high school physics we also encounter the limitations which result from the lack of mathematical knowledge of students, because they don't know how analytically solve the differential equations. We show that when dealing with one-dimensional dynamical systems

  14. Mathematical modeling of mutant transferrin-CRM107 molecular conjugates for cancer therapy.

    PubMed

    Yoon, Dennis J; Chen, Kevin Y; Lopes, André M; Pan, April A; Shiloach, Joseph; Mason, Anne B; Kamei, Daniel T

    2017-03-07

    The transferrin (Tf) trafficking pathway is a promising mechanism for use in targeted cancer therapy due to the overexpression of transferrin receptors (TfRs) on cancerous cells. We have previously developed a mathematical model of the Tf/TfR trafficking pathway to improve the efficiency of Tf as a drug carrier. By using diphtheria toxin (DT) as a model toxin, we found that mutating the Tf protein to change its iron release rate improves cellular association and efficacy of the drug. Though this is an improvement upon using wild-type Tf as the targeting ligand, conjugated toxins like DT are unfortunately still highly cytotoxic at off-target sites. In this work, we address this hurdle in cancer research by developing a mathematical model to predict the efficacy and selectivity of Tf conjugates that use an alternative toxin. For this purpose, we have chosen to study a mutant of DT, cross-reacting material 107 (CRM107). First, we developed a mathematical model of the Tf-DT trafficking pathway by extending our Tf/TfR model to include intracellular trafficking via DT and DT receptors. Using this mathematical model, we subsequently investigated the efficacy of several conjugates in cancer cells: DT and CRM107 conjugated to wild-type Tf, as well as to our engineered mutant Tf proteins (K206E/R632A Tf and K206E/R534A Tf). We also investigated the selectivity of mutant Tf-CRM107 against non-neoplastic cells. Through the use of our mathematical model, we predicted that (i) mutant Tf-CRM107 exhibits a greater cytotoxicity than wild-type Tf-CRM107 against cancerous cells, (ii) this improvement was more drastic with CRM107 conjugates than with DT conjugates, and (iii) mutant Tf-CRM107 conjugates were selective against non-neoplastic cells. These predictions were validated with in vitro cytotoxicity experiments, demonstrating that mutant Tf-CRM107 conjugates is indeed a more suitable therapeutic agent. Validation from in vitro experiments also confirmed that such whole

  15. MATHEMATICAL MODELING OF OZONE ABSORPTION IN THE LOWER RESPIRATORY TRACT

    EPA Science Inventory

    A mathematical O3 dosimetry model has been developed for simulating the local absorption of O3 in the lower respiratory tract (LRT) of animals and man. The model takes into account LRT anatomy, transport in the lumen and air spaces, transport and chemical reactions in the liquid ...

  16. Engaging Students in Mathematical Modeling through Service-Learning

    ERIC Educational Resources Information Center

    Carducci, Olivia M.

    2014-01-01

    I have included a service-learning project in my mathematical modeling course for the last 6 years. This article describes my experience with service-learning in this course. The article includes a description of the course and the service-learning projects. There is a discussion of how to connect with community partners and identify…

  17. The biology and mathematical modelling of glioma invasion: a review

    PubMed Central

    Talkenberger, K.; Seifert, M.; Klink, B.; Hawkins-Daarud, A.; Swanson, K. R.; Hatzikirou, H.

    2017-01-01

    Adult gliomas are aggressive brain tumours associated with low patient survival rates and limited life expectancy. The most important hallmark of this type of tumour is its invasive behaviour, characterized by a markedly phenotypic plasticity, infiltrative tumour morphologies and the ability of malignant progression from low- to high-grade tumour types. Indeed, the widespread infiltration of healthy brain tissue by glioma cells is largely responsible for poor prognosis and the difficulty of finding curative therapies. Meanwhile, mathematical models have been established to analyse potential mechanisms of glioma invasion. In this review, we start with a brief introduction to current biological knowledge about glioma invasion, and then critically review and highlight future challenges for mathematical models of glioma invasion. PMID:29118112

  18. Predicting human chronically paralyzed muscle force: a comparison of three mathematical models.

    PubMed

    Frey Law, Laura A; Shields, Richard K

    2006-03-01

    Chronic spinal cord injury (SCI) induces detrimental musculoskeletal adaptations that adversely affect health status, ranging from muscle paralysis and skin ulcerations to osteoporosis. SCI rehabilitative efforts may increasingly focus on preserving the integrity of paralyzed extremities to maximize health quality using electrical stimulation for isometric training and/or functional activities. Subject-specific mathematical muscle models could prove valuable for predicting the forces necessary to achieve therapeutic loading conditions in individuals with paralyzed limbs. Although numerous muscle models are available, three modeling approaches were chosen that can accommodate a variety of stimulation input patterns. To our knowledge, no direct comparisons between models using paralyzed muscle have been reported. The three models include 1) a simple second-order linear model with three parameters and 2) two six-parameter nonlinear models (a second-order nonlinear model and a Hill-derived nonlinear model). Soleus muscle forces from four individuals with complete, chronic SCI were used to optimize each model's parameters (using an increasing and decreasing frequency ramp) and to assess the models' predictive accuracies for constant and variable (doublet) stimulation trains at 5, 10, and 20 Hz in each individual. Despite the large differences in modeling approaches, the mean predicted force errors differed only moderately (8-15% error; P=0.0042), suggesting physiological force can be adequately represented by multiple mathematical constructs. The two nonlinear models predicted specific force characteristics better than the linear model in nearly all stimulation conditions, with minimal differences between the two nonlinear models. Either nonlinear mathematical model can provide reasonable force estimates; individual application needs may dictate the preferred modeling strategy.

  19. Factors involved in making post-performance judgments in mathematics problem-solving.

    PubMed

    García Fernández, Trinidad; Kroesbergen, Evelyn; Rodríguez Pérez, Celestino; González-Castro, Paloma; González-Pienda, Julio A

    2015-01-01

    This study examines the impact of executive functions, affective-motivational variables related to mathematics, mathematics achievement and task characteristics on fifth and sixth graders’ calibration accuracy after completing two mathematical problems. A sample of 188 students took part in the study. They were divided into two groups as function of their judgment accuracy after completing the two tasks (accurate= 79, inaccurate= 109). Differences between these groups were examined. The discriminative value of these variables to predict group membership was analyzed, as well as the effect of age, gender, and grade level. The results indicated that accurate students showed better levels of executive functioning, and more positive feelings, beliefs, and motivation related to mathematics. They also spent more time on the tasks. Mathematics achievement, perceived usefulness of mathematics, and time spent on Task 1 significantly predicted group membership, classifying 71.3% of the sample correctly. These results support the relationship between academic achievement and calibration accuracy, suggesting the need to consider a wide range of factors when explaining performance judgments.

  20. Progress in Mathematical Modeling of Gastrointestinal Slow Wave Abnormalities

    PubMed Central

    Du, Peng; Calder, Stefan; Angeli, Timothy R.; Sathar, Shameer; Paskaranandavadivel, Niranchan; O'Grady, Gregory; Cheng, Leo K.

    2018-01-01

    Gastrointestinal (GI) motility is regulated in part by electrophysiological events called slow waves, which are generated by the interstitial cells of Cajal (ICC). Slow waves propagate by a process of “entrainment,” which occurs over a decreasing gradient of intrinsic frequencies in the antegrade direction across much of the GI tract. Abnormal initiation and conduction of slow waves have been demonstrated in, and linked to, a number of GI motility disorders. A range of mathematical models have been developed to study abnormal slow waves and applied to propose novel methods for non-invasive detection and therapy. This review provides a general outline of GI slow wave abnormalities and their recent classification using multi-electrode (high-resolution) mapping methods, with a particular emphasis on the spatial patterns of these abnormal activities. The recently-developed mathematical models are introduced in order of their biophysical scale from cellular to whole-organ levels. The modeling techniques, main findings from the simulations, and potential future directions arising from notable studies are discussed. PMID:29379448