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Sample records for based mathematical model

  1. 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

  2. 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.

  3. Information system based on the mathematical model of the EPS

    NASA Astrophysics Data System (ADS)

    Kalimoldayev, Maksat N.; Abdildayeva, Assel A.; Mamyrbayev, Orken Zh.; Akhmetzhanov, Maksat

    2016-11-01

    This article discusses the structure of an information system, the mathematical and information models of electric power systems. Currently, the major application areas include system relaying data communication systems and automation, automated dispatching and technological management of electric power facilities, as well as computer-aided calculation of energy resources. Automatic control of excitation (ARV) synchronous machines is one of the most effective ways to ensure the stability of power systems. However, the variety of possible options and modes even in a single grid pose significant obstacles to the development of the best means of ensuring sustainability. Thus, the use of ARVs to ensure stability in some cases may not be sufficient. Therefore, there is a need to develop an information system based on a mathematical model.

  4. Mathematical model for light scanning system based on circular laser

    NASA Astrophysics Data System (ADS)

    Xu, Peiquan; Yao, Shun; Lu, Fenggui; Tang, Xinhua; Zhang, Wei

    2005-11-01

    A novel light scanning system based on circular laser trajectory for welding robot is developed. With the help of image processing technique, intelligent laser welding could be realized. According to laser triangulation algorithm and Scheimpflug condition, mathematical model for circular laser vision is built. This scanning system projects circular laser onto welded seams and recovers the depth of the welded seams, escapes from shortcomings of less information, explains ambiguity and single tracking direction inherent in "spot" or "line" type laser trajectory. Three-dimensional (3D) model for welded seams could be recognized after depth recovery. The imaging error is investigated also.

  5. A Cellular Automata-Based Mathematical Model for Thymocyte Development

    PubMed Central

    Souza-e-Silva, Hallan; Savino, Wilson; Feijóo, Raúl A.; Vasconcelos, Ana Tereza Ribeiro

    2009-01-01

    Intrathymic T cell development is an important process necessary for the normal formation of cell-mediated immune responses. Importantly, such a process depends on interactions of developing thymocytes with cellular and extracellular elements of the thymic microenvironment. Additionally, it includes a series of oriented and tunely regulated migration events, ultimately allowing mature cells to cross endothelial barriers and leave the organ. Herein we built a cellular automata-based mathematical model for thymocyte migration and development. The rules comprised in this model take into account the main stages of thymocyte development, two-dimensional sections of the normal thymic microenvironmental network, as well as the chemokines involved in intrathymic cell migration. Parameters of our computer simulations with further adjusted to results derived from previous experimental data using sub-lethally irradiated mice, in which thymus recovery can be evaluated. The model fitted with the increasing numbers of each CD4/CD8-defined thymocyte subset. It was further validated since it fitted with the times of permanence experimentally ascertained in each CD4/CD8-defined differentiation stage. Importantly, correlations using the whole mean volume of young normal adult mice revealed that the numbers of cells generated in silico with the mathematical model fall within the range of total thymocyte numbers seen in these animals. Furthermore, simulations made with a human thymic epithelial network using the same mathematical model generated similar profiles for temporal evolution of thymocyte developmental stages. Lastly, we provided in silico evidence that the thymus architecture is important in the thymocyte development, since changes in the epithelial network result in different theoretical profiles for T cell development/migration. This model likely can be used to predict thymocyte evolution following therapeutic strategies designed for recovery of the thymus in diseases

  6. 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…

  7. Mathematical modelling of microtumour infiltration based on in vitro experiments.

    PubMed

    Luján, Emmanuel; Guerra, Liliana N; Soba, Alejandro; Visacovsky, Nicolás; Gandía, Daniel; Calvo, Juan C; Suárez, Cecilia

    2016-08-08

    The present mathematical models of microtumours consider, in general, volumetric growth and spherical tumour invasion shapes. Nevertheless in many cases, such as in gliomas, a need for more accurate delineation of tumour infiltration areas in a patient-specific manner has arisen. The objective of this study was to build a mathematical model able to describe in a case-specific way as well as to predict in a probabilistic way the growth and the real invasion pattern of multicellular tumour spheroids (in vitro model of an avascular microtumour) immersed in a collagen matrix. The two-dimensional theoretical model was represented by a reaction-convection-diffusion equation that considers logistic proliferation, volumetric growth, a rim with proliferative cells at the tumour surface and invasion with diffusive and convective components. Population parameter values of the model were extracted from the experimental dataset and a shape function that describes the invasion area was derived from each experimental case by image processing. New possible and aleatory shape functions were generated by data mining and Monte Carlo tools by means of a satellite EGARCH model, which were fed with all the shape functions of the dataset. Then the main model is used in two different ways: to reproduce the growth and invasion of a given experimental tumour in a case-specific manner when fed with the corresponding shape function (descriptive simulations) or to generate new possible tumour cases that respond to the general population pattern when fed with an aleatory-generated shape function (predictive simulations). Both types of simulations are in good agreement with empirical data, as it was revealed by area quantification and Bland-Altman analysis. This kind of experimental-numerical interaction has wide application potential in designing new strategies able to predict as much as possible the invasive behaviour of a tumour based on its particular characteristics and microenvironment.

  8. PREFACE: Physics-Based Mathematical Models for Nanotechnology

    NASA Astrophysics Data System (ADS)

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

    2008-03-01

    stain-resistant clothing, but with thousands more anticipated. The focus of this interdisciplinary workshop was on determining what kind of new theoretical and computational tools will be needed to advance the science and engineering of nanomaterials and nanostructures. Thanks to the stimulating environment of the BIRS, participants of the workshop had plenty of opportunity to exchange new ideas on one of the main topics of this workshop—physics-based mathematical models for the description of low-dimensional semiconductor nanostructures (LDSNs) that are becoming increasingly important in technological innovations. The main objective of the workshop was to bring together some of the world leading experts in the field from each of the key research communities working on different aspects of LDSNs in order to (a) summarize the state-of-the-art models and computational techniques for modeling LDSNs, (b) identify critical problems of major importance that require solution and prioritize them, (c) analyze feasibility of existing mathematical and computational methodologies for the solution of some such problems, and (d) use some of the workshop working sessions to explore promising approaches in addressing identified challenges. With the possibility of growing practically any shape and size of heterostructures, it becomes essential to understand the mathematical properties of quantum-confined structures including properties of bulk states, interface states, and surface states as a function of shape, size, and internal strain. This workshop put strong emphasis on discussions of the new mathematics needed in nanotechnology especially in relation to geometry and material-combination optimization of device properties such as electronic, optical, and magnetic properties. The problems that were addressed at this meeting are of immense importance in determining such quantum-mechanical properties and the group of invited participants covered very well all the relevant disciplines

  9. Teaching Mathematical Modelling.

    ERIC Educational Resources Information Center

    Jones, Mark S.

    1997-01-01

    Outlines a course at the University of Glamorgan in the United Kingdom in which a computer algebra system (CAS) teaches mathematical modeling. The format is based on continual assessment of group and individual work stating the problem, a feature list, and formulation of the models. No additional mathematical word processing package is necessary.…

  10. Hybrid modelling framework by using mathematics-based and information-based methods

    NASA Astrophysics Data System (ADS)

    Ghaboussi, J.; Kim, J.; Elnashai, A.

    2010-06-01

    Mathematics-based computational mechanics involves idealization in going from the observed behaviour of a system into mathematical equations representing the underlying mechanics of that behaviour. Idealization may lead mathematical models that exclude certain aspects of the complex behaviour that may be significant. An alternative approach is data-centric modelling that constitutes a fundamental shift from mathematical equations to data that contain the required information about the underlying mechanics. However, purely data-centric methods often fail for infrequent events and large state changes. In this article, a new hybrid modelling framework is proposed to improve accuracy in simulation of real-world systems. In the hybrid framework, a mathematical model is complemented by information-based components. The role of informational components is to model aspects which the mathematical model leaves out. The missing aspects are extracted and identified through Autoprogressive Algorithms. The proposed hybrid modelling framework has a wide range of potential applications for natural and engineered systems. The potential of the hybrid methodology is illustrated through modelling highly pinched hysteretic behaviour of beam-to-column connections in steel frames.

  11. 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…

  12. Mathematical modeling of laser based potato cutting and peeling.

    PubMed

    Ferraz, A Carlos O; Mittal, Gauri S; Bilanski, Walter K; Abdullah, Hussein A

    2007-01-01

    A mathematical model is developed and validated to predict the depth of cut in potato tuber slabs as a function of laser power and travel speed. The model considers laser processing parameters such as input power, spot size and exposure time as well as the properties of the material being cut such as specific heat, thermal conductivity, surface reflectance, etc. The model also considers the phase change of water in potato and the ignition temperature of the solid portion. The composition of the potato tuber is assumed to be of water and solid. The model also assumes that the ablation process is accomplished through ejection of liquid water, debris and water vapour, and combustion of solid. A CO(2) laser operating in c.w. mode was chosen for the experimental work because water absorbs laser energy highly at 10.6 microm, and CO(2) laser units with relatively high output power are available. Slabs of potato tuber were chosen to be laser processed since potato contains high moisture and large amounts of relatively homogeneous tissue. The results of the preliminary calculations and experiments concluded that the model is able to predict the depth of cut in potato tuber parenchyma when subjected to a CO(2) laser beam.

  13. A School-Based Professional Development Programme for Teachers of Mathematical Modelling in Singapore

    ERIC Educational Resources Information Center

    Tan, Liang Soon; Ang, Keng Cheng

    2016-01-01

    A school-based professional development programme (SBPD) aimed at developing secondary school mathematics teachers' competencies to teach mathematical modelling in Singapore is presented and evaluated in this article. The SBPD is characterized by two key features--content elements to develop teachers' knowledge and skills, and transformative…

  14. A mathematical framework for agent based models of complex biological networks.

    PubMed

    Hinkelmann, Franziska; Murrugarra, David; Jarrah, Abdul Salam; Laubenbacher, Reinhard

    2011-07-01

    Agent-based modeling and simulation is a useful method to study biological phenomena in a wide range of fields, from molecular biology to ecology. Since there is currently no agreed-upon standard way to specify such models, it is not always easy to use published models. Also, since model descriptions are not usually given in mathematical terms, it is difficult to bring mathematical analysis tools to bear, so that models are typically studied through simulation. In order to address this issue, Grimm et al. proposed a protocol for model specification, the so-called ODD protocol, which provides a standard way to describe models. This paper proposes an addition to the ODD protocol which allows the description of an agent-based model as a dynamical system, which provides access to computational and theoretical tools for its analysis. The mathematical framework is that of algebraic models, that is, time-discrete dynamical systems with algebraic structure. It is shown by way of several examples how this mathematical specification can help with model analysis. This mathematical framework can also accommodate other model types such as Boolean networks and the more general logical models, as well as Petri nets.

  15. Application of an OCT data-based mathematical model of the foveal pit in Parkinson disease.

    PubMed

    Ding, Yin; Spund, Brian; Glazman, Sofya; Shrier, Eric M; Miri, Shahnaz; Selesnick, Ivan; Bodis-Wollner, Ivan

    2014-11-01

    Spectral-domain Optical coherence tomography (OCT) has shown remarkable utility in the study of retinal disease and has helped to characterize the fovea in Parkinson disease (PD) patients. We developed a detailed mathematical model based on raw OCT data to allow differentiation of foveae of PD patients from healthy controls. Of the various models we tested, a difference of a Gaussian and a polynomial was found to have "the best fit". Decision was based on mathematical evaluation of the fit of the model to the data of 45 control eyes versus 50 PD eyes. We compared the model parameters in the two groups using receiver-operating characteristics (ROC). A single parameter discriminated 70 % of PD eyes from controls, while using seven of the eight parameters of the model allowed 76 % to be discriminated. The future clinical utility of mathematical modeling in study of diffuse neurodegenerative conditions that also affect the fovea is discussed.

  16. 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…

  17. 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…

  18. Summer Teacher Enhancement Institute for Science, Mathematics, and Technology Using the Problem-Based Learning Model

    NASA Technical Reports Server (NTRS)

    Petersen, Richard H.

    1997-01-01

    The objectives of the Institute were: (a) increase participants' content knowledge about aeronautics, science, mathematics, and technology, (b) model and promote the use of scientific inquiry through problem-based learning, (c) investigate the use of instructional technologies and their applications to curricula, and (d) encourage the dissemination of TEI experiences to colleagues, students, and parents.

  19. Approaching mathematical model of the immune network based DNA Strand Displacement system.

    PubMed

    Mardian, Rizki; Sekiyama, Kosuke; Fukuda, Toshio

    2013-12-01

    One biggest obstacle in molecular programming is that there is still no direct method to compile any existed mathematical model into biochemical reaction in order to solve a computational problem. In this paper, the implementation of DNA Strand Displacement system based on nature-inspired computation is observed. By using the Immune Network Theory and Chemical Reaction Network, the compilation of DNA-based operation is defined and the formulation of its mathematical model is derived. Furthermore, the implementation on this system is compared with the conventional implementation by using silicon-based programming. From the obtained results, we can see a positive correlation between both. One possible application from this DNA-based model is for a decision making scheme of intelligent computer or molecular robot.

  20. Frequencies as proportions: Using a teaching model based on Pirie and Kieren's model of mathematical understanding

    NASA Astrophysics Data System (ADS)

    Wright, Vince

    2014-03-01

    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 learners develop their mathematical understanding. The model was adapted to create the teaching model used in the New Zealand Numeracy Development Projects (Ministry of Education, 2007). A case study of a 3-week sequence of instruction with a group of eight 12- and 13-year-old students provided the data. The teacher/researcher used folding back to materials and images and progressing from materials to imaging to number properties to assist students to develop their understanding of frequencies as proportions. The data show that successful implementation of the model is dependent on the teacher noticing and responding to the layers of understanding demonstrated by the students and the careful selection of materials, problems and situations. It supports the use of the model as a useful part of teachers' instructional strategies and the importance of pedagogical content knowledge to the quality of the way the model is used.

  1. 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…

  2. Mathematical modeling in neuroendocrinology.

    PubMed

    Bertram, Richard

    2015-04-01

    Mathematical models are commonly used in neuroscience, both as tools for integrating data and as devices for designing new experiments that test model predictions. The wide range of relevant spatial and temporal scales in the neuroendocrine system makes neuroendocrinology a branch of neuroscience with great potential for modeling. This article provides an overview of concepts that are useful for understanding mathematical models of the neuroendocrine system, as well as design principles that have been illuminated through the use of mathematical models. These principles are found over and over again in cellular dynamics, and serve as building blocks for understanding some of the complex temporal dynamics that are exhibited throughout the neuroendocrine system.

  3. Modelers' Perception of Mathematical Modeling in Epidemiology: A Web-Based Survey

    PubMed Central

    Hejblum, Gilles; Setbon, Michel; Temime, Laura; Lesieur, Sophie; Valleron, Alain-Jacques

    2011-01-01

    Background Mathematical modeling in epidemiology (MME) is being used increasingly. However, there are many uncertainties in terms of definitions, uses and quality features of MME. Methodology/Principal Findings To delineate the current status of these models, a 10-item questionnaire on MME was devised. Proposed via an anonymous internet-based survey, the questionnaire was completed by 189 scientists who had published in the domain of MME. A small minority (18%) of respondents claimed to have in mind a concise definition of MME. Some techniques were identified by the researchers as characterizing MME (e.g. Markov models), while others–at the same level of sophistication in terms of mathematics–were not (e.g. Cox regression). The researchers' opinions were also contrasted about the potential applications of MME, perceived as higly relevant for providing insight into complex mechanisms and less relevant for identifying causal factors. The quality criteria were those of good science and were not related to the size and the nature of the public health problems addressed. Conclusions/Significance This study shows that perceptions on the nature, uses and quality criteria of MME are contrasted, even among the very community of published authors in this domain. Nevertheless, MME is an emerging discipline in epidemiology and this study underlines that it is associated with specific areas of application and methods. The development of this discipline is likely to deserve a framework providing recommendations and guidance at various steps of the studies, from design to report. PMID:21304976

  4. Phase errors elimination in compact digital holoscope (CDH) based on a reasonable mathematical model

    NASA Astrophysics Data System (ADS)

    Wen, Yongfu; Qu, Weijuan; Cheng, Cheeyuen; Wang, Zhaomin; Asundi, Anand

    2015-03-01

    In the compact digital holoscope (CDH) measurement process, theoretically, we need to ensure the distances between the reference wave and object wave to the hologram plane exactly match. However, it is not easy to realize in practice due to the human factors. This can lead to a phase error in the reconstruction result. In this paper, the strict theoretical analysis of the wavefront interference is performed to demonstrate the mathematical model of the phase error and then a phase errors elimination method is proposed based on the advanced mathematical model, which has a more explicit physical meaning. Experiments are carried out to verify the performance of the presented method and the results indicate that it is effective and allows the operator can make operation more flexible.

  5. A MULTISTAGE BIOLOGICALLY BASED MATHEMATICAL MODEL FOR MOUSE LIVER TUMORS INDUCED BY DICHLOROACETIC ACID (DCA) - EXPLORATION OF THE MODEL

    EPA Science Inventory

    A biologically based mathematical model for the induction of liver tumors in mice by dichloroacetic acid (DCA) has been developed from histopathologic analysis of the livers of exposed mice. This analysis suggests that following chronic exposure to DCA, carcinomas can arise dire...

  6. Facial plastic surgery area acquisition method based on point cloud mathematical model solution.

    PubMed

    Li, Xuwu; Liu, Fei

    2013-09-01

    It is one of the hot research problems nowadays to find a quick and accurate method of acquiring the facial plastic surgery area to provide sufficient but irredundant autologous or in vitro skin source for covering extensive wound, trauma, and burnt area. At present, the acquisition of facial plastic surgery area mainly includes model laser scanning, point cloud data acquisition, pretreatment of point cloud data, three-dimensional model reconstruction, and computation of area. By using this method, the area can be computed accurately, but it is hard to control the random error, and it requires a comparatively longer computation period. In this article, a facial plastic surgery area acquisition method based on point cloud mathematical model solution is proposed. This method applies symmetric treatment to the point cloud based on the pretreatment of point cloud data, through which the comparison diagram color difference map of point cloud error before and after symmetry is obtained. The slicing mathematical model of facial plastic area is got through color difference map diagram. By solving the point cloud data in this area directly, the facial plastic area is acquired. The point cloud data are directly operated in this method, which can accurately and efficiently complete the surgery area computation. The result of the comparative analysis shows the method is effective in facial plastic surgery area.

  7. SEQAID: a DNA sequence assembling program based on a mathematical model.

    PubMed Central

    Peltola, H; Söderlund, H; Ukkonen, E

    1984-01-01

    A program package, called SEQAID, to support DNA sequencing is presented. The program automatically assembles long DNA sequences from short fragments with minimal user interaction. Various tools for controlling the assembling process are also available. The main novel features of the system are that SEQAID implements several new well-behaved algorithms based on a mathematical model of the problem. It also utilizes available information on restriction fragments to detect illegitimate overlaps and to find relationships between separately assembled sequence blocks. Experiences with the system are reported including an extremely pathological real sequence which offers an interesting benchmark for this kind of programs. PMID:6320092

  8. Differential properties of Van der Pol — Duffing mathematical model of cerebrovascular haemodynamics based on clinical measurements

    NASA Astrophysics Data System (ADS)

    Parshin, D. V.; Ufimtseva, I. V.; Cherevko, A. A.; Khe, A. K.; Orlov, K. Yu; Krivoshapkin, A. L.; Chupakhin, A. P.

    2016-06-01

    The present paper discusses the method of identification (diseased/healthy) human cerebral vessels by using of mathematical model. Human cerebral circulation as a single tuned circuit, which consists of blood flow, elastic vessels and elastic brain gel tissue is under consideration. Non linear Van der Pol-Duffing equation is assumed as mathematical model of cerebrovascular circulation. Hypothesis of vascular pathology existence in some position of blood vessel, based on mathematical model properties for this position is formulated. Good reliability of hypothesis is proved statistically for 7 patients with arterial aneurysms.

  9. 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…

  10. Mathematical model for adaptive evolution of populations based on a complex domain

    PubMed Central

    Ibrahim, Rabha W.; Ahmad, M.Z.; Al-Janaby, Hiba F.

    2015-01-01

    A mutation is ultimately essential for adaptive evolution in all populations. It arises all the time, but is mostly fixed by enzymes. Further, most do consider that the evolution mechanism is by a natural assortment of variations in organisms in line for random variations in their DNA, and the suggestions for this are overwhelming. The altering of the construction of a gene, causing a different form that may be communicated to succeeding generations, produced by the modification of single base units in DNA, or the deletion, insertion, or rearrangement of larger units of chromosomes or genes. This altering is called a mutation. In this paper, a mathematical model is introduced to this reality. The model describes the time and space for the evolution. The tool is based on a complex domain for the space. We show that the evolution is distributed with the hypergeometric function. The Boundedness of the evolution is imposed by utilizing the Koebe function. PMID:26858564

  11. A biophysically based mathematical model for the catalytic mechanism of glutathione reductase.

    PubMed

    Pannala, Venkat R; Bazil, Jason N; Camara, Amadou K S; Dash, Ranjan K

    2013-12-01

    Glutathione reductase (GR) catalyzes the reduction of oxidized glutathione (GSSG) to reduced glutathione (GSH) using NADPH as the reducing cofactor, and thereby maintains a constant GSH level in the system. GSH scavenges superoxide (O2(*-)) and hydroxyl radicals (OH) nonenzymatically or by serving as an electron donor to several enzymes involved in reactive oxygen species (ROS) detoxification. In either case, GSH oxidizes to GSSG and is subsequently regenerated by the catalytic action of GR. Although the GR kinetic mechanism has been extensively studied under various experimental conditions with variable substrates and products, the catalytic mechanism has not been studied in terms of a mechanistic model that accounts for the effects of the substrates and products on the reaction kinetics. The aim of this study is therefore to develop a comprehensive mathematical model for the catalytic mechanism of GR. We use available experimental data on GR kinetics from various species/sources to develop the mathematical model and estimate the associated model parameters. The model simulations are consistent with the experimental observation that GR operates via both ping-pong and sequential branching mechanisms based on relevant concentrations of its reaction substrate GSSG. Furthermore, we show the observed pH-dependent substrate inhibition of GR activity by GSSG and bimodal behavior of GR activity with pH. The model presents a unique opportunity to understand the effects of products on the kinetics of GR. The model simulations show that under physiological conditions, where both substrates and products are present, the flux distribution depends on the concentrations of both GSSG and NADP(+), with ping-pong flux operating at low levels and sequential flux dominating at higher levels. The kinetic model of GR may serve as a key module for the development of integrated models for ROS-scavenging systems to understand protection of cells under normal and oxidative stress

  12. Empirical and physics based mathematical models of uranium hydride decomposition kinetics with quantified uncertainties.

    SciTech Connect

    Salloum, Maher N.; Gharagozloo, Patricia E.

    2013-10-01

    Metal particle beds have recently become a major technique for hydrogen storage. In order to extract hydrogen from such beds, it is crucial to understand the decomposition kinetics of the metal hydride. We are interested in obtaining a a better understanding of the uranium hydride (UH3) decomposition kinetics. We first developed an empirical model by fitting data compiled from different experimental studies in the literature and quantified the uncertainty resulting from the scattered data. We found that the decomposition time range predicted by the obtained kinetics was in a good agreement with published experimental results. Secondly, we developed a physics based mathematical model to simulate the rate of hydrogen diffusion in a hydride particle during the decomposition. We used this model to simulate the decomposition of the particles for temperatures ranging from 300K to 1000K while propagating parametric uncertainty and evaluated the kinetics from the results. We compared the kinetics parameters derived from the empirical and physics based models and found that the uncertainty in the kinetics predicted by the physics based model covers the scattered experimental data. Finally, we used the physics-based kinetics parameters to simulate the effects of boundary resistances and powder morphological changes during decomposition in a continuum level model. We found that the species change within the bed occurring during the decomposition accelerates the hydrogen flow by increasing the bed permeability, while the pressure buildup and the thermal barrier forming at the wall significantly impede the hydrogen extraction.

  13. [Mathematical models of hysteresis

    SciTech Connect

    Mayergoyz, I.D.

    1991-01-01

    The research described in this proposal is currently being supported by the US Department of Energy under the contract Mathematical Models of Hysteresis''. Thus, before discussing the proposed research in detail, it is worthwhile to describe and summarize the main results achieved in the course of our work under the above contract. Our ongoing research has largely been focused on the development of mathematical models of hysteretic nonlinearities with nonlocal memories''. The distinct feature of these nonlinearities is that their current states depend on past histories of input variations. It turns out that memories of hysteretic nonlinearities are quite selective. Indeed, experiments show that only some past input extrema leave their marks upon future states of hysteretic nonlinearities. Thus special mathematical tools are needed in order to describe nonlocal selective memories of hysteretic nonlinearities. Our research has been primarily concerned with Preisach-type models of hysteresis. All these models have a common generic feature; they are constructed as superpositions of simplest hysteretic nonlinearities-rectangular loops. Our study has by and large been centered around the following topics: various generalizations and extensions of the classical Preisach model, finding of necessary and sufficient conditions for the representation of actual hysteretic nonlinearities by various Preisach type models, solution of identification problems for these models, numerical implementation and experimental testing of Preisach type models. Although the study of Preisach type models has constituted the main direction of the research, some effort has also been made to establish some interesting connections between these models and such topics as: the critical state model for superconducting hysteresis, the classical Stoner-Wohlfarth model of vector magnetic hysteresis, thermal activation type models for viscosity, magnetostrictive hysteresis and neural networks.

  14. Mathematical modeling and kinematics: A study of emerging themes and their implications for learning mathematics through an inquiry-based approach

    NASA Astrophysics Data System (ADS)

    Carrejo, David John

    construction of the learners' models included several robust conceptions of average velocity and considerations of what constitutes a "good enough" model to use when describing and predicting motion. The emergence of these themes has implications for teaching and learning mathematics through an inquiry-based approach to kinematics.

  15. 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…

  16. Richardson, mathematical modeller

    NASA Astrophysics Data System (ADS)

    Vreugdenhil, C. B.

    1994-03-01

    On the occasion of the 70th anniversary of Richardson's book Weather Prediction by Numerical Process (Cambridge University Press, Cambridge), a review is given of Richardson's scientific work. He made lasting contributions to very diverse fields of interest, such as finite-difference methods and related numerical methods, weather forecasting by computer, turbulence, international relations, and fractals. Although he was an original experimenter, the main present-day interest is in his mathematical modelling work.

  17. 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…

  18. Analysis of laser remote fusion cutting based on a mathematical model

    SciTech Connect

    Matti, R. S.; Ilar, T.; Kaplan, A. F. H.

    2013-12-21

    Laser remote fusion cutting is analyzed by the aid of a semi-analytical mathematical model of the processing front. By local calculation of the energy balance between the absorbed laser beam and the heat losses, the three-dimensional vaporization front can be calculated. Based on an empirical model for the melt flow field, from a mass balance, the melt film and the melting front can be derived, however only in a simplified manner and for quasi-steady state conditions. Front waviness and multiple reflections are not modelled. The model enables to compare the similarities, differences, and limits between laser remote fusion cutting, laser remote ablation cutting, and even laser keyhole welding. In contrast to the upper part of the vaporization front, the major part only slightly varies with respect to heat flux, laser power density, absorptivity, and angle of front inclination. Statistical analysis shows that for high cutting speed, the domains of high laser power density contribute much more to the formation of the front than for low speed. The semi-analytical modelling approach offers flexibility to simplify part of the process physics while, for example, sophisticated modelling of the complex focused fibre-guided laser beam is taken into account to enable deeper analysis of the beam interaction. Mechanisms like recast layer generation, absorptivity at a wavy processing front, and melt film formation are studied too.

  19. Analysis of laser remote fusion cutting based on a mathematical model

    NASA Astrophysics Data System (ADS)

    Matti, R. S.; Ilar, T.; Kaplan, A. F. H.

    2013-12-01

    Laser remote fusion cutting is analyzed by the aid of a semi-analytical mathematical model of the processing front. By local calculation of the energy balance between the absorbed laser beam and the heat losses, the three-dimensional vaporization front can be calculated. Based on an empirical model for the melt flow field, from a mass balance, the melt film and the melting front can be derived, however only in a simplified manner and for quasi-steady state conditions. Front waviness and multiple reflections are not modelled. The model enables to compare the similarities, differences, and limits between laser remote fusion cutting, laser remote ablation cutting, and even laser keyhole welding. In contrast to the upper part of the vaporization front, the major part only slightly varies with respect to heat flux, laser power density, absorptivity, and angle of front inclination. Statistical analysis shows that for high cutting speed, the domains of high laser power density contribute much more to the formation of the front than for low speed. The semi-analytical modelling approach offers flexibility to simplify part of the process physics while, for example, sophisticated modelling of the complex focused fibre-guided laser beam is taken into account to enable deeper analysis of the beam interaction. Mechanisms like recast layer generation, absorptivity at a wavy processing front, and melt film formation are studied too.

  20. Problem-Based Learning--Buginese Cultural Knowledge Model--Case Study: Teaching Mathematics at Junior High School

    ERIC Educational Resources Information Center

    Cheriani, Cheriani; Mahmud, Alimuddin; Tahmir, Suradi; Manda, Darman; Dirawan, Gufran Darma

    2015-01-01

    This study aims to determine the differences in learning output by using Problem Based Model combines with the "Buginese" Local Cultural Knowledge (PBL-Culture). It is also explores the students activities in learning mathematics subject by using PBL-Culture Models. This research is using Mixed Methods approach that combined quantitative…

  1. Validation of 2DH hydrodynamic and morphological mathematical models. A methodology based on SAR imaging

    NASA Astrophysics Data System (ADS)

    Canelas, Ricardo; Heleno, Sandra; Pestana, Rita; Ferreira, Rui M. L.

    2014-05-01

    The objective of the present work is to devise a methodology to validate 2DH shallow-water models suitable to simulate flow hydrodynamics and channel morphology. For this purpose, a 2DH mathematical model, assembled at CEHIDRO, IST, is employed to model Tagus river floods over a 70 km reach and Synthetic Aperture Radar (SAR) images are collected to retrieve planar inundation extents. The model is suited for highly unsteady discontinuous flows over complex, time-evolving geometries, employing a finite-volume discretization scheme, based on a flux-splitting technique incorporating a reviewed version of the Roe Riemann solver. Novel closure terms for the non-equilibrium sediment transport model are included. New boundary conditions are employed, based on the Riemann variables associated the outgoing characteristic fields, coping with the provided hydrographs in a mathematically coherent manner. A high resolution Digital Elevation Model (DEM) is used and levee structures are considered as fully erodible elements. Spatially heterogeneous roughness characteristics are derived from land-use databases such as CORINE LandCover 2006. SAR satellite imagery of the floods is available and is used to validate the simulation results, with particular emphasis on the 2000/2001 flood. The delimited areas from the satellite and simulations are superimposed. The quality of the adjustment depends on the calibration of roughness coefficients and the spatial discretization of with small structures, with lengths at the order of the spatial discretization. Flow depths and registered discharges are recovered from the simulation and compared with data from a measuring station in the domain, with the comparison revealing remarkably high accuracy, both in terms of amplitudes and phase. Further inclusion of topographical detail should improve the comparison of flood extents regarding satellite data. The validated model was then employed to simulate 100-year floods in the same reach. The

  2. Mathematical Modelling in European Education

    ERIC Educational Resources Information Center

    Ferri, Rita Borromeo

    2013-01-01

    Teaching and learning of mathematical modelling has become a key competence within school curricula and educational standards in many countries of the world. The term mathematical modelling, its meaning, and how it can be implemented in mathematics lessons have been intensively discussed during several Conferences of the European Society for…

  3. 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…

  4. 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…

  5. Investigating mathematical models of immuno-interactions with early-stage cancer under an agent-based modelling perspective

    PubMed Central

    2013-01-01

    Many advances in research regarding immuno-interactions with cancer were developed with the help of ordinary differential equation (ODE) models. These models, however, are not effectively capable of representing problems involving individual localisation, memory and emerging properties, which are common characteristics of cells and molecules of the immune system. Agent-based modelling and simulation is an alternative paradigm to ODE models that overcomes these limitations. In this paper we investigate the potential contribution of agent-based modelling and simulation when compared to ODE modelling and simulation. We seek answers to the following questions: Is it possible to obtain an equivalent agent-based model from the ODE formulation? Do the outcomes differ? Are there any benefits of using one method compared to the other? To answer these questions, we have considered three case studies using established mathematical models of immune interactions with early-stage cancer. These case studies were re-conceptualised under an agent-based perspective and the simulation results were then compared with those from the ODE models. Our results show that it is possible to obtain equivalent agent-based models (i.e. implementing the same mechanisms); the simulation output of both types of models however might differ depending on the attributes of the system to be modelled. In some cases, additional insight from using agent-based modelling was obtained. Overall, we can confirm that agent-based modelling is a useful addition to the tool set of immunologists, as it has extra features that allow for simulations with characteristics that are closer to the biological phenomena. PMID:23734575

  6. Investigating mathematical models of immuno-interactions with early-stage cancer under an agent-based modelling perspective.

    PubMed

    Figueredo, Grazziela P; Siebers, Peer-Olaf; Aickelin, Uwe

    2013-01-01

    Many advances in research regarding immuno-interactions with cancer were developed with the help of ordinary differential equation (ODE) models. These models, however, are not effectively capable of representing problems involving individual localisation, memory and emerging properties, which are common characteristics of cells and molecules of the immune system. Agent-based modelling and simulation is an alternative paradigm to ODE models that overcomes these limitations. In this paper we investigate the potential contribution of agent-based modelling and simulation when compared to ODE modelling and simulation. We seek answers to the following questions: Is it possible to obtain an equivalent agent-based model from the ODE formulation? Do the outcomes differ? Are there any benefits of using one method compared to the other? To answer these questions, we have considered three case studies using established mathematical models of immune interactions with early-stage cancer. These case studies were re-conceptualised under an agent-based perspective and the simulation results were then compared with those from the ODE models. Our results show that it is possible to obtain equivalent agent-based models (i.e. implementing the same mechanisms); the simulation output of both types of models however might differ depending on the attributes of the system to be modelled. In some cases, additional insight from using agent-based modelling was obtained. Overall, we can confirm that agent-based modelling is a useful addition to the tool set of immunologists, as it has extra features that allow for simulations with characteristics that are closer to the biological phenomena.

  7. Identifying potential misfit items in cognitive process of learning engineering mathematics based on Rasch model

    NASA Astrophysics Data System (ADS)

    Ataei, Sh; Mahmud, Z.; Khalid, M. N.

    2014-04-01

    The students learning outcomes clarify what students should know and be able to demonstrate after completing their course. So, one of the issues on the process of teaching and learning is how to assess students' learning. This paper describes an application of the dichotomous Rasch measurement model in measuring the cognitive process of engineering students' learning of mathematics. This study provides insights into the perspective of 54 engineering students' cognitive ability in learning Calculus III based on Bloom's Taxonomy on 31 items. The results denote that some of the examination questions are either too difficult or too easy for the majority of the students. This analysis yields FIT statistics which are able to identify if there is data departure from the Rasch theoretical model. The study has identified some potential misfit items based on the measurement of ZSTD where the removal misfit item was accomplished based on the MNSQ outfit of above 1.3 or less than 0.7 logit. Therefore, it is recommended that these items be reviewed or revised to better match the range of students' ability in the respective course.

  8. Chronology of DIC technique based on the fundamental mathematical modeling and dehydration impact.

    PubMed

    Alias, Norma; Saipol, Hafizah Farhah Saipan; Ghani, Asnida Che Abd

    2014-12-01

    A chronology of mathematical models for heat and mass transfer equation is proposed for the prediction of moisture and temperature behavior during drying using DIC (Détente Instantanée Contrôlée) or instant controlled pressure drop technique. DIC technique has the potential as most commonly used dehydration method for high impact food value including the nutrition maintenance and the best possible quality for food storage. The model is governed by the regression model, followed by 2D Fick's and Fourier's parabolic equation and 2D elliptic-parabolic equation in a rectangular slice. The models neglect the effect of shrinkage and radiation effects. The simulations of heat and mass transfer equations with parabolic and elliptic-parabolic types through some numerical methods based on finite difference method (FDM) have been illustrated. Intel®Core™2Duo processors with Linux operating system and C programming language have been considered as a computational platform for the simulation. Qualitative and quantitative differences between DIC technique and the conventional drying methods have been shown as a comparative.

  9. Mathematical model of biological order state or syndrome in traditional Chinese medicine: based on electromagnetic radiation within the human body.

    PubMed

    Han, Jinxiang; Huang, Jinzhao

    2012-03-01

    In this study, based on the resonator model and exciplex model of electromagnetic radiation within the human body, mathematical model of biological order state, also referred to as syndrome in traditional Chinese medicine, was established and expressed as: "Sy = v/ 1n(6I + 1)". This model provides the theoretical foundation for experimental research addressing the order state of living system, especially the quantitative research syndrome in traditional Chinese medicine.

  10. Causality, mathematical models and statistical association: dismantling evidence-based medicine.

    PubMed

    Thompson, R Paul

    2010-04-01

    From humble beginnings, largely at the medical school at McMaster University, Canada, the evidence-based medicine (EBM) movement has enjoyed a spectacular rise in international acceptance over the last 25 years. Randomized controlled trials (RCTs) and systematic reviews based on them have pride of place (the gold standard) in EBM's hierarchy of evidence; models and theories are relegated to the bottom of the hierarchy. In the last decade, RCTs have been extensively criticized. I briefly rehearse those criticisms because they are an important backdrop to the criticism of EBM developed in this paper. In essence, the argument developed here is that RCTs use mathematics solely as a tool of analysis rather than as the language of the science and that this fundamentally affects the validity of causal claims. As EBM gives pride of place to RCTs and devalues theoretical models - a devaluation that would be incomprehensible to a physicist or biologist - the validity of EBM's causal claims and knowledge claims are weak and far from a 'gold standard'.

  11. Physiologically based mathematical models to optimize therapies against metastatic colorectal cancer: a mini-review.

    PubMed

    Ballesta, Annabelle; Clairambault, Jean

    2014-01-01

    Understanding and improving the effects of combined drug treatments in metastatic colorectal Cancer (mCRC) is a multidisciplinary and multiscale problem, that can benefit from a systems biology approach. Although a quite limited number of active drugs have been approved for clinical applications, a variety of combined delivery regimen options are actually used in the clinic, so that choosing between them, or designing new ones, is not an obvious task, which calls for some rationalization based on physiological principles. We propose some physiologically based molecular pharmacokinetics-pharmacodynamics models for the main cytotoxic drugs used in the clinic and call for others describing more recently used agents, such as associated with monoclonal antibodies. We also advocate simultaneously designing models of the proliferating cell populations under therapeutic control, as cancer is primarily a disruption of physiological control on tissue proliferation. These two types of models are based on differential equations to continuously describe both the fate of drugs in the organism, from infusion until pharmacological effects, and their impact on the proliferation of cell populations, healthy and tumor. The multiscale nature of colorectal cancer, from the disruption of intracellular pathways to tumor growth observed at the macroscopic level, together with its frequent multilocal extension by simultaneous metastases in various healthy tissues of the organism at the time of diagnosis, and later, call for multiscale mathematical models. We thus propose a multi-level vision of cytotoxic drug use in the clinic, in which the weapon in the hands of clinicians, a drug combination regimen, the targets -wanted and unwanted -on which it exerts its effects, molecular pathways in proliferating cell populations, and the environment of the latter in a whole organism, are all considered in order to design a rationale for appropriate shooting, i.e., treatment optimization under

  12. Mathematical models of vaccination.

    PubMed

    Scherer, Almut; McLean, Angela

    2002-01-01

    Mathematical models of epidemics have a long history of contributing to the understanding of the impact of vaccination programmes. Simple, one-line models can predict target vaccination coverage that will eradicate an infectious agent, whilst other questions require complex simulations of stochastic processes in space and time. This review introduces some simple ordinary differential equation models of mass vaccination that can be used to address important questions about the predicted impact of vaccination programmes. We show how to calculate the threshold vaccination coverage rate that will eradicate an infection, explore the impact of vaccine-induced immunity that wanes through time, and study the competitive interactions between vaccine susceptible and vaccine resistant strains of infectious agent.

  13. A mathematical model for crop spectral-temporal trajectories based on a plant growth model

    NASA Technical Reports Server (NTRS)

    Woolford, T. L.

    1983-01-01

    The Kubelka-Munk radiative transfer model is combined with an approximation of Kauth-Thomas greeness and brightness transforms to derive approximate closed form expressions for crop greeness and brightness surrogates in terms of canopy biomass. The greeness relation derived resembles an existing empirical relation between leaf area index and greeness. A simple growth model based on interception and utilization of photosynthetically active radiation is developed and used to describe the time evolution of greeness and brightness. The model developed does not yet yield definitive profile calculations but suggests a conceptual framework which may be found useful for further profile analysis.

  14. Teaching Conceptual Model-Based Word Problem Story Grammar to Enhance Mathematics Problem Solving

    ERIC Educational Resources Information Center

    Xin, Yan Ping; Wiles, Ben; Lin, Yu-Ying

    2008-01-01

    Borrowing the concept of story grammar from reading comprehension literature, the purpose of this study was to examine the effect of teaching "word problem (WP) story grammar" on arithmetic WP solving that emphasizes the algebraic expression of mathematical relations in conceptual models. Participants were five students in Grades 4 and 5 with or…

  15. Mathematical Modelling of Data: Software for Pedagogy.

    ERIC Educational Resources Information Center

    Bellomonte, L.; Sperandeo-Mineo, R. M.

    1993-01-01

    Discussion of mathematical modeling, particularly for high school physics curricula, focuses on software that is connected with laboratory work and the inference of mathematical models based on measurements of physical quantities. Fitting procedures are described, and user interface is explained. (Contains nine references.) (LRW)

  16. 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…

  17. Modeling Zombie Outbreaks: A Problem-Based Approach to Improving Mathematics One Brain at a Time

    ERIC Educational Resources Information Center

    Lewis, Matthew; Powell, James A.

    2016-01-01

    A great deal of educational literature has focused on problem-based learning (PBL) in mathematics at the primary and secondary level, but arguably there is an even greater need for PBL in college math courses. We present a project centered around the Humans versus Zombies moderated tag game played on the Utah State University campus. We discuss…

  18. ADMET: ADipocyte METabolism mathematical model.

    PubMed

    Micheloni, Alessio; Orsi, Gianni; De Maria, Carmelo; Vozzi, Giovanni

    2015-01-01

    White fat cells have an important physiological role in maintaining triglyceride and free fatty acid levels due to their fundamental storage property, as well as determining insulin resistance. ADipocyte METabolism is a mathematical model that mimics the main metabolic pathways of human white fat cell, connecting inputs (composition of culture medium) to outputs (glycerol and free fatty acid release). It is based on a set of nonlinear differential equations, implemented in Simulink® and controlled by cellular energetic state. The validation of this model is based on a comparison between the simulation results and a set of experimental data collected from the literature.

  19. 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…

  20. A Bacteria-based Experimental Platform to Test Parameters Raised by Mathematical Models on Population Dynamics

    NASA Astrophysics Data System (ADS)

    Lage, Claudia; Cardoso, Janine; Czary, Ivan; Leitao, Alvaro; Boatto, Stefanella

    2010-09-01

    Bacterial populations are current models to assay biological effects of a number of different treatments on the basis of a high-number statistics. One typical bacterial inoculum grows at doubling rates as fast as some 30 min per generation, reaching up to ˜109 cells per ml of medium in a few hours. Given the features of such experimental protocol, it is easy to test the impact of environmental modifications during bacteria growth, by scoring doubling rates time, final cell concentration, oxygen consumption, mutagenesis rates, cell viability under different selective pressures, etc. The drawing of a actual dose-response or kinetic curves can feed parameters on a given mathematical model on population dynamics by weighting each equation term. The purpose of this talk is to present experimental schemes with bacterial populations so as to serve as parallel two-hands testing of different mathematical models on populations dynamics.

  1. Teaching and Assessing Mathematical Modelling.

    ERIC Educational Resources Information Center

    Lingefjard, T.

    2002-01-01

    Reports on the observed actions of prospective Swedish secondary mathematics teachers as they were working in a modeling situation. Discusses the way the students tackled the modeling situation and their strategies and attitudes as well as the difficulties in assessing mathematical modeling performance. (KHR)

  2. Mathematical model of orbital and ground-based cross-dispersion spectrographs

    NASA Astrophysics Data System (ADS)

    Yushkin, M. V.; Fatkhullin, T. A.; Panchuk, V. E.

    2016-07-01

    We present the technique and algorithm of numerical modeling of high-resolution spectroscopic equipment. The software is implemented in C++ using nVidia CUDA technology. We report the results of currently developedmodeling of new-generation echelle spectrographs. To validate the algorithms used to construct the mathematical model, we present the results of modeling of NES spectrograph of the 6-m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences. A comparison of simulated and real images of the spectra acquired with NES spectrograph demonstrates good agreement between the model constructed and experimental data.

  3. Calculation procedures for oil free scroll compressors based on mathematical modelling of working process

    NASA Astrophysics Data System (ADS)

    Paranin, Y.; Burmistrov, A.; Salikeev, S.; Fomina, M.

    2015-08-01

    Basic propositions of calculation procedures for oil free scroll compressors characteristics are presented. It is shown that mathematical modelling of working process in a scroll compressor makes it possible to take into account such factors influencing the working process as heat and mass exchange, mechanical interaction in working chambers, leakage through slots, etc. The basic mathematical model may be supplemented by taking into account external heat exchange, elastic deformation of scrolls, inlet and outlet losses, etc. To evaluate the influence of procedure on scroll compressor characteristics calculations accuracy different calculations were carried out. Internal adiabatic efficiency was chosen as a comparative parameter which evaluates the perfection of internal thermodynamic and gas-dynamic compressor processes. Calculated characteristics are compared with experimental values obtained for the compressor pilot sample.

  4. Mathematical Modeling of Kidney Transport

    PubMed Central

    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. PMID:23852667

  5. 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…

  6. Are Clade Specific HIV Vaccines a Necessity? An Analysis Based on Mathematical Models.

    PubMed

    Dimitrov, Dobromir; Kublin, James G; Ramsey, Scott; Corey, Lawrence

    2015-12-01

    As HIV-1 envelope immune responses are critical to vaccine related protection, most candidate HIV vaccines entering efficacy trials are based upon a clade specific design. This need for clade specific vaccine prototypes markedly reduces the implementation of potentially effective HIV vaccines. We utilized a mathematical model to determine the effectiveness of immediate roll-out of a non-clade matched vaccine with reduced efficacy compared to constructing clade specific vaccines, which would take considerable time to manufacture and test in safety and efficacy trials. We simulated the HIV epidemic in San Francisco (SF) and South Africa (SA) and projected effectiveness of three vaccination strategies: i) immediate intervention with a 20-40% vaccine efficacy (VE) non-matched vaccine, ii) delayed intervention by developing a 50% VE clade-specific vaccine, and iii) immediate intervention with a non-matched vaccine replaced by a clade-specific vaccine when developed. Immediate vaccination with a non-clade matched vaccine, even with reduced efficacy, would prevent thousands of new infections in SF and millions in SA over 30 years. Vaccination with 50% VE delayed for five years needs six and 12 years in SA to break-even with immediate 20 and 30% VE vaccination, respectively, while not able to surpass the impact of immediate 40% VE vaccination over 30 years. Replacing a 30% VE with a 50% VE vaccine after 5 years reduces the HIV acquisition by 5% compared to delayed vaccination. The immediate use of an HIV vaccine with reduced VE in high risk communities appears desirable over a short time line but higher VE should be the pursued to achieve strong long-term impact. Our analysis illustrates the importance of developing surrogate markers (correlates of protection) to allow bridging types of immunogenicity studies to support more rapid assessment of clade specific vaccines.

  7. Water network cost optimization in a paper mill based on a new library of mathematical models.

    PubMed

    Lizarralde, I; Claeys, F; Ordóñez, R; de Gracia, M; Sancho, L; Grau, P

    2012-01-01

    The increasing costs associated with water supply and the disposal of wastewater has stimulated industries to seek more efficient water management systems. Mathematical modelling and simulation can be a very valuable tool for the study of the multiple alternatives available whilst assessing optimum solutions for water management in industry. This study introduces a new steady state model library able to reproduce industrial water circuits. It has been implemented in a novel software framework for the representation, simulation and optimization of industrial water networks. A water circuit representing a paper mill has been modelled and simulated showing the capability to reproduce real case studies. Alternative scenarios for the water network have also been tested to assess the capability of the models to optimize water circuits minimizing total cost.

  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. Mathematical modeling of glycerol biotransformation

    NASA Astrophysics Data System (ADS)

    Popova-Krumova, Petya; Yankova, Sofia; Ilieva, Biliana

    2013-12-01

    A method for mathematical modeling of glycerol biotransformation by Klebsiella oxytoca is presented. Glycerol is a renewable resource for it is formed as a by-product during biodiesel production. Because of its large volume production, it seems to be a good idea to develop a technology that converts this waste into products of high value (1, 3-Propanediol; 2, 3-Butanediol). The kinetic model of this process consists of many equations and parameters. The minimization of the least square function will be used for model parameters identification. In cases of parameters identification in multiparameter models the minimization of the least square function is very difficult because it is multiextremal. This is the main problem in the multiextremal function minimization which will be solved on the base a hierarchical approach, using a polynomial approximation of the experimental data.

  10. 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).

  11. Teaching Mathematical Modelling in a Design Context: A Methodology Based on the Mechanical Analysis of a Domestic Cancrusher.

    ERIC Educational Resources Information Center

    Pace, Sydney

    2000-01-01

    Presents a methodology for teaching mathematical modeling skills to A-level students. Gives an example illustrating how mathematics teachers and design teachers can take joint perspective in devising learning opportunities that develop mathematical and design skills concurrently. (Contains 14 references.) (Author/ASK)

  12. Growth of Microbial Populations. Mathematical Modeling, Laboratory Exercises, and Model-Based Data Analysis

    ERIC Educational Resources Information Center

    Juska, Alfonsas; Gedminiene, Genovaite; Ivanec, Ruta

    2006-01-01

    This paper has arisen as a result of teaching Models in Biology to undergraduates of Bioengineering at the Gediminas Technical University of Vilnius. The aim is to teach the students to use a fresh approach to the problems they are familiar with, to come up with an articulate verbal model after a mental effort, to express it in rigorous…

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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…

  18. FINAL PROJECT REPORT DOE Early Career Principal Investigator Program Project Title: Developing New Mathematical Models for Multiphase Flows Based on a Fundamental Probability Density Function Approach

    SciTech Connect

    Shankar Subramaniam

    2009-04-01

    This final project report summarizes progress made towards the objectives described in the proposal entitled “Developing New Mathematical Models for Multiphase Flows Based on a Fundamental Probability Density Function Approach”. Substantial progress has been made in theory, modeling and numerical simulation of turbulent multiphase flows. The consistent mathematical framework based on probability density functions is described. New models are proposed for turbulent particle-laden flows and sprays.

  19. 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…

  20. MAX meets ADAM: a dosimetric comparison between a voxel-based and a mathematical model for external exposure to photons.

    PubMed

    Kramer, R; Vieira, J W; Khoury, H J; de Andrade Lima, F

    2004-03-21

    The International Commission on Radiological Protection intends to revise the organ and tissue equivalent dose conversion coefficients published in various reports. For this purpose the mathematical human medical internal radiation dose (MIRD) phantoms, actually in use, have to be replaced by recently developed voxel-based phantoms. This study investigates the dosimetric consequences, especially with respect to the effective male dose, if not only a MIRD phantom is replaced by a voxel phantom, but also if the tissue compositions and the radiation transport codes are changed. This task will be resolved by systematically replacing in the mathematical ADAM/GSF exposure model, first the radiation transport code, then the tissue composition and finally the phantom anatomy, in order to arrive at the voxel-based MAX/EGS4 exposure model. The results show that the combined effect of these replacements can decrease the effective male dose by up to 25% for external exposures to photons for incident energies above 30 keV for different field geometries, mainly because of increased shielding by a heterogeneous skeleton and by the overlying adipose and muscle tissue, and also because of the positions internal organs have in a realistically designed human body compared to their positions in the mathematically constructed phantom.

  1. The Development of Learning Devices Based Guided Discovery Model to Improve Understanding Concept and Critical Thinking Mathematically Ability of Students at Islamic Junior High School of Medan

    ERIC Educational Resources Information Center

    Yuliani, Kiki; Saragih, Sahat

    2015-01-01

    The purpose of this research was to: 1) development of learning devices based guided discovery model in improving of understanding concept and critical thinking mathematically ability of students at Islamic Junior High School; 2) describe improvement understanding concept and critical thinking mathematically ability of students at MTs by using…

  2. Optimal tuberculosis prevention and control strategy from a mathematical model based on real data.

    PubMed

    Choi, Sunhwa; Jung, Eunok

    2014-07-01

    A mathematical control model for the transmission dynamics of tuberculosis (TB) in South Korea is developed on the basis of the reported active-TB and relapse-TB incidence data. In this work, optimal control theory is used to propose optimal TB prevention and control strategy and rearrange the government TB budget for the best TB elimination plan. The impact of distancing, case finding, and/or case holding controls are investigated when the number of infected and infectious individuals are minimized, while the intervention costs are kept low. The implementation of optimal control measures shows that the distancing control, such as isolation of infectious people, early TB patient detection, and educational program/campaign for healthy control, is the most effective control factor for the prevention of TB transmission in South Korea.

  3. A new mathematical modelling based shape extraction technique for Forensic Odontology.

    PubMed

    G, Jaffino; A, Banumathi; Gurunathan, Ulaganathan; B, Vijayakumari; J, Prabin Jose

    2017-04-01

    Forensic Odontology is a specific means for identifying a person in which deceased, and particularly in fatality incidents. The algorithm can be proposed to identify a person by comparing both postmortem (PM) and antemortem (AM) dental radiographs and photographs. This work aims to introduce a new mathematical algorithm for photographs in addition with radiographs. Isoperimetric graph partitioning method is used to extract the shape of dental images in forensic identification. Shape matching is done by comparing AM and PM dental images using both similarity and distance measures. Experimental results prove that the higher matching distance is observed by distance metric rather than similarity measures. The results of this algorithm show that a high hit rate is observed for distance based performance measures and it is well suited for forensic odontologist to identify a person.

  4. Mathematical models based on transfer functions to estimate tissue temperature during RF cardiac ablation in real time.

    PubMed

    Alba-Martínez, Jose; Trujillo, Macarena; Blasco-Gimenez, Ramon; Berjano, Enrique

    2012-01-01

    Radiofrequency cardiac ablation (RFCA) has been used to treat certain types of cardiac arrhythmias by producing a thermal lesion. Even though a tissue temperature higher than 50ºC is required to destroy the target, thermal mapping is not currently used during RFCA. Our aim was thus to develop mathematical models capable of estimating tissue temperature from tissue characteristics acquired or estimated at the beginning of the procedure (electrical conductivity, thermal conductivity, specific heat and density) and the applied voltage at any time. Biological tissue was considered as a system with an input (applied voltage) and output (tissue temperature), and so the mathematical models were based on transfer functions relating these variables. We used theoretical models based on finite element method to verify the mathematical models. Firstly, we solved finite element models to identify the transfer functions between the temperature at a depth of 4 mm and a constant applied voltage using a 7Fr and 4 mm electrode. The results showed that the relationships can be expressed as first-order transfer functions. Changes in electrical conductivity only affected the static gain of the system, while specific heat variations produced a change in the dynamic system response. In contrast, variations in thermal conductivity modified both the static gain and the dynamic system response. Finally, to assess the performance of the transfer functions obtained, we conducted a new set of computer simulations using a controlled temperature protocol and considering the temperature dependence of the thermal and electrical conductivities, i.e. conditions closer to those found in clinical use. The results showed that the difference between the values estimated from transfer functions and the temperatures obtained from finite element models was less than 4ºC, which suggests that the proposed method could be used to estimate tissue temperature in real time.

  5. And So It Grows: Using a Computer-Based Simulation of a Population Growth Model to Integrate Biology & Mathematics

    ERIC Educational Resources Information Center

    Street, Garrett M.; Laubach, Timothy A.

    2013-01-01

    We provide a 5E structured-inquiry lesson so that students can learn more of the mathematics behind the logistic model of population biology. By using models and mathematics, students understand how population dynamics can be influenced by relatively simple changes in the environment.

  6. 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…

  7. A method of ecological and economic risk assessment during the development of the shelf based on mathematical modelling

    NASA Astrophysics Data System (ADS)

    Solovyova, N. V.; Lobkovsky, L. I.

    2015-09-01

    This paper proposes a method of mathematical modelling of ecological risk based on a synthesis of dynamic and probabilistic risk assessment techniques. The probability of assessment of an acceptable probability of an anthropogenic impact to minimize economic costs is proposed. The dependence of an acceptable probability of an anthropogenic impact on the ecological risk is demonstrated with an example calculation. The results of the modelling of the state of a shelf ecosystem based on the dynamic model are used for the calculation as source information. Based on this synthesis, the calculation results bring about the opportunity to balance ecological-economic goals of achieving safe development of the shelf and to satisfy the involuntary necessity to reduce the costs on environmental protection measures, while maintaining the priority of environmental requirements.

  8. Mathematical modeling in soil science

    NASA Astrophysics Data System (ADS)

    Tarquis, Ana M.; Gasco, Gabriel; Saa-Requejo, Antonio; Méndez, Ana; Andina, Diego; Sánchez, M. Elena; Moratiel, Rubén; Antón, Jose Manuel

    2015-04-01

    Teaching in context can be defined as teaching a mathematical idea or process by using a problem, situation, or data to enhance the teaching and learning process. The same problem or situation may be used many times, at different mathematical levels to teach different objectives. A common misconception exists that assigning/teaching applications is teaching in context. While both use problems, the difference is in timing, in purpose, and in student outcome. In this work, one problem situation is explored thoroughly at different levels of understanding and other ideas are suggested for classroom explorations. Some teachers, aware of the difficulties some students have with mathematical concepts, try to teach quantitative sciences without using mathematical tools. Such attempts are not usually successful. The answer is not in discarding the mathematics, but in finding ways to teach mathematically-based concepts to students who need them but who find them difficult. The computer is an ideal tool for this purpose. To this end, teachers of the Soil Science and Mathematics Departments of the UPM designed a common practice to teach to the students the role of soil on the carbon sequestration. The objective of this work is to explain the followed steps to the design of the practice. Acknowledgement Universidad Politécnica de Madrid (UPM) for the Projects in Education Innovation IE12_13-02009 and IE12_13-02012 is gratefully acknowledge.

  9. Mathematical Models of Gene Regulation

    NASA Astrophysics Data System (ADS)

    Mackey, Michael C.

    2004-03-01

    This talk will focus on examples of mathematical models for the regulation of repressible operons (e.g. the tryptophan operon), inducible operons (e.g. the lactose operon), and the lysis/lysogeny switch in phage λ. These ``simple" gene regulatory elements can display characteristics experimentally of rapid response to perturbations and bistability, and biologically accurate mathematical models capture these aspects of the dynamics. The models, if realistic, are always nonlinear and contain significant time delays due to transcriptional and translational delays that pose substantial problems for the analysis of the possible ranges of dynamics.

  10. 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…

  11. Qualitative mathematical models to support ecosystem-based management of Australia's Northern Prawn Fishery.

    PubMed

    Dambacher, Jeffrey M; Rothlisberg, Peter C; Loneragan, Neil R

    2015-01-01

    A major decline in the catch of the banana prawn [shrimp], Penaeus (Fenneropenaeus) merguiensis, occurred over a six-year period in the Weipa region of the northeastern Gulf of Carpentaria, Australia. Three main hypotheses have been developed to explain this decline: (1) prawn recruitment collapsed due to overfishing; (2) recruitment collapsed due to a change in the prawn's environment; and (3) adult banana prawns were still present, but fishers could no longer effectively find or catch them. Qualitative mathematical models were used to link population biology, environmental factors, and fishery dynamics to evaluate the alternative hypotheses. This modeling approach provides the means to rapidly integrate knowledge across disciplines and consider alternative hypotheses about how the structure and function of an ecosystem affects its dynamics. Alternative models were constructed to address the different hypotheses and also to encompass a diversity of opinion about the underlying dynamics of the system. Key findings from these analyses are that: instability in the system can arise when discarded fishery bycatch supports relatively high predation pressure; system stability can be enhanced by management of fishing effort or stock catchability; catch per unit effort is not necessarily a reliable indicator of stock abundance; a change in early-season rainfall should affect all stages in the banana prawn's life cycle; and a reduced catch in the Weipa region can create and reinforce a shift in fishing effort away from Weipa. Results from the models informed an approach to test the hypotheses (i.e., an experimental fishing program), and promoted understanding of the system among researchers, management agencies, and industry. The analytical tools developed in this work to address stages of a prawn life cycle and fishery dynamics are generally applicable to any exploited natural. resource.

  12. 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.

  13. 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…

  14. 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…

  15. Mathematical modeling based evaluation and simulation of boron removal in bioelectrochemical systems.

    PubMed

    Ping, Qingyun; Abu-Reesh, Ibrahim M; He, Zhen

    2016-11-01

    Boron removal is an arising issue in desalination plants due to boron's toxicity. As an emerging treatment concept, bioelectrochemical systems (BES) can achieve potentially cost-effective boron removal by taking advantage of cathodic-produced alkali. Prior studies have demonstrated successful removal of boron in microbial desalination cells (MDCs) and microbial fuel cells (MFCs), both of which are representative BES. Herein, mathematical models were developed to further evaluate boron removal by different BES and understand the key operating factors. The models delivered very good prediction of the boron concentration in the MDC integrated with Donnan Dialysis (DD) system with the lowest relative root-mean-square error (RMSE) of 0.00%; the predication of the MFC performance generated the highest RMSE of 18.55%. The model results of salt concentration, solution pH, and current generation were well fitted with experimental data for RMSE values mostly below 10%. The long term simulation of the MDC-DD system suggests that the accumulation of salt in the catholyte/stripping solution could have a positive impact on the removal of boron due to osmosis-driven convection. The current generation in the MDC may have little influence on the boron removal, while in the MFC the current-driven electromigration can contribute up to 40% of boron removal. Osmosis-induced convection transport of boron could be the major driving force for boron removal to a low level <2mgL(-1). The ratio between the anolyte and the catholyte flow rates should be kept >22.2 in order to avoid boron accumulation in the anolyte effluent.

  16. Comprehensive Mathematical Model Of Real Fluids

    NASA Technical Reports Server (NTRS)

    Anderson, Peter G.

    1996-01-01

    Mathematical model of thermodynamic properties of water, steam, and liquid and gaseous hydrogen and oxygen developed for use in computational simulations of flows of mass and heat in main engine of space shuttle. Similar models developed for other fluids and applications. Based on HBMS equation of state.

  17. A mathematical model of a cloud

    NASA Astrophysics Data System (ADS)

    Wang, A. P.

    1980-07-01

    The model under consideration is a pencil of radiation incident on a cloud, and the problem is to determine the reflection and transmitted radiation. Based on the method of 'principle of invariance', three mathematical models are constructed. The first is the basic model, which describes the radiation system completely. The second is the flux integral model, in which the integral average intensity is considered. The third is the diffusion model, which gives the most important information about the diffused radiation field.

  18. Mathematical circulatory system model

    NASA Technical Reports Server (NTRS)

    Lakin, William D. (Inventor); Stevens, Scott A. (Inventor)

    2010-01-01

    A system and method of modeling a circulatory system including a regulatory mechanism parameter. In one embodiment, a regulatory mechanism parameter in a lumped parameter model is represented as a logistic function. In another embodiment, the circulatory system model includes a compliant vessel, the model having a parameter representing a change in pressure due to contraction of smooth muscles of a wall of the vessel.

  19. Development of 4D mathematical observer models for the task-based evaluation of gated myocardial perfusion SPECT

    NASA Astrophysics Data System (ADS)

    Lee, Taek-Soo; Frey, Eric C.; Tsui, Benjamin M. W.

    2015-04-01

    This paper presents two 4D mathematical observer models for the detection of motion defects in 4D gated medical images. Their performance was compared with results from human observers in detecting a regional motion abnormality in simulated 4D gated myocardial perfusion (MP) SPECT images. The first 4D mathematical observer model extends the conventional channelized Hotelling observer (CHO) based on a set of 2D spatial channels and the second is a proposed model that uses a set of 4D space-time channels. Simulated projection data were generated using the 4D NURBS-based cardiac-torso (NCAT) phantom with 16 gates/cardiac cycle. The activity distribution modelled uptake of 99mTc MIBI with normal perfusion and a regional wall motion defect. An analytical projector was used in the simulation and the filtered backprojection (FBP) algorithm was used in image reconstruction followed by spatial and temporal low-pass filtering with various cut-off frequencies. Then, we extracted 2D image slices from each time frame and reorganized them into a set of cine images. For the first model, we applied 2D spatial channels to the cine images and generated a set of feature vectors that were stacked for the images from different slices of the heart. The process was repeated for each of the 1,024 noise realizations, and CHO and receiver operating characteristics (ROC) analysis methodologies were applied to the ensemble of the feature vectors to compute areas under the ROC curves (AUCs). For the second model, a set of 4D space-time channels was developed and applied to the sets of cine images to produce space-time feature vectors to which the CHO methodology was applied. The AUC values of the second model showed better agreement (Spearman’s rank correlation (SRC) coefficient = 0.8) to human observer results than those from the first model (SRC coefficient = 0.4). The agreement with human observers indicates the proposed 4D mathematical observer model provides a good predictor of the

  20. Development of 4D mathematical observer models for the task-based evaluation of gated myocardial perfusion SPECT.

    PubMed

    Lee, Taek-Soo; Frey, Eric C; Tsui, Benjamin M W

    2015-04-07

    This paper presents two 4D mathematical observer models for the detection of motion defects in 4D gated medical images. Their performance was compared with results from human observers in detecting a regional motion abnormality in simulated 4D gated myocardial perfusion (MP) SPECT images. The first 4D mathematical observer model extends the conventional channelized Hotelling observer (CHO) based on a set of 2D spatial channels and the second is a proposed model that uses a set of 4D space-time channels. Simulated projection data were generated using the 4D NURBS-based cardiac-torso (NCAT) phantom with 16 gates/cardiac cycle. The activity distribution modelled uptake of (99m)Tc MIBI with normal perfusion and a regional wall motion defect. An analytical projector was used in the simulation and the filtered backprojection (FBP) algorithm was used in image reconstruction followed by spatial and temporal low-pass filtering with various cut-off frequencies. Then, we extracted 2D image slices from each time frame and reorganized them into a set of cine images. For the first model, we applied 2D spatial channels to the cine images and generated a set of feature vectors that were stacked for the images from different slices of the heart. The process was repeated for each of the 1,024 noise realizations, and CHO and receiver operating characteristics (ROC) analysis methodologies were applied to the ensemble of the feature vectors to compute areas under the ROC curves (AUCs). For the second model, a set of 4D space-time channels was developed and applied to the sets of cine images to produce space-time feature vectors to which the CHO methodology was applied. The AUC values of the second model showed better agreement (Spearman's rank correlation (SRC) coefficient = 0.8) to human observer results than those from the first model (SRC coefficient = 0.4). The agreement with human observers indicates the proposed 4D mathematical observer model provides a good predictor of the

  1. 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…

  2. 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…

  3. Mathematical Modelling with Young Children

    ERIC Educational Resources Information Center

    English, Lyn D.; Watters, James J.

    2004-01-01

    This paper addresses the first year of a three-year, longitudinal study which introduces mathematical modeling to young children and provides professional development for their teachers. Four classes of third-graders (8 years of age) and their teachers participated in the first year of the program, which involved several preliminary modeling…

  4. Mathematical modeling of biological ensembles

    SciTech Connect

    Harlow, F.H.; Sandoval, D.L.; Ruppel, H.M.

    1986-07-01

    Mathematical models are proposed for three distinctly different aspects of biophysical dynamics: mental dynamics, mob dynamics, and the evolution of species. Each section is self-contained, but the approaches are unified by the employment of stochastic equations for the interactive dynamics of numerous discrete entities.

  5. Exploring optimal air ambulance base locations in Norway using advanced mathematical modelling

    PubMed Central

    Røislien, Jo; van den Berg, Pieter L; Lindner, Thomas; Zakariassen, Erik; Aardal, Karen; van Essen, J Theresia

    2017-01-01

    Background Helicopter emergency medical services are an important part of many healthcare systems. Norway has a nationwide physician staffed air ambulance service with 12 bases servicing a country with large geographical variations in population density. The aim of the study was to estimate optimal air ambulance base locations. Methods We used high resolution population data for Norway from 2015, dividing Norway into >300 000 1 km×1 km cells. Inhabited cells had a median (5–95 percentile) of 13 (1–391) inhabitants. Optimal helicopter base locations were estimated using the maximal covering location problem facility location optimisation model, exploring the number of bases needed to cover various fractions of the population for time thresholds 30 and 45 min, both in green field scenarios and conditioning on the current base structure. We reanalysed on municipality level data to explore the potential information loss using coarser population data. Results For a 45 min threshold, 90% of the population could be covered using four bases, and 100% using nine bases. Given the existing bases, the calculations imply the need for two more bases to achieve full coverage. Decreasing the threshold to 30 min approximately doubles the number of bases needed. Results using municipality level data were remarkably similar to those using fine grid information. Conclusions The whole population could be reached in 45 min or less using nine optimally placed bases. The current base structure could be improved by moving or adding one or two select bases. Municipality level data appears sufficient for proper analysis. PMID:27325670

  6. Mathematical Modeling of Cellular Metabolism.

    PubMed

    Berndt, Nikolaus; Holzhütter, Hermann-Georg

    Cellular metabolism basically consists of the conversion of chemical compounds taken up from the extracellular environment into energy (conserved in energy-rich bonds of organic phosphates) and a wide array of organic molecules serving as catalysts (enzymes), information carriers (nucleic acids), and building blocks for cellular structures such as membranes or ribosomes. Metabolic modeling aims at the construction of mathematical representations of the cellular metabolism that can be used to calculate the concentration of cellular molecules and the rates of their mutual chemical interconversion in response to varying external conditions as, for example, hormonal stimuli or supply of essential nutrients. Based on such calculations, it is possible to quantify complex cellular functions as cellular growth, detoxification of drugs and xenobiotic compounds or synthesis of exported molecules. Depending on the specific questions to metabolism addressed, the methodological expertise of the researcher, and available experimental information, different conceptual frameworks have been established, allowing the usage of computational methods to condense experimental information from various layers of organization into (self-) consistent models. Here, we briefly outline the main conceptual frameworks that are currently exploited in metabolism research.

  7. 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

  8. Landslide Susceptibility Evaluation on agricultural terraces of DOURO VALLEY (PORTUGAL), using physically based mathematical models.

    NASA Astrophysics Data System (ADS)

    Faria, Ana; Bateira, Carlos; Laura, Soares; Fernandes, Joana; Gonçalves, José; Marques, Fernando

    2016-04-01

    The work focuses the evaluation of landslide susceptibility in Douro Region agricultural terraces, supported by dry stone walls and earth embankments, using two physically based models. The applied models, SHALSTAB (Montgomery et al.,1994; Dietrich et al., 1995) and SINMAP (PACK et al., 2005), combine an infinite slope stability model with a steady state hydrological model, and both use the following geophysical parameters: cohesion, friction angle, specific weight and soil thickness. The definition of the contributing areas is different in both models. The D∞ methodology used by SINMAP model suggests a great influence of the terraces morphology, providing a much more diffuse flow on the internal flow modelling. The MD8 used in SHALSTAB promotes an important degree of flow concentration, representing an internal flow based on preferential paths of the runoff as the areas more susceptible to saturation processes. The model validation is made through the contingency matrix method (Fawcett, 2006; Raia et al., 2014) and implies the confrontation with the inventory of past landslides. The True Positive Rate shows that SHALSTAB classifies 77% of the landslides on the high susceptibility areas, while SINMAP reaches 90%. The SINMAP has a False Positive Rate (represents the percentage of the slipped area that is classified as unstable but without landslides) of 83% and the SHALSTAB has 67%. The reliability (analyzes the areas that were correctly classified on the total area) of SHALSTAB is better (33% against 18% of SINMAP). Relative to Precision (refers to the ratio of the slipped area correctly classified over the whole area classified as unstable) SHALSTAB has better results (0.00298 against 0.00283 of SINMAP). It was elaborate the index TPR/FPR and better results obtained by SHALSTAB (1.14 against 1.09 of SINMAP). SHALSTAB shows a better performance in the definition of susceptibility most prone areas to instability processes. One of the reasons for the difference of

  9. 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…

  10. Mathematical modelling of the human foetal cardiovascular system based on Doppler ultrasound data.

    PubMed

    Pennati, G; Bellotti, M; Fumero, R

    1997-06-01

    A lumped parameter model of the human foetal circulation primarily based on blood velocity data derived from the Doppler analysis was developed in this study. It consists of two major parts, the heart and the foetal vascular circulation. The heart model accounts for both ventricular and atrial contractility. The circulation was divided into 19 compliant vascular compartments in order to describe all of the clinically monitored sites. The model parameters refer to the final gestation period and were derived either from literature on foetal sheep circulation or from anatomical dimension monitoring of the human foetus. No control mechanism is incorporated into the model. The model was validated by comparing several index values of simulated velocity curves to those of the experimental Doppler waveforms. The mean and maximum percentual errors in the estimation of the experimental results by the model are 7.7% and 20.1%, respectively. Velocity and pressure tracings of the foetal circulation were investigated, as well as regional blood flow rate distribution.

  11. 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…

  12. 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…

  13. A Biophysically Based Mathematical Model for the Kinetics of Mitochondrial Na+-Ca2+ Antiporter

    PubMed Central

    Pradhan, Ranjan K.; Beard, Daniel A.; Dash, Ranjan K.

    2010-01-01

    Sodium-calcium antiporter is the primary efflux pathway for Ca2+ in respiring mitochondria, and hence plays an important role in mitochondrial Ca2+ homeostasis. Although experimental data on the kinetics of Na+-Ca2+ antiporter are available, the structure and composition of its functional unit and kinetic mechanisms associated with the Na+-Ca2+ exchange (including the stoichiometry) remains unclear. To gain a quantitative understanding of mitochondrial Ca2+ homeostasis, a biophysical model of Na+-Ca2+ antiporter is introduced that is thermodynamically balanced and satisfactorily describes a number of independent data sets under a variety of experimental conditions. The model is based on a multistate catalytic binding mechanism for carrier-mediated facilitated transport and Eyring's free energy barrier theory for interconversion and electrodiffusion. The model predicts the activating effect of membrane potential on the antiporter function for a 3Na+:1Ca2+ electrogenic exchange as well as the inhibitory effects of both high and low pH seen experimentally. The model is useful for further development of mechanistic integrated models of mitochondrial Ca2+ handling and bioenergetics to understand the mechanisms by which Ca2+ plays a role in mitochondrial signaling pathways and energy metabolism. PMID:20338843

  14. 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.

  15. 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…

  16. 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…

  17. Mathematical models of diabetes progression.

    PubMed

    De Gaetano, Andrea; Hardy, Thomas; Beck, Benoit; Abu-Raddad, Eyas; Palumbo, Pasquale; Bue-Valleskey, Juliana; Pørksen, Niels

    2008-12-01

    Few attempts have been made to model mathematically the progression of type 2 diabetes. A realistic representation of the long-term physiological adaptation to developing insulin resistance is necessary for effectively designing clinical trials and evaluating diabetes prevention or disease modification therapies. Writing a good model for diabetes progression is difficult because the long time span of the disease makes experimental verification of modeling hypotheses extremely awkward. In this context, it is of primary importance that the assumptions underlying the model equations properly reflect established physiology and that the mathematical formulation of the model give rise only to physically plausible behavior of the solutions. In the present work, a model of the pancreatic islet compensation is formulated, its physiological assumptions are presented, some fundamental qualitative characteristics of its solutions are established, the numerical values assigned to its parameters are extensively discussed (also with reference to available cross-sectional epidemiologic data), and its performance over the span of a lifetime is simulated under various conditions, including worsening insulin resistance and primary replication defects. The differences with respect to two previously proposed models of diabetes progression are highlighted, and therefore, the model is proposed as a realistic, robust description of the evolution of the compensation of the glucose-insulin system in healthy and diabetic individuals. Model simulations can be run from the authors' web page.

  18. Mathematical modeling of drug delivery.

    PubMed

    Siepmann, J; Siepmann, F

    2008-12-08

    Due to the significant advances in information technology mathematical modeling of drug delivery is a field of steadily increasing academic and industrial importance with an enormous future potential. The in silico optimization of novel drug delivery systems can be expected to significantly increase in accuracy and easiness of application. Analogous to other scientific disciplines, computer simulations are likely to become an integral part of future research and development in pharmaceutical technology. Mathematical programs can be expected to be routinely used to help optimizing the design of novel dosage forms. Good estimates for the required composition, geometry, dimensions and preparation procedure of various types of delivery systems will be available, taking into account the desired administration route, drug dose and release profile. Thus, the number of required experimental studies during product development can be significantly reduced, saving time and reducing costs. In addition, the quantitative analysis of the physical, chemical and potentially biological phenomena, which are involved in the control of drug release, offers another fundamental advantage: The underlying drug release mechanisms can be elucidated, which is not only of academic interest, but a pre-requisite for an efficient improvement of the safety of the pharmaco-treatments and for effective trouble-shooting during production. This article gives an overview on the current state of the art of mathematical modeling of drug delivery, including empirical/semi-empirical and mechanistic realistic models. Analytical as well as numerical solutions are described and various practical examples are given. One of the major challenges to be addressed in the future is the combination of mechanistic theories describing drug release out of the delivery systems with mathematical models quantifying the subsequent drug transport within the human body in a realistic way. Ideally, the effects of the design

  19. 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…

  20. A universal optimization strategy for ant colony optimization algorithms based on the Physarum-inspired mathematical model.

    PubMed

    Zhang, Zili; Gao, Chao; Liu, Yuxin; Qian, Tao

    2014-09-01

    Ant colony optimization (ACO) algorithms often fall into the local optimal solution and have lower search efficiency for solving the travelling salesman problem (TSP). According to these shortcomings, this paper proposes a universal optimization strategy for updating the pheromone matrix in the ACO algorithms. The new optimization strategy takes advantages of the unique feature of critical paths reserved in the process of evolving adaptive networks of the Physarum-inspired mathematical model (PMM). The optimized algorithms, denoted as PMACO algorithms, can enhance the amount of pheromone in the critical paths and promote the exploitation of the optimal solution. Experimental results in synthetic and real networks show that the PMACO algorithms are more efficient and robust than the traditional ACO algorithms, which are adaptable to solve the TSP with single or multiple objectives. Meanwhile, we further analyse the influence of parameters on the performance of the PMACO algorithms. Based on these analyses, the best values of these parameters are worked out for the TSP.

  1. Mathematical Modelling of Folate Metabolism

    PubMed Central

    Panetta, John C.; Paugh, Steven W.

    2013-01-01

    Folate metabolism is a complex biological process that is influenced by many variables including transporters, co-factors and enzymes. Mathematical models provide a useful tool to evaluate this complex system and to elucidate hypotheses that would be otherwise untenable to test in vitro or in vivo. Forty years of model development and refinement along with enhancements in technology have led to systematic improvement in our biological understanding from these models. However, increased complexity does not always lead to increased understanding, and a balanced approach to modelling the system is often advantageous. This approach should address questions about sensitivity of the model to variation and incorporate genomic data. The folate model is a useful platform for investigating the effects of antifolates on the folate pathway. The utility of the model is demonstrated through interrogation of drug resistance, drug-drug interactions, drug selectivity, and drug doses and schedules. Mathematics can be used to create models with the ability to design and improve rationale therapeutic interventions. PMID:23703958

  2. 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.

  3. Developing mathematical models of neurobehavioral performance for the "real world".

    PubMed

    Dean, Dennis A; Fletcher, Adam; Hursh, Steven R; Klerman, Elizabeth B

    2007-06-01

    Work-related operations requiring extended wake durations, night, or rotating shifts negatively affect worker neurobehavioral performance and health. These types of work schedules are required in many industries, including the military, transportation, and health care. These industries are increasingly using or considering the use of mathematical models of neurobehavioral performance as a means to predict the neurobehavioral deficits due to these operational demands, to develop interventions that decrease these deficits, and to provide additional information to augment existing decision-making processes. Recent advances in mathematical modeling have allowed its application to real-world problems. Developing application-specific expertise is necessary to successfully apply mathematical models, in part because development of new algorithms and methods linking the models to the applications may be required. During a symposium, "Modeling Human Neurobehavioral Performance II: Towards Operational Readiness," at the 2006 SIAM-SMB Conference on the Life Sciences, examples of the process of applying mathematical models, including model construction, model validation, or developing model-based interventions, were presented. The specific applications considered included refining a mathematical model of sleep/wake patterns of airline flight crew, validating a mathematical model using railroad operations data, and adapting a mathematical model to develop appropriate countermeasure recommendations based on known constraints. As mathematical models and their associated analytical methods continue to transition into operational settings, such additional development will be required. However, major progress has been made in using mathematical model outputs to inform those individuals making schedule decisions for their workers.

  4. Trends and techniques for space base electronics. [mathematical models, ion implantation, and semiconductors

    NASA Technical Reports Server (NTRS)

    Gassaway, J. D.; Mahmood, Q.; Trotter, J. D.

    1978-01-01

    A system was developed for depositing aluminum and aluminum alloys by the D.C. sputtering technique. This system which was designed for a high level of cleanliness and ion monitoring the deposition parameters during film preparation is ready for studying the deposition and annealing parameters upon double level metal preparation. The finite element method was studied for use in the computer modeling of two dimensional MOS transistor structures. An algorithm was developed for implementing a computer study which is based upon the finite difference method. The program was modified and used to calculate redistribution data for boron and phosphorous which had been predeposited by ion implantation with range and straggle conditions typical of those used at MSFC. Data were generated for 111 oriented SOS films with redistribution in N2, dry O2 and steam ambients. Data are given showing both two dimensional effects and the evolution of the junction depth, sheet resistance and integrated dose with redistribution time.

  5. Thermodynamics-based mathematical model for solubility prediction of glibenclamide in ethanol-water mixtures.

    PubMed

    Shakeel, Faiyaz; Alanazi, Fars K; Alsarra, Ibrahim A; Haq, Nazrul

    2014-09-01

    Temperature-dependent solubility data of glibenclamide (GBN) in various ethanol-water mixtures is not reported in literature so far. Therefore, the aim of this study was to determine the mole fraction solubility of GBN in various ethanol-water mixtures at the temperature range of 293.15 to 318.15 K. The solubility of GBN was determined by reported shake flask method and the experimental data was fitted in thermodynamics-based modified Apelblat model. The solubility of GBN was found to be increased with increase in temperature and mass fraction of ethanol in ethanol-water mixtures. The experimental data of GBN was well correlated with the modified Apelblat model at each temperature range with correlation coefficient of 0.9940-1.0000. The relative absolute deviation (AD) was found to be less than 0.1% except in pure ethanol and water. The positive values of enthalpies and entropies for GBN dissolution indicated that its dissolution is endothermic and an entropy-driven process.

  6. 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.

  7. A mathematical model to optimize the drain phase in gravity-based peritoneal dialysis systems.

    PubMed

    Akonur, Alp; Lo, Ying-Cheng; Cizman, Borut

    2010-01-01

    Use of patient-specific drain-phase parameters has previously been suggested to improve peritoneal dialysis (PD) adequacy. Improving management of the drain period may also help to minimize intraperitoneal volume (IPV). A typical gravity-based drain profile consists of a relatively constant initial fast-flow period, followed by a transition period and a decaying slow-flow period. That profile was modeled using the equation VD(t) = (V(D0) - Q(MAX) x t) xphi + (V(D0) x e(-alphat)) x (1 - phi), where V(D)(t) is the time-dependent dialysate volume; V(D0), the dialysate volume at the start of the drain; Q(MAX), the maximum drain flow rate; alpha, the exponential drain constant; and phi, the unit step function with respect to the flow transition. We simulated the effects of the assumed patient-specific maximum drain flow (Q(MAX)) and transition volume (psi), and the peritoneal volume percentage when transition occurs,for fixed device-specific drain parameters. Average patient transport parameters were assumed during 5-exchange therapy with 10 L of PD solution. Changes in therapy performance strongly depended on the drain parameters. Comparing 400 mL/85% with 200 mL/65% (Q(MAX/psi), drain time (7.5 min vs. 13.5 min) and IPV (2769 mL vs. 2355 mL) increased when the initial drain flow was low and the transition quick. Ultrafiltration and solute clearances remained relatively similar. Such differences were augmented up to a drain time of 22 minutes and an IPV of more than 3 L when Q(MAX) was 100 mL/min. The ability to model individual drain conditions together with water and solute transport may help to prevent patient discomfort with gravity-based PD. However, it is essential to note that practical difficulties such as displaced catheters and obstructed flow paths cause variability in drain characteristics even for the same patient, limiting the clinical applicability of this model.

  8. 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.

  9. Mathematical Model for Mapping Students' Cognitive Capability

    ERIC Educational Resources Information Center

    Tambunan, Hardi

    2016-01-01

    The quality mapping of educational unit program is important issue in education in Indonesia today in an effort to improve the quality of education. The objective of this study is to make a mathematical model to find out the map of students' capability in mathematics. It has been made a mathematical model to be used in the mapping of students'…

  10. 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.

  11. Inquiry-Based Mathematics Curriculum Design for Young Children-Teaching Experiment and Reflection

    ERIC Educational Resources Information Center

    Wu, Su-Chiao; Lin, Fou-Lai

    2016-01-01

    A group of teacher educators and practitioners in mathematics education and early childhood education generalized a set of inquiry-based mathematics models for Taiwanese young children of ages 3-6 and designed a series of inquiry-based mathematics curriculum tasks in cultivate the children's diverse mathematical concepts and mathematical power. In…

  12. Mathematical models in medicine: Diseases and epidemics

    SciTech Connect

    Witten, M.

    1987-01-01

    This volume presents the numerous applications of mathematics in the life sciences and medicine, and demonstrates how mathematics and computers have taken root in these fields. The work covers a variety of techniques and applications including mathematical and modelling methodology, modelling/simulation technology, and philosophical issues in model formulation, leading to speciality medical modelling, artificial intelligence, psychiatric models, medical decision making, and molecular modelling.

  13. On Religion and Language Evolutions Seen Through Mathematical and Agent Based Models

    NASA Astrophysics Data System (ADS)

    Ausloos, M.

    Religions and languages are social variables, like age, sex, wealth or political opinions, to be studied like any other organizational parameter. In fact, religiosity is one of the most important sociological aspects of populations. Languages are also obvious characteristics of the human species. Religions, languages appear though also disappear. All religions and languages evolve and survive when they adapt to the society developments. On the other hand, the number of adherents of a given religion, or the number of persons speaking a language is not fixed in time, - nor space. Several questions can be raised. E.g. from a oscopic point of view : How many religions/languages exist at a given time? What is their distribution? What is their life time? How do they evolve? From a "microscopic" view point: can one invent agent based models to describe oscopic aspects? Do simple evolution equations exist? How complicated must be a model? These aspects are considered in the present note. Basic evolution equations are outlined and critically, though briefly, discussed. Similarities and differences between religions and languages are summarized. Cases can be illustrated with historical facts and data. It is stressed that characteristic time scales are different. It is emphasized that "external fields" are historically very relevant in the case of religions, rending the study more " interesting" within a mechanistic approach based on parity and symmetry of clusters concepts. Yet the modern description of human societies through networks in reported simulations is still lacking some mandatory ingredients, i.e. the non scalar nature of the nodes, and the non binary aspects of nodes and links, though for the latter this is already often taken into account, including directions. From an analytical point of view one can consider a population independently of the others. It is intuitively accepted, but also found from the statistical analysis of the frequency distribution that an

  14. Identification of the noise using mathematical modelling

    NASA Astrophysics Data System (ADS)

    Dobeš, Josef; Kozubková, Milada; Mahdal, Miroslav

    2016-03-01

    In engineering applications the noisiness of a component or the whole device is a common problem. Currently, a lot of effort is put to eliminate noise of the already produced devices, to prevent generation of acoustic waves during the design of new components, or to specify the operating problems based on noisiness change. The experimental method and the mathematical modelling method belong to these identification methods. With the power of today's computers the ability to identify the sources of the noise on the mathematical modelling level is a very appreciated tool for engineers. For example, the noise itself may be generated by the vibration of the solid object, combustion, shock, fluid flow around an object or cavitation at the fluid flow in an object. For the given task generating the noise using fluid flow on the selected geometry and propagation of the acoustic waves and their subsequent identification are solved and evaluated. In this paper the principle of measurement of variables describing the fluid flow field and acoustic field are described. For the solution of fluid flow a mathematical model implemented into the CFD code is used. The mathematical modelling evaluation of the flow field is compared to the experimental data.

  15. Mathematical Models Of Turbulence In Hypersonic Flow

    NASA Technical Reports Server (NTRS)

    Marvin, J. G.; Coakley, T. J.

    1991-01-01

    Report discusses mathematical models of turbulence used in numerical simulations of complicated viscous, hypersonic flows. Includes survey of essential features of models and their statuses in applications.

  16. Mathematical models of malaria - a review

    PubMed Central

    2011-01-01

    Mathematical models have been used to provide an explicit framework for understanding malaria transmission dynamics in human population for over 100 years. With the disease still thriving and threatening to be a major source of death and disability due to changed environmental and socio-economic conditions, it is necessary to make a critical assessment of the existing models, and study their evolution and efficacy in describing the host-parasite biology. In this article, starting from the basic Ross model, the key mathematical models and their underlying features, based on their specific contributions in the understanding of spread and transmission of malaria have been discussed. The first aim of this article is to develop, starting from the basic models, a hierarchical structure of a range of deterministic models of different levels of complexity. The second objective is to elaborate, using some of the representative mathematical models, the evolution of modelling strategies to describe malaria incidence by including the critical features of host-vector-parasite interactions. Emphasis is more on the evolution of the deterministic differential equation based epidemiological compartment models with a brief discussion on data based statistical models. In this comprehensive survey, the approach has been to summarize the modelling activity in this area so that it helps reach a wider range of researchers working on epidemiology, transmission, and other aspects of malaria. This may facilitate the mathematicians to further develop suitable models in this direction relevant to the present scenario, and help the biologists and public health personnel to adopt better understanding of the modelling strategies to control the disease PMID:21777413

  17. Mathematical modeling of cold cap

    SciTech Connect

    Pokorny, Richard; Hrma, Pavel R.

    2012-10-13

    The ultimate goal of studies of cold cap behavior in glass melters is to increase the rate of glass processing in an energy-efficient manner. Regrettably, mathematical models, which are ideal tools for assessing the responses of melters to process parameters, have not paid adequate attention to the cold cap. In this study, we consider a cold cap resting on a pool of molten glass from which it receives a steady heat flux while temperature, velocity, and extent of conversion are functions of the position along the vertical coordinate. A one-dimensional (1D) mathematical model simulates this process by solving the differential equations for mass and energy balances with appropriate boundary conditions and constitutive relationships for material properties. The sensitivity analyses on the effects of incoming heat fluxes to the cold cap through its lower and upper boundaries show that the cold cap thickness increases as the heat flux from above increases, and decreases as the total heat flux increases. We also discuss the effects of foam, originating from batch reactions and from redox reactions in molten glass and argue that models must represent the foam layer to achieve a reliable prediction of the melting rate as a function of feed properties and melter conditions.

  18. 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).

  19. 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.

  20. Standardized, mathematical model-based and validated in vitro analysis of anthrax lethal toxin neutralization.

    PubMed

    Li, Han; Soroka, Stephen D; Taylor, Thomas H; Stamey, Karen L; Stinson, Kelly Wallace; Freeman, Alison E; Abramson, Darbi R; Desai, Rita; Cronin, Li X; Oxford, J Wade; Caba, Joseph; Pleatman, Cynthia; Pathak, Sonal; Schmidt, Daniel S; Semenova, Vera A; Martin, Sandra K; Wilkins, Patricia P; Quinn, Conrad P

    2008-04-20

    Quantification of anthrax lethal toxin (LTx) neutralization activity (TNA) is pivotal in assessing protective antibody responses to anthrax vaccines and for evaluation of immunotherapies for anthrax. We have adapted and redesigned the TNA assay to establish a unifying, standardized, quantitative and validated technology platform for LTx neutralization in the J774A.1 murine cell line. Critical design features of this platform are 1) the application of a free-form or constrained 4 parameter logistic (4-PL) function to model neutralization responses within and between boundary limits of 100% cell survival and 95% cell lysis and 2) to exploit innovative assay curve recognition algorithms for interpretive endpoints. The assay was validated using human serum ED50 (dilution of serum effecting 50% neutralization) as the primary reportable value (RV). Intra-operator and intermediate precision, expressed as the coefficient of variation (%CV), were high at 10.5-15.5%CV and 13.5-14.5%CV respectively. TNA assay dilutional linearity was demonstrated for human sera using linear regression analysis of log(10) transformed data with slope=0.99, intercept=-0.03 and r(2)=0.985. Assay accuracy, inferred from the precision and linearity data and using a spike-recovery approach, was high with a percent error (%E) range of only 3.4-20.5%E. The lower limit of detection (LLOD) was ED50=12 and the lower limit of quantification (LLOQ) was ED50=36. The cell-based assay was robust, tolerating incubation temperatures from 35 to 39 degrees C, CO(2) concentrations from 3% to 7% and reporter substrate (MTT) concentrations of 2.5-7.5 mg/ml. Strict assay quality control parameters were met for up to 25 cell culture passages. The long term (50 month) assay stability, determined using human reference standards AVR414 and AVR801, indicated high precision, consistent accuracy and no detectable assay drift. A customized software program provided two additional assay metrics, Quantification Titer (QT) and

  1. Examining the Implementation of a Problem-Based Learning and Traditional Hybrid Model of Instruction in Remedial Mathematics Classes Designed for State Testing Preparation of Eleventh Grade Students

    ERIC Educational Resources Information Center

    Rodgers, Lindsay D.

    2011-01-01

    The following paper examined the effects of a new method of teaching for remedial mathematics, named the hybrid model of instruction. Due to increasing importance of high stakes testing, the study sought to determine if this method of instruction, that blends traditional teaching and problem-based learning, had different learning effects on…

  2. On mathematical modelling of flameless combustion

    SciTech Connect

    Mancini, Marco; Schwoeppe, Patrick; Weber, Roman; Orsino, Stefano

    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)

  3. Mathematical model for classification of EEG signals

    NASA Astrophysics Data System (ADS)

    Ortiz, Victor H.; Tapia, Juan J.

    2015-09-01

    A mathematical model to filter and classify brain signals from a brain machine interface is developed. The mathematical model classifies the signals from the different lobes of the brain to differentiate the signals: alpha, beta, gamma and theta, besides the signals from vision, speech, and orientation. The model to develop further eliminates noise signals that occur in the process of signal acquisition. This mathematical model can be used on different platforms interfaces for rehabilitation of physically handicapped persons.

  4. Students' Approaches to Learning a New Mathematical Model

    ERIC Educational Resources Information Center

    Flegg, Jennifer A.; Mallet, Daniel G.; Lupton, Mandy

    2013-01-01

    In this article, we report on the findings of an exploratory study into the experience of undergraduate students as they learn new mathematical models. Qualitative and quantitative data based around the students' approaches to learning new mathematical models were collected. The data revealed that students actively adopt three approaches to…

  5. 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.…

  6. A mathematical description of a growing cell colony based on the mechanical bidomain model

    NASA Astrophysics Data System (ADS)

    Auddya, Debabrata; Roth, Bradley J.

    2017-03-01

    The mechanical bidomain model is used to describe a colony of cells growing on a substrate. Analytical expressions are derived for the intracellular and extracellular displacements. Mechanotransduction events are driven by the difference between the displacements in the two spaces, corresponding to the force acting on integrins. The equation for the displacement consists of two terms: one proportional to the radius that is the same in the intracellular and extracellular spaces (the monodomain term) and one that is proportional to a modified Bessel function that is responsible for mechanotransduction (the bidomain term). The model predicts that mechanotransduction occurs within a few length constants of the colony’s edge, and an expression for the length constant contains the intracellular and extracellular shear moduli and the spring constant of the integrins coupling the two spaces. The model predictions are qualitatively consistent with experiments on human embryonic stem cell colonies, in which differentiation is localized near the edge.

  7. Mathematical modelling of leprosy and its control.

    PubMed

    Blok, David J; de Vlas, Sake J; Fischer, Egil A J; Richardus, Jan Hendrik

    2015-03-01

    Leprosy or Hansen's disease is an infectious disease caused by the bacterium Mycobacterium leprae. The annual number of new leprosy cases registered worldwide has remained stable over the past years at over 200,000. Early case finding and multidrug therapy have not been able interrupt transmission completely. Elimination requires innovation in control and sustained commitment. Mathematical models can be used to predict the course of leprosy incidence and the effect of intervention strategies. Two compartmental models and one individual-based model have been described in the literature. Both compartmental models investigate the course of leprosy in populations and the long-term impact of control strategies. The individual-based model focusses on transmission within households and the impact of case finding among contacts of new leprosy patients. Major improvement of these models should result from a better understanding of individual differences in exposure to infection and developing leprosy after exposure. Most relevant are contact heterogeneity, heterogeneity in susceptibility and spatial heterogeneity. Furthermore, the existing models have only been applied to a limited number of countries. Parameterization of the models for other areas, in particular those with high incidence, is essential to support current initiatives for the global elimination of leprosy. Many challenges remain in understanding and dealing with leprosy. The support of mathematical models for understanding leprosy epidemiology and supporting policy decision making remains vital.

  8. Regulation of amniotic fluid volume: mathematical model based on intramembranous transport mechanisms.

    PubMed

    Brace, Robert A; Anderson, Debra F; Cheung, Cecilia Y

    2014-11-15

    Experimentation in late-gestation fetal sheep has suggested that regulation of amniotic fluid (AF) volume occurs primarily by modulating the rate of intramembranous transport of water and solutes across the amnion into underlying fetal blood vessels. In order to gain insight into intramembranous transport mechanisms, we developed a computer model that allows simulation of experimentally measured changes in AF volume and composition over time. The model included fetal urine excretion and lung liquid secretion as inflows into the amniotic compartment plus fetal swallowing and intramembranous absorption as outflows. By using experimental flows and solute concentrations for urine, lung liquid, and swallowed fluid in combination with the passive and active transport mechanisms of the intramembranous pathway, we simulated AF responses to basal conditions, intra-amniotic fluid infusions, fetal intravascular infusions, urine replacement, and tracheoesophageal occlusion. The experimental data are consistent with four intramembranous transport mechanisms acting in concert: 1) an active unidirectional bulk transport of AF with all dissolved solutes out of AF into fetal blood presumably by vesicles; 2) passive bidirectional diffusion of solutes, such as sodium and chloride, between fetal blood and AF; 3) passive bidirectional water movement between AF and fetal blood; and 4) unidirectional transport of lactate into the AF. Further, only unidirectional bulk transport is dynamically regulated. The simulations also identified areas for future study: 1) identifying intramembranous stimulators and inhibitors, 2) determining the semipermeability characteristics of the intramembranous pathway, and 3) characterizing the vesicles that are the primary mediators of intramembranous transport.

  9. The Activity System of School-Teaching Mathematics and Mathematical Modelling.

    ERIC Educational Resources Information Center

    Julie, Cyril

    2002-01-01

    Focuses on the activity system of school-teaching mathematics and the impact of mathematical modeling. Describes the Applications of and Modeling in School Mathematics Project (AMSMAP) which investigates teachers' mathematical modeling and its relationship to a hypothesized school mathematical modeling activity system. Discusses the notion of an…

  10. Mathematical modeling of deformation during hot rolling

    SciTech Connect

    Jin, D.; Stachowiak, R.G.; Samarasekera, I.V.; Brimacombe, J.K.

    1994-12-31

    The deformation that occurs in the roll bite during the hot rolling of steel, particularly the strain-rate and strain distribution, has been mathematically modeled using finite-element analysis. In this paper three different finite-element models are compared with one another and with industrial measurements. The first model is an Eulerian analysis based on the flow formulation method, while the second utilizes an Updated Lagrangian approach. The third model is based on a commercially available program DEFORM which also utilizes a Lagrangian reference frame. Model predictions of strain and strain-rate distribution, particularly near the surface of the slab, are strongly influenced by the treatment of friction at the boundary and the magnitude of the friction coefficient or shear factor. Roll forces predicted by the model have been compared with industrial rolling loads from a seven-stand hot-strip mill.

  11. How parrots talk: insights based on CT scans, image processing, and mathematical models

    NASA Astrophysics Data System (ADS)

    Patterson, Dianne K.; Pepperberg, Irene M.; Story, Brad H.; Hoffman, Eric A.

    1997-05-01

    Little is known about mechanisms of speech production in parrots. Recently, however, techniques for correlating vocal tract shape with vowel production in humans have become more sophisticated and we have adapted these techniques for use with parrots. We scanned two grey parrot heads with intact vocal tracts. One specimen, 'Oldbird' was fixed with its beak propped open; the second 'Youngbird' was fixed with its beak closed. Using VIDA software, we (1) established that differences in tongue and larynx positioning resulted from opening or closing the beak; and (2) obtained lengths and area functions for the trachea, glottis, pharynx, mouth, and choana for both specimens and esophageal length and area functions for the first specimen. We entered lengths and area functions into a 1D wave propagation model to determine the natural formant frequencies associated with an open versus closed beak. We also determined how manipulating lengths and area functions could affect formant frequency and relative intensity. Finally, by comparing observed grey parrot vowel formant, we predict how the parrot uses its vocal tract to produce speech.

  12. A new mathematical model based on clinical and laboratory variables for the diagnosis of Sjögren's syndrome.

    PubMed

    Martin-Martin, L S; Latini, A; Pagano, A; Ragno, A; Stasi, R; Coppè, A; Davoli, G; Crescenzi, A; Alimonti, A; Migliore, A

    2003-05-01

    Sjögren's syndrome (SS) is a systemic autoimmune disease that mainly affects exocrine glands. A diagnosis of SS in its early stages has a potential clinical relevance, but it is difficult and cannot be made solely on clinical grounds. Several sets of diagnostic criteria have been proposed, but none has met with a general consensus. Minor salivary gland has been judged to be the "gold standard" for the diagnosis of SS. However, it is a painful procedure and has a small but significant proportion of both false positive and false negative results. The aim of our study was to develop a simple mathematical score that uses clinical and laboratory variables for diagnosing SS, thereby reducing the need of minor salivary gland. The following variables were included in the model: ANA, SS-A/SS-B, Schirmer's Test/BUT, C3/C4, serum gammaglobulin levels. One hundred consecutive individuals reporting clinical syndromes consistent with a sicca syndrome were included in the study. The application of our multifactorial mathematical model has shown a high predictive value for SS vs controls or vs patients with other autoimmune disorders (Sensitivity 93%, Specificity 100%), with an estimated minor salivary gland reduction of 77%. We conclude that our mathematical model can be considered a useful non-invasive approach for diagnosing Sjogren's Syndrome and recommend its validation on a larger scale.

  13. A Simple Mathematical Model Based on the Cancer Stem Cell Hypothesis Suggests Kinetic Commonalities in Solid Tumor Growth

    PubMed Central

    Molina-Peña, Rodolfo; Álvarez, Mario Moisés

    2012-01-01

    Background The Cancer Stem Cell (CSC) hypothesis has gained credibility within the cancer research community. According to this hypothesis, a small subpopulation of cells within cancerous tissues exhibits stem-cell-like characteristics and is responsible for the maintenance and proliferation of cancer. Methodologies/Principal Findings We present a simple compartmental pseudo-chemical mathematical model for tumor growth, based on the CSC hypothesis, and derived using a “chemical reaction” approach. We defined three cell subpopulations: CSCs, transit progenitor cells, and differentiated cells. Each event related to cell division, differentiation, or death is then modeled as a chemical reaction. The resulting set of ordinary differential equations was numerically integrated to describe the time evolution of each cell subpopulation and the overall tumor growth. The parameter space was explored to identify combinations of parameter values that produce biologically feasible and consistent scenarios. Conclusions/Significance Certain kinetic relationships apparently must be satisfied to sustain solid tumor growth and to maintain an approximate constant fraction of CSCs in the tumor lower than 0.01 (as experimentally observed): (a) the rate of symmetrical and asymmetrical CSC renewal must be in the same order of magnitude; (b) the intrinsic rate of renewal and differentiation of progenitor cells must be half an order of magnitude higher than the corresponding intrinsic rates for cancer stem cells; (c) the rates of apoptosis of the CSC, transit amplifying progenitor (P) cells, and terminally differentiated (D) cells must be progressively higher by approximately one order of magnitude. Simulation results were consistent with reports that have suggested that encouraging CSC differentiation could be an effective therapeutic strategy for fighting cancer in addition to selective killing or inhibition of symmetric division of CSCs. PMID:22363395

  14. Aircraft engine mathematical model - linear system approach

    NASA Astrophysics Data System (ADS)

    Rotaru, Constantin; Roateşi, Simona; Cîrciu, Ionicǎ

    2016-06-01

    This paper examines a simplified mathematical model of the aircraft engine, based on the theory of linear and nonlinear systems. The dynamics of the engine was represented by a linear, time variant model, near a nominal operating point within a finite time interval. The linearized equations were expressed in a matrix form, suitable for the incorporation in the MAPLE program solver. The behavior of the engine was included in terms of variation of the rotational speed following a deflection of the throttle. The engine inlet parameters can cover a wide range of altitude and Mach numbers.

  15. Conversations about curriculum change: mathematical thinking and team-based learning in a discrete mathematics course

    NASA Astrophysics Data System (ADS)

    Paterson, Judy; Sneddon, Jamie

    2011-10-01

    This article reports on the learning conversations between a mathematician and a mathematics educator as they worked together to change the delivery model of a third year discrete mathematics course from a traditional lecture mode to team-based learning (TBL). This change prompted the mathematician to create team tasks which increasingly focused on what he calls the 'unspoken curriculum': mathematical thinking. We consider the ways in which the TBL model promoted and enabled this in the light of literature on mathematical thinking, sense-making and behaviours, and strongly suggest that this approach warrants more attention from the mathematics teaching community. We also discuss shifts in the mathematician's thinking about task construction as he refined the tasks to encourage students to think and behave like mathematicians.

  16. Mathematics in the Biology Classroom: A Model of Interdisciplinary Education

    ERIC Educational Resources Information Center

    Hodgson, Ted; Keck, Robert; Patterson, Richard; Maki, Dan

    2005-01-01

    This article describes an interdisciplinary course that develops essential mathematical modeling skills within an introductory biology setting. The course embodies recent recommendations regarding the need for interdisciplinary, inquiry-based mathematical preparation of undergraduates in the biological sciences. Evaluation indicates that the…

  17. Constructing a Model of Mathematical Literacy.

    ERIC Educational Resources Information Center

    Pugalee, David K.

    1999-01-01

    Discusses briefly the call for mathematical literacy and the need for a model that articulates the fluid and dynamic nature of this form of literacy. Presents such a model which uses two concentric circles, one depicting the four processes of mathematical literacy (representing, manipulating, reasoning, and problem solving) and enablers that…

  18. 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…

  19. 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…

  20. 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.

  1. 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…

  2. 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…

  3. 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)

  4. A mathematical model of leptin resistance.

    PubMed

    Jacquier, Marine; Soula, Hédi A; Crauste, Fabien

    2015-09-01

    Obesity is often associated with leptin resistance, which leads to a physiological system with high leptin concentration but unable to respond to leptin signals and to regulate food intake. We propose a mathematical model of the leptin-leptin receptors system, based on the assumption that leptin is a regulator of its own receptor activity, and investigate its qualitative behavior. Based on current knowledge and previous models developed for body weight dynamics in rodents, the model includes the dynamics of leptin, leptin receptors and the regulation of food intake and body weight. It displays two stable equilibria, one representing a healthy state and the other one an obese and leptin resistant state. We show that a constant leptin injection can lead to leptin resistance and that a temporal variation in some parameter values influencing food intake can induce a change of equilibrium and a pathway to leptin resistance and obesity.

  5. 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,…

  6. 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.

  7. The mathematical bases for qualitative reasoning

    NASA Technical Reports Server (NTRS)

    Kalagnanam, Jayant; Simon, Herbert A.; Iwasaki, Yumi

    1991-01-01

    The practices of researchers in many fields who use qualitative reasoning are summarized and explained. The goal is to gain an understanding of the formal assumptions and mechanisms that underlie this kind of analysis. The explanations given are based on standard mathematical formalisms, particularly on ordinal properties, continuous differentiable functions, and the mathematics of nonlinear dynamic systems.

  8. Computer-Game-Based Tutoring of Mathematics

    ERIC Educational Resources Information Center

    Ke, Fengfeng

    2013-01-01

    This in-situ, descriptive case study examined the potential of implementing computer mathematics games as an anchor for tutoring of mathematics. Data were collected from middle school students at a rural pueblo school and an urban Hispanic-serving school, through in-field observation, content analysis of game-based tutoring-learning interactions,…

  9. Study of Photovoltaic Cells Engineering Mathematical Model

    NASA Astrophysics Data System (ADS)

    Zhou, Jun; Yu, Zhengping; Lu, Zhengyi; Li, Chenhui; Zhang, Ruilan

    2016-11-01

    The characteristic curve of photovoltaic cells is the theoretical basis of PV Power, which simplifies the existing mathematical model, eventually, obtains a mathematical model used in engineering. The characteristic curve of photovoltaic cells contains both exponential and logarithmic calculation. The exponential and logarithmic spread out through Taylor series, which includes only four arithmetic and use single chip microcontroller as the control center. The result shows that: the use of single chip microcontroller for calculating exponential and logarithmic functions, simplifies mathematical model of PV curve, also can meet the specific conditions’ requirement for engineering applications.

  10. A ‘post-honeymoon’ measles epidemic in Burundi: mathematical model-based analysis and implications for vaccination timing

    PubMed Central

    Corey, Katelyn C.

    2016-01-01

    Using a mathematical model with realistic demography, we analyze a large outbreak of measles in Muyinga sector in rural Burundi in 1988–1989. We generate simulated epidemic curves and age × time epidemic surfaces, which we qualitatively and quantitatively compare with the data. Our findings suggest that supplementary immunization activities (SIAs) should be used in places where routine vaccination cannot keep up with the increasing numbers of susceptible individuals resulting from population growth or from logistical problems such as cold chain maintenance. We use the model to characterize the relationship between SIA frequency and SIA age range necessary to suppress measles outbreaks. If SIAs are less frequent, they must expand their target age range. PMID:27672515

  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 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.

  13. 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

  14. A mathematical model of elastic fin micromotors

    NASA Astrophysics Data System (ADS)

    Lu, Pin; Lee, Kwok Hong; Piang Lim, Siak; Dong, Shuxiang; Zhong Lin, Wu

    2000-08-01

    In the present work, a simplified mathematical model of ultrasonic elastic fin micromotors has been developed. According to the operating principle of this type of motor, the motions of a rotor in each cycle of the stator vibration are divided into several stages based on whether the fin tip and the stator are in contact with slip, contact without slip or separation. The equations of motion of the rotor in each stage are derived. The valid range of the model has been discussed through numerical examples. This work provides an initial effort to construct a model for the elastic fin motor by considering the dynamical deformation of the rotor as well as the intermittent contacts.

  15. A mathematical model for Vertical Attitude Takeoff and Landing (VATOL) aircraft simulation. Volume 2: Model equations and base aircraft data

    NASA Technical Reports Server (NTRS)

    Fortenbaugh, R. L.

    1980-01-01

    Equations incorporated in a VATOL six degree of freedom off-line digital simulation program and data for the Vought SF-121 VATOL aircraft concept which served as the baseline for the development of this program are presented. The equations and data are intended to facilitate the development of a piloted VATOL simulation. The equation presentation format is to state the equations which define a particular model segment. Listings of constants required to quantify the model segment, input variables required to exercise the model segment, and output variables required by other model segments are included. In several instances a series of input or output variables are followed by a section number in parentheses which identifies the model segment of origination or termination of those variables.

  16. 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

  17. 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.

  18. A mathematical model of aortic aneurysm formation.

    PubMed

    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.

  19. Mathematical Modeling of Chemical Stoichiometry

    ERIC Educational Resources Information Center

    Croteau, Joshua; Fox, William P.; Varazo, Kristofoland

    2007-01-01

    In beginning chemistry classes, students are taught a variety of techniques for balancing chemical equations. The most common method is inspection. This paper addresses using a system of linear mathematical equations to solve for the stoichiometric coefficients. Many linear algebra books carry the standard balancing of chemical equations as an…

  20. Mathematical Modelling as Problem Solving for Children in the Singapore Mathematics Classrooms

    ERIC Educational Resources Information Center

    Eric, Chan Chun Ming

    2009-01-01

    The newly revised mathematics curriculum in Singapore has recently factored Applications and Modelling to be part of the teaching and learning of mathematics. Its implication is that even children should now be involved in works of mathematical modelling. However, to be able to implement modelling activities in the primary mathematics classroom,…

  1. 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.

  2. 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)

  3. 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…

  4. Genetic demographic networks: Mathematical model and applications.

    PubMed

    Kimmel, Marek; Wojdyła, Tomasz

    2016-10-01

    Recent improvement in the quality of genetic data obtained from extinct human populations and their ancestors encourages searching for answers to basic questions regarding human population history. The most common and successful are model-based approaches, in which genetic data are compared to the data obtained from the assumed demography model. Using such approach, it is possible to either validate or adjust assumed demography. Model fit to data can be obtained based on reverse-time coalescent simulations or forward-time simulations. In this paper we introduce a computational method based on mathematical equation that allows obtaining joint distributions of pairs of individuals under a specified demography model, each of them characterized by a genetic variant at a chosen locus. The two individuals are randomly sampled from either the same or two different populations. The model assumes three types of demographic events (split, merge and migration). Populations evolve according to the time-continuous Moran model with drift and Markov-process mutation. This latter process is described by the Lyapunov-type equation introduced by O'Brien and generalized in our previous works. Application of this equation constitutes an original contribution. In the result section of the paper we present sample applications of our model to both simulated and literature-based demographies. Among other we include a study of the Slavs-Balts-Finns genetic relationship, in which we model split and migrations between the Balts and Slavs. We also include another example that involves the migration rates between farmers and hunters-gatherers, based on modern and ancient DNA samples. This latter process was previously studied using coalescent simulations. Our results are in general agreement with the previous method, which provides validation of our approach. Although our model is not an alternative to simulation methods in the practical sense, it provides an algorithm to compute pairwise

  5. 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.

  6. Mathematical Modeling of Circadian and Homeostatic Interaction

    DTIC Science & Technology

    2011-11-16

    REM ) sleep , and non- REM ( NREM ) sleep states. Using this mathematical modeling framework, the Pis conducted modeling studies on several...The model network exhibits realistic polyphasic sleep -wake behavior consisting of wake, rapid eye movement ( REM ) sleep , and non- REM ( NREM ) sleep ...states. In addition, the model captures stereotypical sleep patterning including cycling between NREM and REM sleep . Using this

  7. Mathematical modelling of the MAP kinase pathway using proteomic datasets.

    PubMed

    Tian, Tianhai; Song, Jiangning

    2012-01-01

    The advances in proteomics technologies offer an unprecedented opportunity and valuable resources to understand how living organisms execute necessary functions at systems levels. However, little work has been done up to date to utilize the highly accurate spatio-temporal dynamic proteome data generated by phosphoprotemics for mathematical modeling of complex cell signaling pathways. This work proposed a novel computational framework to develop mathematical models based on proteomic datasets. Using the MAP kinase pathway as the test system, we developed a mathematical model including the cytosolic and nuclear subsystems; and applied the genetic algorithm to infer unknown model parameters. Robustness property of the mathematical model was used as a criterion to select the appropriate rate constants from the estimated candidates. Quantitative information regarding the absolute protein concentrations was used to refine the mathematical model. We have demonstrated that the incorporation of more experimental data could significantly enhance both the simulation accuracy and robustness property of the proposed model. In addition, we used the MAP kinase pathway inhibited by phosphatases with different concentrations to predict the signal output influenced by different cellular conditions. Our predictions are in good agreement with the experimental observations when the MAP kinase pathway was inhibited by phosphatase PP2A and MKP3. The successful application of the proposed modeling framework to the MAP kinase pathway suggests that our method is very promising for developing accurate mathematical models and yielding insights into the regulatory mechanisms of complex cell signaling pathways.

  8. Mathematical biology modules based on modern molecular biology and modern discrete mathematics.

    PubMed

    Robeva, Raina; Davies, Robin; Hodge, Terrell; Enyedi, Alexander

    2010-01-01

    We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. For the majority of projects, calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. Open-source software is used to facilitate the relevant computations. As a detailed example, we outline a module that focuses on Boolean models of the lac operon network.

  9. Mathematical Biology Modules Based on Modern Molecular Biology and Modern Discrete Mathematics

    PubMed Central

    Davies, Robin; Hodge, Terrell; Enyedi, Alexander

    2010-01-01

    We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. For the majority of projects, calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. Open-source software is used to facilitate the relevant computations. As a detailed example, we outline a module that focuses on Boolean models of the lac operon network. PMID:20810955

  10. Mathematical model of tumor-immune surveillance.

    PubMed

    Mahasa, Khaphetsi Joseph; Ouifki, Rachid; Eladdadi, Amina; Pillis, Lisette de

    2016-09-07

    We present a novel mathematical model involving various immune cell populations and tumor cell populations. The model describes how tumor cells evolve and survive the brief encounter with the immune system mediated by natural killer (NK) cells and the activated CD8(+) cytotoxic T lymphocytes (CTLs). The model is composed of ordinary differential equations describing the interactions between these important immune lymphocytes and various tumor cell populations. Based on up-to-date knowledge of immune evasion and rational considerations, the model is designed to illustrate how tumors evade both arms of host immunity (i.e. innate and adaptive immunity). The model predicts that (a) an influx of an external source of NK cells might play a crucial role in enhancing NK-cell immune surveillance; (b) the host immune system alone is not fully effective against progression of tumor cells; (c) the development of immunoresistance by tumor cells is inevitable in tumor immune surveillance. Our model also supports the importance of infiltrating NK cells in tumor immune surveillance, which can be enhanced by NK cell-based immunotherapeutic approaches.

  11. 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…

  12. 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…

  13. 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…

  14. Mathematical biodynamic feedthrough model applied to rotorcraft.

    PubMed

    Venrooij, Joost; Mulder, Mark; Abbink, David A; van Paassen, Marinus M; Mulder, Max; van der Helm, Frans C T; Bulthoff, Heinrich H

    2014-07-01

    Biodynamic feedthrough (BDFT) occurs when vehicle accelerations feed through the human body and cause involuntary control inputs. This paper proposes a model to quantitatively predict this effect in rotorcraft. This mathematical BDFT model aims to fill the gap between the currently existing black box BDFT models and physical BDFT models. The model structure was systematically constructed using asymptote modeling, a procedure described in detail in this paper. The resulting model can easily be implemented in many typical rotorcraft BDFT studies, using the provided model parameters. The model's performance was validated in both the frequency and time domain. Furthermore, it was compared with several recent BDFT models. The results show that the proposed mathematical model performs better than typical black box models and is easier to parameterize and implement than a recent physical model.

  15. Assessing the Effectiveness of STAD Model and Problem Based Learning in Mathematics Learning Achievement and Problem Solving Ability

    ERIC Educational Resources Information Center

    Rattanatumma, Tawachai; Puncreobutr, Vichian

    2016-01-01

    The objective of this study was to compare the effectiveness of teaching methods in improving Mathematics Learning Achievement and Problem solving ability of students at an international college. This is a Quasi-Experimental Research which was done the study with the first year students who have registered to study Mathematics subject at St.…

  16. Identifying Subtypes among Children with Developmental Coordination Disorder and Mathematical Learning Disabilities, Using Model-Based Clustering

    ERIC Educational Resources Information Center

    Pieters, Stefanie; Roeyers, Herbert; Rosseel, Yves; Van Waelvelde, Hilde; Desoete, Annemie

    2015-01-01

    A relationship between motor and mathematical skills has been shown by previous research. However, the question of whether subtypes can be differentiated within developmental coordination disorder (DCD) and/or mathematical learning disability (MLD) remains unresolved. In a sample of children with and without DCD and/or MLD, a data-driven…

  17. Mathematical model for contemplative amoeboid locomotion

    NASA Astrophysics Data System (ADS)

    Ueda, Kei-Ichi; Takagi, Seiji; Nishiura, Yasumasa; Nakagaki, Toshiyuki

    2011-02-01

    It has recently been reported that even single-celled organisms appear to be “indecisive” or “contemplative” when confronted with an obstacle. When the amoeboid organism Physarum plasmodium encounters the chemical repellent quinine during migration along a narrow agar lane, it stops for a period of time (typically several hours) and then suddenly begins to move again. When movement resumes, three distinct types of behavior are observed: The plasmodium continues forward, turns back, or migrates in both directions simultaneously. Here, we develop a continuum mathematical model of the cell dynamics of contemplative amoeboid movement. Our model incorporates the dynamics of the mass flow of the protoplasmic sol, in relation to the generation of pressure based on the autocatalytic kinetics of pseudopod formation and retraction (mainly, sol-gel conversion accompanying actin-myosin dynamics). The biological justification of the model is tested by comparing with experimentally measured spatiotemporal profiles of the cell thickness. The experimentally observed types of behavior are reproduced in simulations based on our model, and the core logic of the modeled behavior is clarified by means of nonlinear dynamics. An on-off transition between the refractory and activated states of the chemical reactivity that takes place at the leading edge of the plasmodium plays a key role in the emergence of contemplative behavior.

  18. Mathematical Modelling with 9-Year-Olds

    ERIC Educational Resources Information Center

    English, Lyn D.; Watters, James J.

    2005-01-01

    This paper reports on the mathematical modelling of four classes of 4th-grade children as they worked on a modelling problem involving the selection of an Australian swimming team for the 2004 Olympics. The problem was implemented during the second year of the children's participation in a 3-year longitudinal program of modelling experiences…

  19. Incorporating neurophysiological concepts in mathematical thermoregulation models

    NASA Astrophysics Data System (ADS)

    Kingma, Boris R. M.; Vosselman, M. J.; Frijns, A. J. H.; van Steenhoven, A. A.; van Marken Lichtenbelt, W. D.

    2014-01-01

    Skin blood flow (SBF) is a key player in human thermoregulation during mild thermal challenges. Various numerical models of SBF regulation exist. However, none explicitly incorporates the neurophysiology of thermal reception. This study tested a new SBF model that is in line with experimental data on thermal reception and the neurophysiological pathways involved in thermoregulatory SBF control. Additionally, a numerical thermoregulation model was used as a platform to test the function of the neurophysiological SBF model for skin temperature simulation. The prediction-error of the SBF-model was quantified by root-mean-squared-residual (RMSR) between simulations and experimental measurement data. Measurement data consisted of SBF (abdomen, forearm, hand), core and skin temperature recordings of young males during three transient thermal challenges (1 development and 2 validation). Additionally, ThermoSEM, a thermoregulation model, was used to simulate body temperatures using the new neurophysiological SBF-model. The RMSR between simulated and measured mean skin temperature was used to validate the model. The neurophysiological model predicted SBF with an accuracy of RMSR < 0.27. Tskin simulation results were within 0.37 °C of the measured mean skin temperature. This study shows that (1) thermal reception and neurophysiological pathways involved in thermoregulatory SBF control can be captured in a mathematical model, and (2) human thermoregulation models can be equipped with SBF control functions that are based on neurophysiology without loss of performance. The neurophysiological approach in modelling thermoregulation is favourable over engineering approaches because it is more in line with the underlying physiology.

  20. Mathematical Models of Tuberculosis Reactivation and Relapse

    PubMed Central

    Wallis, Robert S.

    2016-01-01

    The natural history of human infection with Mycobacterium tuberculosis (Mtb) is highly variable, as is the response to treatment of active tuberculosis. There is presently no direct means to identify individuals in whom Mtb infection has been eradicated, whether by a bactericidal immune response or sterilizing antimicrobial chemotherapy. Mathematical models can assist in such circumstances by measuring or predicting events that cannot be directly observed. The 3 models discussed in this review illustrate instances in which mathematical models were used to identify individuals with innate resistance to Mtb infection, determine the etiologic mechanism of tuberculosis in patients treated with tumor necrosis factor blockers, and predict the risk of relapse in persons undergoing tuberculosis treatment. These examples illustrate the power of various types of mathematic models to increase knowledge and thereby inform interventions in the present global tuberculosis epidemic. PMID:27242697

  1. 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…

  2. Mathematical modeling in metal metabolism: overview and perspectives.

    PubMed

    Curis, Emmanuel; Nicolis, Ioannis; Bensaci, Jalil; Deschamps, Patrick; Bénazeth, Simone

    2009-10-01

    A review of mathematical modeling in metal metabolism is presented. Both endogenous and exogenous metals are considered. Four classes of methods are considered: Petri nets, multi-agent systems, determinist models based on differential equations and stochastic models. For each, a basic theoretical background is given, then examples of applications are given, detailed and commented. Advantages and disadvantages of each class of model are presented. A special attention is given to determinist differential equation models, since almost all models belong to this class.

  3. Mathematical Modeling in Continuum Mechanics

    NASA Astrophysics Data System (ADS)

    Temam, Roger; Miranville, Alain

    2005-06-01

    Temam and Miranville present core topics within the general themes of fluid and solid mechanics. The brisk style allows the text to cover a wide range of topics including viscous flow, magnetohydrodynamics, atmospheric flows, shock equations, turbulence, nonlinear solid mechanics, solitons, and the nonlinear Schrödinger equation. This second edition will be a unique resource for those studying continuum mechanics at the advanced undergraduate and beginning graduate level whether in engineering, mathematics, physics or the applied sciences. Exercises and hints for solutions have been added to the majority of chapters, and the final part on solid mechanics has been substantially expanded. These additions have now made it appropriate for use as a textbook, but it also remains an ideal reference book for students and anyone interested in continuum mechanics.

  4. TOWARDS A BIOLOGICALLY BASED DOSE-RESPONSE MODEL FOR DEVELOPMENTAL TOXICITY OF 5-FLUOROUACIL IN THE RAT: A MATHEMATICAL CONSTRUCT

    EPA Science Inventory

    CREATING A BIOLOGICALLY-BASED DOSE-RESPONSE MODEL FOR DEVELOPMENTAL TOXICITY OF 5-FLUOROURACIL IN THE RAT. R W Setzer1, C Lau2, M L Mole2, M F Copeland2, J M Rogers2 and R J Kavlock2. 1ETD, 2RTD, NHEERL, ORD, US EPA, Research Triangle Park, NC, USA.
    Biologically based dose-...

  5. 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.

  6. 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.

  7. Mathematical Model For Scattering From Mirrors

    NASA Technical Reports Server (NTRS)

    Wang, Yaujen

    1988-01-01

    Additional terms account for effects of particulate contamination. Semiempirical mathematical model of scattering of light from surface of mirror gives improved account of effects of particulate contamination. Models that treated only scattering by microscopic irregularities in surface gave bidirectional reflectance distribution functions differing from measured scattering intensities over some ranges of angles.

  8. Mathematical Modeling of Electrochemical Flow Capacitors

    SciTech Connect

    Hoyt, NC; Wainright, JS; Savinell, RF

    2015-01-13

    Electrochemical flow capacitors (EFCs) for grid-scale energy storage are a new technology that is beginning to receive interest. Prediction of the expected performance of such systems is important as modeling can be a useful avenue in the search for design improvements. Models based off of circuit analogues exist to predict EFC performance, but these suffer from deficiencies (e.g. a multitude of fitting constants that are required and the ability to analyze only one spatial direction at a time). In this paper mathematical models based off of three-dimensional macroscopic balances (similar to models for porous electrodes) are reported. Unlike existing three-dimensional porous electrode-based approaches for modeling slurry electrodes, advection (i.e., transport associated with bulk fluid motion) of the overpotential is included in order to account for the surface charge at the interface between flowing particles and the electrolyte. Doing so leads to the presence of overpotential boundary layers that control the performance of EFCs. These models were used to predict the charging behavior of an EFC under both flowing and non-flowing conditions. Agreement with experimental data was good, including proper prediction of the steady-state current that is achieved during charging of a flowing EFC. (C) The Author(s) 2015. Published by ECS. This is an open access article distributed under the terms of the Creative Commons Attribution Non-Commercial No Derivatives 4.0 License (CC BY-NC-ND, http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial reuse, distribution, and reproduction in any medium, provided the original work is not changed in any way and is properly cited. For permission for commercial reuse, please email: oa@electrochem.org. All rights reserved.

  9. A Taxonomy-Based Approach to Shed Light on the Babel of Mathematical Models for Rice Simulation

    NASA Technical Reports Server (NTRS)

    Confalonieri, Roberto; Bregaglio, Simone; Adam, Myriam; Ruget, Francoise; Li, Tao; Hasegawa, Toshihiro; Yin, Xinyou; Zhu, Yan; Boote, Kenneth; Buis, Samuel; Ruane, Alex C.

    2016-01-01

    For most biophysical domains, differences in model structures are seldom quantified. Here, we used a taxonomy-based approach to characterise thirteen rice models. Classification keys and binary attributes for each key were identified, and models were categorised into five clusters using a binary similarity measure and the unweighted pair-group method with arithmetic mean. Principal component analysis was performed on model outputs at four sites. Results indicated that (i) differences in structure often resulted in similar predictions and (ii) similar structures can lead to large differences in model outputs. User subjectivity during calibration may have hidden expected relationships between model structure and behaviour. This explanation, if confirmed, highlights the need for shared protocols to reduce the degrees of freedom during calibration, and to limit, in turn, the risk that user subjectivity influences model performance.

  10. University Mathematics and Science Faculty Modeling Their Understanding of Reform Based Instruction in a Teacher Preparation Program: Voices of Faculty and Teacher Candidates

    ERIC Educational Resources Information Center

    McGinnis, J. Randy; Watanabe, Tad; McDuffie, Amy Roth

    2005-01-01

    This study was conducted in a reform-based mathematics and science teacher education program in the USA, the Maryland Collaborative for Teacher Preparation (MCTP). The goal of the undergraduate program was to prepare upper elementary/middle level specialists in mathematics and science. One significant aspect of the MCTP was the expectation that…

  11. 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.

  12. Mathematical modeling relevant to closed artificial ecosystems.

    PubMed

    DeAngelis, Donald 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.

  13. Voters' Fickleness:. a Mathematical Model

    NASA Astrophysics Data System (ADS)

    Boccara, Nino

    This paper presents a spatial agent-based model in order to study the evolution of voters' choice during the campaign of a two-candidate election. Each agent, represented by a point inside a two-dimensional square, is under the influence of its neighboring agents, located at a Euclidean distance less than or equal to d, and under the equal influence of both candidates seeking to win its support. Moreover, each agent located at time t at a given point moves at the next timestep to a randomly selected neighboring location distributed normally around its position at time t. Besides their location in space, agents are characterized by their level of awareness, a real a ∈ [0, 1], and their opinion ω ∈ {-1, 0, +1}, where -1 and +1 represent the respective intentions to cast a ballot in favor of one of the two candidates while 0 indicates either disinterest or refusal to vote. The essential purpose of the paper is qualitative; its aim is to show that voters' fickleness is strongly correlated to the level of voters' awareness and the efficiency of candidates' propaganda.

  14. Environmental factors in breast cancer invasion: a mathematical modelling review.

    PubMed

    Simmons, Alex; Burrage, Pamela M; Nicolau, Dan V; Lakhani, Sunil R; Burrage, Kevin

    2017-02-01

    This review presents a brief overview of breast cancer, focussing on its heterogeneity and the role of mathematical modelling and simulation in teasing apart the underlying biophysical processes. Following a brief overview of the main known pathophysiological features of ductal carcinoma, attention is paid to differential equation-based models (both deterministic and stochastic), agent-based modelling, multi-scale modelling, lattice-based models and image-driven modelling. A number of vignettes are presented where these modelling approaches have elucidated novel aspects of breast cancer dynamics, and we conclude by offering some perspectives on the role mathematical modelling can play in understanding breast cancer development, invasion and treatment therapies.

  15. 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…

  16. Cocaine addiction and personality: a mathematical model.

    PubMed

    Caselles, Antonio; Micó, Joan C; Amigó, Salvador

    2010-05-01

    The existence of a close relation between personality and drug consumption is recognized, but the corresponding causal connection is not well known. Neither is it well known whether personality exercises an influence predominantly at the beginning and development of addiction, nor whether drug consumption produces changes in personality. This paper presents a dynamic mathematical model of personality and addiction based on the unique personality trait theory (UPTT) and the general modelling methodology. This model attempts to integrate personality, the acute effect of drugs, and addiction. The UPTT states the existence of a unique trait of personality called extraversion, understood as a dimension that ranges from impulsive behaviour and sensation-seeking (extravert pole) to fearful and anxious behaviour (introvert pole). As a consequence of drug consumption, the model provides the main patterns of extraversion dynamics through a system of five coupled differential equations. It combines genetic extraversion, as a steady state, and dynamic extraversion in a unique variable measured on the hedonic scale. The dynamics of this variable describes the effects of stimulant drugs on a short-term time scale (typical of the acute effect); while its mean time value describes the effects of stimulant drugs on a long-term time scale (typical of the addiction effect). This understanding may help to develop programmes of prevention and intervention in drug misuse.

  17. Mathematical modelling of animate and intentional motion.

    PubMed Central

    Rittscher, Jens; Blake, Andrew; Hoogs, Anthony; Stein, Gees

    2003-01-01

    Our aim is to enable a machine to observe and interpret the behaviour of others. Mathematical models are employed to describe certain biological motions. The main challenge is to design models that are both tractable and meaningful. In the first part we will describe how computer vision techniques, in particular visual tracking, can be applied to recognize a small vocabulary of human actions in a constrained scenario. Mainly the problems of viewpoint and scale invariance need to be overcome to formalize a general framework. Hence the second part of the article is devoted to the question whether a particular human action should be captured in a single complex model or whether it is more promising to make extensive use of semantic knowledge and a collection of low-level models that encode certain motion primitives. Scene context plays a crucial role if we intend to give a higher-level interpretation rather than a low-level physical description of the observed motion. A semantic knowledge base is used to establish the scene context. This approach consists of three main components: visual analysis, the mapping from vision to language and the search of the semantic database. A small number of robust visual detectors is used to generate a higher-level description of the scene. The approach together with a number of results is presented in the third part of this article. PMID:12689374

  18. Mathematical modeling plasma transport in tokamaks

    SciTech Connect

    Quiang, Ji

    1997-01-01

    In this work, the author applied a systematic calibration, validation and application procedure based on the methodology of mathematical modeling to international thermonuclear experimental reactor (ITER) ignition studies. The multi-mode plasma transport model used here includes a linear combination of drift wave branch and ballooning branch instabilities with two a priori uncertain constants to account for anomalous plasma transport in tokamaks. A Bayesian parameter estimation method is used including experimental calibration error/model offsets and error bar rescaling factors to determine the two uncertain constants in the transport model with quantitative confidence level estimates for the calibrated parameters, which gives two saturation levels of instabilities. This method is first tested using a gyroBohm multi-mode transport model with a pair of DIII-D discharge experimental data, and then applied to calibrating a nominal multi-mode transport model against a broad database using twelve discharges from seven different tokamaks. The calibrated transport model is then validated on five discharges from JT-60 with no adjustable constants. The results are in a good agreement with experimental data. Finally, the resulting class of multi-mode tokamak plasma transport models is applied to the transport analysis of the ignition probability in a next generation machine, ITER. A reference simulation of basic ITER engineering design activity (EDA) parameters shows that a self-sustained thermonuclear burn with 1.5 GW output power can be achieved provided that impurity control makes radiative losses sufficiently small at an average plasma density of 1.2 X 1020/m3 with 50 MW auxiliary heating. The ignition probability of ITER for the EDA parameters, can be formally as high as 99.9% in the present context. The same probability for concept design activity (CDA) parameters of ITER, which has smaller size and lower current, is only 62.6%.

  19. 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…

  20. Mathematics Literacy on Problem Based Learning with Indonesian Realistic Mathematics Education Approach Assisted E-Learning Edmodo

    NASA Astrophysics Data System (ADS)

    Wardono; Waluya, S. B.; Mariani, Scolastika; Candra D, S.

    2016-02-01

    This study aims to find out that there are differences in mathematical literacy ability in content Change and Relationship class VII Junior High School 19, Semarang by Problem Based Learning (PBL) model with an Indonesian Realistic Mathematics Education (called Pendidikan Matematika Realistik Indonesia or PMRI in Indonesia) approach assisted Elearning Edmodo, PBL with a PMRI approach, and expository; to know whether the group of students with learning PBL models with PMRI approach and assisted E-learning Edmodo can improve mathematics literacy; to know that the quality of learning PBL models with a PMRI approach assisted E-learning Edmodo has a good category; to describe the difficulties of students in working the problems of mathematical literacy ability oriented PISA. This research is a mixed methods study. The population was seventh grade students of Junior High School 19, Semarang Indonesia. Sample selection is done by random sampling so that the selected experimental class 1, class 2 and the control experiment. Data collected by the methods of documentation, tests and interviews. From the results of this study showed average mathematics literacy ability of students in the group PBL models with a PMRI approach assisted E-learning Edmodo better than average mathematics literacy ability of students in the group PBL models with a PMRI approach and better than average mathematics literacy ability of students in the expository models; Mathematics literacy ability in the class using the PBL model with a PMRI approach assisted E-learning Edmodo have increased and the improvement of mathematics literacy ability is higher than the improvement of mathematics literacy ability of class that uses the model of PBL learning with PMRI approach and is higher than the improvement of mathematics literacy ability of class that uses the expository models; The quality of learning using PBL models with a PMRI approach assisted E-learning Edmodo have very good category.

  1. 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.

  2. Three dimensional mathematical modeling of violin plate surfaces: An approach based on an ensemble of contour lines.

    PubMed

    Piantadosi, Steven

    2017-01-01

    This paper presents an approach to describing the three dimensional shape of a violin plate in mathematical form. The shape description begins with standard contour lines and ends with an equation for a surface in three dimensional space. The traditional specification of cross sectional arching is unnecessary. Advantages of this approach are that it employs simple and universal description of plate geometry and yields a complete, smoothed, precise mathematical equation of the plate that is suitable for modern three dimensional production. It is quite general and suitable for both exterior and interior plate surfaces, yielding the ability to control thicknesses along with shape. This method can produce mathematical descriptions with tolerances easily less than 0.001 millimeters suitable for modern computerized numerical control carving and hand finishing.

  3. Three dimensional mathematical modeling of violin plate surfaces: An approach based on an ensemble of contour lines

    PubMed Central

    2017-01-01

    This paper presents an approach to describing the three dimensional shape of a violin plate in mathematical form. The shape description begins with standard contour lines and ends with an equation for a surface in three dimensional space. The traditional specification of cross sectional arching is unnecessary. Advantages of this approach are that it employs simple and universal description of plate geometry and yields a complete, smoothed, precise mathematical equation of the plate that is suitable for modern three dimensional production. It is quite general and suitable for both exterior and interior plate surfaces, yielding the ability to control thicknesses along with shape. This method can produce mathematical descriptions with tolerances easily less than 0.001 millimeters suitable for modern computerized numerical control carving and hand finishing. PMID:28166230

  4. 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.

  5. A mathematical model of the CH-53 helicopter

    NASA Technical Reports Server (NTRS)

    Sturgeon, W. R.; Phillips, J. D.

    1980-01-01

    A mathematical model suitable for real time simulation of the CH-53 helicopter is presented. This model, which is based on modified nonlinear classical rotor theory and nonlinear fuselage aerodynamics, will be used to support terminal-area guidance and navigation studies on a fixed-base simulator. Validation is achieved by comparing the model response with that of a similar aircraft and by a qualitative comparison of the handling characteristics made by experienced pilots.

  6. 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.

  7. 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

  8. Turbulent motion of mass flows. Mathematical modeling

    NASA Astrophysics Data System (ADS)

    Eglit, Margarita; Yakubenko, Alexander; Yakubenko, Tatiana

    2016-04-01

    New mathematical models for unsteady turbulent mass flows, e.g., dense snow avalanches and landslides, are presented. Such models are important since most of large scale flows are turbulent. In addition to turbulence, the two other important points are taken into account: the entrainment of the underlying material by the flow and the nonlinear rheology of moving material. The majority of existing models are based on the depth-averaged equations and the turbulent character of the flow is accounted by inclusion of drag proportional to the velocity squared. In this paper full (not depth-averaged) equations are used. It is assumed that basal entrainment takes place if the bed friction equals the shear strength of the underlying layer (Issler D, M. Pastor Peréz. 2011). The turbulent characteristics of the flow are calculated using a three-parameter differential model (Lushchik et al., 1978). The rheological properties of moving material are modeled by one of the three types of equations: 1) Newtonian fluid with high viscosity, 2) power-law fluid and 3) Bingham fluid. Unsteady turbulent flows down long homogeneous slope are considered. The flow dynamical parameters and entrainment rate behavior in time as well as their dependence on properties of moving and underlying materials are studied numerically. REFERENCES M.E. Eglit and A.E. Yakubenko, 2014. Numerical modeling of slope flows entraining bottom material. Cold Reg. Sci. Technol., 108, 139-148 Margarita E. Eglit and Alexander E. Yakubenko, 2016. The effect of bed material entrainment and non-Newtonian rheology on dynamics of turbulent slope flows. Fluid Dynamics, 51(3) Issler D, M. Pastor Peréz. 2011. Interplay of entrainment and rheology in snow avalanches; a numerical study. Annals of Glaciology, 52(58), 143-147 Lushchik, V.G., Paveliev, A.A. , and Yakubenko, A.E., 1978. Three-parameter model of shear turbulence. Fluid Dynamics, 13, (3), 350-362

  9. TOWARD A BIOLOGICALLY BASED DOSE-RESPONSE MODEL FOR DEVELOPMENTAL TOXICITY OF 5-FLUOROURACIL IN THE RAT: A MATHEMATICAL CONSTRUCT

    EPA Science Inventory

    Biologically based dose-response (BBDR) models comprise one way to incorporate mechanistic information into a dose-response assessment to be used for risk assessments. The chemotherapeutic drug 5-fluorouracil (5-FU) has been used as a prototypic compound for the construction of ...

  10. On Mathematical Modeling Of Quantum Systems

    SciTech Connect

    Achuthan, P.; Narayanankutty, Karuppath

    2009-07-02

    The world of physical systems at the most fundamental levels is replete with efficient, interesting models possessing sufficient ability to represent the reality to a considerable extent. So far, quantum mechanics (QM) forming the basis of almost all natural phenomena, has found beyond doubt its intrinsic ingenuity, capacity and robustness to stand the rigorous tests of validity from and through appropriate calculations and experiments. No serious failures of quantum mechanical predictions have been reported, yet. However, Albert Einstein, the greatest theoretical physicist of the twentieth century and some other eminent men of science have stated firmly and categorically that QM, though successful by and large, is incomplete. There are classical and quantum reality models including those based on consciousness. Relativistic quantum theoretical approaches to clearly understand the ultimate nature of matter as well as radiation have still much to accomplish in order to qualify for a final theory of everything (TOE). Mathematical models of better, suitable character as also strength are needed to achieve satisfactory explanation of natural processes and phenomena. We, in this paper, discuss some of these matters with certain apt illustrations as well.

  11. On Mathematical Modeling Of Quantum Systems

    NASA Astrophysics Data System (ADS)

    Achuthan, P.; Narayanankutty, Karuppath

    2009-07-01

    The world of physical systems at the most fundamental levels is replete with efficient, interesting models possessing sufficient ability to represent the reality to a considerable extent. So far, quantum mechanics (QM) forming the basis of almost all natural phenomena, has found beyond doubt its intrinsic ingenuity, capacity and robustness to stand the rigorous tests of validity from and through appropriate calculations and experiments. No serious failures of quantum mechanical predictions have been reported, yet. However, Albert Einstein, the greatest theoretical physicist of the twentieth century and some other eminent men of science have stated firmly and categorically that QM, though successful by and large, is incomplete. There are classical and quantum reality models including those based on consciousness. Relativistic quantum theoretical approaches to clearly understand the ultimate nature of matter as well as radiation have still much to accomplish in order to qualify for a final theory of everything (TOE). Mathematical models of better, suitable character as also strength are needed to achieve satisfactory explanation of natural processes and phenomena. We, in this paper, discuss some of these matters with certain apt illustrations as well.

  12. Mathematical Models of Cardiac Pacemaking Function

    NASA Astrophysics Data System (ADS)

    Li, Pan; Lines, Glenn T.; Maleckar, Mary M.; Tveito, Aslak

    2013-10-01

    Over the past half century, there has been intense and fruitful interaction between experimental and computational investigations of cardiac function. This interaction has, for example, led to deep understanding of cardiac excitation-contraction coupling; how it works, as well as how it fails. However, many lines of inquiry remain unresolved, among them the initiation of each heartbeat. The sinoatrial node, a cluster of specialized pacemaking cells in the right atrium of the heart, spontaneously generates an electro-chemical wave that spreads through the atria and through the cardiac conduction system to the ventricles, initiating the contraction of cardiac muscle essential for pumping blood to the body. Despite the fundamental importance of this primary pacemaker, this process is still not fully understood, and ionic mechanisms underlying cardiac pacemaking function are currently under heated debate. Several mathematical models of sinoatrial node cell membrane electrophysiology have been constructed as based on different experimental data sets and hypotheses. As could be expected, these differing models offer diverse predictions about cardiac pacemaking activities. This paper aims to present the current state of debate over the origins of the pacemaking function of the sinoatrial node. Here, we will specifically review the state-of-the-art of cardiac pacemaker modeling, with a special emphasis on current discrepancies, limitations, and future challenges.

  13. Dog Mathematics: Exploring Base-4

    ERIC Educational Resources Information Center

    Kurz, Terri L.; Yanik, H. Bahadir; Lee, Mi Yeon

    2016-01-01

    Using a dog's paw as a basis for numerical representation, sixth grade students explored how to count and regroup using the dog's four digital pads. Teachers can connect these base-4 explorations to the conceptual meaning of place value and regrouping using base-10.

  14. 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.

  15. 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…

  16. Mathematical Modeling of Wildfire Dynamics

    NASA Astrophysics Data System (ADS)

    Del Bene, Kevin; Drew, Donald

    2012-11-01

    Wildfires have been a long-standing problem in today's society. In this paper, we derive and solve a fluid dynamics model to study a specific type of wildfire, namely, a two dimensional flow around a rising plume above a concentrated heat source, modeling a fire line. This flow assumes a narrow plume of hot gas rising and entraining the surrounding air. The surrounding air is assumed to have constant density and is irrotational far from the fire line. The flow outside the plume is described by a Biot-Savart integral with jump conditions across the position of the plume. The plume model describes the unsteady evolution of the mass, momentum, energy, and vorticity inside the plume, with sources derived to model mixing in the style of Morton, et al. 1956]. The fire is then modeled using a conservation derivation, allowing the fire to propagate, coupling back to the plume model. The results show that this model is capable of capturing the complex interaction of the plume with the surrounding air and fuel layer. Funded by NSF GRFP.

  17. Introduction to mathematical models and methods

    SciTech Connect

    Siddiqi, A. H.; Manchanda, P.

    2012-07-17

    Some well known mathematical models in the form of partial differential equations representing real world systems are introduced along with fundamental concepts of Image Processing. Notions such as seismic texture, seismic attributes, core data, well logging, seismic tomography and reservoirs simulation are discussed.

  18. An Examination of the Effects of Collaborative Scientific Visualization via Model-based Reasoning on Science, Technology, Engineering, and Mathematics (STEM) Learning Within an Immersive 3D World

    NASA Astrophysics Data System (ADS)

    Soleimani, Ali

    Immersive 3D worlds can be designed to effectively engage students in peer-to-peer collaborative learning activities, supported by scientific visualization, to help with understanding complex concepts associated with learning science, technology, engineering, and mathematics (STEM). Previous research studies have shown STEM learning benefits associated with the use of scientific visualization tools involving model-based reasoning (MBR). Little is known, however, about collaborative use of scientific visualization, via MBR, within an immersive 3D-world learning environment for helping to improve perceived value of STEM learning and knowledge acquisition in a targeted domain such as geothermal energy. Geothermal energy was selected as the study's STEM focus, because understanding in the domain is highly dependent on successfully integrating science and mathematics concepts. This study used a 2x2 Mixed ANOVA, with repeated measures, design to analyze collaborative usage of a geothermal energy MBR model and its effects on learning within an immersive 3D world. The immersive 3D world used for the study is supported by the Open Simulator platform. Findings from this study can suggest ways to improve STEM learning and inform the design of MBR activities when conducted within an immersive 3D world.

  19. Determining the Views of Mathematics Student Teachers Related to Mathematical Modelling

    ERIC Educational Resources Information Center

    Tekin, Ayse; Kula, Semiha; Hidiroglu, Caglar Naci; Bukova-Guzel, Esra; Ugurel, Isikhan

    2012-01-01

    The purpose of this qualitative research is to examine the views of 21 secondary mathematics student teachers attending Mathematical Modelling Course regarding mathematical modelling in a state university in Turkey; reasons why they chose this course and their expectations from the course in question. For this reason, three open-ended questions…

  20. 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…

  1. Study on the Comparisons of the Establishment of Two Mathematical Modeling Methods for Soil Organic Matter Content Based on Spectral Reflectance.

    PubMed

    Zhang, Pei; Li, Yi

    2016-03-01

    Existing prediction models of soil organic matter content (SOC) are restricted by some factors, such as sampling scale, soil type and spectral parameters of samples. Therefore, it is necessary to make a comparative analysis on larger scales to build a quantitative model with better feasibility and greater accuracy. A total of 225 soil samples were collected in an extensive region of the upper reaches of Heihe river basin. SOC and spectral reflectance were being measured. All the samples were divided into 2 subsets--a modeling subset (180 samples) and a validation subset (45 samples). Six indices were obtained through transformation of soil spectral reflectance (R), continuum-removal (CR), reciprocal (REC), logarithm of reciprocal (LR), first-order differential (FDR) and Kubelka-Munck transformation coefficient (K-M). To build the mathematical model of SOC with 12 spectral indices, two methods, i. e., stepwise linear regression and partial least-square regression were used based on the modeling subset, respectively; the validation subset is used for model evaluation. The results indicated that, (1) Regardless of different modeling methods, model between SOC and LR index was always the best among the 6 reflectance-related indices. LR was the best index for predicting SOC; (2) For the model based on the LR index, the accuracy of model using partial least-square regression method was better than that using stepwise linear regression method; (3) 225 samples were compared to verify the former available published SOC model. Both the predicted and measured values passed the mean value t-test, and the Pearson correlation coefficient reached 0.826. It shows that local prediction model can be applied to the research of predicting SOC in the larger scale.

  2. Toxin detection based on action potential shape analysis using a realistic mathematical model of differentiated NG108-15 cells

    PubMed Central

    Mohan, Dinesh K; Molnar, Peter; Hickman, James J.

    2010-01-01

    The NG108-15 neuroblastoma / glioma hybrid cell line has been frequently used for toxin detection, pharmaceutical screening and as a whole-cell biosensor. However, detailed analysis of its action potentials during toxin or drug administration has not been accomplished previously using patch clamp electrophysiology. In order to explore the possibility of identifying toxins based on their effect on the shape of intracellularly or extracellularly detected action potentials, we created a computer model of the action potential generation of this cell type. To generate the experimental data to validate the model, voltage dependent sodium, potassium and high-threshold calcium currents, as well as action potentials, were recorded from NG108-15 cells with conventional whole-cell patch-clamp methods. Based on the classic Hodgkin-Huxley formalism and the linear thermodynamic description of the rate constants, ion-channel parameters were estimated using an automatic fitting method. Utilizing the established parameters, action potentials were generated in the model and were optimized to represent the actual recorded action potentials to establish baseline conditions. To demonstrate the applicability of the method for toxin detection and discrimination, the effect of tetrodotoxin (a sodium channel blocker) and tefluthrin (a pyrethroid that is a sodium channel opener) were studied. The two toxins affected the shape of the action potentials differently and their respective effects were identified based on the changes in the fitted parameters. Our results represent one of the first steps to establish a complex model of NG108-15 cells for quantitative toxin detection based on action potential shape analysis of the experimental results. PMID:16460924

  3. A Mathematical Model of Forgetting and Amnesia

    PubMed Central

    Murre, Jaap M. J.; Chessa, Antonio G.; Meeter, Martijn

    2013-01-01

    We describe a mathematical model of learning and memory and apply it to the dynamics of forgetting and amnesia. The model is based on the hypothesis that the neural systems involved in memory at different time scales share two fundamental properties: (1) representations in a store decline in strength (2) while trying to induce new representations in higher-level more permanent stores. This paper addresses several types of experimental and clinical phenomena: (i) the temporal gradient of retrograde amnesia (Ribot’s Law), (ii) forgetting curves with and without anterograde amnesia, and (iii) learning and forgetting curves with impaired cortical plasticity. Results are in the form of closed-form expressions that are applied to studies with mice, rats, and monkeys. In order to analyze human data in a quantitative manner, we also derive a relative measure of retrograde amnesia that removes the effects of non-equal item difficulty for different time periods commonly found with clinical retrograde amnesia tests. Using these analytical tools, we review studies of temporal gradients in the memory of patients with Korsakoff’s Disease, Alzheimer’s Dementia, Huntington’s Disease, and other disorders. PMID:23450438

  4. A Mathematical Model for Suppression Subtractive Hybridization

    PubMed Central

    Gadgil, Chetan; Rink, Anette; Beattie, Craig

    2002-01-01

    Suppression subtractive hybridization (SSH) is frequently used to unearth differentially expressed genes on a whole-genome scale. Its versatility is based on combining cDNA library subtraction and normalization, which allows the isolation of sequences of varying degrees of abundance and differential expression. SSH is a complex process with many adjustable parameters that affect the outcome of gene isolation.We present a mathematical model of SSH based on DNA hybridization kinetics for assessing the effect of various parameters to facilitate its optimization. We derive an equation for the probability that a particular differentially expressed species is successfully isolated and use this to quantify the effect of the following parameters related to the cDNA sample: (a) mRNA abundance; (b) partial sequence complementarity to other species; and (3) degree of differential expression. We also evaluate the effect of parameters related to the process, including: (a) reaction times; and (b) extent of driver excess used in the two hybridization reactions. The optimum set of process parameters for successful isolation of differentially expressed species depends on transcript abundance. We show that the reaction conditions have a significant effect on the occurrence of false-positives and formulate strategies to isolate specific subsets of differentially expressed genes. We also quantify the effect of non-specific hybridization on the false-positive results and present strategies for spiking cDNA sequences to address this problem. PMID:18629052

  5. Prospective Mathematics Teachers' Views about Using Computer-Based Instructional Materials in Constructing Mathematical Concepts

    ERIC Educational Resources Information Center

    Bukova-Guzel, Esra; Canturk-Gunhan, Berna

    2011-01-01

    The purpose of the study is to determine prospective mathematics teachers' views about using computer-based instructional materials in constructing mathematical concepts and to reveal how the sample computer-based instructional materials for different mathematical concepts altered their views. This is a qualitative study involving twelve…

  6. Mathematical modeling of the aerodynamic characteristics in flight dynamics

    NASA Technical Reports Server (NTRS)

    Tobak, M.; Chapman, G. T.; Schiff, L. B.

    1984-01-01

    Basic concepts involved in the mathematical modeling of the aerodynamic response of an aircraft to arbitrary maneuvers are reviewed. The original formulation of an aerodynamic response in terms of nonlinear functionals is shown to be compatible with a derivation based on the use of nonlinear functional expansions. Extensions of the analysis through its natural connection with ideas from bifurcation theory are indicated.

  7. Gifted Learners and Mathematical Achievement: An Analysis of Gifted Instructional Models

    ERIC Educational Resources Information Center

    Anderson, Lezley Barker

    2013-01-01

    The purpose of this causal-comparative study was to examine whether differences exist in the mathematics achievement of fifth grade gifted students based on the instructional delivery model used for mathematics instruction, cluster or collaborative, as defined by the Georgia Department of Education. The content area of mathematics, an area…

  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. Mathematical Modeling for Preservice Teachers: A Problem from Anesthesiology.

    ERIC Educational Resources Information Center

    Lingefjard, Thomas

    2002-01-01

    Addresses the observed actions of prospective Swedish mathematics teachers as they worked with a modeling situation. Explores prospective teachers' preparation to teach in grades 4-12 during a course of mathematical modeling. Focuses on preservice teachers' understanding of modeling and how they relate mathematical models to the real world.…

  10. Implementing the Standards: Incorporating Mathematical Modeling into the Curriculum.

    ERIC Educational Resources Information Center

    Swetz, Frank

    1991-01-01

    Following a brief historical review of the mechanism of mathematical modeling, examples are included that associate a mathematical model with given data (changes in sea level) and that model a real-life situation (process of parallel parking). Also provided is the rationale for the curricular implementation of mathematical modeling. (JJK)

  11. Mathematical Modelling of Turbidity Currents

    NASA Astrophysics Data System (ADS)

    Fay, G. L.; Fowler, A.; Howell, P.

    2011-12-01

    A turbidity current is a submarine sediment flow which propagates downslope through the ocean into the deep sea. Turbidity currents can occur randomly and without much warning and consequently are hard to observe and measure. The driving force in a turbidity current is the presence of sediment in the current - gravity acts on the sediment in suspension, causing it to move downstream through the ocean water. A phenomenon known as ignition or autosuspension has been observed in turbidity currents in submarine canyons, and it occurs when a current travelling downslope gathers speed as it erodes sediment from the sea floor in a self-reinforcing cycle. Using the turbidity current model of Parker et al. (Journal of Fluid Mechanics, 1986) we investigate the evolution of a 1-D turbidity current as it moves downstream. To seek a better understanding of the dynamics of flow as the current evolves in space and time, we present analytical results alongside computed numerical solutions, incorporating entrainment of water and erosion and deposition of sediment. We consider varying slope functions and inlet conditions and attempt to predict when the current will become extinct. We examine currents which are in both supercritical and subcritical flow regimes and consider the dynamics of the flow as the current switches regime.

  12. Mathematical Models of College Myopia

    PubMed Central

    Greene, Peter R.; Grill, Zachary W.; Medina, Antonio

    2015-01-01

    Experimental design phase of a pilot study at Annapolis is described, using reading glasses, +1.5 D. to +3.0 D. to alleviate college myopia. College students often become 1.0 to 2.0 diopters more myopic, so reading glasses were explored to partially cancel the effects of the study environment. N = 25 different sets of (+)Add lenses are evaluated, for required adjustment period and reading comfort. Three computer models are developed to predict refraction versus time. Basic control system equations predict exponential myopia shift of refractive state R(t) with time constant t0 = 100 days. Linear, exponential and Gompertz computer results are compared calculating refraction R(t) during the college years, showing correlation coefficients |r| = 0.96 to 0.97, accurate +/−0.31 D. over a 14 year interval. Typical college myopia rate is −0.3 to −0.4 D/yr. Reading glasses may be a simple, practical solution to stabilize college myopia. PMID:26709316

  13. Mathematical Models Of Turbulence In Transonic Flow

    NASA Technical Reports Server (NTRS)

    Rubesin, Morris W.; Viegas, John R.

    1989-01-01

    Predictions of several models compared with measurements of well-documented flow. Report reviews performances of variety of mathematical models of turbulence in transonic flow. Predictions of models compared with measurements of flow in wind tunnel along outside of cylinder having axisymmetric bump of circular-arc cross section in meridional plane. Review part of continuing effort to calibrate and verify computer codes for prediction of transonic flows about airfoils. Johnson-and-King model proved superior in predicting transonic flow over bumpy cylinder.

  14. 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)

  15. Multi-Objective Ant Colony Optimization Based on the Physarum-Inspired Mathematical Model for Bi-Objective Traveling Salesman Problems

    PubMed Central

    Zhang, Zili; Gao, Chao; Lu, Yuxiao; Liu, Yuxin; Liang, Mingxin

    2016-01-01

    Bi-objective Traveling Salesman Problem (bTSP) is an important field in the operations research, its solutions can be widely applied in the real world. Many researches of Multi-objective Ant Colony Optimization (MOACOs) have been proposed to solve bTSPs. However, most of MOACOs suffer premature convergence. This paper proposes an optimization strategy for MOACOs by optimizing the initialization of pheromone matrix with the prior knowledge of Physarum-inspired Mathematical Model (PMM). PMM can find the shortest route between two nodes based on the positive feedback mechanism. The optimized algorithms, named as iPM-MOACOs, can enhance the pheromone in the short paths and promote the search ability of ants. A series of experiments are conducted and experimental results show that the proposed strategy can achieve a better compromise solution than the original MOACOs for solving bTSPs. PMID:26751562

  16. Multi-Objective Ant Colony Optimization Based on the Physarum-Inspired Mathematical Model for Bi-Objective Traveling Salesman Problems.

    PubMed

    Zhang, Zili; Gao, Chao; Lu, Yuxiao; Liu, Yuxin; Liang, Mingxin

    2016-01-01

    Bi-objective Traveling Salesman Problem (bTSP) is an important field in the operations research, its solutions can be widely applied in the real world. Many researches of Multi-objective Ant Colony Optimization (MOACOs) have been proposed to solve bTSPs. However, most of MOACOs suffer premature convergence. This paper proposes an optimization strategy for MOACOs by optimizing the initialization of pheromone matrix with the prior knowledge of Physarum-inspired Mathematical Model (PMM). PMM can find the shortest route between two nodes based on the positive feedback mechanism. The optimized algorithms, named as iPM-MOACOs, can enhance the pheromone in the short paths and promote the search ability of ants. A series of experiments are conducted and experimental results show that the proposed strategy can achieve a better compromise solution than the original MOACOs for solving bTSPs.

  17. Aspects Of Multicriterial Mathematical Modeling And Of The Fuzzy Formalism For The Hierarchization Of Study Programs Based On Several Quality Characteristics

    NASA Astrophysics Data System (ADS)

    Bucur, Amelia

    2015-09-01

    The aim of this paper is to present aspects of mathematical modeling for the hierarchization of study programs from universities, based on several quality characteristics. The tools used pertain to multicriterial optimization, to the different methods of assessing importance coefficients, to the utility theory, the fuzzy formalism, and to the fuzzy simple additive weighting method. The conclusion is that multicriterial decision-making methods can be efficiently used in assessing the quality of study programs, noting that, just like other methods from the decision theory, the multicriterial decision-making methods highlight aspects of problems differently, therefore, there can be no comparison or competitiveness between them, and choosing one over the other is up to the decision-maker.

  18. Mathematical modeling of vertebrate limb development.

    PubMed

    Zhang, Yong-Tao; Alber, Mark S; Newman, Stuart A

    2013-05-01

    In this paper, we review the major mathematical and computational models of vertebrate limb development and their roles in accounting for different aspects of this process. The main aspects of limb development that have been modeled include outgrowth and shaping of the limb bud, establishment of molecular gradients within the bud, and formation of the skeleton. These processes occur interdependently during development, although (as described in this review), there are various interpretations of the biological relationships among them. A wide range of mathematical and computational methods have been used to study these processes, including ordinary and partial differential equation systems, cellular automata and discrete, stochastic models, finite difference methods, finite element methods, the immersed boundary method, and various combinations of the above. Multiscale mathematical modeling and associated computational simulation have become integrated into the study of limb morphogenesis and pattern formation to an extent with few parallels in the field of developmental biology. These methods have contributed to the design and analysis of experiments employing microsurgical and genetic manipulations, evaluation of hypotheses for limb bud outgrowth, interpretation of the effects of natural mutations, and the formulation of scenarios for the origination and evolution of the limb skeleton.

  19. Generalizing in Interaction: Middle School Mathematics Students Making Mathematical Generalizations in a Population-Modeling Project

    ERIC Educational Resources Information Center

    Jurow, A. Susan

    2004-01-01

    Generalizing or making claims that extend beyond particular situations is a central mathematical practice and a focus of classroom mathematics instruction. This study examines how aspects of generality are produced through the situated activities of a group of middle school mathematics students working on an 8-week population-modeling project. The…

  20. Assessing Science Students' Attitudes to Mathematics: A Case Study on a Modelling Project with Mathematical Software

    ERIC Educational Resources Information Center

    Lim, L. L.; Tso, T. -Y.; Lin, F. L.

    2009-01-01

    This article reports the attitudes of students towards mathematics after they had participated in an applied mathematical modelling project that was part of an Applied Mathematics course. The students were majoring in Earth Science at the National Taiwan Normal University. Twenty-six students took part in the project. It was the first time a…

  1. "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…

  2. Mathematical modelling of the lower urinary tract.

    PubMed

    Paya, Antonio Soriano; Fernandez, Daniel Ruiz; Gil, David; Garcia Chamizo, Juan Manuel; Perez, Francisco Macia

    2013-03-01

    The lower urinary tract is one of the most complex biological systems of the human body as it involved hydrodynamic properties of urine and muscle. Moreover, its complexity is increased to be managed by voluntary and involuntary neural systems. In this paper, a mathematical model of the lower urinary tract it is proposed as a preliminary study to better understand its functioning. Furthermore, another goal of that mathematical model proposal is to provide a basis for developing artificial control systems. Lower urinary tract is comprised of two interacting systems: the mechanical system and the neural regulator. The latter has the function of controlling the mechanical system to perform the voiding process. The results of the tests reproduce experimental data with high degree of accuracy. Also, these results indicate that simulations not only with healthy patients but also of patients with dysfunctions with neurological etiology present urodynamic curves very similar to those obtained in clinical studies.

  3. 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.

  4. Mathematical Model For Deposition Of Soot

    NASA Technical Reports Server (NTRS)

    Makel, Darby B.

    1991-01-01

    Semiempirical mathematical model predicts deposition of soot in tubular gas generator in which hydrocarbon fuel burned in very-fuel-rich mixture with pure oxygen. Developed in response to concern over deposition of soot in gas generators and turbomachinery of rocket engines. Also of interest in terrestrial applications involving fuel-rich combustion or analogous process; e.g., purposeful deposition of soot to manufacture carbon black pigments.

  5. Mathematical Models and the Experimental Analysis of Behavior

    ERIC Educational Resources Information Center

    Mazur, James E.

    2006-01-01

    The use of mathematical models in the experimental analysis of behavior has increased over the years, and they offer several advantages. Mathematical models require theorists to be precise and unambiguous, often allowing comparisons of competing theories that sound similar when stated in words. Sometimes different mathematical models may make…

  6. Mathematical Programming Model for Fighter Training Squadron Pilot Scheduling

    DTIC Science & Technology

    2007-03-01

    of Defense, or the United States Government. AFIT/GOR/ENS/07-17 MATHEMATICAL PROGAMMING MODEL FOR...March 2007 APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED. AFIT/GOR/ENS/07-17 MATHEMATICAL PROGAMMING MODEL FOR FIGHTER...80 x MATHEMATICAL PROGAMMING MODEL FOR FIGHTER TRAINING SQUADRON PILOT

  7. 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.

  8. A Computational and Mathematical Model for Device Induced Thrombosis

    NASA Astrophysics Data System (ADS)

    Wu, Wei-Tao; Aubry, Nadine; Massoudi, Mehrdad; Antaki, James

    2015-11-01

    Based on the Sorenson's model of thrombus formation, a new mathematical model describing the process of thrombus growth is developed. In this model the blood is treated as a Newtonian fluid, and the transport and reactions of the chemical and biological species are modeled using CRD (convection-reaction-diffusion) equations. A computational fluid dynamic (CFD) solver for the mathematical model is developed using the libraries of OpenFOAM. Applying the CFD solver, several representative benchmark problems are studied: rapid thrombus growth in vivo by injecting Adenosine diphosphate (ADP) using iontophoretic method and thrombus growth in rectangular microchannel with a crevice which usually appears as a joint between components of devices and often becomes nidus of thrombosis. Very good agreements between the numerical and the experimental results validate the model and indicate its potential to study a host of complex and practical problems in the future, such as thrombosis in blood pumps and artificial lungs.

  9. Agent-based mathematical modeling as a tool for estimating Trypanosoma cruzi vector-host contact rates.

    PubMed

    Yong, Kamuela E; Mubayi, Anuj; Kribs, Christopher M

    2015-11-01

    The parasite Trypanosoma cruzi, spread by triatomine vectors, affects over 100 mammalian species throughout the Americas, including humans, in whom it causes Chagas' disease. In the U.S., only a few autochthonous cases have been documented in humans, but prevalence is high in sylvatic hosts (primarily raccoons in the southeast and woodrats in Texas). The sylvatic transmission of T. cruzi is spread by the vector species Triatoma sanguisuga and Triatoma gerstaeckeri biting their preferred hosts and thus creating multiple interacting vector-host cycles. The goal of this study is to quantify the rate of contacts between different host and vector species native to Texas using an agent-based model framework. The contact rates, which represent bites, are required to estimate transmission coefficients, which can be applied to models of infection dynamics. In addition to quantitative estimates, results confirm host irritability (in conjunction with host density) and vector starvation thresholds and dispersal as determining factors for vector density as well as host-vector contact rates.

  10. Biology by numbers: mathematical modelling in developmental biology.

    PubMed

    Tomlin, Claire J; Axelrod, Jeffrey D

    2007-05-01

    In recent years, mathematical modelling of developmental processes has earned new respect. Not only have mathematical models been used to validate hypotheses made from experimental data, but designing and testing these models has led to testable experimental predictions. There are now impressive cases in which mathematical models have provided fresh insight into biological systems, by suggesting, for example, how connections between local interactions among system components relate to their wider biological effects. By examining three developmental processes and corresponding mathematical models, this Review addresses the potential of mathematical modelling to help understand development.

  11. Preservice Mathematics Teachers' Perceptions of Drama Based Instruction

    ERIC Educational Resources Information Center

    Bulut, Neslihan

    2016-01-01

    The purpose of this study was to determine the perceptions of pre-service mathematics teachers related to drama-based instruction. For this purpose, effects of a drama-based mathematics course on senior class pre-service mathematics teachers' knowledge about drama-based instruction and teacher candidates' competencies for developing and…

  12. Mathematical models for quantifying eruption velocity in degassing pipes based on exsolution of a single gas and simultaneous exsolution of multiple gases

    NASA Astrophysics Data System (ADS)

    Leon, Arturo S.

    2016-09-01

    After the limnic eruptions at Nyos and Monoun in the 1980s, degassing pipes were installed to reduce the continuous increase of CO2 at the bottom of these lakes. The degassing system consists of a vertical pipe from the lake bottom to the surface and a small pump located near the top of the pipe, which raises water in the pipe up to a level where it becomes saturated with gas, which in turn leads to volume expansion and eruption. This paper describes two new mathematical models for predicting eruption velocity in degassing pipes based on exsolution of a single gas and the simultaneous exsolution of multiple gases. The models were applied to the degassing system of lakes Nyos and Monoun, which contain two main gases, namely CO2 and CH4. Because the volume proportion of CH4 is significant only in Lake Monoun, the Lake Nyos test case considered the CO2 gas only, while as the Lake Monoun test case considered the simultaneous exsolution of CO2 and CH4. Good agreement between the results of the models and observed data is found for both test cases. The results for the eruption in Lake Monoun considering the two main gases measured in this lake (CO2 and CH4) were found to have a better agreement with the measurements compared to the model results obtained considering the main gas only (CO2).

  13. Mathematics.

    ERIC Educational Resources Information Center

    Costellano, Janet; Scaffa, Matthew

    The product of a Special Studies Institute, this teacher developed resource guide for the emotionally handicapped (K-6) presents 37 activities designed to develop mathematics concepts and skills utilizing the urban out-of-doors. Focus is on experiencing math models, patterns, problems, and relationships found in an urban environment. Activities…

  14. Mathematical model of induced flow on the airplane vertical tail

    NASA Astrophysics Data System (ADS)

    Rotaru, Constantin; Cîrciu, Ionicǎ; Edu, Raluca Ioana

    2016-06-01

    In this paper is presented a mathematical model of the flow around the vertical tail of an airplane, based on the general elements of the aerodynamic design, with details leading to the separate formulation of the Fourier coefficients in the series solution of the Prandtl's lifting-line equation. Numerical results are obtained in Maple soft environment, for a standard configuration of an airplane geometry. The results include the discussion of the vortex model for the sidewash gradient on the vertical stabilizer.

  15. Mathematical models of human african trypanosomiasis epidemiology.

    PubMed

    Rock, Kat S; Stone, Chris M; Hastings, Ian M; Keeling, Matt J; Torr, Steve J; Chitnis, Nakul

    2015-03-01

    Human African trypanosomiasis (HAT), commonly called sleeping sickness, is caused by Trypanosoma spp. and transmitted by tsetse flies (Glossina spp.). HAT is usually fatal if untreated and transmission occurs in foci across sub-Saharan Africa. Mathematical modelling of HAT began in the 1980s with extensions of the Ross-Macdonald malaria model and has since consisted, with a few exceptions, of similar deterministic compartmental models. These models have captured the main features of HAT epidemiology and provided insight on the effectiveness of the two main control interventions (treatment of humans and tsetse fly control) in eliminating transmission. However, most existing models have overestimated prevalence of infection and ignored transient dynamics. There is a need for properly validated models, evolving with improved data collection, that can provide quantitative predictions to help guide control and elimination strategies for HAT.

  16. 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.

  17. Modelling of and Conjecturing on a Soccer Ball in a Korean Eighth Grade Mathematics Classroom

    ERIC Educational Resources Information Center

    Lee, Kyeong-Hwa

    2011-01-01

    The purpose of this article was to describe the task design and implementation of cultural artefacts in a mathematics lesson based on the integration of modelling and conjecturing perspectives. The conceived process of integrating a soccer ball into mathematics lessons via modelling- and conjecturing-based instruction was first detailed. Next, the…

  18. Exploring the Relationship between Mathematical Modelling and Classroom Discourse

    ERIC Educational Resources Information Center

    Redmond, Trevor; Sheehy, Joanne; Brown, Raymond

    2010-01-01

    This paper explores the notion that the discourse of the mathematics classroom impacts on the practices that students engage when modelling mathematics. Using excerpts of a Year 12 student's report on modelling Newton's law of cooling, this paper argues that when students engage with the discourse of their mathematics classroom in a manner that…

  19. Assessment of Primary 5 Students' Mathematical Modelling Competencies

    ERIC Educational Resources Information Center

    Chan, Chun Ming Eric; Ng, Kit Ee Dawn; Widjaja, Wanty; Seto, Cynthia

    2012-01-01

    Mathematical modelling is increasingly becoming part of an instructional approach deemed to develop students with competencies to function as 21st century learners and problem solvers. As mathematical modelling is a relatively new domain in the Singapore primary school mathematics curriculum, many teachers may not be aware of the learning outcomes…

  20. Declarative representation of uncertainty in mathematical models.

    PubMed

    Miller, Andrew K; Britten, Randall D; Nielsen, Poul M F

    2012-01-01

    An important aspect of multi-scale modelling is the ability to represent mathematical models in forms that can be exchanged between modellers and tools. While the development of languages like CellML and SBML have provided standardised declarative exchange formats for mathematical models, independent of the algorithm to be applied to the model, to date these standards have not provided a clear mechanism for describing parameter uncertainty. Parameter uncertainty is an inherent feature of many real systems. This uncertainty can result from a number of situations, such as: when measurements include inherent error; when parameters have unknown values and so are replaced by a probability distribution by the modeller; when a model is of an individual from a population, and parameters have unknown values for the individual, but the distribution for the population is known. We present and demonstrate an approach by which uncertainty can be described declaratively in CellML models, by utilising the extension mechanisms provided in CellML. Parameter uncertainty can be described declaratively in terms of either a univariate continuous probability density function or multiple realisations of one variable or several (typically non-independent) variables. We additionally present an extension to SED-ML (the Simulation Experiment Description Markup Language) to describe sampling sensitivity analysis simulation experiments. We demonstrate the usability of the approach by encoding a sample model in the uncertainty markup language, and by developing a software implementation of the uncertainty specification (including the SED-ML extension for sampling sensitivty analyses) in an existing CellML software library, the CellML API implementation. We used the software implementation to run sampling sensitivity analyses over the model to demonstrate that it is possible to run useful simulations on models with uncertainty encoded in this form.

  1. 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.

  2. Mathematical description of nonstationary aerodynamic characteristics of a passenger aircraft model in longitudinal motion at large angles of attack

    NASA Astrophysics Data System (ADS)

    Petoshin, V. I.; Chasovnikov, E. A.

    2011-05-01

    Aerodynamic loads in problems of flight dynamics of passenger aircraft in stalled flow regimes are described using a mathematical model that includes an ordinary linear first-order differential equation. A procedure for determining the parameters of the mathematical model is proposed which is based on approximating experimental frequency characteristics with the frequency characteristics of the linearized mathematical model. The mathematical model was verified by tests of a modern passenger aircraft model in a wind tunnel.

  3. A mathematical prognosis model for pancreatic cancer patients receiving immunotherapy.

    PubMed

    Li, Xuefang; Xu, Jian-Xin

    2016-10-07

    Pancreatic cancer is one of the most deadly types of cancer since it typically spreads rapidly and can seldom be detected in its early stage. Pancreatic cancer therapy is thus a challenging task, and appropriate prognosis or assessment for pancreatic cancer therapy is of critical importance. In this work, based on available clinical data in Niu et al. (2013) we develop a mathematical prognosis model that can predict the overall survival of pancreatic cancer patients who receive immunotherapy. The mathematical model incorporates pancreatic cancer cells, pancreatic stellate cells, three major classes of immune effector cells CD8+ T cells, natural killer cells, helper T cells, and two major classes of cytokines interleukin-2 (IL-2) and interferon-γ (IFN-γ). The proposed model describes the dynamic interaction between tumor and immune cells. In order for the model to be able to generate appropriate prognostic results for disease progression, the distribution and stability properties of equilibria in the mathematical model are computed and analysed in absence of treatments. In addition, numerical simulations for disease progression with or without treatments are performed. It turns out that the median overall survival associated with CIK immunotherapy is prolonged from 7 to 13months compared with the survival without treatment, this is consistent with the clinical data observed in Niu et al. (2013). The validity of the proposed mathematical prognosis model is thus verified. Our study confirms that immunotherapy offers a better prognosis for pancreatic cancer patients. As a direct extension of this work, various new therapy methods that are under exploration and clinical trials could be assessed or evaluated using the newly developed mathematical prognosis model.

  4. Mathematical Modeling and Simulation of Seated Stability

    PubMed Central

    Tanaka, Martin L.; Ross, Shane D.; Nussbaum, Maury A.

    2009-01-01

    Various methods have been used to quantify the kinematic variability or stability of the human spine. However, each of these methods evaluates dynamic behavior within the stable region of state space. In contrast, our goal was to determine the extent of the stable region. A 2D mathematical model was developed for a human sitting on an unstable seat apparatus (i.e., the “wobble chair”). Forward dynamic simulations were used to compute trajectories based on the initial state. From these trajectories, a scalar field of trajectory divergence was calculated, specifically a finite time Lyapunov exponent (FTLE) field. Theoretically, ridges of local maxima within this field are expected to partition the state space into regions of qualitatively different behavior. We found that ridges formed at the boundary between regions of stability and failure (i.e., falling). The location of the basin of stability found using the FTLE field matched well with the basin of stability determined by an alternative method. In addition, an equilibrium manifold was found, which describes a set of equilibrium configurations that act as a low dimensional attractor in the controlled system. These simulations are a first step in developing a method to locate state space boundaries for torso stability. Identifying these boundaries may provide a framework for assessing factors that contribute to health risks associated with spinal injury and poor balance recovery (e.g., age, fatigue, load/weight and distribution). Furthermore, an approach is presented that can be adapted to find state space boundaries in other biomechanical applications. PMID:20018288

  5. Mathematical modelling of submarine landslide motion

    NASA Astrophysics Data System (ADS)

    Burminskij, A.

    2012-04-01

    Mathematical modelling of submarine landslide motion The paper presents a mathematical model to calculate dynamic parameters of a submarine landslide. The problem of estimation possible submarine landslides dynamic parameters and run-out distances as well as their effect on submarine structures becomes more and more actual because they can have significant impacts on infrastructure such as the rupture of submarine cables and pipelines, damage to offshore drilling platforms, cause a tsunami. In this paper a landslide is considered as a viscoplastic flow and is described by continuum mechanics equations, averaged over the flow depth. The model takes into account friction at the bottom and at the landslide-water boundary, as well as the involvement of bottom material in motion. A software was created and series of test calculations were performed. Calculations permitted to estimate the contribution of various model coefficients and initial conditions. Motion down inclined bottom was studied both for constant and variable slope angle. Examples of typical distributions of the flow velocity, thickness and density along the landslide body at different stages of motion are given.

  6. Lipid Raft Size and Lipid Mobility in Non-raft Domains Increase during Aging and Are Exacerbated in APP/PS1 Mice Model of Alzheimer's Disease. Predictions from an Agent-Based Mathematical Model

    PubMed Central

    Santos, Guido; Díaz, Mario; Torres, Néstor V.

    2016-01-01

    A connection between lipid rafts and Alzheimer's disease has been studied during the last decades. Mathematical modeling approaches have recently been used to correlate the effects of lipid composition changes in the physicochemical properties of raft-like membranes. Here we propose an agent based model to assess the effect of lipid changes in lipid rafts on the evolution and progression of Alzheimer's disease using lipid profile data obtained in an established model of familial Alzheimer's disease. We have observed that lipid raft size and lipid mobility in non-raft domains are two main factors that increase during age and are accelerated in the transgenic Alzheimer's disease mouse model. The consequences of these changes are discussed in the context of neurotoxic amyloid β production. Our agent based model predicts that increasing sterols (mainly cholesterol) and long-chain polyunsaturated fatty acids (LCPUFA) (mainly DHA, docosahexaenoic acid) proportions in the membrane composition might delay the onset and progression of the disease. PMID:27014089

  7. Lipid Raft Size and Lipid Mobility in Non-raft Domains Increase during Aging and Are Exacerbated in APP/PS1 Mice Model of Alzheimer's Disease. Predictions from an Agent-Based Mathematical Model.

    PubMed

    Santos, Guido; Díaz, Mario; Torres, Néstor V

    2016-01-01

    A connection between lipid rafts and Alzheimer's disease has been studied during the last decades. Mathematical modeling approaches have recently been used to correlate the effects of lipid composition changes in the physicochemical properties of raft-like membranes. Here we propose an agent based model to assess the effect of lipid changes in lipid rafts on the evolution and progression of Alzheimer's disease using lipid profile data obtained in an established model of familial Alzheimer's disease. We have observed that lipid raft size and lipid mobility in non-raft domains are two main factors that increase during age and are accelerated in the transgenic Alzheimer's disease mouse model. The consequences of these changes are discussed in the context of neurotoxic amyloid β production. Our agent based model predicts that increasing sterols (mainly cholesterol) and long-chain polyunsaturated fatty acids (LCPUFA) (mainly DHA, docosahexaenoic acid) proportions in the membrane composition might delay the onset and progression of the disease.

  8. Mathematical Modeling of Extinction of Inhomogeneous Populations

    PubMed Central

    Karev, G.P.; Kareva, I.

    2016-01-01

    Mathematical models of population extinction have a variety of applications in such areas as ecology, paleontology and conservation biology. Here we propose and investigate two types of sub-exponential models of population extinction. Unlike the more traditional exponential models, the life duration of sub-exponential models is finite. In the first model, the population is assumed to be composed clones that are independent from each other. In the second model, we assume that the size of the population as a whole decreases according to the sub-exponential equation. We then investigate the “unobserved heterogeneity”, i.e. the underlying inhomogeneous population model, and calculate the distribution of frequencies of clones for both models. We show that the dynamics of frequencies in the first model is governed by the principle of minimum of Tsallis information loss. In the second model, the notion of “internal population time” is proposed; with respect to the internal time, the dynamics of frequencies is governed by the principle of minimum of Shannon information loss. The results of this analysis show that the principle of minimum of information loss is the underlying law for the evolution of a broad class of models of population extinction. Finally, we propose a possible application of this modeling framework to mechanisms underlying time perception. PMID:27090117

  9. Development of a mathematical model of the human circulatory system.

    PubMed

    Conlon, Martin J; Russell, Donald L; Mussivand, Tofy

    2006-09-01

    A mathematical lumped parameter model of the human circulatory system (HCS) has been developed to complement in vitro testing of ventricular assist devices. Components included in this model represent the major parts of the systemic HCS loop, with all component parameters based on physiological data available in the literature. Two model configurations are presented in this paper, the first featuring elements with purely linear constitutive relations, and the second featuring nonlinear constitutive relations for the larger vessels. Three different aortic compliance functions are presented, and a pressure-dependent venous flow resistance is used to simulate venous collapse. The mathematical model produces reasonable systemic pressure and flow behaviour, and graphs of this data are included.

  10. Mathematical modeling to predict residential solid waste generation

    SciTech Connect

    Ojeda Benitez, Sara; Vega, Carolina Armijo de

    2008-07-01

    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{sup 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.

  11. Mathematical modeling of the coating process.

    PubMed

    Toschkoff, Gregor; Khinast, Johannes G

    2013-12-05

    Coating of tablets is a common unit operation in the pharmaceutical industry. In most cases, the final product must meet strict quality requirements; to meet them, a detailed understanding of the coating process is required. To this end, numerous experiment studies have been performed. However, to acquire a mechanistic understanding, experimental data must be interpreted in the light of mathematical models. In recent years, a combination of analytical modeling and computational simulations enabled deeper insights into the nature of the coating process. This paper presents an overview of modeling and simulation approaches of the coating process, covering various relevant aspects from scale-up considerations to coating mass uniformity investigations and models for drop atomization. The most important analytical and computational concepts are presented and the findings are compared.

  12. Mathematical modelling of hepatic lipid metabolism.

    PubMed

    Pratt, Adrian C; Wattis, Jonathan A D; Salter, Andrew M

    2015-04-01

    The aim of this paper is to develop a mathematical model capable of simulating the metabolic response to a variety of mixed meals in fed and fasted conditions with particular emphasis placed on the hepatic triglyceride element of the model. Model validation is carried out using experimental data for the ingestion of three mixed composition meals over a 24-h period. Comparison with experimental data suggests the model predicts key plasma lipids accurately given a prescribed insulin profile. One counter-intuitive observation to arise from simulations is that liver triglyceride initially decreases when a high fat meal is ingested, a phenomenon potentially explained by the carbohydrate portion of the meal raising plasma insulin.

  13. Predictive mathematical models of cancer signalling pathways.

    PubMed

    Bachmann, J; Raue, A; Schilling, M; Becker, V; Timmer, J; Klingmüller, U

    2012-02-01

    Complex intracellular signalling networks integrate extracellular signals and convert them into cellular responses. In cancer cells, the tightly regulated and fine-tuned dynamics of information processing in signalling networks is altered, leading to uncontrolled cell proliferation, survival and migration. Systems biology combines mathematical modelling with comprehensive, quantitative, time-resolved data and is most advanced in addressing dynamic properties of intracellular signalling networks. Here, we introduce different modelling approaches and their application to medical systems biology, focusing on the identifiability of parameters in ordinary differential equation models and their importance in network modelling to predict cellular decisions. Two related examples are given, which include processing of ligand-encoded information and dual feedback regulation in erythropoietin (Epo) receptor signalling. Finally, we review the current understanding of how systems biology could foster the development of new treatment strategies in the context of lung cancer and anaemia.

  14. 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.

  15. Mathematics of tsunami: modelling and identification

    NASA Astrophysics Data System (ADS)

    Krivorotko, Olga; Kabanikhin, Sergey

    2015-04-01

    Tsunami (long waves in the deep water) motion caused by underwater earthquakes is described by shallow water equations ( { ηtt = div (gH (x,y)-gradη), (x,y) ∈ Ω, t ∈ (0,T ); η|t=0 = q(x,y), ηt|t=0 = 0, (x,y) ∈ Ω. ( (1) Bottom relief H(x,y) characteristics and the initial perturbation data (a tsunami source q(x,y)) are required for the direct simulation of tsunamis. The main difficulty problem of tsunami modelling is a very big size of the computational domain (Ω = 500 × 1000 kilometres in space and about one hour computational time T for one meter of initial perturbation amplitude max|q|). The calculation of the function η(x,y,t) of three variables in Ω × (0,T) requires large computing resources. We construct a new algorithm to solve numerically the problem of determining the moving tsunami wave height S(x,y) which is based on kinematic-type approach and analytical representation of fundamental solution. Proposed algorithm of determining the function of two variables S(x,y) reduces the number of operations in 1.5 times than solving problem (1). If all functions does not depend on the variable y (one dimensional case), then the moving tsunami wave height satisfies of the well-known Airy-Green formula: S(x) = S(0)° --- 4H (0)/H (x). The problem of identification parameters of a tsunami source using additional measurements of a passing wave is called inverse tsunami problem. We investigate two different inverse problems of determining a tsunami source q(x,y) using two different additional data: Deep-ocean Assessment and Reporting of Tsunamis (DART) measurements and satellite altimeters wave-form images. These problems are severely ill-posed. The main idea consists of combination of two measured data to reconstruct the source parameters. We apply regularization techniques to control the degree of ill-posedness such as Fourier expansion, truncated singular value decomposition, numerical regularization. The algorithm of selecting the truncated number of

  16. Mathematical model of laser PUVA psoriasis treatment

    NASA Astrophysics Data System (ADS)

    Medvedev, Boris A.; Tuchin, Valery V.; Yaroslavsky, Ilya V.

    1991-05-01

    In order to optimize laser PUVA psoriasis treatment we develop the mathematical model of the dynamics of cell processes within epidermis. We consider epidermis as a structure consisting of N cell monolayers. There are four kinds of cells that correspond to four epidermal strata. The different kinds of cells can exist within a given monolayer. We assume that the following cell processes take place: division, death and transition from one stratum to the following. Discrete transition of cells from stratum j to j + 1 approximates to real differentiation.

  17. Mathematical modelling of risk reduction in reinsurance

    NASA Astrophysics Data System (ADS)

    Balashov, R. B.; Kryanev, A. V.; Sliva, D. E.

    2017-01-01

    The paper presents a mathematical model of efficient portfolio formation in the reinsurance markets. The presented approach provides the optimal ratio between the expected value of return and the risk of yield values below a certain level. The uncertainty in the return values is conditioned by use of expert evaluations and preliminary calculations, which result in expected return values and the corresponding risk levels. The proposed method allows for implementation of computationally simple schemes and algorithms for numerical calculation of the numerical structure of the efficient portfolios of reinsurance contracts of a given insurance company.

  18. 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

  19. Precision Landing System Mathematical Modeling Study Report for Andrews Air Force Base, Runway 19L, Camp Springs, MD.

    DTIC Science & Technology

    1994-11-01

    aircraft, and terrain. Results are provided as plots illustrating the predicted multipath levels, separation angles, and the resulting error plots from the...worst case contributors. Scenarios were modeled to determine the effects of the multipath sources in the modeled environment. These resulting errors ...were analyzed and compared to error tolerances (FAA-STD-022d) to determine if the errors are acceptable. The effects of the ADW environment were

  20. Mathematical modeling of COD removal via the combined treatment of domestic wastewater and landfill leachate based on the PACT process.

    PubMed

    Fernández Bou, Ángel S; Nascentes, Alexandre Lioi; Costa Pereira, Barbara; Da Silva, Leonardo Duarte Batista; Alberto Ferreira, João; Campos, Juacyara Carbonelli

    2015-01-01

    The experiments performed in this study consisted of 16 batch reactors fed different mixtures of landfill leachate combined with synthetic wastewater treated using the Powdered Activated Carbon Treatment (PACT) process. The objective was to measure the COD mass removal per liter each day for each reactor using two models: the first model combined the variables PAC concentration (0 g·L(-1), 2 g·L(-1), 4 g·L(-1), and 6 g·L(-1)) and leachate rate in the wastewater (0%, 2%, 5%, and 10%), and the second model combined the PAC concentration and the influent COD. The Response Surface Methodology with Central Composite Design was used to describe the response surface of both models considered in this study. Domestic wastewater was produced under controlled conditions in the laboratory where the experiments were performed. The results indicated that the PAC effect was null when the influent did not contain leachate; however, as the concentration of leachate applied to the mixture was increased, the addition of a higher PAC concentration resulted in a better COD mass removal in the reactors. The adjusted R(2) values of the two models were greater than 0.95, and the predicted R(2) values were greater than 0.93. The models may be useful for wastewater treatment companies to calculate PAC requirements in order to meet COD mass removal objectives in combined treatment.

  1. 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.

  2. A community effort towards a knowledge-base and mathematical model of the human pathogen Salmonella Typhimurium LT2

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Metabolic reconstructions (MRs) are common denominators in systems biology and represent biochemical, genetic, and genomic (BiGG) knowledge-bases for target organisms by capturing currently available information in a consistent, structured manner. Salmonella enterica subspecies I serovar Typhimurium...

  3. Development of a Mathematical Model of Crevice Corrosion Propagation on Nickel Base Alloys in Natural and Chlorinated Sea Water

    DTIC Science & Technology

    1994-08-30

    then bromamines and chloramines are formed and the processes become even more complicated. [10]. 0 From the point of view of crevice corrosion ... Corrosion Propagation on Nickel Base Alloys in Natural and Chlorinated Sea Water Thi! os 7 -= n %:ý 7e~~r: :-ppcved tor piU&* : e --I . " dcktr!u-,J...Summary Crevice corrosion initiation and propagation of nickel base alloys Inconel 625, Hastelloy C276 and Hastelloy 22 in sea water and chlorinated sea

  4. Adequate mathematical modelling of environmental processes

    NASA Astrophysics Data System (ADS)

    Chashechkin, Yu. D.

    2012-04-01

    In environmental observations and laboratory visualization both large scale flow components like currents, jets, vortices, waves and a fine structure are registered (different examples are given). The conventional mathematical modeling both analytical and numerical is directed mostly on description of energetically important flow components. The role of a fine structures is still remains obscured. A variety of existing models makes it difficult to choose the most adequate and to estimate mutual assessment of their degree of correspondence. The goal of the talk is to give scrutiny analysis of kinematics and dynamics of flows. A difference between the concept of "motion" as transformation of vector space into itself with a distance conservation and the concept of "flow" as displacement and rotation of deformable "fluid particles" is underlined. Basic physical quantities of the flow that are density, momentum, energy (entropy) and admixture concentration are selected as physical parameters defined by the fundamental set which includes differential D'Alembert, Navier-Stokes, Fourier's and/or Fick's equations and closing equation of state. All of them are observable and independent. Calculations of continuous Lie groups shown that only the fundamental set is characterized by the ten-parametric Galilelian groups reflecting based principles of mechanics. Presented analysis demonstrates that conventionally used approximations dramatically change the symmetries of the governing equations sets which leads to their incompatibility or even degeneration. The fundamental set is analyzed taking into account condition of compatibility. A high order of the set indicated on complex structure of complete solutions corresponding to physical structure of real flows. Analytical solutions of a number problems including flows induced by diffusion on topography, generation of the periodic internal waves a compact sources in week-dissipative media as well as numerical solutions of the same

  5. Development of a new version of the Liverpool Malaria Model. I. Refining the parameter settings and mathematical formulation of basic processes based on a literature review

    PubMed Central

    2011-01-01

    Background A warm and humid climate triggers several water-associated diseases such as malaria. Climate- or weather-driven malaria models, therefore, allow for a better understanding of malaria transmission dynamics. The Liverpool Malaria Model (LMM) is a mathematical-biological model of malaria parasite dynamics using daily temperature and precipitation data. In this study, the parameter settings of the LMM are refined and a new mathematical formulation of key processes related to the growth and size of the vector population are developed. Methods One of the most comprehensive studies to date in terms of gathering entomological and parasitological information from the literature was undertaken for the development of a new version of an existing malaria model. The knowledge was needed to allow the justification of new settings of various model parameters and motivated changes of the mathematical formulation of the LMM. Results The first part of the present study developed an improved set of parameter settings and mathematical formulation of the LMM. Important modules of the original LMM version were enhanced in order to achieve a higher biological and physical accuracy. The oviposition as well as the survival of immature mosquitoes were adjusted to field conditions via the application of a fuzzy distribution model. Key model parameters, including the mature age of mosquitoes, the survival probability of adult mosquitoes, the human blood index, the mosquito-to-human (human-to-mosquito) transmission efficiency, the human infectious age, the recovery rate, as well as the gametocyte prevalence, were reassessed by means of entomological and parasitological observations. This paper also revealed that various malaria variables lack information from field studies to be set properly in a malaria modelling approach. Conclusions Due to the multitude of model parameters and the uncertainty involved in the setting of parameters, an extensive literature survey was carried out

  6. Mathematical Modeling of Microbial Community Dynamics: A Methodological Review

    SciTech Connect

    Song, Hyun-Seob; Cannon, William R.; Beliaev, Alex S.; Konopka, Allan

    2014-10-17

    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 be 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.

  7. Preparing Secondary Mathematics Teachers: A Focus on Modeling in Algebra

    ERIC Educational Resources Information Center

    Jung, Hyunyi; Mintos, Alexia; Newton, Jill

    2015-01-01

    This study addressed the opportunities to learn (OTL) modeling in algebra provided to secondary mathematics pre-service teachers (PSTs). To investigate these OTL, we interviewed five instructors of required mathematics and mathematics education courses that had the potential to include opportunities for PSTs to learn algebra at three universities.…

  8. Mathematical Model of the Jet Engine Fuel System

    NASA Astrophysics Data System (ADS)

    Klimko, Marek

    2015-05-01

    The paper discusses the design of a simplified mathematical model of the jet (turbo-compressor) engine fuel system. The solution will be based on the regulation law, where the control parameter is a fuel mass flow rate and the regulated parameter is the rotational speed. A differential equation of the jet engine and also differential equations of other fuel system components (fuel pump, throttle valve, pressure regulator) will be described, with respect to advanced predetermined simplifications.

  9. Place-Based Mathematics Education: A Conflated Pedagogy?

    ERIC Educational Resources Information Center

    Showalter, Daniel A.

    2013-01-01

    Place-based mathematics education (PBME) has the potential to engage students with the mathematics inherent in the local land, culture, and community. However, research has identified daunting barriers to this pedagogy, especially in abstract mathematics courses such as algebra and beyond. In this study, 15 graduates of a doctoral program in rural…

  10. Effectiveness of cervical cancer screening based on a mathematical screening model using data from the Hiroshima Prefecture Cancer Registry.

    PubMed

    Ito, Katsura; Tsunematsu, Miwako; Satoh, Kenichi; Kakehashi, Masayuki; Nagata, Yasushi

    2013-01-01

    Here we assessed the effectiveness of cervical cancer screening using data from the Hiroshima Prefecture Cancer Registry regarding patient age at the start of screening and differences in screening intervals. A screening model was created to calculate the health status in relation to prognosis following cervical cancer screening and its influence on life expectancy. Epidemiological data on the mortality rate of cervical cancer by age groups and mortality rates from the Hiroshima Prefecture Cancer Registry were used for the model projections. Our results showed that life expectancy when screening rate was 100% compared with 0% was extended by approximately 1 month. Furthermore, when the incidence of cervical cancer was 0% compared with the screening rate was 100%, life expectancy was extended by a maximum of 3 months. Moreover, among individuals affected by cervical cancer, a difference of 13 years in life expectancy was calculated between screened and unscreened groups.

  11. A novel mathematical model for controllable near-field electrospinning

    NASA Astrophysics Data System (ADS)

    Ru, Changhai; Chen, Jie; Shao, Zhushuai; Pang, Ming; Luo, Jun

    2014-01-01

    Near-field electrospinning (NFES) had better controllability than conventional electrospinning. However, due to the lack of guidance of theoretical model, precise deposition of micro/nano fibers could only accomplished by experience. To analyze the behavior of charged jet in NFES using mathematical model, the momentum balance equation was simplified and a new expression between jet cross-sectional radius and axial position was derived. Using this new expression and mass conservation equation, expressions for jet cross-sectional radius and velocity were derived in terms of axial position and initial jet acceleration in the form of exponential functions. Based on Slender-body theory and Giesekus model, a quadratic equation for initial jet acceleration was acquired. With the proposed model, it was able to accurately predict the diameter and velocity of polymer fibers in NFES, and mathematical analysis rather than experimental methods could be applied to study the effects of the process parameters in NFES. Moreover, the movement velocity of the collector stage can be regulated by mathematical model rather than experience. Therefore, the model proposed in this paper had important guiding significance to precise deposition of polymer fibers.

  12. A novel mathematical model for controllable near-field electrospinning

    SciTech Connect

    Ru, Changhai E-mail: luojun@shu.edu.cn; Chen, Jie; Shao, Zhushuai; Pang, Ming; Luo, Jun E-mail: luojun@shu.edu.cn

    2014-01-15

    Near-field electrospinning (NFES) had better controllability than conventional electrospinning. However, due to the lack of guidance of theoretical model, precise deposition of micro/nano fibers could only accomplished by experience. To analyze the behavior of charged jet in NFES using mathematical model, the momentum balance equation was simplified and a new expression between jet cross-sectional radius and axial position was derived. Using this new expression and mass conservation equation, expressions for jet cross-sectional radius and velocity were derived in terms of axial position and initial jet acceleration in the form of exponential functions. Based on Slender-body theory and Giesekus model, a quadratic equation for initial jet acceleration was acquired. With the proposed model, it was able to accurately predict the diameter and velocity of polymer fibers in NFES, and mathematical analysis rather than experimental methods could be applied to study the effects of the process parameters in NFES. Moreover, the movement velocity of the collector stage can be regulated by mathematical model rather than experience. Therefore, the model proposed in this paper had important guiding significance to precise deposition of polymer fibers.

  13. Mathematical modelling of carbohydrate degradation by human colonic microbiota.

    PubMed

    Muñoz-Tamayo, Rafael; Laroche, Béatrice; Walter, Eric; Doré, Joël; Leclerc, Marion

    2010-09-07

    The human colon is an anaerobic ecosystem that remains largely unexplored as a result of its limited accessibility and its complexity. Mathematical models can play a central role for a better insight into its dynamics. In this context, this paper presents the development of a mathematical model of carbohydrate degradation. Our aim was to provide an in silico approach to contribute to a better understanding of the fermentation patterns in such an ecosystem. Our mathematical model is knowledge-based, derived by writing down mass-balance equations. It incorporates physiology of the intestine, metabolic reactions and transport phenomena. The model was used to study various nutritional scenarios and to assess the role of the mucus on the system behavior. Model simulations provided an adequate qualitative representation of the human colon. Our model is complementary to experimental studies on human colonic fermentation, which, of course, is not meant to replace. It may be helpful to gain insight on questions that are still difficult to elucidate by experimentation and suggest future experiments.

  14. Exploration of the R code-based mathematical model for PMI estimation using profiling of RNA degradation in rat brain tissue at different temperatures.

    PubMed

    Ma, Jianlong; Pan, Hui; Zeng, Yan; Lv, Yehui; Zhang, Heng; Xue, Aimin; Jiang, Jieqing; Ma, Kaijun; Chen, Long

    2015-12-01

    Precise estimation of postmortem interval (PMI) is crucial in some criminal cases. This study aims to find some optimal markers for PMI estimation and build a mathematical model that could be used in various temperature conditions. Different mRNA and microRNA markers in rat brain samples were detected using real-time fluorescent quantitative PCR at 12 time points within 144 h postmortem and at temperatures of 4, 15, 25, and 35 °C. Samples from 36 other rats were used to verify the animal mathematical model. Brain-specific mir-9 and mir-125b are effective endogenous control markers that are not affected by PMI up to 144 h postmortem under these temperatures, whereas the commonly used U6 is not a suitable endogenous control in this study. Among all the candidate markers, ΔCt (β-actin) has the best correlation coefficient with PMI and was used to build a new model using R software which can simultaneously manage both PMI and temperature parameters. This animal mathematical model is verified using samples from 36 other rats and shows increased accuracy for higher temperatures and longer PMI. In this study, β-actin was found to be an optimal marker to estimate PMI and some other markers were found to be suitable to act as endogenous controls. Additionally, we have used R code software to build a model of PMI estimation that could be used in various temperature conditions.

  15. 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

  16. A community effort towards a knowledge-base and mathematical model of the human pathogen Salmonella Typhimurium LT2

    SciTech Connect

    Thiele, Ines; Hyduke, Daniel R.; Steeb, Benjamin; Fankam, Guy; Allen, Douglas K.; Bazzani, Susanna; Charusanti, Pep; Chen, Feng-Chi; Fleming, Ronan MT; Hsiung, Chao A.; De Keersmaecker, Sigrid CJ; Liao, Yu-Chieh; Marchal, Kathleen; Mo, Monica L.; Özdemir, Emre; Raghunathan, Anu; Reed, Jennifer L.; Shin, Sook-Il; Sigurbjörnsdóttir, Sara; Steinmann, Jonas; Sudarsan, Suresh; Swainston, Neil; Thijs, Inge M.; Zengler, Karsten; Palsson, Bernhard O.; Adkins, Joshua N.; Bumann, Dirk

    2011-01-01

    Metabolic reconstructions (MRs) are common denominators in systems biology and represent biochemical, genetic, and genomic (BiGG) knowledge-bases for target organisms by capturing currently available information in a consistent, structured manner. Salmonella enterica subspecies I serovar Typhimurium is a human pathogen, causes various diseases and its increasing antibiotic resistance poses a public health problem. Here, we describe a community-driven effort, in which more than 20 experts in S. Typhimurium biology and systems biology collaborated to reconcile and expand the S. Typhimurium BiGG knowledge-base. The consensus MR was obtained starting from two independently developed MRs for S. Typhimurium. Key results of this reconstruction jamboree include i) development and implementation of a community-based workflow for MR annotation and reconciliation; ii) incorporation of thermodynamic information; and iii) use of the consensus MR to identify potential multi-target drug therapy approaches. Finally, taken together, with the growing number of parallel MRs a structured, community-driven approach will be necessary to maximize quality while increasing adoption of MRs in experimental design and interpretation.

  17. 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.

  18. 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…

  19. Mathematical modeling and simulation in animal health - Part II: principles, methods, applications, and value of physiologically based pharmacokinetic modeling in veterinary medicine and food safety assessment.

    PubMed

    Lin, Z; Gehring, R; Mochel, J P; Lavé, T; Riviere, J E

    2016-10-01

    This review provides a tutorial for individuals interested in quantitative veterinary pharmacology and toxicology and offers a basis for establishing guidelines for physiologically based pharmacokinetic (PBPK) model development and application in veterinary medicine. This is important as the application of PBPK modeling in veterinary medicine has evolved over the past two decades. PBPK models can be used to predict drug tissue residues and withdrawal times in food-producing animals, to estimate chemical concentrations at the site of action and target organ toxicity to aid risk assessment of environmental contaminants and/or drugs in both domestic animals and wildlife, as well as to help design therapeutic regimens for veterinary drugs. This review provides a comprehensive summary of PBPK modeling principles, model development methodology, and the current applications in veterinary medicine, with a focus on predictions of drug tissue residues and withdrawal times in food-producing animals. The advantages and disadvantages of PBPK modeling compared to other pharmacokinetic modeling approaches (i.e., classical compartmental/noncompartmental modeling, nonlinear mixed-effects modeling, and interspecies allometric scaling) are further presented. The review finally discusses contemporary challenges and our perspectives on model documentation, evaluation criteria, quality improvement, and offers solutions to increase model acceptance and applications in veterinary pharmacology and toxicology.

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

    PubMed

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

    2016-07-08

    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.

  1. Mechanical-mathematical modeling for landslide process

    NASA Astrophysics Data System (ADS)

    Svalova, V.

    2009-04-01

    500 m and displacement of a landslide in the plan over 1 m. Last serious activization of a landslide has taken place in 2002 with a motion on 53 cm. Catastrophic activization of the deep blockglide landslide in the area of Khoroshevo in Moscow took place in 2006-2007. A crack of 330 m long appeared in the old sliding circus, along which a new 220 m long creeping block was separated from the plateau and began sinking with a displaced surface of the plateau reaching to 12 m. Such activization of the landslide process was not observed in Moscow since mid XIX century. The sliding area of Khoroshevo was stable during long time without manifestations of activity. Revealing of the reasons of deformation and development of ways of protection from deep landslide motions is extremely actual and difficult problem which decision is necessary for preservation of valuable historical monuments and modern city constructions. The reasons of activization and protective measures are discussed. Structure of monitoring system for urban territories is elaborated. Mechanical-mathematical model of high viscous fluid was used for modeling of matter behavior on landslide slopes. Equation of continuity and an approximated equation of the Navier-Stockes for slow motions in a thin layer were used. The results of modelling give possibility to define the place of highest velocity on landslide surface, which could be the best place for monitoring post position. Model can be used for calibration of monitoring equipment and gives possibility to investigate some fundamental aspects of matter movement on landslide slope.

  2. 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.

  3. The force-frequency relationship: insights from mathematical modeling.

    PubMed

    Puglisi, Jose L; Negroni, Jorge A; Chen-Izu, Ye; Bers, Donald M

    2013-03-01

    The force-frequency relationship has intrigued researchers since its discovery by Bowditch in 1871. Many attempts have been made to construct mathematical descriptions of this phenomenon, beginning with the simple formulation of Koch-Wesser and Blinks in 1963 to the most sophisticated ones of today. This property of cardiac muscle is amplified by β-adrenergic stimulation, and, in a coordinated way, the neurohumoral state alters both frequency (acting on the sinoatrial node) as well as force generation (modifying ventricular myocytes). This synchronized tuning is needed to meet new metabolic demands. Cardiac modelers have already linked mechanical and electrical activity in their formulations and showed how those activities feedback on each other. However, now it is necessary to include neurological control to have a complete description of heart performance, especially when changes in frequency are involved. Study of arrhythmias (or antiarrhythmic drugs) based on mathematical models should incorporate this effect to make useful predictions or point out potential pharmaceutical targets.

  4. 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…

  5. Mathematical Modelling: A Path to Political Reflection in the Mathematics Class

    ERIC Educational Resources Information Center

    Jacobini, Otavio Roberto; Wodewotzki, Maria Lucia L.

    2006-01-01

    This paper describes the construction of pedagogical environments in mathematics classes, centred on mathematical modelling and denominated "investigative scenarios", which stimulate students to investigation, to formulation of problems and to political reflection, as well as the sharing of acquired knowledge with other persons in the community.…

  6. 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…

  7. 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…

  8. Mathematical foundations of the dendritic growth models.

    PubMed

    Villacorta, José A; Castro, Jorge; Negredo, Pilar; Avendaño, Carlos

    2007-11-01

    At present two growth models describe successfully the distribution of size and topological complexity in populations of dendritic trees with considerable accuracy and simplicity, the BE model (Van Pelt et al. in J. Comp. Neurol. 387:325-340, 1997) and the S model (Van Pelt and Verwer in Bull. Math. Biol. 48:197-211, 1986). This paper discusses the mathematical basis of these models and analyzes quantitatively the relationship between the BE model and the S model assumed in the literature by developing a new explicit equation describing the BES model (a dendritic growth model integrating the features of both preceding models; Van Pelt et al. in J. Comp. Neurol. 387:325-340, 1997). In numerous studies it is implicitly presupposed that the S model is conditionally linked to the BE model (Granato and Van Pelt in Brain Res. Dev. Brain Res. 142:223-227, 2003; Uylings and Van Pelt in Network 13:397-414, 2002; Van Pelt, Dityatev and Uylings in J. Comp. Neurol. 387:325-340, 1997; Van Pelt and Schierwagen in Math. Biosci. 188:147-155, 2004; Van Pelt and Uylings in Network. 13:261-281, 2002; Van Pelt, Van Ooyen and Uylings in Modeling Dendritic Geometry and the Development of Nerve Connections, pp 179, 2000). In this paper we prove the non-exactness of this assumption, quantify involved errors and determine the conditions under which the BE and S models can be separately used instead of the BES model, which is more exact but considerably more difficult to apply. This study leads to a novel expression describing the BE model in an analytical closed form, much more efficient than the traditional iterative equation (Van Pelt et al. in J. Comp. Neurol. 387:325-340, 1997) in many neuronal classes. Finally we propose a new algorithm in order to obtain the values of the parameters of the BE model when this growth model is matched to experimental data, and discuss its advantages and improvements over the more commonly used procedures.

  9. Mathematical analysis of epidemiological models with heterogeneity

    SciTech Connect

    Van Ark, J.W.

    1992-01-01

    For many diseases in human populations the disease shows dissimilar characteristics in separate subgroups of the population; for example, the probability of disease transmission for gonorrhea or AIDS is much higher from male to female than from female to male. There is reason to construct and analyze epidemiological models which allow this heterogeneity of population, and to use these models to run computer simulations of the disease to predict the incidence and prevalence of the disease. In the models considered here the heterogeneous population is separated into subpopulations whose internal and external interactions are homogeneous in the sense that each person in the population can be assumed to have all average actions for the people of that subpopulation. The first model considered is an SIRS models; i.e., the Susceptible can become Infected, and if so he eventually Recovers with temporary immunity, and after a period of time becomes Susceptible again. Special cases allow for permanent immunity or other variations. This model is analyzed and threshold conditions are given which determine whether the disease dies out or persists. A deterministic model is presented; this model is constructed using difference equations, and it has been used in computer simulations for the AIDS epidemic in the homosexual population in San Francisco. The homogeneous version and the heterogeneous version of the differential-equations and difference-equations versions of the deterministic model are analyzed mathematically. In the analysis, equilibria are identified and threshold conditions are set forth for the disease to die out if the disease is below the threshold so that the disease-free equilibrium is globally asymptotically stable. Above the threshold the disease persists so that the disease-free equilibrium is unstable and there is a unique endemic equilibrium.

  10. Mathematical and computer modeling of component surface shaping

    NASA Astrophysics Data System (ADS)

    Lyashkov, A.

    2016-04-01

    The process of shaping technical surfaces is an interaction of a tool (a shape element) and a component (a formable element or a workpiece) in their relative movements. It was established that the main objects of formation are: 1) a discriminant of a surfaces family, formed by the movement of the shape element relatively the workpiece; 2) an enveloping model of the real component surface obtained after machining, including transition curves and undercut lines; 3) The model of cut-off layers obtained in the process of shaping. When modeling shaping objects there are a lot of insufficiently solved or unsolved issues that make up a single scientific problem - a problem of qualitative shaping of the surface of the tool and then the component surface produced by this tool. The improvement of known metal-cutting tools, intensive development of systems of their computer-aided design requires further improvement of the methods of shaping the mating surfaces. In this regard, an important role is played by the study of the processes of shaping of technical surfaces with the use of the positive aspects of analytical and numerical mathematical methods and techniques associated with the use of mathematical and computer modeling. The author of the paper has posed and has solved the problem of development of mathematical, geometric and algorithmic support of computer-aided design of cutting tools based on computer simulation of the shaping process of surfaces.

  11. Mathematical Modeling of the Origins of Life

    NASA Technical Reports Server (NTRS)

    Pohorille, Andrew

    2006-01-01

    The emergence of early metabolism - a network of catalyzed chemical reactions that supported self-maintenance, growth, reproduction and evolution of the ancestors of contemporary cells (protocells) was a critical, but still very poorly understood step on the path from inanimate to animate matter. Here, it is proposed and tested through mathematical modeling of biochemically plausible systems that the emergence of metabolism and its initial evolution towards higher complexity preceded the emergence of a genome. Even though the formation of protocellular metabolism was driven by non-genomic, highly stochastic processes the outcome was largely deterministic, strongly constrained by laws of chemistry. It is shown that such concepts as speciation and fitness to the environment, developed in the context of genomic evolution, also held in the absence of a genome.

  12. Is Mathematical Representation of Problems an Evidence-Based Strategy for Students with Mathematics Difficulties?

    ERIC Educational Resources Information Center

    Jitendra, Asha K.; Nelson, Gena; Pulles, Sandra M.; Kiss, Allyson J.; Houseworth, James

    2016-01-01

    The purpose of the present review was to evaluate the quality of the research and evidence base for representation of problems as a strategy to enhance the mathematical performance of students with learning disabilities and those at risk for mathematics difficulties. The authors evaluated 25 experimental and quasiexperimental studies according to…

  13. Balancing Classroom Management with Mathematical Learning: Using Practice-Based Task Design in Mathematics Teacher Education

    ERIC Educational Resources Information Center

    Biza, Irene; Nardi, Elena; Joel, Gareth

    2015-01-01

    In this paper we present the results from a study in which 21 mathematics trainee teachers engage with two practice-based tasks in which classroom management interferes with mathematical learning. We investigate the trainees' considerations when they make decisions in classroom situations and how these tasks can trigger their reflections on the…

  14. 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…

  15. 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.

  16. The Aircraft Availability Model: Conceptual Framework and Mathematics

    DTIC Science & Technology

    1983-06-01

    THE AIRCRAFT AVAILABILITY MODEL: CONCEPTUAL FRAMEWORK AND MATHEMATICS June 1983 T. J. O’Malley Prepared pursuant to Department of Defense Contract No...OF REPORT & PERIOD COVERED The Aircraft Availability Model: Model Documentation Conceptual Framework and Mathematics 6. PERFORMING ORG. REPORT NUMBER

  17. Noise in restaurants: levels and mathematical model.

    PubMed

    To, Wai Ming; Chung, Andy

    2014-01-01

    Noise affects the dining atmosphere and is an occupational hazard to restaurant service employees worldwide. This paper examines the levels of noise in dining areas during peak hours in different types of restaurants in Hong Kong SAR, China. A mathematical model that describes the noise level in a restaurant is presented. The 1-h equivalent continuous noise level (L(eq,1-h)) was measured using a Type-1 precision integral sound level meter while the occupancy density, the floor area of the dining area, and the ceiling height of each of the surveyed restaurants were recorded. It was found that the measured noise levels using Leq,1-h ranged from 67.6 to 79.3 dBA in Chinese restaurants, from 69.1 to 79.1 dBA in fast food restaurants, and from 66.7 to 82.6 dBA in Western restaurants. Results of the analysis of variance show that there were no significant differences between means of the measured noise levels among different types of restaurants. A stepwise multiple regression analysis was employed to determine the relationships between geometrical and operational parameters and the measured noise levels. Results of the regression analysis show that the measured noise levels depended on the levels of occupancy density only. By reconciling the measured noise levels and the mathematical model, it was found that people in restaurants increased their voice levels when the occupancy density increased. Nevertheless, the maximum measured hourly noise level indicated that the noise exposure experienced by restaurant service employees was below the regulated daily noise exposure value level of 85 dBA.

  18. Why finite mathematics is the most fundamental and ultimate quantum theory will be based on finite mathematics

    NASA Astrophysics Data System (ADS)

    Lev, Felix M.

    2017-01-01

    Classical mathematics (involving such notions as infinitely small/large and continuity) is usually treated as fundamental while finite mathematics is treated as inferior which is used only in special applications. We first argue that the situation is the opposite: classical mathematics is only a degenerate special case of finite one and finite mathematics is more pertinent for describing nature than standard one. Then we describe results of a quantum theory based on finite mathematics. Implications for foundation of mathematics are discussed.

  19. Mathematical Model for the Mineralization of Bone

    NASA Technical Reports Server (NTRS)

    Martin, Bruce

    1994-01-01

    A mathematical model is presented for the transport and precipitation of mineral in refilling osteons. One goal of this model was to explain calcification 'halos,' in which the bone near the haversian canal is more highly mineralized than the more peripheral lamellae, which have been mineralizing longer. It was assumed that the precipitation rate of mineral is proportional to the difference between the local concentration of calcium ions and an equilibrium concentration and that the transport of ions is by either diffusion or some other concentration gradient-dependent process. Transport of ions was assumed to be slowed by the accumulation of mineral in the matrix along the transport path. ne model also mimics bone apposition, slowing of apposition during refilling, and mineralization lag time. It was found that simple diffusion cannot account for the transport of calcium ions into mineralizing bone, because the diffusion coefficient is two orders of magnitude too low. If a more rapid concentration gradient-driven means of transport exists, the model demonstrates that osteonal geometry and variable rate of refilling work together to produce calcification halos, as well as the primary and secondary calcification effect reported in the literature.

  20. Mathematical Model for the Mineralization of Bone

    NASA Technical Reports Server (NTRS)

    Martin, Bruce

    1994-01-01

    A mathematical model is presented for the transport and precipitation of mineral in refilling osteons. One goal of this model was to explain calcification 'halos,' in which the bone near the haversian canal is more highly mineralized than the more peripheral lamellae, which have been mineralizing longer. It was assumed that the precipitation rate of mineral is proportional to the difference between the local concentration of calcium ions and an equilibrium concentration and that the transport of ions is by either diffusion or some other concentration gradient-dependent process. Transport of ions was assumed to be slowed by the accumulation of mineral in the matrix along the transport path. The model also mimics bone apposition, slowing of apposition during refilling, and mineralization lag time. It was found that simple diffusion cannot account for the transport of calcium ions into mineralizing bone, because the diffusion coefficient is two orders of magnitude too low. If a more rapid concentration gradient-driven means of transport exists, the model demonstrates that osteonal geometry and variable rate of refilling work together to produce calcification halos, as well as the primary and secondary calcification effect reported in the literature.

  1. Mathematical modelling of physical and chemical processes of coal combustion in chamber furnaces of boiler aggregates based on the package of applied programs FIRE 3D

    NASA Astrophysics Data System (ADS)

    Gil, A. V.; Starchenko, A. V.

    2012-09-01

    The furnace processes of the combustion of poly-fraction high-ashes Ekibastuz coal in the furnace chamber of the boiler aggregate PK-39 and of the combustion of highly humid brown Berezov's coal in the furnace of the BKZ-210-140 boiler are investigated by mathematical modeling using the package of applied programs FIRE 3D [1-3]. Results of the numerical modeling of the processes of aerodynamics, heat exchange, and combustion in the furnace volume and their comparison with the results of nature tests are presented.

  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. Mathematical model insights into arsenic detoxification

    PubMed Central

    2011-01-01

    Background Arsenic in drinking water, a major health hazard to millions of people in South and East Asia and in other parts of the world, is ingested primarily as trivalent inorganic arsenic (iAs), which then undergoes hepatic methylation to methylarsonic acid (MMAs) and a second methylation to dimethylarsinic acid (DMAs). Although MMAs and DMAs are also known to be toxic, DMAs is more easily excreted in the urine and therefore methylation has generally been considered a detoxification pathway. A collaborative modeling project between epidemiologists, biologists, and mathematicians has the purpose of explaining existing data on methylation in human studies in Bangladesh and also testing, by mathematical modeling, effects of nutritional supplements that could increase As methylation. Methods We develop a whole body mathematical model of arsenic metabolism including arsenic absorption, storage, methylation, and excretion. The parameters for arsenic methylation in the liver were taken from the biochemical literature. The transport parameters between compartments are largely unknown, so we adjust them so that the model accurately predicts the urine excretion rates of time for the iAs, MMAs, and DMAs in single dose experiments on human subjects. Results We test the model by showing that, with no changes in parameters, it predicts accurately the time courses of urinary excretion in mutiple dose experiments conducted on human subjects. Our main purpose is to use the model to study and interpret the data on the effects of folate supplementation on arsenic methylation and excretion in clinical trials in Bangladesh. Folate supplementation of folate-deficient individuals resulted in a 14% decrease in arsenicals in the blood. This is confirmed by the model and the model predicts that arsenicals in the liver will decrease by 19% and arsenicals in other body stores by 26% in these same individuals. In addition, the model predicts that arsenic methyltransferase has been

  4. 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.

  5. Mathematical model of one-man air revitalization system

    NASA Technical Reports Server (NTRS)

    1976-01-01

    A mathematical model was developed for simulating the steady state performance in electrochemical CO2 concentrators which utilize (NMe4)2 CO3 (aq.) electrolyte. This electrolyte, which accommodates a wide range of air relative humidity, is most suitable for one-man air revitalization systems. The model is based on the solution of coupled nonlinear ordinary differential equations derived from mass transport and rate equations for the processes which take place in the cell. The boundary conditions are obtained by solving the mass and energy transport equations. A shooting method is used to solve the differential equations.

  6. A review on mathematical models for estimating indoor radon concentrations.

    PubMed

    Park, Ji Hyun; Kang, Dae Ryong; Kim, Jinheum

    2016-01-01

    Radiation from natural sources is one of causes of the environmental diseases. Radon is the leading environmental cause of lung cancer next to smoking. To investigate the relationship between indoor radon concentrations and lung cancer, researchers must be able to estimate an individual's cumulative level of indoor radon exposure and to do so, one must first be able to assess indoor radon concentrations. In this article, we outline factors affecting indoor radon concentrations and review related mathematical models based on the mass balance equation and the differential equations. Furthermore, we suggest the necessities of applying time-dependent functions for indoor radon concentrations and developing stochastic models.

  7. A 6DOF mathematical model of parachute in Mars EDL

    NASA Astrophysics Data System (ADS)

    Shen, Ganghui; Xia, Yuanqing; Sun, Haoran

    2015-04-01

    The base of the dynamics characteristic research on the parachute and vehicle system is to establish a dynamics model, during the parachute descent phase, which can accurately display the relationship among the velocity, altitude and attitude angles as well as the variation of time. This paper starts with a new tracking law - ADRC in Mars entry guidance, which affects the initial states of the parachute deployment point and determines precision landing capability. Then, the influence of unsteady resistance to the parachute in Martian air is considered as the added mass, and a 6DOF nonlinear mathematical model of the parachute and vehicle system is established.

  8. Assessment of mathematical models for the flow in directional solidification

    NASA Astrophysics Data System (ADS)

    Lu, Jay W.; Chen, Falin

    1997-02-01

    In a binary solution unidirectionally solidified from below, the bulk melt and the eutectic solid is separated by a dendritic mushy zone. The mathematical formulation governing the fluid motion shall thus consist of the equations in the bulk melt and the mushy zone and the associated boundary conditions. In the bulk melt, assuming that the melt is a Newtonian fluid, the governing equations are the continuity equation, the Navier-Stokes equations, the heat conservation equation, and the solute conservation equation. In the mushy layer, however, the formulation of the momentum equation and the associated boundary conditions are diversified in previous investigations. In this paper, we discuss three mathematical models, which had been previously applied to study the flow induced by the solidification of binary solutions cooling from below. The assessment is given on the bases of the stability characteristics of the convective flow and the comparison between the numerical and experimental results.

  9. Prediction Assessments: Using Video-Based Predictions to Assess Prospective Teachers' Knowledge of Students' Mathematical Thinking

    ERIC Educational Resources Information Center

    Norton, Anderson; McCloskey, Andrea; Hudson, Rick A.

    2011-01-01

    In order to evaluate the effectiveness of an experimental elementary mathematics field experience course, we have designed a new assessment instrument. These video-based prediction assessments engage prospective teachers in a video analysis of a child solving mathematical tasks. The prospective teachers build a model of that child's mathematics…

  10. Learning Mathematics by Designing, Programming, and Investigating with Interactive, Dynamic Computer-Based Objects

    ERIC Educational Resources Information Center

    Marshall, Neil; Buteau, Chantal

    2014-01-01

    As part of their undergraduate mathematics curriculum, students at Brock University learn to create and use computer-based tools with dynamic, visual interfaces, called Exploratory Objects, developed for the purpose of conducting pure or applied mathematical investigations. A student's Development Process Model of creating and using an Exploratory…

  11. Mathematical modelling of the composting process: a review.

    PubMed

    Mason, I G

    2006-01-01

    In this paper mathematical models of the composting process are examined and their performance evaluated. Mathematical models of the composting process have been derived from both energy and mass balance considerations, with solutions typically derived in time, and in some cases, spatially. Both lumped and distributed parameter models have been reported, with lumped parameter models presently predominating in the literature. Biological energy production functions within the models included first-order, Monod-type or empirical expressions, and these have predicted volatile solids degradation, oxygen consumption or carbon dioxide production, with heat generation derived using heat quotient factors. Rate coefficient correction functions for temperature, moisture, oxygen and/or free air space have been incorporated in a number of the first-order and Monod-type expressions. The most successful models in predicting temperature profiles were those which incorporated either empirical kinetic expressions for volatile solids degradation or CO2 production, or which utilised a first-order model for volatile solids degradation, with empirical corrections for temperature and moisture variations. Models incorporating Monod-type kinetic expressions were less successful. No models were able to predict maximum, average and peak temperatures to within criteria of 5, 2 and 2 degrees C, respectively, or to predict the times to reach peak temperatures to within 8 h. Limitations included the modelling of forced aeration systems only and the generation of temperature validation data for relatively short time periods in relation to those used in full-scale composting practice. Moisture and solids profiles were well predicted by two models, but oxygen and carbon dioxide profiles were generally poorly modelled. Further research to obtain more extensive substrate degradation data, develop improved first-order biological heat production models, investigate mechanistically-based moisture

  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. Evaluation of a Mentor Teacher Model for Enhancing Mathematics Instruction through the Use of Computers.

    ERIC Educational Resources Information Center

    Holahan, Patricia J.; Jurkat, M. Peter; Friedman, Edward A.

    2000-01-01

    Describes the development of the Mentor Teacher Model that trained middle school and high school mathematics teachers in New Jersey as mentor teachers in the effective use of computer-based technologies for teaching mathematics. Highlights include student-centered teaching methods; cooperative learning; problem-solving activities; and technology…

  14. The Reciprocal Relationship between Parental Involvement and Mathematics Achievement: Autoregressive Cross-Lagged Modeling

    ERIC Educational Resources Information Center

    Hong, Sehee; Yoo, Sung-Kyung; You, Sukkyung; Wu, Chih-Chun

    2010-01-01

    This study focused on comparing the longitudinal associations between two types of parental involvement (i.e., mathematics value and academic reinforcement) and high school students' mathematics achievement, using data from the Longitudinal Study of American Youth (LSAY). Results, based on multivariate autoregressive cross-lagged modeling,…

  15. Modelling Mathematical Reasoning in Physics Education

    ERIC Educational Resources Information Center

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

    2012-01-01

    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…

  16. Model Learner Outcomes for Mathematics Education.

    ERIC Educational Resources Information Center

    Halvorson, Judith K.; Stenglein, Sharon M.

    Awareness of the need for essential reforms within mathematics education evolved fundamentally as the consequence of several national reports, culminating in the documentation of this need with "Everybody Counts" in January 1989. The publication of "Curriculum and Evaluation Standards for School Mathematics" by the National…

  17. Mathematical model of frost heave and thaw settlement in pavements

    NASA Astrophysics Data System (ADS)

    Guymon, Gary L.; Berg, Richard L.; Hromadka, Theodore V.

    1993-04-01

    Since 1975 the U.S. Army Corps of Engineers, the Federal Highway Administration and the Federal Aviation Administration have been working cooperatively to develop a mathematical model to estimate frost heave and thaw weakening under various environmental conditions and for various pavement designs. A model has been developed. It is a one-dimensional representation of vertical heat and moisture flux. It is based on a numerical solution technique termed the nodal domain integration method, and it estimates frost heave and frost penetration reasonably well for a variety of situations. The model is now ready for additional field evaluation and implementation in appropriate cases. The main objectives of this report are: (1) to describe the model, FROST, including modeling uncertainties and errors; (2) to summarize recent comparisons between measured and computed values for frost heave and frost penetration; and (3) to describe parameters necessary for input into the model.

  18. 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…

  19. 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…

  20. 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…

  1. Mathematical Models of the Value of Achievement Testing.

    ERIC Educational Resources Information Center

    Pinsky, Paul D.

    The mathematical models of this paper were developed as an outgrowth of working with the Comprehensive Achievement Monitoring project (Project CAM) which was conceived as a model and application of sampling procedures such as those used in industrial quality control techniques to educational measurement. This paper explores mathematical modeling…

  2. Mathematical modeling of Chikungunya fever control

    NASA Astrophysics Data System (ADS)

    Hincapié-Palacio, Doracelly; Ospina, Juan

    2015-05-01

    Chikungunya fever is a global concern due to the occurrence of large outbreaks, the presence of persistent arthropathy and its rapid expansion throughout various continents. Globalization and climate change have contributed to the expansion of the geographical areas where mosquitoes Aedes aegypti and Aedes albopictus (Stegomyia) remain. It is necessary to improve the techniques of vector control in the presence of large outbreaks in The American Region. We derive measures of disease control, using a mathematical model of mosquito-human interaction, by means of three scenarios: a) a single vector b) two vectors, c) two vectors and human and non-human reservoirs. The basic reproductive number and critical control measures were deduced by using computer algebra with Maple (Maplesoft Inc, Ontario Canada). Control measures were simulated with parameter values obtained from published data. According to the number of households in high risk areas, the goals of effective vector control to reduce the likelihood of mosquito-human transmission would be established. Besides the two vectors, if presence of other non-human reservoirs were reported, the monthly target of effective elimination of the vector would be approximately double compared to the presence of a single vector. The model shows the need to periodically evaluate the effectiveness of vector control measures.

  3. Mathematical model I. Electron and quantum mechanics

    NASA Astrophysics Data System (ADS)

    Gadre, Nitin Ramchandra

    2011-03-01

    The basic particle electron obeys various theories like electrodynamics, quantum mechanics and special relativity. Particle under different experimental conditions behaves differently, allowing us to observe different characteristics which become basis for these theories. In this paper, we have made an attempt to suggest a classical picture by studying the requirements of these three modern theories. The basic presumption is: There must be certain structural characteristics in a particle like electron which make it obey postulates of modern theories. As it is `difficult' to find structure of electron experimentally, we make a mathematical attempt. For a classical approach, we require well defined systems and we have studied a system with two charged particles, proton and electron in a hydrogen atom. An attempt has been made to give a model to describe electron as seen by the proton. We then discuss how the model can satisfy the requirements of the three modern theories in a classical manner. The paper discusses basic aspects of relativity and electrodynamics. However the focus of the paper is on quantum mechanics.

  4. Mathematical modeling of the neuron morphology using two dimensional images.

    PubMed

    Rajković, Katarina; Marić, Dušica L; Milošević, Nebojša T; Jeremic, Sanja; Arsenijević, Valentina Arsić; Rajković, Nemanja

    2016-02-07

    In this study mathematical analyses such as the analysis of area and length, fractal analysis and modified Sholl analysis were applied on two dimensional (2D) images of neurons from adult human dentate nucleus (DN). Using mathematical analyses main morphological properties were obtained including the size of neuron and soma, the length of all dendrites, the density of dendritic arborization, the position of the maximum density and the irregularity of dendrites. Response surface methodology (RSM) was used for modeling the size of neurons and the length of all dendrites. However, the RSM model based on the second-order polynomial equation was only possible to apply to correlate changes in the size of the neuron with other properties of its morphology. Modeling data provided evidence that the size of DN neurons statistically depended on the size of the soma, the density of dendritic arborization and the irregularity of dendrites. The low value of mean relative percent deviation (MRPD) between the experimental data and the predicted neuron size obtained by RSM model showed that model was suitable for modeling the size of DN neurons. Therefore, RSM can be generally used for modeling neuron size from 2D images.

  5. TriBITS lifecycle model. Version 1.0, a lean/agile software lifecycle model for research-based computational science and engineering and applied mathematical software.

    SciTech Connect

    Willenbring, James M.; Bartlett, Roscoe Ainsworth; Heroux, Michael Allen

    2012-01-01

    Software lifecycles are becoming an increasingly important issue for computational science and engineering (CSE) software. The process by which a piece of CSE software begins life as a set of research requirements and then matures into a trusted high-quality capability is both commonplace and extremely challenging. Although an implicit lifecycle is obviously being used in any effort, the challenges of this process - respecting the competing needs of research vs. production - cannot be overstated. Here we describe a proposal for a well-defined software lifecycle process based on modern Lean/Agile software engineering principles. What we propose is appropriate for many CSE software projects that are initially heavily focused on research but also are expected to eventually produce usable high-quality capabilities. The model is related to TriBITS, a build, integration and testing system, which serves as a strong foundation for this lifecycle model, and aspects of this lifecycle model are ingrained in the TriBITS system. Here, we advocate three to four phases or maturity levels that address the appropriate handling of many issues associated with the transition from research to production software. The goals of this lifecycle model are to better communicate maturity levels with customers and to help to identify and promote Software Engineering (SE) practices that will help to improve productivity and produce better software. An important collection of software in this domain is Trilinos, which is used as the motivation and the initial target for this lifecycle model. However, many other related and similar CSE (and non-CSE) software projects can also make good use of this lifecycle model, especially those that use the TriBITS system. Indeed this lifecycle process, if followed, will enable large-scale sustainable integration of many complex CSE software efforts across several institutions.

  6. 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.

  7. Mathematical Modeling Tools to Study Preharvest Food Safety.

    PubMed

    Lanzas, Cristina; Chen, Shi

    2016-08-01

    This article provides an overview of the emerging field of mathematical modeling in preharvest food safety. We describe the steps involved in developing mathematical models, different types of models, and their multiple applications. The introduction to modeling is followed by several sections that introduce the most common modeling approaches used in preharvest systems. We finish the chapter by outlining potential future directions for the field.

  8. Mathematical models in biology: from molecules to life.

    PubMed

    Kaznessis, Yiannis N

    2011-01-01

    A vexing question in the biological sciences is the following: can biological phenotypes be explained with mathematical models of molecules that interact according to physical laws? At the crux of the matter lies the doubt that humans can develop physically faithful mathematical representations of living organisms. We discuss advantages that synthetic biological systems confer that may help us describe life's distinctiveness with tractable mathematics that are grounded on universal laws of thermodynamics and molecular biology.

  9. Mathematical models in biology: from molecules to life

    PubMed Central

    Kaznessis, Yiannis N.

    2011-01-01

    A vexing question in the biological sciences is the following: can biological phenotypes be explained with mathematical models of molecules that interact according to physical laws? At the crux of the matter lies the doubt that humans can develop physically faithful mathematical representations of living organisms. We discuss advantages that synthetic biological systems confer that may help us describe life’s distinctiveness with tractable mathematics that are grounded on universal laws of thermodynamics and molecular biology. PMID:21472998

  10. 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

  11. 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.

  12. Mathematical modeling and the neuroscience of metaphor

    NASA Astrophysics Data System (ADS)

    Rising, Hawley K., III

    2008-02-01

    We look at a characterization of metaphor from cognitive linguistics, extracting the salient features of metaphorical processing. We examine the neurobiology of dendrites, specifically spike timing-dependent plasticity (STDP), and the modulation of backpropagating action potentials (bAPs), to generate a neuropil-centric model of cortical processing based on signal timing and reverberation between regions. We show how this model supports the basic features of metaphorical processing previously extracted. Finally, we model this system using a combination of euclidean, projective, and hyperbolic geometries, and show how the resulting model accounts for this processing, and relates to other neural network models

  13. Mathematical modeling of the West Africa Ebola epidemic

    PubMed Central

    Chretien, Jean-Paul; Riley, Steven; George, Dylan B

    2015-01-01

    As of November 2015, the Ebola virus disease (EVD) epidemic that began in West Africa in late 2013 is waning. The human toll includes more than 28,000 EVD cases and 11,000 deaths in Guinea, Liberia, and Sierra Leone, the most heavily-affected countries. We reviewed 66 mathematical modeling studies of the EVD epidemic published in the peer-reviewed literature to assess the key uncertainties models addressed, data used for modeling, public sharing of data and results, and model performance. Based on the review, we suggest steps to improve the use of modeling in future public health emergencies. DOI: http://dx.doi.org/10.7554/eLife.09186.001 PMID:26646185

  14. The roughness surface expressed by the mathematical model

    NASA Astrophysics Data System (ADS)

    Macurova, Anna

    2010-07-01

    The work investigates the effect of some characteristics of a cut surface and studies roughness of the cutting process. There is elaborated theoretical information and new aspects on calculation of the theoretical values of the roughness of the cut surface for the chosen materials are formulated. In the area of the experimental investigation, results on characteristics of the chosen materials are formulated in this work. Obtained results are fundamental for the mathematical modulation and mathematical analysis for the investigated dependencies for the cut surfaces. The mathematical model also represents the specific dependencies of the technological process. The characteristics of the observed parameters are approximated by characteristics of the quasi-linear models. The solution of this model offers acceptable results. The mathematical models of the roughness of the cut surface are a mathematical description of the dependency of the maximum roughness of the cut surface of the feed represented by the differential equation and by the integral curves.

  15. Mathematical modelling for nanotube bundle oscillators

    NASA Astrophysics Data System (ADS)

    Thamwattana, Ngamta; Cox, Barry J.; Hill, James M.

    2009-07-01

    This paper investigates the mechanics of a gigahertz oscillator comprising a nanotube oscillating within the centre of a uniform concentric ring or bundle of nanotubes. The study is also extended to the oscillation of a fullerene inside a nanotube bundle. In particular, certain fullerene-nanotube bundle oscillators are studied, namely C60-carbon nanotube bundle, C60-boron nitride nanotube bundle, B36N36-carbon nanotube bundle and B36N36-boron nitride nanotube bundle. Using the Lennard-Jones potential and the continuum approach, we obtain a relation between the bundle radius and the radii of the nanotubes forming the bundle, as well as the optimum bundle size which gives rise to the maximum oscillatory frequency for both the fullerene and the nanotube bundle oscillators. While previous studies in this area have been undertaken through molecular dynamics simulations, this paper emphasizes the use of applied mathematical modelling techniques which provides considerable insight into the underlying mechanisms. The paper presents a synopsis of the major results derived in detail by the present authors in [1, 2].

  16. Mathematical modeling of the human knee joint

    SciTech Connect

    Ricafort, Juliet

    1996-05-01

    A model was developed to determine the forces exerted by several flexor and extensor muscles of the human knee under static conditions. The following muscles were studied: the gastrocnemius, biceps femoris, semitendinosus, semimembranosus, and the set of quadricep muscles. The tibia and fibula were each modeled as rigid bodies; muscles were modeled by their functional lines of action in space. Assumptions based on previous data were used to resolve the indeterminacy.

  17. Helping Students Become Better Mathematical Modelers: Pseudosteady-State Approximations.

    ERIC Educational Resources Information Center

    Bunge, Annette L.; Miller, Ronald L.

    1997-01-01

    Undergraduate and graduate students are often confused about several aspects of modeling physical systems. Describes an approach to address these issues using a single physical transport problem that can be analyzed with multiple mathematical models. (DKM)

  18. A mathematical model of stress generation in microtubule pair interactions

    NASA Astrophysics Data System (ADS)

    Fang, Fang; Betterton, Meredith; Shelley, Michael

    2014-11-01

    Microtubules and motor proteins are basic ingredients in many cellular structures and of new biosynthetic ``active'' suspensions. The interaction of microtubules with their surrounding fluid medium depends fundamentally upon the force generation afforded them through cross-linking motile motor proteins. Here we develop a simple mathematical model, based on the statistical mechanics, motor proteins binding and unbinding, to study the generation of active fluid stresses. We study the role and contributions of ``polarity sorting'' and ``tether'' relaxation on the generation of intrinsic, destabilizing stresses.

  19. Mathematical modeling of heat transfer problems in the permafrost

    NASA Astrophysics Data System (ADS)

    Gornov, V. F.; Stepanov, S. P.; Vasilyeva, M. V.; Vasilyev, V. I.

    2014-11-01

    In this work we present results of numerical simulation of three-dimensional temperature fields in soils for various applied problems: the railway line in the conditions of permafrost for different geometries, the horizontal tunnel underground storage and greenhouses of various designs in the Far North. Mathematical model of the process is described by a nonstationary heat equation with phase transitions of pore water. The numerical realization of the problem is based on the finite element method using a library of scientific computing FEniCS. For numerical calculations we use high-performance computing systems.

  20. The development and evaluation of a mathematical nutrition model to predict digestible energy intake of broodmares based on body condition changes.

    PubMed

    Cordero, V V; Cavinder, C A; Tedeschi, L O; Sigler, D H; Vogelsang, M M; Arnold, C E

    2013-05-01

    Mathematical nutrition models have been developed for beef and dairy cattle to estimate dietary energy intake needed to change BCS. Similar technology has not been used to improve nutrition and feeding strategies for horses. An accurate equine nutrition model may enhance feeding management and reduce the costs of unnecessary overfeeding and promote an optimal level of fatness to achieve reproductive efficiency. The objectives of this study were to develop and evaluate a mathematical nutrition model capable of accurately predicting dietary energy changes to alter BW, rump fat (RF) thickness, and overall body fat (BF), which is needed to maximize profitability and productivity of mares. Model structure was similar to a previously developed model for cattle, and literature data for Quarter Horse mares were used to parameterize the horse model in predicting DE requirement associated with BCS changes. Evaluation of the horse model was performed using an independent dataset comprising 20 nonlactating Quarter Horse mares. Pretrial BCS was used to assign mares to 1 of 4 treatment groups and fed to alter BCS by 1 unit as follows: from 4 to 5 (Group 1), 5 to 4 (Group 2), 6 to 7 (Group 3), and 7 to 6 (Group 4). The BCS, RF thickness, and BW were measured for each mare before the commencement of the feeding trial and once per week thereafter for the duration of a 30-d feeding trial. Initial and target BCS, percent BF, and BW data were collected from each mare and inputted into the model. Mares were individually fed according to the DE suggestions proposed by the model to achieve the targeted BCS change within 30 d. The coefficient of determination of observed and model-predicted values (model precision) was 0.907 (P < 0.001) for BCS, 0.607 (P < 0.001) for percent BF, and 0.94 (P < 0.001) for BW. The BCS was highly correlated to percent BF (r = 0.808; P = 0.01). We concluded the reparameterized model was reliable to predict changes in BW and BCS, but more work is needed to

  1. Typhoid transmission: a historical perspective on mathematical model development.

    PubMed

    Bakach, Iurii; Just, Matthew R; Gambhir, Manoj; Fung, Isaac Chun-Hai

    2015-11-01

    Mathematical models of typhoid transmission were first developed nearly half a century ago. To facilitate a better understanding of the historical development of this field, we reviewed mathematical models of typhoid and summarized their structures and limitations. Eleven models, published in 1971 to 2014, were reviewed. While models of typhoid vaccination are well developed, we highlight the need to better incorporate water, sanitation and hygiene interventions into models of typhoid and other foodborne and waterborne diseases. Mathematical modeling is a powerful tool to test and compare different intervention strategies which is important in the world of limited resources. By working collaboratively, epidemiologists and mathematicians should build better mathematical models of typhoid transmission, including pharmaceutical and non-pharmaceutical interventions, which will be useful in epidemiological and public health practice.

  2. Mathematics and Astronomy: Inquire Based Scientific Education at School

    NASA Astrophysics Data System (ADS)

    de Castro, Ana I. Gómez

    2010-10-01

    Mathematics is the language of science however, in secondary and high school education students are not made aware of the strong implications behind this statement. This is partially caused because mathematical training and the modelling of nature are not taught together. Astronomy provides firm scientific grounds for this joint training; the mathematics needed is simple, the data can be acquired with simple instrumentation in any place on the planet and the physics is rich with a broad range of levels. In addition, astronomy and space exploration are extremely appealing to young (14-17 years old) students helping to motivate them to study science doing science, i.e. to introduce Inquiry Based Scientific Education (IBSE). Since 1997 a global consortium is being developed to introduce IBSE techniques in secondary/high school education on a global scale: the Global Hands-On Universe association (www.globalhou.org) making use of the astronomical universe as a training lab. This contribution is a brief update on the current activities of the HOU consortium. Relevant URLS: www.globalhou.org, www.euhou.net, www.houspain.com.

  3. towards a theory-based multi-dimensional framework for assessment in mathematics: The "SEA" framework

    NASA Astrophysics Data System (ADS)

    Anku, Sitsofe E.

    1997-09-01

    Using the reform documents of the National Council of Teachers of Mathematics (NCTM) (NCTM, 1989, 1991, 1995), a theory-based multi-dimensional assessment framework (the "SEA" framework) which should help expand the scope of assessment in mathematics is proposed. This framework uses a context based on mathematical reasoning and has components that comprise mathematical concepts, mathematical procedures, mathematical communication, mathematical problem solving, and mathematical disposition.

  4. 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…

  5. 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…

  6. The Berlin-White Integrated Science and Mathematics Model.

    ERIC Educational Resources Information Center

    Berlin, Donna F.; White, Arthur L.

    1994-01-01

    Discusses six aspects of the Berlin-White Integrated Science and Mathematics Model developed to address the need for a definition of the integration of science and mathematics education. These aspects are ways of learning; ways of knowing; process and thinking skills; content knowledge; attitudes and perceptions; and teaching strategies. (MKR)

  7. 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…

  8. Modelling Reality in Mathematics Classrooms: The Case of Word Problems.

    ERIC Educational Resources Information Center

    Greer, Brian

    1997-01-01

    Word problems as used within the culture of mathematics education often promote a suspension of sense making by the students. In the papers in this issue, an alternative conceptualization of word problems is proposed that calls for mathematical modelling that takes real world knowledge into account. (SLD)

  9. An Assessment Model for Proof Comprehension in Undergraduate Mathematics

    ERIC Educational Resources Information Center

    Mejia-Ramos, Juan Pablo; Fuller, Evan; Weber, Keith; Rhoads, Kathryn; Samkoff, Aron

    2012-01-01

    Although proof comprehension is fundamental in advanced undergraduate mathematics courses, there has been limited research on what it means to understand a mathematical proof at this level and how such understanding can be assessed. In this paper, we address these issues by presenting a multidimensional model for assessing proof comprehension in…

  10. Pattern formation in stromatolites: insights from mathematical modelling

    PubMed Central

    Cuerno, R.; Escudero, C.; García-Ruiz, J. M.; Herrero, M. A.

    2012-01-01

    To this day, computer models for stromatolite formation have made substantial use of the Kardar–Parisi–Zhang (KPZ) equation. Oddly enough, these studies yielded mutually exclusive conclusions about the biotic or abiotic origin of such structures. We show in this paper that, at our current state of knowledge, a purely biotic origin for stromatolites can neither be proved nor disproved by means of a KPZ-based model. What can be shown, however, is that whatever their (biotic or abiotic) origin might be, some morphologies found in actual stromatolite structures (e.g. overhangs) cannot be formed as a consequence of a process modelled exclusively in terms of the KPZ equation and acting over sufficiently large times. This suggests the need to search for alternative mathematical approaches to model these structures, some of which are discussed in this paper. PMID:21993008

  11. Description of a tilt wing mathematical model for piloted simulation

    NASA Technical Reports Server (NTRS)

    Totah, Joseph J.

    1991-01-01

    A tilt-wing mathematical model that was used in a piloted six-deg-of-freedom flight simulation application is presented. Two types of control systems developed for the model - a conventional programmed-flap wing-tilt control system and a geared-flap wing-tilt control system - are discussed. The objective of this effort was to develop the capability to study tilt-wing aircraft. Experienced tilt-wing pilots subjectively evaluated the model using programmed-flap control to assess the quality of the simulation. The objective was met and the model was then applied to study geared-flap control to investigate the possibility of eliminating the need for auxiliary pitch control devices. This was performed in the moving-base simulation environment, and the vehicle responses with programmed-flap and geared-flap control were compared.

  12. Mathematical Model of a Lithium/Thionyl Chloride Battery

    SciTech Connect

    Jain, M.; Jungst, R.G.; Nagasubramanian, G.; Weidner, J.W.

    1998-11-24

    A mathematical model of a spirally wound lithium/thionyl chloride primary battery has been developed ~d used for parameter estimation and design studies. The model formulation is based on the fimdarnental Consemation laws using porous electrode theory and concentrated solution theory. The model is used to estimate the difision coefficient and the kinetic parameters for the reactions at the anode and the cathode as a function of temperature. These parameters are obtained by fitting the simulated capacity and average cell voltage to experimental data over a wide range of temperatures (-55 to 49"C) and discharge loads (10 to 250 ohms). The experiments were performed on D-sized, cathode-limited, spirally wound lithium/thionyl chloride cells. The model is also used to study the effkct of cathode thickness on the cell capacity as a finction of temperature, and it was found that the optimum thickness for the cathode- limited design is temperature and load dependent.

  13. 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

  14. Mathematical model and software for control of commissioning blast furnace

    NASA Astrophysics Data System (ADS)

    Spirin, N. A.; Onorin, O. P.; Shchipanov, K. A.; Lavrov, V. V.

    2016-09-01

    Blowing-in is a starting period of blast furnace operation after construction or major repair. The current approximation methods of blowing-in burden analysis are based on blowing-in practice of previously commissioned blast furnaces. This area is theoretically underexplored; there are no common scientifically based methods for selection of the burden composition and blast parameters. The purpose of this paper is development and scientific substantiation of the methods for selection of the burden composition and blast parameters in the blast furnace during the blowing-in period. Research methods are based on physical regularities of main processes running in the blast furnace, system analysis, and application of modern principles for development and construction of mathematical models, algorithms and software designed for automated control of complex production processes in metallurgy. As consequence of the research made by the authors the following results have been achieved: 1. A set of mathematical models for analysis of burden arrangement throughout the height of the blast furnace and for selection of optimal blast and gas dynamic parameters has been developed. 2. General principles for selection of the blowing-in burden composition and blast and gas dynamic parameters have been set up. 3. The software for the engineering and process staff of the blast furnace has been developed and introduced in the industry.

  15. Evolvable mathematical models: A new artificial Intelligence paradigm

    NASA Astrophysics Data System (ADS)

    Grouchy, Paul

    We develop a novel Artificial Intelligence paradigm to generate autonomously artificial agents as mathematical models of behaviour. Agent/environment inputs are mapped to agent outputs via equation trees which are evolved in a manner similar to Symbolic Regression in Genetic Programming. Equations are comprised of only the four basic mathematical operators, addition, subtraction, multiplication and division, as well as input and output variables and constants. From these operations, equations can be constructed that approximate any analytic function. These Evolvable Mathematical Models (EMMs) are tested and compared to their Artificial Neural Network (ANN) counterparts on two benchmarking tasks: the double-pole balancing without velocity information benchmark and the challenging discrete Double-T Maze experiments with homing. The results from these experiments show that EMMs are capable of solving tasks typically solved by ANNs, and that they have the ability to produce agents that demonstrate learning behaviours. To further explore the capabilities of EMMs, as well as to investigate the evolutionary origins of communication, we develop NoiseWorld, an Artificial Life simulation in which interagent communication emerges and evolves from initially noncommunicating EMM-based agents. Agents develop the capability to transmit their x and y position information over a one-dimensional channel via a complex, dialogue-based communication scheme. These evolved communication schemes are analyzed and their evolutionary trajectories examined, yielding significant insight into the emergence and subsequent evolution of cooperative communication. Evolved agents from NoiseWorld are successfully transferred onto physical robots, demonstrating the transferability of EMM-based AIs from simulation into physical reality.

  16. Inquiry-Based Learning and the Art of Mathematical Discourse

    ERIC Educational Resources Information Center

    von Renesse, Christine; Ecke, Volker

    2015-01-01

    Our particular flavor of inquiry-based learning (IBL) uses mathematical discourse, conversations, and discussions to empower students to deepen their mathematical thinking, building on strengths of students in the humanities. We present an organized catalog of powerful questions, discussion prompts, and talk moves that can help faculty facilitate…

  17. College Students Attitude and Mathematics Achievement Using Web Based Homework

    ERIC Educational Resources Information Center

    Leong, Kwan Eu; Alexander, Nathan

    2014-01-01

    The goal of this study was to understand how students' attitudes were connected to their mathematics learning and achievement. This investigation of students (n = 78) and their attitudes was specific to web-based homework in developmental mathematics courses in a two-year community college located in a large urban city in the United States. A…

  18. Language-Based Prior Knowledge and Transition to Mathematics

    ERIC Educational Resources Information Center

    Dogan-Dunlap, Hamide; Torres, Cristina; Chen, Fan

    2005-01-01

    The paper provides a college mathematics student's concept maps, definitions, and essays to support the thesis that language-based prior knowledge can influence students' cognitive processes of mathematical concepts. A group of intermediate algebra students who displayed terms mainly from the spoken language on the first and the second concept…

  19. Mathematical modeling in wound healing, bone regeneration and tissue engineering.

    PubMed

    Geris, Liesbet; Gerisch, Alf; Schugart, Richard C

    2010-12-01

    The processes of wound healing and bone regeneration and problems in tissue engineering have been an active area for mathematical modeling in the last decade. Here we review a selection of recent models which aim at deriving strategies for improved healing. In wound healing, the models have particularly focused on the inflammatory response in order to improve the healing of chronic wound. For bone regeneration, the mathematical models have been applied to design optimal and new treatment strategies for normal and specific cases of impaired fracture healing. For the field of tissue engineering, we focus on mathematical models that analyze the interplay between cells and their biochemical cues within the scaffold to ensure optimal nutrient transport and maximal tissue production. Finally, we briefly comment on numerical issues arising from simulations of these mathematical models.

  20. Mathematical Modeling of Intestinal Iron Absorption Using Genetic Programming

    PubMed Central

    Colins, Andrea; Gerdtzen, Ziomara P.; Nuñez, Marco T.; Salgado, J. Cristian

    2017-01-01

    Iron is a trace metal, key for the development of living organisms. Its absorption process is complex and highly regulated at the transcriptional, translational and systemic levels. Recently, the internalization of the DMT1 transporter has been proposed as an additional regulatory mechanism at the intestinal level, associated to the mucosal block phenomenon. The short-term effect of iron exposure in apical uptake and initial absorption rates was studied in Caco-2 cells at different apical iron concentrations, using both an experimental approach and a mathematical modeling framework. This is the first report of short-term studies for this system. A non-linear behavior in the apical uptake dynamics was observed, which does not follow the classic saturation dynamics of traditional biochemical models. We propose a method for developing mathematical models for complex systems, based on a genetic programming algorithm. The algorithm is aimed at obtaining models with a high predictive capacity, and considers an additional parameter fitting stage and an additional Jackknife stage for estimating the generalization error. We developed a model for the iron uptake system with a higher predictive capacity than classic biochemical models. This was observed both with the apical uptake dataset used for generating the model and with an independent initial rates dataset used to test the predictive capacity of the model. The model obtained is a function of time and the initial apical iron concentration, with a linear component that captures the global tendency of the system, and a non-linear component that can be associated to the movement of DMT1 transporters. The model presented in this paper allows the detailed analysis, interpretation of experimental data, and identification of key relevant components for this complex biological process. This general method holds great potential for application to the elucidation of biological mechanisms and their key components in other complex

  1. Mathematical models and their applications in medicine and health.

    PubMed

    Verma, B l; Ray, S K; Srivastava, R N

    1981-01-01

    Mathematical models have great potentialities as regards their utility in different disciplines of medicine and health. This paper attempts to elucidate their uses in the field. A brief mention of some models has also been made. Mathematical models are useful in epidemiologic research, planning and evaluation of preventive and control programmes, clinical trials, measurement of health, cost-benefit analysis, diagnosis of patients and in maximizing effectiveness of operations aimed at attaining specified goals within existing resources.

  2. Computer-Based Mathematics Instructions for Engineering Students

    NASA Technical Reports Server (NTRS)

    Khan, Mustaq A.; Wall, Curtiss E.

    1996-01-01

    Almost every engineering course involves mathematics in one form or another. The analytical process of developing mathematical models is very important for engineering students. However, the computational process involved in the solution of some mathematical problems may be very tedious and time consuming. There is a significant amount of mathematical software such as Mathematica, Mathcad, and Maple designed to aid in the solution of these instructional problems. The use of these packages in classroom teaching can greatly enhance understanding, and save time. Integration of computer technology in mathematics classes, without de-emphasizing the traditional analytical aspects of teaching, has proven very successful and is becoming almost essential. Sample computer laboratory modules are developed for presentation in the classroom setting. This is accomplished through the use of overhead projectors linked to graphing calculators and computers. Model problems are carefully selected from different areas.

  3. Mathematical model of cancer with competition

    NASA Astrophysics Data System (ADS)

    Chrobak, Joanna M.; Herrero, Henar

    2009-05-01

    In this paper we present a model of tumor based on the use of an autonomous system of ordinary differential equations (ODE). The model assumes that normal cells and cancer cells coexist in an environment as two different species which compete for nutrients and space. The immune system and the tumor cells fight against each other. The analysis of the linear stability of the fixed points of the model yields to two groups of solutions. In the first one, the immune system wins against the tumor cells, so the cancer disappears. In the second one, the cancer grows until some fixed level and then stabilizes.

  4. 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.

  5. Modelling Of Flotation Processes By Classical Mathematical Methods - A Review

    NASA Astrophysics Data System (ADS)

    Jovanović, Ivana; Miljanović, Igor

    2015-12-01

    Flotation process modelling is not a simple task, mostly because of the process complexity, i.e. the presence of a large number of variables that (to a lesser or a greater extent) affect the final outcome of the mineral particles separation based on the differences in their surface properties. The attempts toward the development of the quantitative predictive model that would fully describe the operation of an industrial flotation plant started in the middle of past century and it lasts to this day. This paper gives a review of published research activities directed toward the development of flotation models based on the classical mathematical rules. The description and systematization of classical flotation models were performed according to the available references, with emphasize exclusively given to the flotation process modelling, regardless of the model application in a certain control system. In accordance with the contemporary considerations, models were classified as the empirical, probabilistic, kinetic and population balance types. Each model type is presented through the aspects of flotation modelling at the macro and micro process levels.

  6. A mathematical model and numerical method for thermoelectric DNA sequencing

    NASA Astrophysics Data System (ADS)

    Shi, Liwei; Guilbeau, Eric J.; Nestorova, Gergana; Dai, Weizhong

    2014-05-01

    Single nucleotide polymorphisms (SNPs) are single base pair variations within the genome that are important indicators of genetic predisposition towards specific diseases. This study explores the feasibility of SNP detection using a thermoelectric sequencing method that measures the heat released when DNA polymerase inserts a deoxyribonucleoside triphosphate into a DNA strand. We propose a three-dimensional mathematical model that governs the DNA sequencing device with a reaction zone that contains DNA template/primer complex immobilized to the surface of the lower channel wall. The model is then solved numerically. Concentrations of reactants and the temperature distribution are obtained. Results indicate that when the nucleoside is complementary to the next base in the DNA template, polymerization occurs lengthening the complementary polymer and releasing thermal energy with a measurable temperature change, implying that the thermoelectric conceptual device for sequencing DNA may be feasible for identifying specific genes in individuals.

  7. 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

  8. Innovative mathematical modeling in environmental remediation.

    PubMed

    Yeh, Gour-Tsyh; Gwo, Jin-Ping; Siegel, Malcolm D; Li, Ming-Hsu; Fang, Yilin; Zhang, Fan; Luo, Wensui; Yabusaki, Steve B

    2013-05-01

    There are two different ways to model reactive transport: ad hoc and innovative reaction-based approaches. The former, such as the Kd simplification of adsorption, has been widely employed by practitioners, while the latter has been mainly used in scientific communities for elucidating mechanisms of biogeochemical transport processes. It is believed that innovative mechanistic-based models could serve as protocols for environmental remediation as well. This paper reviews the development of a mechanistically coupled fluid flow, thermal transport, hydrologic transport, and reactive biogeochemical model and example-applications to environmental remediation problems. Theoretical bases are sufficiently described. Four example problems previously carried out are used to demonstrate how numerical experimentation can be used to evaluate the feasibility of different remediation approaches. The first one involved the application of a 56-species uranium tailing problem to the Melton Branch Subwatershed at Oak Ridge National Laboratory (ORNL) using the parallel version of the model. Simulations were made to demonstrate the potential mobilization of uranium and other chelating agents in the proposed waste disposal site. The second problem simulated laboratory-scale system to investigate the role of natural attenuation in potential off-site migration of uranium from uranium mill tailings after restoration. It showed inadequacy of using a single Kd even for a homogeneous medium. The third example simulated laboratory experiments involving extremely high concentrations of uranium, technetium, aluminum, nitrate, and toxic metals (e.g., Ni, Cr, Co). The fourth example modeled microbially-mediated immobilization of uranium in an unconfined aquifer using acetate amendment in a field-scale experiment. The purposes of these modeling studies were to simulate various mechanisms of mobilization and immobilization of radioactive wastes and to illustrate how to apply reactive transport

  9. Modeling Students' Interest in Mathematics Homework

    ERIC Educational Resources Information Center

    Xu, Jianzhong; Yuan, Ruiping; Xu, Brian; Xu, Melinda

    2016-01-01

    The authors examine the factors influencing mathematics homework interest for Chinese students and compare the findings with a recent study involving U.S. students. The findings from multilevel analyses revealed that some predictors for homework interest functioned similarly (e.g., affective attitude toward homework, learning-oriented reasons,…

  10. Key Concept Mathematics and Management Science Models

    ERIC Educational Resources Information Center

    Macbeth, Thomas G.; Dery, George C.

    1973-01-01

    The presentation of topics in calculus and matrix algebra to second semester freshmen along with a treatment of exponential and power functions would permit them to cope with a significant portion of the mathematical concepts that comprise the essence of several disciplines in a business school curriculum. (Author)

  11. Making Insulation Decisions through Mathematical Modeling

    ERIC Educational Resources Information Center

    Yanik, H. Bahadir; Memis, Yasin

    2014-01-01

    Engaging students in studies about conservation and sustainability can support their understanding of making environmental conscious decisions to conserve Earth. This article aims to contribute these efforts and direct students' attention to how they can use mathematics to make environmental decisions. Contributors to iSTEM: Integrating…

  12. The Answering Process for Multiple-Choice Questions in Collaborative Learning: A Mathematical Learning Model Analysis

    ERIC Educational Resources Information Center

    Nakamura, Yasuyuki; Nishi, Shinnosuke; Muramatsu, Yuta; Yasutake, Koichi; Yamakawa, Osamu; Tagawa, Takahiro

    2014-01-01

    In this paper, we introduce a mathematical model for collaborative learning and the answering process for multiple-choice questions. The collaborative learning model is inspired by the Ising spin model and the model for answering multiple-choice questions is based on their difficulty level. An intensive simulation study predicts the possibility of…

  13. Mathematical modeling of the growth and development of the mussel Mytilus galloprovincialis on artificial substrates

    NASA Astrophysics Data System (ADS)

    Vasechkina, E. F.; Kazankova, I. I.

    2014-11-01

    A mathematical model simulating the growth and development of the mussel Mytilus galloprovincialis Lam. on artificial substrates has been constructed. The model is based on experimental data and contains mathematical descriptions of the filtration, respiration, excretion, spawning, and growth of an individual during its ontogenesis from the moment it attaches to a solid substrate to the attainment of a marketable size. The test computations have been compared to the available observation data for mussel farms.

  14. MAPCLUS: A Mathematical Programming Approach to Fitting the ADCLUS Model.

    ERIC Educational Resources Information Center

    Arabie, Phipps

    1980-01-01

    A new computing algorithm, MAPCLUS (Mathematical Programming Clustering), for fitting the Shephard-Arabie ADCLUS (Additive Clustering) model is presented. Details and benefits of the algorithm are discussed. (Author/JKS)

  15. The Mathematical Concept of Set and the 'Collection' Model.

    ERIC Educational Resources Information Center

    Fischbein, Efraim; Baltsan, Madlen

    1999-01-01

    Hypothesizes that various misconceptions held by students with regard to the mathematical set concept may be explained by the initial collection model. Study findings confirm the hypothesis. (Author/ASK)

  16. 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

  17. Mathematical Modelling of Mixed-Model Assembly Line Balancing Problem with Resources Constraints

    NASA Astrophysics Data System (ADS)

    Magffierah Razali, Muhamad; Rashid, Mohd Fadzil Faisae Ab.; Razif Abdullah Make, Muhammad

    2016-11-01

    Modern manufacturing industries nowadays encounter with the challenges to provide a product variety in their production at a cheaper cost. This situation requires for a system that flexible with cost competent such as Mixed-Model Assembly Line. This paper developed a mathematical model for Mixed-Model Assembly Line Balancing Problem (MMALBP). In addition to the existing works that consider minimize cycle time, workstation and product rate variation, this paper also consider the resources constraint in the problem modelling. Based on the finding, the modelling results achieved by using computational method were in line with the manual calculation for the evaluated objective functions. Hence, it provided an evidence to verify the developed mathematical model for MMALBP. Implications of the results and future research directions were also presented in this paper.

  18. [Mathematical models of decision making and learning].

    PubMed

    Ito, Makoto; Doya, Kenji

    2008-07-01

    Computational models of reinforcement learning have recently been applied to analysis of brain imaging and neural recording data to identity neural correlates of specific processes of decision making, such as valuation of action candidates and parameters of value learning. However, for such model-based analysis paradigms, selecting an appropriate model is crucial. In this study we analyze the process of choice learning in rats using stochastic rewards. We show that "Q-learning," which is a standard reinforcement learning algorithm, does not adequately reflect the features of choice behaviors. Thus, we propose a generalized reinforcement learning (GRL) algorithm that incorporates the negative reward effect of reward loss and forgetting of values of actions not chosen. Using the Bayesian estimation method for time-varying parameters, we demonstrated that the GRL algorithm can predict an animal's choice behaviors as efficiently as the best Markov model. The results suggest the usefulness of the GRL for the model-based analysis of neural processes involved in decision making.

  19. Searching for new mathematical growth model approaches for Listeria monocytogenes.

    PubMed

    Valero, A; Hervás, C; García-Gimeno, R M; Zurera, G

    2007-01-01

    Different secondary modeling approaches for the estimation of Listeria monocytogenes growth rate as a function of temperature (4 to 30 degrees C), citric acid (0% to 0.4% w/v), and ascorbic acid (0% to 0.4% w/v) are presented. Response surface (RS) and square-root (SR) models are proposed together with different artificial neural networks (ANN) based on product functions units (PU), sigmoidal functions units (SU), and a novel approach based on the use of hybrid functions units (PSU), which results from a combination of PU and SU. In this study, a significantly better goodness-of-fit was obtained in the case of the ANN models presented, reflected by the lower SEP values obtained (< 24.23 for both training and generalization datasets). Among these models, the SU model provided the best generalization capacity, displaying lower RMSE and SEP values, with fewer parameters compared to the PU and PSU models. The bias factor (B(f)) and accuracy factor (A(f)) of the mathematical validation dataset were above 1 in all cases, providing fail-safe predictions. The balance between generalization properties and the ease of use is the main consideration when applying secondary modeling approaches to achieve accurate predictions about the behavior of microorganisms.

  20. Mathematical Model of an Air Cushion Vehicle

    DTIC Science & Technology

    1975-05-01

    otion, cushion dynamics, control and machinery dynamics and water wave effects are mwdeled. DD IJ එ 1473 EOITION OF I NOV 6 IS OBSOLETE U...cushion pressure model, the calculations are based on scanty experimental and analytical evidence that should not be taken for more than what it is...updates are readily incorporated. Many of the forces acting on the vehicle are curve fits to experimental4data obtained by Bell Aerospace and used in their

  1. Discrete Mathematical Approaches to Graph-Based Traffic Analysis

    SciTech Connect

    Joslyn, Cliff A.; Cowley, Wendy E.; Hogan, Emilie A.; Olsen, Bryan K.

    2014-04-01

    Modern cyber defense and anlaytics requires general, formal models of cyber systems. Multi-scale network models are prime candidates for such formalisms, using discrete mathematical methods based in hierarchically-structured directed multigraphs which also include rich sets of labels. An exemplar of an application of such an approach is traffic analysis, that is, observing and analyzing connections between clients, servers, hosts, and actors within IP networks, over time, to identify characteristic or suspicious patterns. Towards that end, NetFlow (or more generically, IPFLOW) data are available from routers and servers which summarize coherent groups of IP packets flowing through the network. In this paper, we consider traffic analysis of Netflow using both basic graph statistics and two new mathematical measures involving labeled degree distributions and time interval overlap measures. We do all of this over the VAST test data set of 96M synthetic Netflow graph edges, against which we can identify characteristic patterns of simulated ground-truth network attacks.

  2. 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…

  3. Academic Libraries as a Context for Teaching Mathematical Modeling

    ERIC Educational Resources Information Center

    Warwick, Jon

    2008-01-01

    The teaching of mathematical modeling to undergraduate students requires that students are given ample opportunity to develop their own models and experience first-hand the process of model building. Finding an appropriate context within which modeling can be undertaken is not a simple task as it needs to be readily understandable and seen as…

  4. The force-frequency relationship: insights from mathematical modeling

    PubMed Central

    Negroni, Jorge A.; Chen-Izu, Ye; Bers, Donald M.

    2013-01-01

    The force-frequency relationship has intrigued researchers since its discovery by Bowditch in 1871. Many attempts have been made to construct mathematical descriptions of this phenomenon, beginning with the simple formulation of Koch-Wesser and Blinks in 1963 to the most sophisticated ones of today. This property of cardiac muscle is amplified by β-adrenergic stimulation, and, in a coordinated way, the neurohumoral state alters both frequency (acting on the sinoatrial node) as well as force generation (modifying ventricular myocytes). This synchronized tuning is needed to meet new metabolic demands. Cardiac modelers have already linked mechanical and electrical activity in their formulations and showed how those activities feedback on each other. However, now it is necessary to include neurological control to have a complete description of heart performance, especially when changes in frequency are involved. Study of arrhythmias (or antiarrhythmic drugs) based on mathematical models should incorporate this effect to make useful predictions or point out potential pharmaceutical targets. PMID:23471245

  5. Mathematical modeling of drug release from lipid dosage forms.

    PubMed

    Siepmann, J; Siepmann, F

    2011-10-10

    Lipid dosage forms provide an interesting potential for controlled drug delivery. In contrast to frequently used poly(ester) based devices for parenteral administration, they do not lead to acidification upon degradation and potential drug inactivation, especially in the case of protein drugs and other acid-labile active agents. The aim of this article is to give an overview on the current state of the art of mathematical modeling of drug release from this type of advanced drug delivery systems. Empirical and semi-empirical models are described as well as mechanistic theories, considering diffusional mass transport, potentially limited drug solubility and the leaching of other, water-soluble excipients into the surrounding bulk fluid. Various practical examples are given, including lipid microparticles, beads and implants, which can successfully be used to control the release of an incorporated drug during periods ranging from a few hours up to several years. The great benefit of mechanistic mathematical theories is the possibility to quantitatively predict the effects of different formulation parameters and device dimensions on the resulting drug release kinetics. Thus, in silico simulations can significantly speed up product optimization. This is particularly useful if long release periods (e.g., several months) are targeted, since experimental trial-and-error studies are highly time-consuming in these cases. In the future it would be highly desirable to combine mechanistic theories with the quantitative description of the drug fate in vivo, ideally including the pharmacodynamic efficacy of the treatments.

  6. Mathematical modelling methodologies in predictive food microbiology: a SWOT analysis.

    PubMed

    Ferrer, Jordi; Prats, Clara; López, Daniel; Vives-Rego, Josep

    2009-08-31

    Predictive microbiology is the area of food microbiology that attempts to forecast the quantitative evolution of microbial populations over time. This is achieved to a great extent through models that include the mechanisms governing population dynamics. Traditionally, the models used in predictive microbiology are whole-system continuous models that describe population dynamics by means of equations applied to extensive or averaged variables of the whole system. Many existing models can be classified by specific criteria. We can distinguish between survival and growth models by seeing whether they tackle mortality or cell duplication. We can distinguish between empirical (phenomenological) models, which mathematically describe specific behaviour, and theoretical (mechanistic) models with a biological basis, which search for the underlying mechanisms driving already observed phenomena. We can also distinguish between primary, secondary and tertiary models, by examining their treatment of the effects of external factors and constraints on the microbial community. Recently, the use of spatially explicit Individual-based Models (IbMs) has spread through predictive microbiology, due to the current technological capacity of performing measurements on single individual cells and thanks to the consolidation of computational modelling. Spatially explicit IbMs are bottom-up approaches to microbial communities that build bridges between the description of micro-organisms at the cell level and macroscopic observations at the population level. They provide greater insight into the mesoscale phenomena that link unicellular and population levels. Every model is built in response to a particular question and with different aims. Even so, in this research we conducted a SWOT (Strength, Weaknesses, Opportunities and Threats) analysis of the different approaches (population continuous modelling and Individual-based Modelling), which we hope will be helpful for current and future

  7. Full-Range Mathematical Modeling of Turboshaft Engine in Aerospace

    NASA Astrophysics Data System (ADS)

    Sheng, Hanlin; Zhang, Tianhong; Jiang, Wei

    2016-12-01

    In this paper, an approximate computation method of low-speed component characteristics in aeroengine is used and full-range component characteristics is obtained by combining experimental data above idle. Moreover, based on components matching method and variable specific heat method, a full-range static and dynamic mathematical model of turboshaft engine is built, including start-up state. And the numerical simulation result of the engine whole working process is also showed in this paper. The comparison result between the simulation result and the experimental data shows that, the full-range model built by the computation method of low-speed component characteristics is of a certain accuracy, which can meet the needs of a turboshaft engine semi-physical simulation.

  8. A mathematical model for the iron/chromium redox battery

    NASA Technical Reports Server (NTRS)

    Fedkiw, P. S.; Watts, R. W.

    1984-01-01

    A mathematical model has been developed to describe the isothermal operation of a single anode-separator-cathode unit cell in a redox-flow battery and has been applied to the NASA iron/chromium system. The model, based on porous electrode theory, incorporates redox kinetics, mass transfer, and ohmic effects as well as the parasitic hydrogen reaction which occurs in the chromium electrode. A numerical parameter study was carried out to predict cell performance to aid in the rational design, scale-up, and operation of the flow battery. The calculations demonstrate: (1) an optimum electrode thickness and electrolyte flow rate exist; (2) the amount of hydrogen evolved and, hence, cycle faradaic efficiency, can be affected by cell geometry, flow rate, and charging procedure; (3) countercurrent flow results in enhanced cell performance over cocurrent flow; and (4) elevated temperature operation enhances cell performance.

  9. Mathematical modelling of flow distribution in the human cardiovascular system

    NASA Technical Reports Server (NTRS)

    Sud, V. K.; Srinivasan, R. S.; Charles, J. B.; Bungo, M. W.

    1992-01-01

    The paper presents a detailed model of the entire human cardiovascular system which aims to study the changes in flow distribution caused by external stimuli, changes in internal parameters, or other factors. The arterial-venous network is represented by 325 interconnected elastic segments. The mathematical description of each segment is based on equations of hydrodynamics and those of stress/strain relationships in elastic materials. Appropriate input functions provide for the pumping of blood by the heart through the system. The analysis employs the finite-element technique which can accommodate any prescribed boundary conditions. Values of model parameters are from available data on physical and rheological properties of blood and blood vessels. As a representative example, simulation results on changes in flow distribution with changes in the elastic properties of blood vessels are discussed. They indicate that the errors in the calculated overall flow rates are not significant even in the extreme case of arteries and veins behaving as rigid tubes.

  10. Innovative mathematical modeling in environmental remediation

    SciTech Connect

    Yeh, Gour T.; Gwo, Jin Ping; Siegel, Malcolm D.; Li, Ming-Hsu; Fang, Yilin; Zhang, Fan; Luo, Wensui; Yabusaki, Steven B.

    2013-05-01

    There are two different ways to model reactive transport: ad hoc and innovative reaction-based approaches. The former, such as the Kd simplification of adsorption, has been widely employed by practitioners, while the latter has been mainly used in scientific communities for elucidating mechanisms of biogeochemical transport processes. It is believed that innovative mechanistic-based models could serve as protocols for environmental remediation as well. This paper reviews the development of a mechanistically coupled fluid flow, thermal transport, hydrologic transport, and reactive biogeochemical model and example-applications to environmental remediation problems. Theoretical bases are sufficiently described. Four example problems previously carried out are used to demonstrate how numerical experimentation can be used to evaluate the feasibility of different remediation approaches. The first one involved the application of a 56-species uranium tailing problem to the Melton Branch Subwatershed at Oak Ridge National Laboratory (ORNL) using the parallel version of the model. Simulations were made to demonstrate the potential mobilization of uranium and other chelating agents in the proposed waste disposal site. The second problem simulated laboratory-scale system to investigate the role of natural attenuation in potential off-site migration of uranium from uranium mill tailings after restoration. It showed inadequacy of using a single Kd even for a homogeneous medium. The third example simulated laboratory experiments involving extremely high concentrations of uranium, technetium, aluminum, nitrate, and toxic metals (e.g.,Ni, Cr, Co).The fourth example modeled microbially-mediated immobilization of uranium in an unconfined aquifer using acetate amendment in a field-scale experiment. The purposes of these modeling studies were to simulate various mechanisms of mobilization and immobilization of radioactive wastes and to illustrate how to apply reactive transport models

  11. Membrane transport of several ions during peritoneal dialysis: mathematical modeling.

    PubMed

    Galach, Magda; Waniewski, Jacek

    2012-09-01

    Peritoneal dialysis utilizes a complex mass exchange device created by natural permselective membranes of the visceral and abdominal muscle tissues. In mathematical modeling of solute transport during peritoneal dialysis, each solute is typically considered as a neutral, independent particle. However, such mathematical models cannot predict transport parameters for small ions. Therefore, the impact of the electrostatic interactions between ions on the estimated transport parameters needs to be investigated. In this study, transport of sodium, chloride, and a third ion through a permselective membrane with characteristics of the peritoneal transport barrier was described using two models: a model with the Nernst-Planck (NP) equations for a set of interacting ions and a model with combined diffusive and convective transport of each ion separately (DC). Transport parameters for the NP model were calculated using the pore theory, while the parameters for the DC model were estimated by fitting the model to the predictions from the NP model. Solute concentration profiles in the membrane obtained by computer simulations based on these two models were similar, whereas the transport parameters (diffusive mass transport parameters and sieving coefficients) were generally different. The presence of the third ion could substantially modify the values of diffusive mass parameter for sodium and chloride ions estimated using the DC model compared with those predicted by NP. The extent of this modification depended on the molecular mass and concentration of the third ion, and the rate of volumetric flow. Closed formulas for the transport parameters of the DC model in terms of the NP model parameters, ion concentration profiles in the membrane, and volumetric flow across the membrane were derived. Their reliable approximations, which include only boundary ion concentrations instead of spatial intramembrane concentration profiles, were formulated. The precision of this approximation

  12. Comprehensive Mathematical Model for Simulating Electroslag Remelting

    NASA Astrophysics Data System (ADS)

    Dong, Yan-Wu; Jiang, Zhou-Hua; Fan, Jin-Xi; Cao, Yu-Long; Hou, Dong; Cao, Hai-Bo

    2016-04-01

    Droplet formation and departure from an electrode tip affect the temperature distribution in liquid slag and a molten steel pool, as well as the removal of nonmetallic inclusions in the electroslag remelting process. In this article, magneto-hydrodynamics modules coupled with a volume of fluid (VOF) model (as described in VOF model theory) for tracking phase distribution have been employed to develop the electrode fusion model and to investigate formation and departure of a droplet from the electrode tip. Subsequently, the remelting rate and molten steel pool have been achieved based on the electrode fusion model. Results indicate that a droplet can increase the flow rate of liquid slag, especially the region of droplet fall through the slag pool; yet it has little impact on the flow distribution. Asymmetric flow can take place in a slag pool due to the action of the droplet. The depth of the molten steel pool increases in the presence of droplets, but the width of the mushy zone decreases. In addition, the shape of the electrode tip is not constant but changes with its fusion. The remelting rate is calculated instead of being imposed in this work. The development of the model supports further understanding of the process and the ability to set the appropriate operating parameters, especially for expensive and easy segregation materials.

  13. Mathematical modelling for the new millenium: medicine by numbers.

    PubMed

    Smye, Stephen W; Clayton, Richard H

    2002-11-01

    Physicists, engineers and mathematicians are accustomed to the combination of elegance, rigour and utility that characterise mathematical models. They are familiar with the need to dip into their mathematical toolbox to select the technique of choice. However, medicine and biology have not been characterised, in general, by a mathematical formalism. The relative paucity of mathematical models in biology and medicine reflects in part the difficulty in making accurate and appropriate experimental measurements in the field. Signal noise, the lack of appropriate sensors, and uncertainty as to what constitutes the significant measurements are largely to blame for this. The purpose of this paper is to characterise a 'good' model, encourage the development and application of such models to new areas, and outline future developments in the field. It is proposed that a good model will be accurate, predictive, economical, unique and elegant. These principles will be illustrated with reference to four models: radiosensitisation of tumours, modelling solute clearance in haemodialysis, the myogenic response in reactive hyperaemia and cardiac electrical activity. It is suggested that, in the immediate future, the mathematical model will become a useful adjunct to laboratory experiment (and possibly clinical trial), and the provision of 'in silico' models will become routine.

  14. Mathematical models for nonparametric inferences from line transect data

    USGS Publications Warehouse

    Burnham, K.P.; Anderson, D.R.

    1976-01-01

    A general mathematical theory of line transects is develoepd which supplies a framework for nonparametric density estimation based on either right angle or sighting distances. The probability of observing a point given its right angle distance (y) from the line is generalized to an arbitrary function g(y). Given only that g(O) = 1, it is shown there are nonparametric approaches to density estimation using the observed right angle distances. The model is then generalized to include sighting distances (r). Let f(y/r) be the conditional distribution of right angle distance given sighting distance. It is shown that nonparametric estimation based only on sighting distances requires we know the transformation of r given by f(O/r).

  15. A mathematical model of pH, based on the total stoichiometric concentration of acids, bases and ampholytes dissolved in water.

    PubMed

    Mioni, Roberto; Mioni, Giuseppe

    2015-10-01

    In chemistry and in acid-base physiology, the Henderson-Hasselbalch equation plays a pivotal role in studying the behaviour of the buffer solutions. However, it seems that the general function to calculate the valence of acids, bases and ampholytes, N = f(pH), at any pH, has only been provided by Kildeberg. This equation can be applied to strong acids and bases, pluriprotic weak acids, bases and ampholytes, with an arbitrary number of acid strength constants, pKA, including water. By differentiating this function with respect to pH, we obtain the general equation for the buffer value. In addition, by integrating the titration curve, TA, proposed by Kildeberg, and calculating its Legendre transform, we obtain the Gibbs free energy of pH (or pOH)-dependent titratable acid. Starting from the law of electroneutrality and applying suitable simplifications, it is possible to calculate the pH of the buffer solutions by numerical methods, available in software packages such as Excel. The concept of buffer capacity has also been clarified by Urbansky, but, at variance with our approach, not in an organic manner. In fact, for each set of monobasic, dibasic, tribasic acids, etc., various equations are presented which independently fit each individual acid-base category. Consequently, with the increase in acid groups (pKA), the equations become more and more difficult, both in practice and in theory. Some examples are proposed to highlight the boundary that exists between acid-base physiology and the thermodynamic concepts of energy, chemical potential, amount of substance and acid resistance.

  16. 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…

  17. Evaluation of limb load asymmetry using two new mathematical models.

    PubMed

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

    2014-09-25

    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.

  18. [Mathematical approach to modeling of the treatment of suppurative processes].

    PubMed

    Men'shikov, D D; Enileev, R Kh

    1989-03-01

    Consideration of an inflammation focus as an "open system" provided analogy between microbiological processes in inflamed wounds and in systems of continuous cultivation of microorganisms. Mathematical modeling of such systems is widely used. Some of the methods for the mathematical modeling were applied to chemoprophylaxis and chemotherapy of postoperative wounds. In modeling continuous cultivation of microorganisms it is usually necessary to determine optimal conditions for the maximum yield of their biomass. In modeling of wound treatment the aim was to determine the process parameters providing the minimum biomass. The described simple models showed that there could be certain optimal flow rate of the washing fluid in the aspiration-washing procedure for wound treatment at which the drug was not completely washed out while the growth rate of the microbial population was minimal. Such mathematical models were shown valuable in optimizing the use of bactericidal and bacteriostatic antibiotics.

  19. Mathematical Modelling of the Infusion Test

    NASA Astrophysics Data System (ADS)

    Cieslicki, Krzysztof

    2007-01-01

    The objective of this paper was to improve the well established in clinical practice Marmarou model for intracranial volume-pressure compensation by adding the pulsatile components. It was demonstrated that complicated pulsation and growth in intracranial pressure during infusion test could be successfully modeled by the relatively simple analytical expression derived in this paper. The CSF dynamics were tested in 25 patients with clinical symptoms of hydrocephalus. Basing on the frequency spectrum of the patient's baseline pressure and identified parameters of CSF dynamic, for each patient an "ideal" infusion test curve free from artefacts and slow waves was simulated. The degree of correlation between simulated and real curves obtained from clinical observations gave insight into the adequacy of assumptions of Marmarou model. The proposed method of infusion tests analysis designates more exactly the value of the reference pressure, which is usually treated as a secondary and of uncertain significance. The properly identified value of the reference pressure decides on the degree of pulsation amplitude growth during IT, as well as on the value of elastance coefficient. The artificially generated tests with various pulsation components were also applied to examine the correctness of the used algorithm of identification of the original Marmarou model parameters.

  20. 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.

  1. Teachers' Temporary Support and Worked-Out Examples as Elements of Scaffolding in Mathematical Modeling

    ERIC Educational Resources Information Center

    Tropper, Natalie; Leiss, Dominik; Hänze, Martin

    2015-01-01

    Empirical findings show that students have manifold difficulties when dealing with mathematical modeling problems. Accordingly, approaches for supporting students in modeling-based learning environments have to be investigated. In the research presented here, we adopted a scaffolding perspective on teaching modeling with the aim of both providing…

  2. Experimental research on mathematical modelling and unconventional control of clinker kiln in cement plants

    NASA Astrophysics Data System (ADS)

    Rusu-Anghel, S.

    2017-01-01

    Analytical modeling of the flow of manufacturing process of the cement is difficult because of their complexity and has not resulted in sufficiently precise mathematical models. In this paper, based on a statistical model of the process and using the knowledge of human experts, was designed a fuzzy system for automatic control of clinkering process.

  3. Mathematical Modelling and the Learning Trajectory: Tools to Support the Teaching of Linear Algebra

    ERIC Educational Resources Information Center

    Cárcamo Bahamonde, Andrea Dorila; Fortuny Aymemí, Josep Maria; Gómez i Urgellés, Joan Vicenç

    2017-01-01

    In this article we present a didactic proposal for teaching linear algebra based on two compatible theoretical models: emergent models and mathematical modelling. This proposal begins with a problematic situation related to the creation and use of secure passwords, which leads students toward the construction of the concepts of spanning set and…

  4. Mathematical modeling of MILD combustion of pulverized coal

    SciTech Connect

    Schaffel, N.; Mancini, M.; Weber, R.; Szlek, A.

    2009-09-15

    MILD (flameless) combustion is a new rapidly developing technology. The IFRF trials have demonstrated high potential of this technology also for N-containing fuels. In this work the IFRF experiments are analyzed using the CFD-based mathematical model. Both the Chemical Percolation Devolatilization (CPD) model and the char combustion intrinsic reactivity model have been adapted to Guasare coal combusted. The flow-field as well as the temperature and the oxygen fields have been accurately predicted by the CFD-based model. The predicted temperature and gas composition fields have been uniform demonstrating that slow combustion occurs in the entire furnace volume. The CFD-based predictions have highlighted the NO{sub x} reduction potential of MILD combustion through the following mechanism. Before the coal devolatilization proceeds, the coal jet entrains a substantial amount of flue gas so that its oxygen content is typically not higher than 3-5%. The volatiles are given off in a highly sub-stoichiometric environment and their N-containing species are preferentially converted to molecular nitrogen rather than to NO. Furthermore, there exists a strong NO-reburning mechanism within the fuel jet and in the air jet downstream of the position where these two jets merge. In other words, less NO is formed from combustion of volatiles and stronger NO-reburning mechanisms exist in the MILD combustion if compared to conventional coal combustion technology. (author)

  5. Development of Learning Devices through Problem Based Learning Model Based on the Context of Aceh Cultural to Improve Mathematical Communication Skills and Social Skills of SMPN 1 Muara Batu Students

    ERIC Educational Resources Information Center

    Aufa, Mahrani; Saragih, Sahat; Minarni, Ani

    2016-01-01

    The purposes of this study were:1) Developed problem-based on learning tools in the cultural context of Aceh (PBM-BKBA) who meet the criteria are valid, practical and effective; 2) Described the improvement of communication capabilities mathematics and social skills of students using the PBM-BKBA developed; and 3) Described the process of student…

  6. Mathematical modeling and application of removal functions during deterministic ion beam figuring of optical surfaces. Part 1: Mathematical modeling.

    PubMed

    Liao, Wenlin; Dai, Yifan; Xie, Xuhui; Zhou, Lin

    2014-07-01

    Ion beam figuring (IBF) is established for the final precision figuring of high-performance optical components, where the figuring accuracy is guaranteed by the stability of the removal function and the solution accuracy of the dwell time. In this deterministic method, the figuring process can be represented by a two-dimensional (2D) convolution operation of a constant removal function and the dwell time. However, we have found that the current 2D convolution operation cannot factually describe the IBF process of curved surfaces, which neglects the influences of the projection distortion and the workpiece geometry on the removal function. Consequently, the current 2D convolution algorithm would influence the solution accuracy for the dwell time and reduce the convergence of the figuring process. In this part, based on the material removal characteristics of IBF, a mathematical model of the removal function is developed theoretically and verified experimentally. Research results show that the removal function during IBF of a curved surface is actually a dynamic function in the 2D convolution algorithm. The mathematical modeling of the dynamic removal function provides theoretical foundations for our proposed new algorithm in the next part, and final verification experiments indicate that this algorithm can effectively improve the accuracy of the dwell time solution for the IBF of curved surfaces.

  7. 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?"

  8. Mathematical modeling of physiological systems: An essential tool for discovery

    PubMed Central

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

    2014-01-01

    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?” PMID:25064823

  9. A Novel Mathematical Model for Determining Faculty Workload

    PubMed Central

    Millette-Snodgrass, Carol; Atef, Eman

    2016-01-01

    Objective. To develop a mathematical model for determining faculty workload at a college of pharmacy with a team-based learning curriculum. Methods. Using faculty provided data, our model calculated activity and weighted means in teaching, scholarship and service. Subsequently, these data were used to develop departmental and institutional workload models. Results. For the pharmaceutical and biomedical sciences department, percent faculty activity mean values were greatest for service followed by teaching and scholarship. These values in the clinical sciences department were greatest for teaching followed by service and scholarship. Overall, the institutional workload model had the largest maximum faculty activity value for teaching, followed by service and then scholarship. Conclusions. A novel faculty workload model proved to be effective in optimizing faculty workload within a college of pharmacy. Since the workload analysis, the faculty service commitment has been substantially changed, by reducing the number of committees at our institution. This type of workload analysis may particularly benefit colleges of pharmacy that employ a team based learning curriculum, with a large time commitment to teaching. PMID:28090101

  10. Mathematical Models for Manpower and Personnel Planning, Research Report.

    ERIC Educational Resources Information Center

    Charnes, A.; And Others

    Current work in mathematical modeling for manpower planning and personnel administration is reviewed with special reference to selected cases in the U.S. Navy. This included: (1) assignment models and their dynamic extensions, (2) Stochastic models with special reference to Markoff Processes, including the Office of Civilian Manpower and…

  11. 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.

  12. Modal test and analysis: Multiple tests concept for improved validation of large space structure mathematical models

    NASA Technical Reports Server (NTRS)

    Wada, B. K.; Kuo, C-P.; Glaser, R. J.

    1986-01-01

    For the structural dynamic analysis of large space structures, the technology in structural synthesis and the development of structural analysis software have increased the capability to predict the dynamic characteristics of the structural system. The various subsystems which comprise the system are represented by various displacement functions; the displacement functions are then combined to represent the total structure. Experience has indicated that even when subsystem mathematical models are verified by test, the mathematical representations of the total system are often in error because the mathematical model of the structural elements which are significant when loads are applied at the interconnection points are not adequately verified by test. A multiple test concept, based upon the Multiple Boundary Condition Test (MBCT), is presented which will increase the accuracy of the system mathematical model by improving the subsystem test and test/analysis correlation procedure.

  13. 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.

  14. A mathematical model for evolution and SETI.

    PubMed

    Maccone, Claudio

    2011-12-01

    Darwinian evolution theory may be regarded as a part of SETI theory in that the factor f(l) in the Drake equation represents the fraction of planets suitable for life on which life actually arose. In this paper we firstly provide a statistical generalization of the Drake equation where the factor f(l) is shown to follow the lognormal probability distribution. This lognormal distribution is a consequence of the Central Limit Theorem (CLT) of Statistics, stating that the product of a number of independent random variables whose probability densities are unknown and independent of each other approached the lognormal distribution when the number of factors increased to infinity. In addition we show that the exponential growth of the number of species typical of Darwinian Evolution may be regarded as the geometric locus of the peaks of a one-parameter family of lognormal distributions (b-lognormals) constrained between the time axis and the exponential growth curve. Finally, since each b-lognormal distribution in the family may in turn be regarded as the product of a large number (actually "an infinity") of independent lognormal probability distributions, the mathematical way is paved to further cast Darwinian Evolution into a mathematical theory in agreement with both its typical exponential growth in the number of living species and the Statistical Drake Equation.

  15. Mathematical modeling of HIV-like particle assembly in vitro.

    PubMed

    Liu, Yuewu; Zou, Xiufen

    2017-02-22

    In vitro, the recombinant HIV-1 Gag protein can generate spherical particles with a diameter of 25-30 nm in a fully defined system. It has approximately 80 building blocks, and its intermediates for assembly are abundant in geometry. Accordingly, there are a large number of nonlinear equations in the classical model. Therefore, it is difficult to compute values of geometry parameters for intermediates and make the mathematical analysis using the model. In this work, we develop a new model of HIV-like particle assembly in vitro by using six-fold symmetry of HIV-like particle assembly to decrease the number of geometry parameters. This method will greatly reduce computational costs and facilitate the application of the model. Then, we prove the existence and uniqueness of the positive equilibrium solution for this model with 79 nonlinear equations. Based on this model, we derive the interesting result that concentrations of all intermediates at equilibrium are independent of three important parameters, including two microscopic on-rate constants and the size of nucleating structure. Before equilibrium, these three parameters influence the concentration variation rates of all intermediates. We also analyze the relationship between the initial concentration of building blocks and concentrations of all intermediates. Furthermore, the bounds of concentrations of free building blocks and HIV-like particles are estimated. These results will be helpful to guide HIV-like particle assembly experiments and improve our understanding of the assembly dynamics of HIV-like particles in vitro.

  16. The Concept of Model. What is Remarkable in Mathematical Models

    NASA Astrophysics Data System (ADS)

    Bezruchko, Boris P.; Smirnov, Dmitry A.

    Dictionaries tell us that the word "model" originates from the Latin word "modulus" which means "measure, template, norm". This term was used in proceedings on civil engineering several centuries BC. Currently, it relates to an enormously wide range of material objects, symbolic structures and ideal images ranging from models of clothes, small copies of ships and aeroplanes, different pictures and plots to mathematical equations and computational algorithms. Starting to define the concept of "model", we would like to remind about the difficulty to give strict definitions of basic concepts. Thus, when university professors define "oscillations" and "waves" in their lectures on this subject, it is common for many of them to repeat the joke of Russian academician L.I. Mandel'shtam, who illustrated the problem with the example of the term "heap": How many objects, and of which kind, deserve such a name? As well, he compared strict definitions at the beginning of studying any topic to "swaddling oneself with barbed wire". Among classical examples of impossibility to give exhaustive formulations, one can mention the terms "bald spot", "forest", etc. Therefore, we will not consider variety of existing definitions of "model" and "modelling" in detail. Any of them relates to the purposes and subjective preferences of an author and is valid in a certain sense. However, it is restricted since it ignores some objects or properties that deserve attention from other points of view.

  17. Mathematical modeling of fluid-electrolyte alterations during weightlessness

    NASA Technical Reports Server (NTRS)

    Leonard, J. I.

    1984-01-01

    Fluid electrolyte metabolism and renal endocrine control as it pertains to adaptation to weightlessness were studied. The mathematical models that have been particularly useful are discussed. However, the focus of the report is on the physiological meaning of the computer studies. A discussion of the major ground based analogs of weightlessness are included; for example, head down tilt, water immersion, and bed rest, and a comparison of findings. Several important zero g phenomena are described, including acute fluid volume regulation, blood volume regulation, circulatory changes, longer term fluid electrolyte adaptations, hormonal regulation, and body composition changes. Hypotheses are offered to explain the major findings in each area and these are integrated into a larger hypothesis of space flight adaptation. A conceptual foundation for fluid electrolyte metabolism, blood volume regulation, and cardiovascular regulation is reported.

  18. Predictions of cardiovascular responses during STS reentry using mathematical models

    NASA Technical Reports Server (NTRS)

    Leonard, J. I.; Srinivasan, R.

    1985-01-01

    The physiological adaptation to weightless exposure includes cardiovascular deconditioning arising in part from a loss of total circulating blood volume and resulting in a reduction of orthostatic tolerance. The crew of the Shuttle orbiter are less tolerant to acceleration forces in the head-to-foot direction during the reentry phase of the flight at a time they must function at a high level of performance. The factors that contribute to orthostatic intolerance during and following reentry and to predict the likelihood of impaired crew performance are evaluated. A computer simulation approach employing a mathematical model of the cardiovascular system is employed. It is shown that depending on the severity of blood volume loss, the reentry acceleration stress may be detrimental to physiologic function and may place the physiologic status of the crew near the borderline of some type of impairment. They are in agreement with conclusions from early ground-based experiments and from observations of early Shuttle flights.

  19. A mathematical model for mesenchymal and chemosensitive cell dynamics.

    PubMed

    Häcker, Anita

    2012-01-01

    The structure of an underlying tissue network has a strong impact on cell dynamics. If, in addition, cells alter the network by mechanical and chemical interactions, their movement is called mesenchymal. Important examples for mesenchymal movement include fibroblasts in wound healing and metastatic tumour cells. This paper is focused on the latter. Based on the anisotropic biphasic theory of Barocas and Tranquillo, which models a fibre network and interstitial solution as two-component fluid, a mathematical model for the interactions of cells with a fibre network is developed. A new description for fibre reorientation is given and orientation-dependent proteolysis is added to the model. With respect to cell dynamics, the equation, based on anisotropic diffusion, is extended by haptotaxis and chemotaxis. The chemoattractants are the solute network fragments, emerging from proteolysis, and the epidermal growth factor which may guide the cells to a blood vessel. Moreover the cell migration is impeded at either high or low network density. This new model enables us to study chemotactic cell migration in a complex fibre network and the consequential network deformation. Numerical simulations for the cell migration and network deformation are carried out in two space dimensions. Simulations of cell migration in underlying tissue networks visualise the impact of the network structure on cell dynamics. In a scenario for fibre reorientation between cell clusters good qualitative agreement with experimental results is achieved. The invasion speeds of cells in an aligned and an isotropic fibre network are compared.

  20. Mathematical model of layered metallurgical furnaces and units

    NASA Astrophysics Data System (ADS)

    Shvydkiy, V. S.; Spirin, N. A.; Lavrov, V. V.

    2016-09-01

    The basic approaches to mathematical modeling of the layered steel furnaces and units are considered. It is noted that the particular importance have the knowledge about the mechanisms and physical nature of processes of the charge column movement and the gas flow in the moving layer, as well as regularities of development of heat- and mass-transfer in them. The statement and mathematical description of the problem solution targeting the potential gas flow in the layered unit of an arbitrary profile are presented. On the basis of the proposed mathematical model the software implementation of information-modeling system of BF gas dynamics is carried out. The results of the computer modeling of BF non-isothermal gas dynamics with regard to the cohesion zone, gas dynamics of the combustion zone and calculation of hot-blast stoves are provided

  1. Mathematical and Computational Modeling of Polymer Exchange Membrane Fuel Cells

    NASA Astrophysics Data System (ADS)

    Ulusoy, Sehribani

    In this thesis a comprehensive review of fuel cell modeling has been given and based on the review, a general mathematical fuel cell model has been developed in order to understand the physical phenomena governing the fuel cell behavior and in order to contribute to the efforts investigating the optimum performance at different operating conditions as well as with different physical parameters. The steady state, isothermal model presented here accounts for the combined effects of mass and species transfer, momentum conservation, electrical current distribution through the gas channels, the electrodes and the membrane, and the electrochemical kinetics of the reactions in the anode and cathode catalyst layers. One of the important features of the model is that it proposes a simpler modified pseudo-homogeneous/agglomerate catalyst layer model which takes the advantage of the simplicity of pseudo-homogenous modeling while taking into account the effects of the agglomerates in the catalyst layer by using experimental geometric parameters published. The computation of the general mathematical model can be accomplished in 3D, 2D and 1D with the proper assumptions. Mainly, there are two computational domains considered in this thesis. The first modeling domain is a 2D Membrane Electrode Assembly (MEA) model including the modified agglomerate/pseudo-homogeneous catalyst layer modeling with consistent treatment of water transport in the MEA while the second domain presents a 3D model with different flow filed designs: straight, stepped and tapered. COMSOL Multiphysics along with Batteries and Fuel Cell Module have been used for 2D & 3D model computations while ANSYS FLUENT PEMFC Module has been used for only 3D two-phase computation. Both models have been validated with experimental data. With 2D MEA model, the effects of temperature and water content of the membrane as well as the equivalent weight of the membrane on the performance have been addressed. 3D COMSOL simulation

  2. On a Mathematical Model of Brain Activities

    SciTech Connect

    Fichtner, K.-H.; Fichtner, L.; Freudenberg, W.; Ohya, M.

    2007-12-03

    The procedure of recognition can be described as follows: There is a set of complex signals stored in the memory. Choosing one of these signals may be interpreted as generating a hypothesis concerning an 'expexted view of the world'. Then the brain compares a signal arising from our senses with the signal chosen from the memory leading to a change of the state of both signals. Furthermore, measurements of that procedure like EEG or MEG are based on the fact that recognition of signals causes a certain loss of excited neurons, i.e. the neurons change their state from 'excited' to 'nonexcited'. For that reason a statistical model of the recognition process should reflect both--the change of the signals and the loss of excited neurons. A first attempt to explain the process of recognition in terms of quantum statistics was given. In the present note it is not possible to present this approach in detail. In lieu we will sketch roughly a few of the basic ideas and structures of the proposed model of the recognition process (Section). Further, we introduce the basic spaces and justify the choice of spaces used in this approach. A more elaborate presentation including all proofs will be given in a series of some forthcoming papers. In this series also the procedures of creation of signals from the memory, amplification, accumulation and transformation of input signals, and measurements like EEG and MEG will be treated in detail.

  3. Nonlinear mathematical model for a biaxial MOEMS scanning mirror

    NASA Astrophysics Data System (ADS)

    Ma, Yunfei; Davis, Wyatt O.; Ellis, Matt; Brown, Dean

    2010-02-01

    In this paper, a nonlinear mathematic model for Microvision's MOEMS scanning mirror is presented. The pixel placement accuracy requirement for scanned laser spot displays translates into a roughly 80dB signal to noise ratio, noise being a departure from the ideal trajectory. To provide a tool for understanding subtle nonidealities, a detailed nonlinear mathematical model is derived, using coefficients derived from physics, finite element analysis, and experiments. Twelve degrees of freedom parameterize the motion of a gimbal plate and a suspended micromirror; a thirteenth is the device temperature. Illustrations of the application of the model to capture subtleties about the device dynamics and transfer functions are presented.

  4. Mathematical Modeling of Primary Wood Processing

    NASA Astrophysics Data System (ADS)

    Szyszka, Barbara; Rozmiarek, Klaudyna

    2008-09-01

    This work presents a way of optimizing wood logs' conversion into semi-products. Calculating algorithms have been used in order to choose the cutting patterns and the number of logs needed to realize an order, including task specification. What makes it possible for the author's computer program TARPAK1 to be written is the visualization of the results, the generation pattern of wood logs' conversion for given entry parameters and prediction of sawn timber manufacture. This program has been created with the intention of being introduced to small and medium sawmills in Poland. The Project has been financed from government resources and written by workers of the Institute of Mathematics (Poznan University of Technology) and the Department of Mechanical Wood Technology (Poznan University of Life Sciences).

  5. A mathematical model of population dynamics for Batesian mimicry system.

    PubMed

    Seno, Hiromi; Kohno, Takahiro

    2012-01-01

    We analyse a mathematical model of the population dynamics among a mimic, a corresponding model, and their common predator populations. Predator changes its search-and-attack probability by forming and losing its search image. It cannot distinguish the mimic from the model. Once a predator eats a model individual, it comes to omit both the model and the mimic species from its diet menu. If a predator eats a mimic individual, it comes to increase the search-and-attack probability for both model and mimic. The predator may lose the repulsive/attractive search image with a probability per day. By analysing our model, we can derive the mathematical condition for the persistence of model and mimic populations, and then get the result that the condition for the persistence of model population does not depend on the mimic population size, while the condition for the persistence of mimic population does depend the predator's memory of search image.

  6. A mathematical model of calcium dynamics in HSY cells

    PubMed Central

    Han, Jung Min; Tanimura, Akihiko; Kirk, Vivien; Sneyd, James

    2017-01-01

    Saliva is an essential part of activities such as speaking, masticating and swallowing. Enzymes in salivary fluid protect teeth and gums from infectious diseases, and also initiate the digestion process. Intracellular calcium (Ca2+) plays a critical role in saliva secretion and regulation. Experimental measurements of Ca2+ and inositol trisphosphate (IP3) concentrations in HSY cells, a human salivary duct cell line, show that when the cells are stimulated with adenosine triphosphate (ATP) or carbachol (CCh), they exhibit coupled oscillations with Ca2+ spike peaks preceding IP3 spike peaks. Based on these data, we construct a mathematical model of coupled Ca2+ and IP3 oscillations in HSY cells and perform model simulations of three different experimental settings to forecast Ca2+ responses. The model predicts that when Ca2+ influx from the extracellular space is removed, oscillations gradually slow down until they stop. The model simulation of applying a pulse of IP3 predicts that photolysis of caged IP3 causes a transient increase in the frequency of the Ca2+ oscillations. Lastly, when Ca2+-dependent activation of PLC is inhibited, we see an increase in the oscillation frequency and a decrease in the amplitude. These model predictions are confirmed by experimental data. We conclude that, although concentrations of Ca2+ and IP3 oscillate, Ca2+ oscillations in HSY cells are the result of modulation of the IP3 receptor by intracellular Ca2+, and that the period is modulated by the accompanying IP3 oscillations. PMID:28199326

  7. Mathematical modelling of the degradation behaviour of biodegradable metals.

    PubMed

    Bajger, P; Ashbourn, J M A; Manhas, V; Guyot, Y; Lietaert, K; Geris, L

    2017-02-01

    A mathematical model for the biodegradation of magnesium is developed in this study to inspect the corrosion behaviour of biodegradable implants. The aim of this study was to provide a suitable framework for the assessment of the corrosion rate of magnesium which includes the process of formation/dissolution of the protective film. The model is intended to aid the design of implants with suitable geometries. The level-set method is used to follow the changing geometry of the implants during the corrosion process. A system of partial differential equations is formulated based on the physical and chemical processes that occur at the implant-medium boundary in order to simulate the effect of the formation of a protective film on the degradation rate. The experimental data from the literature on the corrosion of a high-purity magnesium sample immersed in simulated body fluid is used to calibrate the model. The model is then used to predict the degradation behaviour of a porous orthopaedic implant. The model successfully reproduces the precipitation of the corrosion products on the magnesium surface and the effect on the degradation rate. It can be used to simulate the implant degradation and the formation of the corrosion products on the surface of biodegradable magnesium implants with complex geometries.

  8. 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.

  9. The Mathematics Workshop Model: An Interview with Uri Treisman.

    ERIC Educational Resources Information Center

    Garland, May; Treisman, Uri

    1993-01-01

    Uri Treisman describes the development of his model to help minority students succeed and progress in mathematics, emphasizing group work and integrated instruction and student services. Explains his influences, core ideas informing the workshop model, structural impediments to success in the curriculum, existing programs, and other related…

  10. 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.

  11. Mathematical and computational modeling simulation of solar drying Systems

    Technology Transfer Automated Retrieval System (TEKTRAN)

    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...

  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. 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.

  14. Diagnostic Models for Procedural Bugs in Basic Mathematics Skills.

    ERIC Educational Resources Information Center

    Brown, John Seely; Burton, Richard R.

    A new diagnostic modeling system for automatically synthesizing a deep structure model of a student's misconceptions or bugs in his/her basic mathematics skills provides a mechanism for explaining why a student is making a mistake as opposed to simply identifying the mistake. This report consists of four sections. The first provides examples of…

  15. 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.

  16. Mathematical modeling of steel fiber concrete under dynamic impact

    NASA Astrophysics Data System (ADS)

    Belov, N. N.; Yugov, N. T.; Kopanitsa, D. G.; Kopanitsa, G. D.; Yugov, A. A.; Shashkov, V. V.

    2015-01-01

    This paper introduces a continuum mechanics mathematical model that describes the processes of deformation and destruction of steel-fiber-concrete under a shock wave impact. A computer modeling method was applied to study the processes of shock wave impact of a steel cylindrical rod and concrete and steel fiber concrete plates. The impact speeds were within 100-500 m/s.

  17. Computer Support for Learning Mathematics: A Learning Environment Based on Recreational Learning Objects

    ERIC Educational Resources Information Center

    Lopez-Morteo, Gabriel; Lopez, Gilberto

    2007-01-01

    In this paper, we introduce an electronic collaborative learning environment based on Interactive Instructors of Recreational Mathematics (IIRM), establishing an alternative approach for motivating students towards mathematics. The IIRM are educational software components, specializing in mathematical concepts, presented through recreational…

  18. 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.

  19. Mathematical modeling of moving contact lines in heat transfer applications

    NASA Astrophysics Data System (ADS)

    Ajaev, Vladimir S.; Klentzman, J.; Sodtke, C.; Stephan, P.

    2007-10-01

    We provide an overview of research on the mathematical modeling of apparent contact lines in non-isothermal systems conducted over the past several decades and report a number of recent developments in the field. The latter involve developing mathematical models of evaporating liquid droplets that account not only for liquid flow and evaporation, but also for unsteady heat conduction in the substrate. The droplet is placed on a flat heated solid substrate and is assumed to be in contact with a saturated vapor. Furthermore, we discuss a careful comparison between mathematical models and experimental work that involves simultaneous measurement of shapes of evaporating droplets and temperature profiles in the solid substrate. The latter is accomplished using thermochromic liquid crystals. Applications to new research areas, such as studies of the effect of evaporation on fingering instabilities in gravity-driven liquid films, are also discussed.

  20. Teaching Mathematical Modelling: Demonstrating Enrichment and Elaboration

    ERIC Educational Resources Information Center

    Warwick, Jon

    2015-01-01

    This paper uses a series of models to illustrate one of the fundamental processes of model building--that of enrichment and elaboration. The paper describes how a problem context is given which allows a series of models to be developed from a simple initial model using a queuing theory framework. The process encourages students to think about the…

  1. Mathematical Modelling in the International Baccalaureate, Teacher Beliefs and Technology Usage.

    ERIC Educational Resources Information Center

    Brown, R.

    2002-01-01

    Investigates the introduction of mathematical modeling into the mathematics assessment program of the International Baccalaureate Diploma. Considers structured and open modeling in the pre-university mathematics program. Discusses influences of the use of hand-held technology on mathematical modeling and teacher and assessor beliefs about modeling…

  2. Light driven microactuators: Design, fabrication, and mathematical modeling

    NASA Astrophysics Data System (ADS)

    Han, Li-Hsin

    This dissertation is concerned with design, fabrication, and mathematical modeling of three different microactuators driven by light. Compared to electricity, electromagnetic wave is a wireless source of power. A distant light source can be delivered, absorbed, and converted to generate a driving force for a microactuator. The study of light-driven microsystems, still at its early stage, is already expanding the horizon for the research of microsystems. The microactuators of this dissertation include micro-cantilevers driven by pulsed laser, photo-deformable microshells coated with gold nanospheres, and a nano-particles coated micro-turbine driven by visible light. Experimental investigation and theoretical analysis of these microactuators showed interesting results. These microactuators were functioned based on cross-linked, multiple physics phenomenon, such as photo-heating, thermal expansion, photo-chemistry effect, plasomonics enhancement, and thermal convection in rarefied gas. These multiple physics effects dominate the function of a mechanical system, when the system size becomes small. The modeling results of the microactuators suggest that, to simulate a microscale mechanical system accurately, one has to take account the minimum dimension of the system and to consider the validity of a theoretical model. Examples of the building of different microstructures were shown to demonstrate the capacity of a digital-micromirror-device (DMD) based apparatus for three-dimensional, heterogeneous fabrication of polymeric microstructures.

  3. Mathematical model of galactose regulation and metabolic consumption in yeast.

    PubMed

    Mitre, Tina M; Mackey, Michael C; Khadra, Anmar

    2016-10-21

    The galactose network has been extensively studied at the unicellular level to broaden our understanding of the regulatory mechanisms governing galactose metabolism in multicellular organisms. Although the key molecular players involved in the metabolic and regulatory processes of this system have been known for decades, their interactions and chemical kinetics remain incompletely understood. Mathematical models can provide an alternative method to study the dynamics of this network from a quantitative and a qualitative perspective. Here, we employ this approach to unravel the main properties of the galactose network, including equilibrium binary and temporal responses, as a way to decipher its adaptation to actively-changing inputs. We combine its two main components: the genetic branch, which allows for bistable responses, and a metabolic branch, encompassing the relevant metabolic processes that can be repressed by glucose. We use both computational tools to estimate model parameters based on published experimental data, as well as bifurcation analysis to decipher the properties of the system in various parameter regimes. Our model analysis reveals that the interplay between the inducer (galactose) and the repressor (glucose) creates a bistable regime which dictates the temporal responses of the system. Based on the same bifurcation techniques, we explain why the system is robust to genetic mutations and molecular instabilities. These findings may provide experimentalists with a theoretical framework with which they can determine how the galactose network functions under various conditions.

  4. The Mathematical Structure of Error Correction Models.

    DTIC Science & Technology

    1985-05-01

    The error correction model for a vector valued time series has been proposed and applied in the economic literature with the papers by Sargan (1964...the notion of cointegratedness of a vector process and showed the relation between cointegration and error correction models. This paper defines a...general error correction model, that encompasses the usual error correction model as well as the integral correction model by allowing a finite number of

  5. Inquiry Based-Computational Experiment, Acquisition of Threshold Concepts and Argumentation in Science and Mathematics Education

    ERIC Educational Resources Information Center

    Psycharis, Sarantos

    2016-01-01

    Computational experiment approach considers models as the fundamental instructional units of Inquiry Based Science and Mathematics Education (IBSE) and STEM Education, where the model take the place of the "classical" experimental set-up and simulation replaces the experiment. Argumentation in IBSE and STEM education is related to the…

  6. Teaching for Meaningful Understanding: A School-Based Science and Mathematics Teacher Development Project.

    ERIC Educational Resources Information Center

    Wang, Sea-Yu Patrick; Guo, Chorng-Jee; Chiang, Wu-Hsiung; Cheng, Shiu-Shan

    The purpose of this ongoing project is to establish a model for school-based teacher development for secondary science and mathematics teachers in Taiwan. The model uses an action research approach with emphasis on constructivist perspectives of teaching and learning and the idea that teachers are to be taken as researchers and reflective…

  7. Web-Based Progress Monitoring in First Grade Mathematics

    ERIC Educational Resources Information Center

    Salaschek, Martin; Souvignier, Elmar

    2013-01-01

    The purpose of our research was to examine a web-based tool for mathematics progress monitoring in first grade. The newly developed assessment tool uses several robust indicators and curriculum-based measures forming three competences (Basic Precursors, Advanced Precursors, and Computation) to determine comprehensive early numeracy skills in…

  8. On the injectivity of the generalized Radon transform arising in a model of mathematical economics

    NASA Astrophysics Data System (ADS)

    Agaltsov, A. D.

    2016-11-01

    In the present article we consider the uniqueness problem for the generalized Radon transform arising in a mathematical model of production. We prove uniqueness theorems for this transform and for the profit function in the corresponding model of production. Our approach is based on the multidimensional Wiener’s approximation theorems.

  9. A full body mathematical model of an oil palm harvester

    NASA Astrophysics Data System (ADS)

    Tumit, NP; Rambely, A. S.; BMT, Shamsul; Shahriman A., B.; Ng Y., G.; Deros, B. M.; Zailina, H.; Goh Y., M.; Arumugam, Manohar; Ismail I., A.; Abdul Hafiz A., R.

    2015-09-01

    The main purpose of this article is to develop a mathematical model of human body during harvesting via Kane's method. This paper is an extension model of previous biomechanical model representing a harvester movement during harvesting a Fresh Fruit Bunch (FFB) from a palm oil tree. The ten segment model consists of foot, leg, trunk, the head and the arms segment. Finally, the inverse dynamic equations are represented in a matrix form.

  10. Mathematically modelling proportions of Japanese populations by industry

    NASA Astrophysics Data System (ADS)

    Hirata, Yoshito

    2016-10-01

    I propose a mathematical model for temporal changes of proportions for industrial sectors. I prove that the model keeps the proportions for the primary, the secondary, and the tertiary sectors between 0 and 100% and preserves their total as 100%. The model fits the Japanese historical data between 1950 and 2005 for the population proportions by industry very well. The model also predicts that the proportion for the secondary industry becomes negligible and becomes less than 1% at least around 2080.

  11. Mathematical model in controlling dengue transmission with sterile mosquito strategies

    NASA Astrophysics Data System (ADS)

    Aldila, D.; Nuraini, N.; Soewono, E.

    2015-09-01

    In this article, we propose a mathematical model for controlling dengue disease transmission with sterile mosquito techniques (SIT). Sterile male introduced from lab in to habitat to compete with wild male mosquito for mating with female mosquito. Our aim is to displace gradually the natural mosquito from the habitat. Mathematical model analysis for steady states and the basic reproductive ratio are performed analytically. Numerical simulation are shown in some different scenarios. We find that SIT intervention is potential to controlling dengue spread among humans population

  12. A mathematical look at a physical power prediction model

    SciTech Connect

    Landberg, L.

    1997-12-31

    This paper takes a mathematical look at a physical model used to predict the power produced from wind farms. The reason is to see whether simple mathematical expressions can replace the original equations, and to give guidelines as to where the simplifications can be made and where they can not. This paper shows that there is a linear dependence between the geostrophic wind and the wind at the surface, but also that great care must be taken in the selection of the models since physical dependencies play a very important role, e.g. through the dependence of the turning of the wind on the wind speed.

  13. Mathematical modelling in the computer-aided process planning

    NASA Astrophysics Data System (ADS)

    Mitin, S.; Bochkarev, P.

    2016-04-01

    This paper presents new approaches to organization of manufacturing preparation and mathematical models related to development of the computer-aided multi product process planning (CAMPP) system. CAMPP system has some peculiarities compared to the existing computer-aided process planning (CAPP) systems: fully formalized developing of the machining operations; a capacity to create and to formalize the interrelationships among design, process planning and process implementation; procedures for consideration of the real manufacturing conditions. The paper describes the structure of the CAMPP system and shows the mathematical models and methods to formalize the design procedures.

  14. Using mathematical models to understand the AIDS spidemic. [None

    SciTech Connect

    Hyman, J.M.; Stanley, E.A.

    1987-01-01

    The most urgent public health problem today is to devise effective strategies to minimize the destruction caused by the AIDS epidemic. This complex problem will involve medical advances and new public health and education initiatives. Mathematical models based on the underlying transmission mechanisms of the AIDS virus can help the medical/scientific community understand and anticipate its spread in different populations and evaluate the potential effectiveness of different approaches for bringing the epidemic under control. Before we can use models to predict the future, we must carefully test them against the past spread of the infection and for sensitivity to parameter changes. The long and extremely variable incubation period and the low probability of transmitting the AIDS virus in a single contact imply that population structure and variations in infectivity both play an important role in its spread. This structure occurs because of differences between people in numbers of sexual partners and the use of intravenous drugs and because of the way in which people mix among age, ethnic, and social groups. We use a simplified approach to investigate the effects of variation in incubation periods and infectivity specific to the AIDS virus and we compare a model of random partner choices with a model in which partners both come from similar behavior groups. 60 refs., 15 figs.

  15. Mathematical Modelling in Engineering: An Alternative Way to Teach Linear Algebra

    ERIC Educational Resources Information Center

    Domínguez-García, S.; García-Planas, M. I.; Taberna, J.

    2016-01-01

    Technological advances require that basic science courses for engineering, including Linear Algebra, emphasize the development of mathematical strengths associated with modelling and interpretation of results, which are not limited only to calculus abilities. Based on this consideration, we have proposed a project-based learning, giving a dynamic…

  16. A mathematical space mapping model for ballistic carbon nanotube field-effect transistors

    NASA Astrophysics Data System (ADS)

    Emamifar, Farnousha; Yousefi, Reza

    2016-11-01

    In this study, a mathematical model is presented based on mathematical space mapping for ballistic carbon nanotube field-effect transistors. This model is generalized from another model that was based on the concept of neural space mapping to calculate the three parameters of a coarse model. These parameters were the threshold voltage, the Early voltage, and assumed constant k of a modified "level 1" MOSFET model in simulation program with integrated circuit emphasis (SPICE). In this work, three analytical relations are introduced to replace the neural networks of the main model. The comparisons between the proposed model and a well-known reference model, named FETToy, show that the proposed model had reasonable accuracy in terms of different biases and physical parameters.

  17. Integrating Mathematical Modeling for Undergraduate Pre-Service Science Education Learning and Instruction in Middle School Classrooms

    ERIC Educational Resources Information Center

    Carrejo, David; Robertson, William H.

    2011-01-01

    Computer-based mathematical modeling in physics is a process of constructing models of concepts and the relationships between them in the scientific characteristics of work. In this manner, computer-based modeling integrates the interactions of natural phenomenon through the use of models, which provide structure for theories and a base for…

  18. An Examination of the Effects of Collaborative Scientific Visualization via Model-Based Reasoning on Science, Technology, Engineering, and Mathematics (STEM) Learning within an Immersive 3D World

    ERIC Educational Resources Information Center

    Soleimani, Ali

    2013-01-01

    Immersive 3D worlds can be designed to effectively engage students in peer-to-peer collaborative learning activities, supported by scientific visualization, to help with understanding complex concepts associated with learning science, technology, engineering, and mathematics (STEM). Previous research studies have shown STEM learning benefits…

  19. Mathematical modeling of the effects of glutathione on arsenic methylation

    PubMed Central

    2014-01-01

    Background Arsenic is a major environmental toxin that is detoxified in the liver by biochemical mechanisms that are still under study. In the traditional metabolic pathway, arsenic undergoes two methylation reactions, each followed by a reduction, after which it is exported and released in the urine. Recent experiments show that glutathione plays an important role in arsenic detoxification and an alternative biochemical pathway has been proposed in which arsenic is first conjugated by glutathione after which the conjugates are methylated. In addition, in rats arsenic-glutathione conjugates can be exported into the plasma and removed by the liver in the bile. Methods We have developed a mathematical model for arsenic biochemistry that includes three mechanisms by which glutathione affects arsenic methylation: glutathione increases the speed of the reduction steps; glutathione affects the activity of arsenic methyltranferase; glutathione sequesters inorganic arsenic and its methylated downstream products. The model is based as much as possible on the known biochemistry of arsenic methylation derived from cellular and experimental studies. Results We show that the model predicts and helps explain recent experimental data on the effects of glutathione on arsenic methylation. We explain why the experimental data imply that monomethyl arsonic acid inhibits the second methylation step. The model predicts time course data from recent experimental studies. We explain why increasing glutathione when it is low increases arsenic methylation and that at very high concentrations increasing glutathione decreases methylation. We explain why the possible temporal variation of the glutathione concentration affects the interpretation of experimental studies that last hours. Conclusions The mathematical model aids in the interpretation of data from recent experimental studies and shows that the Challenger pathway of arsenic methylation, supplemented by the glutathione effects

  20. GAMMA-400 Space Gamma-telescope Mathematical Model with Engineering Elements Included

    NASA Astrophysics Data System (ADS)

    Chasovikov, E. N.; Arkhangelskaja, I. V.; Perfil`ev, A. A.; Arkhangelskiy, A. I.; Galper, A. M.; Topchiev, N. P.; Gusakov, Yu. V.; Kheymits, M. D.; Yurkin, Yu. T.

    Mathematical model creation is a necessary stage in scientific apparatus development. The mathematical model of gamma-ray telescope GAMMA-400 is used to emulate transport of various elementary particles through the apparatus. The new iteration of the model is based on precise technical drawings and includes all the elements of the real gamma-telescope. It is created in Geant4 environment. This model allows calculation of energy deposition not only in detectors, but in any part of the apparatus, including construction elements. Moreover, it supports creation of virtual sensitive volumes, allowing determination of the number and properties of particles passing through an arbitrary part of the construction. Software for automated creation of Geant4 model based on technical drawings in STEP 3D Model format was developed. This software is capable of making models of other apparatus based particularly on scintillation and strip detectors.