NASA Technical Reports Server (NTRS)
Wade, Rose C.
1989-01-01
The NASA Controlled Ecological Life Support System (CELSS) Program is involved in developing a biogenerative life support system that will supply food, air, and water to space crews on long-duration missions. An important part of this effort is in development of the knowledge and technological capability of producing and processing foods to provide optimal diets for space crews. This involves such interrelated factors as determination of the diet, based on knowledge of nutrient needs of humans and adjustments in those needs that may be required as a result of the conditions of long-duration space flight; determination of the optimal mixture of crops required to provide nutrients at levels that are sufficient but not excessive or toxic; and consideration of the critical issues of spacecraft space and power limitations, which impose a phytomass minimization requirement. The complex interactions among these factors are examined with the goal of supplying a diet that will satisfy human needs while minimizing the total phytomass requirement. The approach taken was to collect plant nutritional composition and phytomass production data, identify human nutritional needs and estimate the adjustments to the nutrient requirements likely to result from space flight, and then to generate mathematical models from these data.
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…
Curriculum integration in nutrition and mathematics.
James, D C; Adams, T L
1998-01-01
Today's school-aged children face a multitude of health issues that affect their well-being and academic performance. Partnerships have developed between health and education agencies to help American children succeed at math and science and to prepare them to make healthful, lifelong decisions. Curriculum integration provides a framework for children to apply knowledge from several disciplines and to use this knowledge to solve real-life problems at work and at play. Goals for instruction focus on the needs not only of the individual but also of society. Nutrition science and mathematics form a natural partnership. Nutrition science incorporates numerous mathematical concepts and procedures such as sorting, classifying, statistics, probability, estimation, and rates and proportion. In preparation for participation in a global and technological society that will require citizens to be quantitative thinkers, educators must endeavor to assist all children in becoming adults who are mathematically literate and competent. PMID:9553899
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
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…
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…
Mathematical Modelling: A New Approach to Teaching Applied Mathematics.
ERIC Educational Resources Information Center
Burghes, D. N.; Borrie, M. S.
1979-01-01
Describes the advantages of mathematical modeling approach in teaching applied mathematics and gives many suggestions for suitable material which illustrates the links between real problems and mathematics. (GA)
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…
Mathematical models of hysteresis
1998-08-01
The 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 (not the entire input variations) 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. The origin of such tools can be traced back to the landmark paper of Preisach. Their 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. During the past four years, the study has been by and large centered around the following topics: (1) further development of Scalar and vector Preisach-type models of hysteresis; (2) experimental testing of Preisach-type models of hysteresis; (3) development of new models for viscosity (aftereffect) in hysteretic systems; (4) development of mathematical models for superconducting hysteresis in the case of gradual resistive transitions; (5) software implementation of Preisach-type models of hysteresis; and (6) development of new ideas which have emerged in the course of the research work. The author briefly describes the main scientific results obtained in the areas outlined above.
[Mathematical models of hysteresis
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.
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…
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…
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…
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…
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…
Students' Mathematical Modeling of Motion
ERIC Educational Resources Information Center
Marshall, Jill A.; Carrejo, David J.
2008-01-01
We present results of an investigation of university students' development of mathematical models of motion in a physical science course for preservice teachers and graduate students in science and mathematics education. Although some students were familiar with the standard concepts of position, velocity, and acceleration from physics classes,…
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.
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…
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.
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…
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…
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.
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…
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.
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…
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…
Mathematical modelling in nuclear medicine
Kuikka, Jyrki T.; Bassingthwaighte, James B.; Henrich, Michael M.; Feinendegen, Ludwig E.
2010-01-01
Modern imaging techniques can provide sequences of images giving signals proportional to the concentrations of tracers (by emission tomography), of X-ray-absorbing contrast materials (fast CT or perhaps NMR contrast), or of native chemical substances (NMR) in tissue regions at identifiable locations in 3D space. Methods for the analysis of the concentration-time curves with mathematical models describing the physiological processes and the appropriate anatomy are now available to give a quantitative portrayal of both structure and function: such is the approach to metabolic or functional imaging. One formulates a model first by defining what it should represent: this is the hypothesis. When translated into a self-consistent set of differential equations, the model becomes a mathematical model, a quantitative version of the hypothesis. This is what one would like to test against data. However, the next step is to reduce the mathematical model to a computable form; anatomically and physiologically realistic models account of the spatial gradients in concentrations within blood-tissue exchange units, while compartmental models simplify the equations by using the average concentrations. The former are known as distributed models and the latter as lumped compartmental or mixing chamber models. Since both are derived from the same ideas, the parameters are usually the same; their differences are in their ability to represent the hypothesis correctly, quantitatively, and sometimes in their computability. In this essay we review the philosophical and practical aspects of such modelling analysis for translating image sequences into physiological terms. PMID:1936044
Mathematical modeling of piezoresistive elements
NASA Astrophysics Data System (ADS)
Geremias, M.; Moreira, R. C.; Rasia, L. A.; Moi, A.
2015-10-01
This article presents the longitudinal piezoresistive coefficients for thin film amorphous semiconductor type a-C:H. Experimental data and mathematical models have been used in computer simulations. The results show that a reduction of the longitudinal piezoresistive coefficient occurs due to the increased concentration of impurities in the films analyzed.
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…
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…
Modeling-Enabled Systems Nutritional Immunology
Verma, Meghna; Hontecillas, Raquel; Abedi, Vida; Leber, Andrew; Tubau-Juni, Nuria; Philipson, Casandra; Carbo, Adria; Bassaganya-Riera, Josep
2016-01-01
This review highlights the fundamental role of nutrition in the maintenance of health, the immune response, and disease prevention. Emerging global mechanistic insights in the field of nutritional immunology cannot be gained through reductionist methods alone or by analyzing a single nutrient at a time. We propose to investigate nutritional immunology as a massively interacting system of interconnected multistage and multiscale networks that encompass hidden mechanisms by which nutrition, microbiome, metabolism, genetic predisposition, and the immune system interact to delineate health and disease. The review sets an unconventional path to apply complex science methodologies to nutritional immunology research, discovery, and development through “use cases” centered around the impact of nutrition on the gut microbiome and immune responses. Our systems nutritional immunology analyses, which include modeling and informatics methodologies in combination with pre-clinical and clinical studies, have the potential to discover emerging systems-wide properties at the interface of the immune system, nutrition, microbiome, and metabolism. PMID:26909350
Modeling-Enabled Systems Nutritional Immunology.
Verma, Meghna; Hontecillas, Raquel; Abedi, Vida; Leber, Andrew; Tubau-Juni, Nuria; Philipson, Casandra; Carbo, Adria; Bassaganya-Riera, Josep
2016-01-01
This review highlights the fundamental role of nutrition in the maintenance of health, the immune response, and disease prevention. Emerging global mechanistic insights in the field of nutritional immunology cannot be gained through reductionist methods alone or by analyzing a single nutrient at a time. We propose to investigate nutritional immunology as a massively interacting system of interconnected multistage and multiscale networks that encompass hidden mechanisms by which nutrition, microbiome, metabolism, genetic predisposition, and the immune system interact to delineate health and disease. The review sets an unconventional path to apply complex science methodologies to nutritional immunology research, discovery, and development through "use cases" centered around the impact of nutrition on the gut microbiome and immune responses. Our systems nutritional immunology analyses, which include modeling and informatics methodologies in combination with pre-clinical and clinical studies, have the potential to discover emerging systems-wide properties at the interface of the immune system, nutrition, microbiome, and metabolism. PMID:26909350
Mathematical Models for Somite Formation
Baker, Ruth E.; Schnell, Santiago; Maini, Philip K.
2009-01-01
Somitogenesis is the process of division of the anterior–posterior vertebrate embryonic axis into similar morphological units known as somites. These segments generate the prepattern which guides formation of the vertebrae, ribs and other associated features of the body trunk. In this work, we review and discuss a series of mathematical models which account for different stages of somite formation. We begin by presenting current experimental information and mechanisms explaining somite formation, highlighting features which will be included in the models. For each model we outline the mathematical basis, show results of numerical simulations, discuss their successes and shortcomings and avenues for future exploration. We conclude with a brief discussion of the state of modeling in the field and current challenges which need to be overcome in order to further our understanding in this area. PMID:18023728
Physical and mathematical cochlear models
NASA Astrophysics Data System (ADS)
Lim, Kian-Meng
2000-10-01
The cochlea is an intricate organ in the inner ear responsible for our hearing. Besides acting as a transducer to convert mechanical sound vibrations to electrical neural signals, the cochlea also amplifies and separates the sound signal into its spectral components for further processing in the brain. It operates over a broad-band of frequency and a huge dynamic range of input while maintaining a low power consumption. The present research takes the approach of building cochlear models to study and understand the underlying mechanics involved in the functioning of the cochlea. Both physical and mathematical models of the cochlea are constructed. The physical model is a first attempt to build a life- sized replica of the human cochlea using advanced micro- machining techniques. The model takes a modular design, with a removable silicon-wafer based partition membrane encapsulated in a plastic fluid chamber. Preliminary measurements in the model are obtained and they compare roughly with simulation results. Parametric studies on the design parameters of the model leads to an improved design of the model. The studies also revealed that the width and orthotropy of the basilar membrane in the cochlea have significant effects on the sharply tuned responses observed in the biological cochlea. The mathematical model is a physiologically based model that includes three-dimensional viscous fluid flow and a tapered partition with variable properties along its length. A hybrid asymptotic and numerical method provides a uniformly valid and efficient solution to the short and long wave regions in the model. Both linear and non- linear activity are included in the model to simulate the active cochlea. The mathematical model has successfully reproduced many features of the response in the biological cochlea, as observed in experiment measurements performed on animals. These features include sharply tuned frequency responses, significant amplification with inclusion of activity
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…
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…
Mathematical modeling of genome replication
NASA Astrophysics Data System (ADS)
Retkute, Renata; Nieduszynski, Conrad A.; de Moura, Alessandro
2012-09-01
Eukaryotic DNA replication is initiated from multiple sites on the chromosome, but little is known about the global and local regulation of replication. We present a mathematical model for the spatial dynamics of DNA replication, which offers insight into the kinetics of replication in different types of organisms. Most biological experiments involve average quantities over large cell populations (typically >107 cells) and therefore can mask the cell-to-cell variability present in the system. Although the model is formulated in terms of a population of cells, using mathematical analysis we show that one can obtain signatures of stochasticity in individual cells from averaged quantities. This work generalizes the result by Retkute [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.107.068103 107, 068103 (2011)] to a broader set of parameter regimes.
Mathematical models of diabetes progression.
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. PMID:18780774
Mathematical modelling in MHD technology
Scheindlin, A.E.; Medin, S.A. )
1990-01-01
The technological scheme and the general parameters of the commercial scale pilot MHD power plant are described. The characteristics of the flow train components and the electrical equipment are discussed. The basic ideas of the mathematical modelling of the processes and the devices operation in MHD systems are considered. The application of different description levels in computer simulation is analyzed and the examples of typical solutions are presented.
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…
[Mathematical model of mental time].
Glasko, A V; Sadykhova, L G
2014-01-01
On the basis of Ernst Mach's ideas and developed before the mathematical theory of mental processes, mathematical definition of duration of an interval of mental time, all over again for perception (experience) of separate event, and then--generally, i.e. for perception (experience) of sequence of events is entered. Its dependence on duration of an appropriating interval of physical time is investigated. Communication of mental time with perception of time (for two cases: "greater" and "small" intervals) is investigated. Comparison of theoretical formulas with results of experimental measurements is spent. Is defined process time which can be used, in particular, as a measure of work. The effect of the inverse of the psychological time, described in works of the Mach is analyzed and modelled. PMID:25723024
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.
Mathematical models in medicine: Diseases and epidemics
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.
Technology Transfer Automated Retrieval System (TEKTRAN)
This paper describes the derivation and application of a new functional mathematical index that was used to evaluate the nutritional, safety, and processing quality aspects of potatoes. The index introduces the concept of an “optimal potato”, using appropriate distance and N-dimensional parameter sp...
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.
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).
Mathematical modeling of cold cap
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.
A Generative Model of Mathematics Learning
ERIC Educational Resources Information Center
Wittrock, M. C.
1974-01-01
The learning of mathematics is presented as a cognitive process rather than as a behavioristic one. A generative model of mathematics learning is described. Learning with understanding can occur with discovery or reception treatments. Relevant empirical research is discussed and implications for teaching mathematics as a generative process are…
On Fences, Forms and Mathematical Modeling
ERIC Educational Resources Information Center
Lege, Jerry
2009-01-01
The white picket fence is an integral component of the iconic American townscape. But, for mathematics students, it can be a mathematical challenge. Picket fences in a variety of styles serve as excellent sources to model constant, step, absolute value, and sinusoidal functions. "Principles and Standards for School Mathematics" (NCTM 2000)…
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.
Mathematical model for alopecia areata.
Dobreva, Atanaska; Paus, Ralf; Cogan, N G
2015-09-01
Alopecia areata (AA) is an autoimmune disease, and its clinical phenotype is characterized by the formation of distinct hairless patterns on the scalp or other parts of the body. In most cases hair falls out in round patches. A well-established hypothesis for the pathogenesis of AA states that collapse of hair follicle immune privilege is one of the essential elements in disease development. To investigate the dynamics of alopecia areata, we develop a mathematical model that incorporates immune system components and hair follicle immune privilege agents whose involvement in AA has been confirmed in clinical studies and experimentally. We perform parameter sensitivity analysis in order to determine which inputs have the greatest effect on outcome variables. Our findings suggest that, among all processes reflected in the model, immune privilege guardians and the pro-inflammatory cytokine interferon-γ govern disease dynamics. These results agree with the immune privilege collapse hypothesis for the development of AA. PMID:26047853
Mathematical model for bone mineralization
Komarova, Svetlana V.; Safranek, Lee; Gopalakrishnan, Jay; Ou, Miao-jung Yvonne; McKee, Marc D.; Murshed, Monzur; Rauch, Frank; Zuhr, Erica
2015-01-01
Defective bone mineralization has serious clinical manifestations, including deformities and fractures, but the regulation of this extracellular process is not fully understood. We have developed a mathematical model consisting of ordinary differential equations that describe collagen maturation, production and degradation of inhibitors, and mineral nucleation and growth. We examined the roles of individual processes in generating normal and abnormal mineralization patterns characterized using two outcome measures: mineralization lag time and degree of mineralization. Model parameters describing the formation of hydroxyapatite mineral on the nucleating centers most potently affected the degree of mineralization, while the parameters describing inhibitor homeostasis most effectively changed the mineralization lag time. Of interest, a parameter describing the rate of matrix maturation emerged as being capable of counter-intuitively increasing both the mineralization lag time and the degree of mineralization. We validated the accuracy of model predictions using known diseases of bone mineralization such as osteogenesis imperfecta and X-linked hypophosphatemia. The model successfully describes the highly nonlinear mineralization dynamics, which includes an initial lag phase when osteoid is present but no mineralization is evident, then fast primary mineralization, followed by secondary mineralization characterized by a continuous slow increase in bone mineral content. The developed model can potentially predict the function for a mutated protein based on the histology of pathologic bone samples from mineralization disorders of unknown etiology. PMID:26347868
Analysis of Physiological Systems via Mathematical Models.
ERIC Educational Resources Information Center
Hazelrig, Jane B.
1983-01-01
Discusses steps to be executed when studying physiological systems with theoretical mathematical models. Steps considered include: (1) definition of goals; (2) model formulation; (3) mathematical description; (4) qualitative evaluation; (5) parameter estimation; (6) model fitting; (7) evaluation; and (8) design of new experiments based on the…
Mathematical models for exotic wakes
NASA Astrophysics Data System (ADS)
Basu, Saikat; Stremler, Mark
2014-11-01
Vortex wakes are a common occurrence in the environment around us; the most famous example being the von Kármán vortex street with two vortices being shed by the bluff body in each cycle. However, frequently there can be many other more exotic wake configurations with different vortex arrangements, based on the flow parameters and the bluff body dimensions and/or its oscillation characteristics. Some examples include wakes with periodic shedding of three vortices (`P+S' mode) and four vortices (symmetric `2P' mode, staggered `2P' mode, `2C' mode). We present mathematical models for such wakes assuming two-dimensional potential flows with embedded point vortices. The spatial alignment of the vortices is inspired by the experimentally observed wakes. The idealized system follows a Hamiltonian formalism. Model-based analysis reveals a rich dynamics pertaining to the relative vortex motion in the mid-wake region. Downstream evolution of the vortices, as predicted from the model results, also show good correspondence with wake-shedding experiments performed on flowing soap films.
Mathematical Modeling of Cellular Metabolism.
Berndt, Nikolaus; Holzhütter, Hermann-Georg
2016-01-01
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. PMID:27557541
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…
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…
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…
Mathematical Modelling and New Theories of Learning.
ERIC Educational Resources Information Center
Boaler, Jo
2001-01-01
Demonstrates the importance of expanding notions of learning beyond knowledge to the practices in mathematics classrooms. Considers a three-year study of students who learned through mathematical modeling. Shows that a modeling approach encouraged the development of a range of important practices in addition to knowledge that were useful in real…
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…
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.
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.
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…
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)
The mathematics of cancer: integrating quantitative models.
Altrock, Philipp M; Liu, Lin L; Michor, Franziska
2015-12-01
Mathematical modelling approaches have become increasingly abundant in cancer research. The complexity of cancer is well suited to quantitative approaches as it provides challenges and opportunities for new developments. In turn, mathematical modelling contributes to cancer research by helping to elucidate mechanisms and by providing quantitative predictions that can be validated. The recent expansion of quantitative models addresses many questions regarding tumour initiation, progression and metastases as well as intra-tumour heterogeneity, treatment responses and resistance. Mathematical models can complement experimental and clinical studies, but also challenge current paradigms, redefine our understanding of mechanisms driving tumorigenesis and shape future research in cancer biology. PMID:26597528
Technical note: Bayesian calibration of dynamic ruminant nutrition models.
Reed, K F; Arhonditsis, G B; France, J; Kebreab, E
2016-08-01
Mechanistic models of ruminant digestion and metabolism have advanced our understanding of the processes underlying ruminant animal physiology. Deterministic modeling practices ignore the inherent variation within and among individual animals and thus have no way to assess how sources of error influence model outputs. We introduce Bayesian calibration of mathematical models to address the need for robust mechanistic modeling tools that can accommodate error analysis by remaining within the bounds of data-based parameter estimation. For the purpose of prediction, the Bayesian approach generates a posterior predictive distribution that represents the current estimate of the value of the response variable, taking into account both the uncertainty about the parameters and model residual variability. Predictions are expressed as probability distributions, thereby conveying significantly more information than point estimates in regard to uncertainty. Our study illustrates some of the technical advantages of Bayesian calibration and discusses the future perspectives in the context of animal nutrition modeling. PMID:27179874
Mathematical Models for Library Systems Analysis.
ERIC Educational Resources Information Center
Leimkuhler, F. F.
1967-01-01
The paper reviews the research on design and operation of research libraries sponsored by the Purdue University Libraries and the Purdue School of Industrial Engineering. The use of mathematical models in library operations research is discussed. Among the mathematical methods discussed are marginal analysis or cost minimization, computer…
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,…
Mathematical modeling of ligaments and tendons.
Woo, S L; Johnson, G A; Smith, B A
1993-11-01
Ligaments and tendons serve a variety of important functions in maintaining the structure of the human body. Although abundant literature exists describing experimental investigations of these tissues, mathematical modeling of ligaments and tendons also contributes significantly to understanding their behavior. This paper presents a survey of developments in mathematical modeling of ligaments and tendons over the past 20 years. Mathematical descriptions of ligaments and tendons are identified as either elastic or viscoelastic, and are discussed in chronological order. Elastic models assume that ligaments and tendons do not display time dependent behavior and thus, they focus on describing the nonlinear aspects of their mechanical response. On the other hand, viscoelastic models incorporate time dependent effects into their mathematical description. In particular, two viscoelastic models are discussed in detail; quasi-linear viscoelasticity (QLV), which has been widely used in the past 20 years, and the recently proposed single integral finite strain (SIFS) model. PMID:8302027
ERIC Educational Resources Information Center
Peretz, Dvora
2005-01-01
This article conceptualises a real-like model of a mathematical model as an inverse model. The inverse model draws on the un-complexity of concrete real life operations in order to help students to add concrete meaning to mathematical algorithms. The inverse model is described in the context of a pedagogical perception, which grants students in…
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…
Mathematical modelling of cucumber (cucumis sativus) drying
NASA Astrophysics Data System (ADS)
Shahari, N.; Hussein, S. M.; Nursabrina, M.; Hibberd, S.
2014-07-01
This paper investigates the applicability of using an experiment based mathematical model (empirical model) and a single phase mathematical model with shrinkage to describe the drying curve of cucumis sativus (cucumber). Drying experiments were conducted using conventional air drying and data obtained from these experiments were fitted to seven empirical models using non-linear least square regression based on the Levenberg Marquardt algorithm. The empirical models were compared according to their root mean square error (RMSE), sum of square error (SSE) and coefficient of determination (R2). A logarithmic model was found to be the best empirical model to describe the drying curve of cucumber. The numerical result of a single phase mathematical model with shrinkage was also compared with experiment data for cucumber drying. A good agreement was obtained between the model predictions and the experimental data.
Mathematical Modeling and the Presidential Election.
ERIC Educational Resources Information Center
Witkowski, Joseph C.
1992-01-01
Looks at the solution to the mathematical-modeling problem asking students to find the smallest percent of the popular vote needed to elect a President. Provides assumptions from which to work the problem. (MDH)
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.
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,…
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.
Baron, V
1990-11-01
This analysis examined references to foods mentioned in elementary school textbooks used in Montreal English schools. A study of 58 language arts and mathematics textbooks used in grades one-six revealed 4,391 references to foods in words and pictures. A large proportion of the references were to sugar-rich foods. Eating with peers was depicted more frequently than eating with family, while a surprising number of children were depicted consuming their food alone in texts used in grades one-three. Results suggest that, because unintended information may influence children's nutritional habits, more attention should be directed at concomitant messages in elementary school textbooks. PMID:2283875
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…
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…
Mathematical biodynamic feedthrough model applied to rotorcraft.
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. PMID:24013832
Mathematical Models of Tuberculosis Reactivation and Relapse
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
Development of Mathematical Models to Estimate Animal Performance and Feed Biological Values
Technology Transfer Automated Retrieval System (TEKTRAN)
Mathematical modeling in nutrition is important because the human mind is able to formulate concepts and hypothesis but lack the ability to track quantitative relationships of complex, nonlinear, and dynamic systems. It provides us with a tool to analyze huge amounts of data and information about nu...
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…
Planning Single-Event Nutrition Education: A New Model
ERIC Educational Resources Information Center
Brown, Lora Beth
2011-01-01
A theoretical model for planning single-event nutrition education contrasts a Practical, Foods, and Positive (PFP) emphasis to an Abstract, Nutrient, and Negative (ANN) focus on nutrition topics. Use of this model makes messages more appealing to consumers and may increase the likelihood that people will apply the nutrition information in their…
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.
Mathematical Modeling of Viral Zoonoses in Wildlife
Allen, L. J. S.; Brown, V. L.; Jonsson, C. B.; Klein, S. L.; Laverty, S. M.; Magwedere, K.; Owen, J. C.; van den Driessche, P.
2011-01-01
Zoonoses are a worldwide public health concern, accounting for approximately 75% of human infectious diseases. In addition, zoonoses adversely affect agricultural production and wildlife. We review some mathematical models developed for the study of viral zoonoses in wildlife and identify areas where further modeling efforts are needed. PMID:22639490
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.
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.
Mathematical modeling relevant to closed artificial ecosystems
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.
Mathematical modeling of molecular diffusion through mucus
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
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…
The (Mathematical) Modeling Process in Biosciences
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
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.
Mathematical model of self-cycling fermentation
Wincure, B.M.; Cooper, D.G.; Rey, A.
1995-04-20
This article presents a mathematical model for biomass, limiting substrate, and dissolved oxygen concentrations during stable operation of self-cycling fermentation (SCF). Laboratory experiments using the bacterium Acinetobacter calcoaceticus RAG-1 and ethanol as the limiting substrate were performed to validate the model. A computer simulation developed from the model successfully matched experimental SCF intracycle trends and end-of-cycle results and, most importantly, settled into an unimposed periodicity characteristic of stable SCF operation.
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.
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…
Mathematical Model Of Nerve/Muscle Interaction
NASA Technical Reports Server (NTRS)
Hannaford, Blake
1990-01-01
Phasic Excitation/Activation (PEA) mathematical model simulates short-term nonlinear dynamics of activation and control of muscle by nerve. Includes electronic and mechanical elements. Is homeomorphic at level of its three major building blocks, which represent motoneuron, dynamics of activation of muscle, and mechanics of muscle.
Mathematical and physical modelling of materials processing
NASA Technical Reports Server (NTRS)
1982-01-01
Mathematical and physical modeling of turbulence phenomena in metals processing, electromagnetically driven flows in materials processing, gas-solid reactions, rapid solidification processes, the electroslag casting process, the role of cathodic depolarizers in the corrosion of aluminum in sea water, and predicting viscoelastic flows are described.
Introduction to mathematical models and methods
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.
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.
Some mathematical tools for a modeller's workbench
NASA Technical Reports Server (NTRS)
Cohen, E.
1984-01-01
The development of a mathematical software tools in workbench environment to model related objects more straightforward is outlined. A computer model from informal drawings and a plastic model of a helicopter is discussed. Lofting was the predominant, characteristic modelling technique. Ships and airplane designs use lofting as a technique because they have defined surfaces, (hulls and fuselages) from vertical station cuts perpendicular to the vertical center plane defining the major axis of reflective symmetry. A turbine blade from a jet engine was modelled in this way. The aerodynamic portion and the root comes from different paradigms. The union of these two parts into a coherent model is shown.
Mathematical challenges in glacier modeling (Invited)
NASA Astrophysics Data System (ADS)
jouvet, G.
2013-12-01
Many of Earth's glaciers are currently shrinking and it is expected that this trend will continue as global warming progresses. To virtually reproduce the evolution of glaciers and finally to predict their future, one needs to couple models of different disciplines and scales. Indeed, the slow motion of ice is described by fluid mechanics equations while the daily snow precipitations and melting are described by hydrological and climatic models. Less visible, applied mathematics are essential to run such a coupling at two different levels: by solving numerically the underlying equations and by seeking parameters using optimisation methods. This talk aims to make visible the role of mathematics in this area. I will first present a short educational film I have made for the "Mathematics of Planet Earth 2013", which is an introduction to the topic. To go further, solving the mechanical model of ice poses several mathematical challenges due to the complexity of the equations and geometries of glaciers. Then, I will describe some strategies to deal with such difficulties and design robust simulation tools. Finally, I will present some simulations of the largest glacier of the European Alps, the Aletsch glacier. As a less unexpected application, I will show how these results allowed us to make a major advance in a police investigation started in 1926.
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…
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…
NASA Astrophysics Data System (ADS)
Smith, Erick; Haarer, Shawn; Confrey, Jere
Although reform efforts in mathematics education have called for more diverse views of mathematics, there have been few studies of how mathematics is used and takes form in practices outside of mathematics itself. Thus legitimate diverse models have largely been missing in education. This study attempts to broaden our understanding of mathematics by investigating how applied mathematicians and biologists, working together to construct dynamic population models, understand these models within the framework of their perspective practices, that is how these models take on a role as ''boundary objects'' between the two practices. By coming to understand how these models function within the practice of biology, the paper suggests that mathematics educators have the opportunity both to reevaluate their own assumptions about modeling and to build an understanding of the dialectic process necessary for these models to develop an epistemological basis that is shared across practices. Investigating this dialectic process is both important and missing in most mathematical classrooms.1
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.
Mathematical models of malaria - a review
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
The stability of colorectal cancer mathematical models
NASA Astrophysics Data System (ADS)
Khairudin, Nur Izzati; Abdullah, Farah Aini
2013-04-01
Colorectal cancer is one of the most common types of cancer. To better understand about the kinetics of cancer growth, mathematical models are used to provide insight into the progression of this natural process which enables physicians and oncologists to determine optimal radiation and chemotherapy schedules and develop a prognosis, both of which are indispensable for treating cancer. This thesis investigates the stability of colorectal cancer mathematical models. We found that continuous saturating feedback is the best available model of colorectal cancer growth. We also performed stability analysis. The result shows that cancer progress in sequence of genetic mutations or epigenetic which lead to a very large number of cells population until become unbounded. The cell population growth initiate and its saturating feedback is overcome when mutation changes causing the net per-capita growth rate of stem or transit cells exceed critical threshold.
Mathematical modeling of normal pharyngeal bolus transport: a preliminary study.
Chang, M W; Rosendall, B; Finlayson, B A
1998-07-01
Dysphagia (difficulty in swallowing) is a common clinical symptom associated with many diseases, such as stroke, multiple sclerosis, neuromuscular diseases, and cancer. Its complications include choking, aspiration, malnutrition, cachexia, and dehydration. The goal in dysphagia management is to provide adequate nutrition and hydration while minimizing the risk of choking and aspiration. It is important to advance the individual toward oral feeding in a timely manner to enhance the recovery of swallowing function and preserve the quality of life. Current clinical assessments of dysphagia are limited in providing adequate guidelines for oral feeding. Mathematical modeling of the fluid dynamics of pharyngeal bolus transport provides a unique opportunity for studying the physiology and pathophysiology of swallowing. Finite element analysis (FEA) is a special case of computational fluid dynamics (CFD). In CFD, the flow of a fluid in a space is modeled by covering the space with a grid and predicting how the fluid moves from grid point to grid point. FEA is capable of solving problems with complex geometries and free surfaces. A preliminary pharyngeal model has been constructed using FEA. This model incorporates literature-reported, normal, anatomical data with time-dependent pharyngeal/upper esophageal sphincter (UES) wall motion obtained from videofluorography (VFG). This time-dependent wall motion can be implemented as a moving boundary condition in the model. Clinical kinematic data can be digitized from VFG studies to construct and test the mathematical model. The preliminary model demonstrates the feasibility of modeling pharyngeal bolus transport, which, to our knowledge, has not been attempted before. This model also addresses the need and the potential for CFD in understanding the physiology and pathophysiology of the pharyngeal phase of swallowing. Improvements of the model are underway. Combining the model with individualized clinical data should potentially
Computing Linear Mathematical Models Of Aircraft
NASA Technical Reports Server (NTRS)
Duke, Eugene L.; Antoniewicz, Robert F.; Krambeer, Keith D.
1991-01-01
Derivation and Definition of Linear Aircraft Model (LINEAR) computer program provides user with powerful, and flexible, standard, documented, and verified software tool for linearization of mathematical models of aerodynamics of aircraft. Intended for use in software tool to drive linear analysis of stability and design of control laws for aircraft. Capable of both extracting such linearized engine effects as net thrust, torque, and gyroscopic effects, and including these effects in linear model of system. Designed to provide easy selection of state, control, and observation variables used in particular model. Also provides flexibility of allowing alternate formulations of both state and observation equations. Written in FORTRAN.
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.…
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.…
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)
Mathematical modeling of vertebrate limb development.
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. PMID:23219575
Editorial: Mathematical modelling of infectious diseases.
Fenton, Andy
2016-06-01
The field of disease ecology - the study of the spread and impact of parasites and pathogens within their host populations and communities - has a long history of using mathematical models. Dating back over 100 years, researchers have used mathematics to describe the spread of disease-causing agents, understand the relationship between host density and transmission and plan control strategies. The use of mathematical modelling in disease ecology exploded in the late 1970s and early 1980s through the work of Anderson and May (Anderson and May, 1978, 1981, 1992; May and Anderson, 1978), who developed the fundamental frameworks for studying microparasite (e.g. viruses, bacteria and protozoa) and macroparasite (e.g. helminth) dynamics, emphasizing the importance of understanding features such as the parasite's basic reproduction number (R 0) and critical community size that form the basis of disease ecology research to this day. Since the initial models of disease population dynamics, which primarily focused on human diseases, theoretical disease research has expanded hugely to encompass livestock and wildlife disease systems, and also to explore evolutionary questions such as the evolution of parasite virulence or drug resistance. More recently there have been efforts to broaden the field still further, to move beyond the standard 'one-host-one-parasite' paradigm of the original models, to incorporate many aspects of complexity of natural systems, including multiple potential host species and interactions among multiple parasite species. PMID:27027318
A mathematical model of collagen lattice contraction
Dallon, J. C.; Evans, E. J.; Ehrlich, H. Paul
2014-01-01
Two mathematical models for fibroblast–collagen interaction are proposed which reproduce qualitative features of fibroblast-populated collagen lattice contraction. Both models are force based and model the cells as individual entities with discrete attachment sites; however, the collagen lattice is modelled differently in each model. In the collagen lattice model, the lattice is more interconnected and formed by triangulating nodes to form the fibrous structure. In the collagen fibre model, the nodes are not triangulated, are less interconnected, and the collagen fibres are modelled as a string of nodes. Both models suggest that the overall increase in stress of the lattice as it contracts is not the cause of the reduced rate of contraction, but that the reduced rate of contraction is due to inactivation of the fibroblasts. PMID:25142520
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)
Mathematical Models for HIV Transmission Dynamics
Cassels, Susan; Clark, Samuel J.; Morris, Martina
2012-01-01
Summary HIV researchers have long appreciated the need to understand the social and behavioral determinants of HIV-related risk behavior, but the cumulative impact of individual behaviors on population-level HIV outcomes can be subtle and counterintuitive, and the methods for studying this are rarely part of a traditional social science or epidemiology training program. Mathematical models provide a way to examine the potential effects of the proximate biologic and behavioral determinants of HIV transmission dynamics, alone and in combination. The purpose of this article is to show how mathematical modeling studies have contributed to our understanding of the dynamics and disparities in the global spread of HIV. Our aims are to demonstrate the value that these analytic tools have for social and behavioral sciences in HIV prevention research, to identify gaps in the current literature, and to suggest directions for future research. PMID:18301132
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…
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…
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…
Mathematical modelling of leprosy and its control.
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. PMID:25765193
On mathematical modelling of flameless combustion
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)
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.
Basic Perforator Flap Hemodynamic Mathematical Model
Tao, Youlun; Ding, Maochao; Wang, Aiguo; Zhuang, Yuehong; Chang, Shi-Min; Mei, Jin; Hallock, Geoffrey G.
2016-01-01
Background: A mathematical model to help explain the hemodynamic characteristics of perforator flaps based on blood flow resistance systems within the flap will serve as a theoretical guide for the future study and clinical applications of these flaps. Methods: There are 3 major blood flow resistance network systems of a perforator flap. These were defined as the blood flow resistance of an anastomosis between artery and artery of adjacent perforasomes, between artery and vein within a perforasome, and then between vein and vein corresponding to the outflow of that perforasome. From this, a calculation could be made of the number of such blood flow resistance network systems that must be crossed for all perforasomes within a perforator flap to predict whether that arrangement would be viable. Results: The summation of blood flow resistance networks from each perforasome in a given perforator flap could predict which portions would likely survive. This mathematical model shows how this is directly dependent on the location of the vascular pedicle to the flap and whether supercharging or superdrainage maneuvers have been added. These configurations will give an estimate of the hemodynamic characteristics for the given flap design. Conclusions: This basic mathematical model can (1) conveniently determine the degree of difficulty for each perforasome within a perforator flap to survive; (2) semiquantitatively allow the calculation of basic hemodynamic parameters; and (3) allow the assessment of the pros and cons expected for each pattern of perforasomes encountered clinically based on predictable hemodynamic observations.
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…
Mathematical models of breast and ovarian cancers.
Botesteanu, Dana-Adriana; Lipkowitz, Stanley; Lee, Jung-Min; Levy, Doron
2016-07-01
Women constitute the majority of the aging United States (US) population, and this has substantial implications on cancer population patterns and management practices. Breast cancer is the most common women's malignancy, while ovarian cancer is the most fatal gynecological malignancy in the US. In this review, we focus on these subsets of women's cancers, seen more commonly in postmenopausal and elderly women. In order to systematically investigate the complexity of cancer progression and response to treatment in breast and ovarian malignancies, we assert that integrated mathematical modeling frameworks viewed from a systems biology perspective are needed. Such integrated frameworks could offer innovative contributions to the clinical women's cancers community, as answers to clinical questions cannot always be reached with contemporary clinical and experimental tools. Here, we recapitulate clinically known data regarding the progression and treatment of the breast and ovarian cancers. We compare and contrast the two malignancies whenever possible in order to emphasize areas where substantial contributions could be made by clinically inspired and validated mathematical modeling. We show how current paradigms in the mathematical oncology community focusing on the two malignancies do not make comprehensive use of, nor substantially reflect existing clinical data, and we highlight the modeling areas in most critical need of clinical data integration. We emphasize that the primary goal of any mathematical study of women's cancers should be to address clinically relevant questions. WIREs Syst Biol Med 2016, 8:337-362. doi: 10.1002/wsbm.1343 For further resources related to this article, please visit the WIREs website. PMID:27259061
Mathematical modeling of deformation during hot rolling
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.
Mathematical and computational models of plasma flows
NASA Astrophysics Data System (ADS)
Brushlinsky, K. V.
Investigations of plasma flows are of interest, firstly, due to numerous applications, and secondly, because of their general principles, which form a special branch of physics: the plasma dynamics. Numerical simulation and computation, together with theoretic and experimental methods, play an important part in these investigations. Speaking on flows, a relatively dense plasma is mentioned, so its mathematical models appertain to the fluid mechanics, i.e., they are based on the magnetohydrodynamic description of plasma. Time dependent two dimensional models of plasma flows of two wide-spread types are considered: the flows across the magnetic field and those in the magnetic field plane.
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.
Mathematical Modeling of Ultraporous Nonmetallic Reticulated Materials
NASA Astrophysics Data System (ADS)
Alifanov, O. M.; Cherepanov, V. V.; Morzhukhina, A. V.
2015-01-01
We have developed an imitation statistical mathematical model reflecting the structure and the thermal, electrophysical, and optical properties of nonmetallic ultraporous reticulated materials. This model, in combination with a nonstationary thermal experiment and methods of the theory of inverse heat transfer problems, permits determining the little-studied characteristics of the above materials such as the radiative and conductive heat conductivities, the spectral scattering and absorption coefficients, the scattering indicatrix, and the dielectric constants, which are of great practical interest but are difficult to investigate.
A mathematical model of 'Pride and Prejudice'.
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. PMID:24560011
Nutrition Health Education During the 2 years preceding the study: • The percentage of states that provided funding for staff development or offered staff development on nutrition and dietary behavior to those who teach health ...
... into your diet. These include brightly colored and dark fruits and vegetables. Balance the food you eat ... can also order your free copy of Nutrition Matters and visit our Ask about Nutrition forum. << Back ...
A mathematical model of adult subventricular neurogenesis
Ashbourn, J. M. A.; Miller, J. J.; Reumers, V.; Baekelandt, V.; Geris, L.
2012-01-01
Neurogenesis has been the subject of active research in recent years and many authors have explored the phenomenology of the process, its regulation and its purported purpose. Recent developments in bioluminescent imaging (BLI) allow direct in vivo imaging of neurogenesis, and in order to interpret the experimental results, mathematical models are necessary. This study proposes such a mathematical model that describes adult mammalian neurogenesis occurring in the subventricular zone and the subsequent migration of cells through the rostral migratory stream to the olfactory bulb (OB). This model assumes that a single chemoattractant is responsible for cell migration, secreted both by the OB and in an endocrine fashion by the cells involved in neurogenesis. The solutions to the system of partial differential equations are compared with the physiological rodent process, as previously documented in the literature and quantified through the use of BLI, and a parameter space is described, the corresponding solution to which matches that of the rodent model. A sensitivity analysis shows that this parameter space is stable to perturbation and furthermore that the system as a whole is sloppy. A large number of parameter sets are stochastically generated, and it is found that parameter spaces corresponding to physiologically plausible solutions generally obey constraints similar to the conditions reported in vivo. This further corroborates the model and its underlying assumptions based on the current understanding of the investigated phenomenon. Concomitantly, this leaves room for further quantitative predictions pertinent to the design of future proposed experiments. PMID:22572029
Social Network Analysis and Nutritional Behavior: An Integrated Modeling Approach
Senior, Alistair M.; Lihoreau, Mathieu; Buhl, Jerome; Raubenheimer, David; Simpson, Stephen J.
2016-01-01
Animals have evolved complex foraging strategies to obtain a nutritionally balanced diet and associated fitness benefits. Recent research combining state-space models of nutritional geometry with agent-based models (ABMs), show how nutrient targeted foraging behavior can also influence animal social interactions, ultimately affecting collective dynamics and group structures. Here we demonstrate how social network analyses can be integrated into such a modeling framework and provide a practical analytical tool to compare experimental results with theory. We illustrate our approach by examining the case of nutritionally mediated dominance hierarchies. First we show how nutritionally explicit ABMs that simulate the emergence of dominance hierarchies can be used to generate social networks. Importantly the structural properties of our simulated networks bear similarities to dominance networks of real animals (where conflicts are not always directly related to nutrition). Finally, we demonstrate how metrics from social network analyses can be used to predict the fitness of agents in these simulated competitive environments. Our results highlight the potential importance of nutritional mechanisms in shaping dominance interactions in a wide range of social and ecological contexts. Nutrition likely influences social interactions in many species, and yet a theoretical framework for exploring these effects is currently lacking. Combining social network analyses with computational models from nutritional ecology may bridge this divide, representing a pragmatic approach for generating theoretical predictions for nutritional experiments. PMID:26858671
Social Network Analysis and Nutritional Behavior: An Integrated Modeling Approach.
Senior, Alistair M; Lihoreau, Mathieu; Buhl, Jerome; Raubenheimer, David; Simpson, Stephen J
2016-01-01
Animals have evolved complex foraging strategies to obtain a nutritionally balanced diet and associated fitness benefits. Recent research combining state-space models of nutritional geometry with agent-based models (ABMs), show how nutrient targeted foraging behavior can also influence animal social interactions, ultimately affecting collective dynamics and group structures. Here we demonstrate how social network analyses can be integrated into such a modeling framework and provide a practical analytical tool to compare experimental results with theory. We illustrate our approach by examining the case of nutritionally mediated dominance hierarchies. First we show how nutritionally explicit ABMs that simulate the emergence of dominance hierarchies can be used to generate social networks. Importantly the structural properties of our simulated networks bear similarities to dominance networks of real animals (where conflicts are not always directly related to nutrition). Finally, we demonstrate how metrics from social network analyses can be used to predict the fitness of agents in these simulated competitive environments. Our results highlight the potential importance of nutritional mechanisms in shaping dominance interactions in a wide range of social and ecological contexts. Nutrition likely influences social interactions in many species, and yet a theoretical framework for exploring these effects is currently lacking. Combining social network analyses with computational models from nutritional ecology may bridge this divide, representing a pragmatic approach for generating theoretical predictions for nutritional experiments. PMID:26858671
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…
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…
Development of a Multidisciplinary Middle School Mathematics Infusion Model
ERIC Educational Resources Information Center
Russo, Maria; Hecht, Deborah; Burghardt, M. David; Hacker, Michael; Saxman, Laura
2011-01-01
The National Science Foundation (NSF) funded project "Mathematics, Science, and Technology Partnership" (MSTP) developed a multidisciplinary instructional model for connecting mathematics to science, technology and engineering content areas at the middle school level. Specifically, the model infused mathematics into middle school curriculum…
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.
Mathematical model to predict drivers' reaction speeds.
Long, Benjamin L; Gillespie, A Isabella; Tanaka, Martin L
2012-02-01
Mental distractions and physical impairments can increase the risk of accidents by affecting a driver's ability to control the vehicle. In this article, we developed a linear mathematical model that can be used to quantitatively predict drivers' performance over a variety of possible driving conditions. Predictions were not limited only to conditions tested, but also included linear combinations of these tests conditions. Two groups of 12 participants were evaluated using a custom drivers' reaction speed testing device to evaluate the effect of cell phone talking, texting, and a fixed knee brace on the components of drivers' reaction speed. Cognitive reaction time was found to increase by 24% for cell phone talking and 74% for texting. The fixed knee brace increased musculoskeletal reaction time by 24%. These experimental data were used to develop a mathematical model to predict reaction speed for an untested condition, talking on a cell phone with a fixed knee brace. The model was verified by comparing the predicted reaction speed to measured experimental values from an independent test. The model predicted full braking time within 3% of the measured value. Although only a few influential conditions were evaluated, we present a general approach that can be expanded to include other types of distractions, impairments, and environmental conditions. PMID:22431214
Mathematical Modeling of Extinction of Inhomogeneous Populations.
Karev, G P; Kareva, I
2016-04-01
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 of 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
Mathematical Modeling of Extinction of Inhomogeneous Populations
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
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.
Mathematical modeling of diesel fuel hydrotreating
NASA Astrophysics Data System (ADS)
Tataurshikov, A.; Ivanchina, E.; Krivtcova, N.; Krivtsov, E.; Syskina, A.
2015-11-01
Hydrotreating of the diesel fraction with the high initial sulfur content of 1,4 mass% is carried out in the flow-through laboratory setup with the industrial GKD-202 catalyst at various process temperature. On the basis of the experimental data the regularities of the hydrogenation reactions are revealed, and the formalized scheme of sulfur-containing components (sulfides, benzothiophenes, and dibenzothiophenes) transformations is made. The mathematical model of hydrotreating process is developed, the constant values for the reaction rate of hydrodesulfurization of the specified components are calculated.
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.
Mathematical modeling of infectious disease dynamics
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
A Mathematical Model of Idiopathic Pulmonary Fibrosis
Hao, Wenrui; Marsh, Clay; Friedman, Avner
2015-01-01
Idiopathic pulmonary fibrosis (IPF) is a disease of unknown etiology, and life expectancy of 3-5 years after diagnosis. The incidence rate in the United States is estimated as high as 15 per 100,000 persons per year. The disease is characterized by repeated injury to the alveolar epithelium, resulting in inflammation and deregulated repair, leading to scarring of the lung tissue, resulting in progressive dyspnea and hypoxemia. The disease has no cure, although new drugs are in clinical trials and two agents have been approved for use by the FDA. In the present paper we develop a mathematical model based on the interactions among cells and proteins that are involved in the progression of the disease. The model simulations are shown to be in agreement with available lung tissue data of human patients. The model can be used to explore the efficacy of potential drugs. PMID:26348490
Animal models to study neonatal nutrition in humans
Technology Transfer Automated Retrieval System (TEKTRAN)
The impact of neonatal nutrition on the health status of the newborn and incidence of disease in later life is a topic of intense interest. Animal models are an invaluable tool to identify mechanisms that mediate the effect of nutrition on neonatal development and metabolic function. This review hig...
Mathematical modelling of eukaryotic DNA replication.
Hyrien, Olivier; Goldar, Arach
2010-01-01
Eukaryotic DNA replication is a complex process. Replication starts at thousand origins that are activated at different times in S phase and terminates when converging replication forks meet. Potential origins are much more abundant than actually fire within a given S phase. The choice of replication origins and their time of activation is never exactly the same in any two cells. Individual origins show different efficiencies and different firing time probability distributions, conferring stochasticity to the DNA replication process. High-throughput microarray and sequencing techniques are providing increasingly huge datasets on the population-averaged spatiotemporal patterns of DNA replication in several organisms. On the other hand, single-molecule replication mapping techniques such as DNA combing provide unique information about cell-to-cell variability in DNA replication patterns. Mathematical modelling is required to fully comprehend the complexity of the chromosome replication process and to correctly interpret these data. Mathematical analysis and computer simulations have been recently used to model and interpret genome-wide replication data in the yeast Saccharomyces cerevisiae and Schizosaccharomyces pombe, in Xenopus egg extracts and in mammalian cells. These works reveal how stochasticity in origin usage confers robustness and reliability to the DNA replication process. PMID:20205354
Mathematical Modelling: Transitions between the Real World and the Mathematical Model
ERIC Educational Resources Information Center
Crouch, Rosalind; Haines, Christopher
2004-01-01
Applications in engineering, science and technology within undergraduate programmes can be difficult for students to understand. In this paper, new results are presented which go some way to demonstrate and explain the problems faced by students in linking mathematical models to real-world applications. The study is based on student responses to…
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.…
Building Mathematics Achievement Models in Four Countries Using TIMSS 2003
ERIC Educational Resources Information Center
Wang, Ze; Osterlind, Steven J.; Bergin, David A.
2012-01-01
Using the Trends in International Mathematics and Science Study 2003 data, this study built mathematics achievement models of 8th graders in four countries: the USA, Russia, Singapore and South Africa. These 4 countries represent the full spectrum of mathematics achievement. In addition, they represent 4 continents, and they include 2 countries…
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.
Mathematical modeling of a rotary hearth calciner
Meisingset, H.C.; Balchen, J.G.; Fernandez, R.
1996-10-01
Calcination of petroleum coke is a thermal process where green petroleum coke is heat-treated to a pre-determined temperature. During heat treatment the associated moisture is removed and the volatile combustible matter (VCM) is released. The VCM is burned in the gas phase giving the energy to sustain the process. In addition, structural changes take place. The combination of the final calcination temperature and the residence time determine the final real density of the calcined coke. Depending on its further use, different real density requirements may arise. It is important to control the dynamics of the calcination process so that the specified final quality is achieved. A dynamic mathematical model of a Rotary Hearth Calciner is presented. The model is based on physicochemical laws involving the most important phenomena taking place and the relevant calcination parameters. The temperature profile in the coke bed is predicted which in terms is related to the real density of the coke.
Mathematics Teacher Education: A Model from Crimea.
ERIC Educational Resources Information Center
Ferrucci, Beverly J.; Evans, Richard C.
1993-01-01
Reports on the mathematics teacher preparation program at Simferopol State University, the largest institution of higher education in the Crimea. The article notes the value of investigating what other countries consider essential in mathematics teacher education to improve the mathematical competence of students in the United States. (SM)
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…
Mathematical modeling of acid-base physiology
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
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.
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).
Mathematical model of tumor-immune surveillance.
Mahasa, Khaphetsi Joseph; Ouifki, Rachid; Eladdadi, Amina; Pillis, Lisette de
2016-09-01
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. PMID:27317864
Mathematical Model of Evolution of Brain Parcellation.
Ferrante, Daniel D; Wei, Yi; Koulakov, Alexei A
2016-01-01
We study the distribution of brain and cortical area sizes [parcellation units (PUs)] obtained for three species: mouse, macaque, and human. We find that the distribution of PU sizes is close to lognormal. We propose the mathematical model of evolution of brain parcellation based on iterative fragmentation and specialization. In this model, each existing PU has a probability to be split that depends on PU size only. This model suggests that the same evolutionary process may have led to brain parcellation in these three species. Within our model, region-to-region (macro) connectivity is given by the outer product form. We show that most experimental data on non-zero macaque cortex macroscopic-level connections can be explained by the outer product power-law form suggested by our model (62% for area V1). We propose a multiplicative Hebbian learning rule for the macroconnectome that could yield the correct scaling of connection strengths between areas. We thus propose an evolutionary model that may have contributed to both brain parcellation and mesoscopic level connectivity in mammals. PMID:27378859
Mathematical Model of Evolution of Brain Parcellation
Ferrante, Daniel D.; Wei, Yi; Koulakov, Alexei A.
2016-01-01
We study the distribution of brain and cortical area sizes [parcellation units (PUs)] obtained for three species: mouse, macaque, and human. We find that the distribution of PU sizes is close to lognormal. We propose the mathematical model of evolution of brain parcellation based on iterative fragmentation and specialization. In this model, each existing PU has a probability to be split that depends on PU size only. This model suggests that the same evolutionary process may have led to brain parcellation in these three species. Within our model, region-to-region (macro) connectivity is given by the outer product form. We show that most experimental data on non-zero macaque cortex macroscopic-level connections can be explained by the outer product power-law form suggested by our model (62% for area V1). We propose a multiplicative Hebbian learning rule for the macroconnectome that could yield the correct scaling of connection strengths between areas. We thus propose an evolutionary model that may have contributed to both brain parcellation and mesoscopic level connectivity in mammals. PMID:27378859
Mathematical modeling of electrocardiograms: a numerical study.
Boulakia, Muriel; Cazeau, Serge; Fernández, Miguel A; Gerbeau, Jean-Frédéric; Zemzemi, Nejib
2010-03-01
This paper deals with the numerical simulation of electrocardiograms (ECG). Our aim is to devise a mathematical model, based on partial differential equations, which is able to provide realistic 12-lead ECGs. The main ingredients of this model are classical: the bidomain equations coupled to a phenomenological ionic model in the heart, and a generalized Laplace equation in the torso. The obtention of realistic ECGs relies on other important features--including heart-torso transmission conditions, anisotropy, cell heterogeneity and His bundle modeling--that are discussed in detail. The numerical implementation is based on state-of-the-art numerical methods: domain decomposition techniques and second order semi-implicit time marching schemes, offering a good compromise between accuracy, stability and efficiency. The numerical ECGs obtained with this approach show correct amplitudes, shapes and polarities, in all the 12 standard leads. The relevance of every modeling choice is carefully discussed and the numerical ECG sensitivity to the model parameters investigated. PMID:20033779
NASA Technical Reports Server (NTRS)
Lane, Helen W.
1990-01-01
This is a collection of viewgraphs on the Johnson Space Center's work on nutrition for long duration space missions. Nutritional requirements are affected by isolation, workloads, and cold as well as the psychological needs, metabolism, and fluid balance of an individual.
Mathematical modelling of the anaerobic hybrid reactor.
Soroa, S; Gomez, J; Ayesa, E; Garcia-Heras, J L
2006-01-01
This paper presents a new mathematical model for the anaerobic hybrid reactor (AHR) (a UASB reactor and an anaerobic filter in series) and its experimental calibration and verification. The model includes a biochemical part and a mass transport one, which considers the AHR as two contact reactors in series. The anaerobic process transformations are described by the model developed by Siegrist et al. The fraction (F) of solids in the clarification zone of the UASB reactor that leaves this first reactor is the key physical parameter to be estimated. The main parameters of the model were calibrated using experimental results from a bench-scale AHR fed with real slaughterhouse wastewater. The fraction of inert particulate COD in the influent and the factor F were estimated by a trial and error procedure comparing experimental and simulated results of the mass of solids in the lower tank and the VSS concentration in the AHR effluent. A good fit was obtained. The final verification was carried out by comparing a set of experiments with simulated data. The model's capability to predict the process performance was thus proved. PMID:16939085
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.
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…
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…
Mathematical analysis of epidemiological models with heterogeneity
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.
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.
Mathematical modeling of endovenous laser treatment (ELT)
Mordon, Serge R; Wassmer, Benjamin; Zemmouri, Jaouad
2006-01-01
Background and objectives Endovenous laser treatment (ELT) has been recently proposed as an alternative in the treatment of reflux of the Great Saphenous Vein (GSV) and Small Saphenous Vein (SSV). Successful ELT depends on the selection of optimal parameters required to achieve an optimal vein damage while avoiding side effects. Mathematical modeling of ELT could provide a better understanding of the ELT process and could determine the optimal dosage as a function of vein diameter. Study design/materials and methods The model is based on calculations describing the light distribution using the diffusion approximation of the transport theory, the temperature rise using the bioheat equation and the laser-induced injury using the Arrhenius damage model. The geometry to simulate ELT was based on a 2D model consisting of a cylindrically symmetric blood vessel including a vessel wall and surrounded by an infinite homogenous tissue. The mathematical model was implemented using the Macsyma-Pdease2D software (Macsyma Inc., Arlington, MA, USA). Damage to the vein wall for CW and single shot energy was calculated for 3 and 5 mm vein diameters. In pulsed mode, the pullback distance (3, 5 and 7 mm) was considered. For CW mode simulation, the pullback speed (1, 2, 3 mm/s) was the variable. The total dose was expressed as joules per centimeter in order to perform comparison to results already reported in clinical studies. Results In pulsed mode, for a 3 mm vein diameter, irrespective of the pullback distance (2, 5 or 7 mm), a minimum fluence of 15 J/cm is required to obtain a permanent damage of the intima. For a 5 mm vein diameter, 50 J/cm (15W-2s) is required. In continuous mode, for a 3 mm and 5 mm vein diameter, respectively 65 J/cm and 100 J/cm are required to obtain a permanent damage of the vessel wall. Finally, the use of different wavelengths (810 nm or 980 nm) played only a minor influence on these results. Discussion and conclusion The parameters determined by
Mathematical modeling of human secondary osteons.
Ascenzi, Maria-Grazia; Andreuzzi, Marta; Kabo, J Michael
2004-01-01
This investigation explores the structural dimensions and patterns within single secondary osteons, with consideration of their biological variation. New data from images obtained previously of osteons observed through linearly polarized light, electron microscopy, and micro-x-ray, combined with recent findings on lamellae by circularly polarized light, confocal microscopy, synchrotron x-ray diffraction, and micro-x-ray, provide the basis for novel computerized models of single osteons and single lamellae. The novelty of such models is the concurrent representation of (1) collagen-hydroxyapatite orientation, (2) relative hydroxyapatite percentage, (3) distributions of osteocytes' lacunae and canaliculae, and (4) biological variations in dimensions of the relevant structures. The mathematical software Maple realizes the computerized models. While the parts of the models are constructed on a personal computer, the voluminous data associated with the representation of lacunar and canalicular distributions require a supercomputer for assembly of the models and final analysis. The programming used to define the models affords the option to randomize the dimensional specifications of osteons, lamellae, lacunae, and canaliculae within the experimentally observed numeric ranges and distributions. Through this option, the program can operate so that each run of the file produces a unique random model within the observed biological variations. The program can also be run to implement specific dimensional requirements. The modeling has applications in the microstructural study of fracture propagation and remodeling, as well as in the simulation of mechanical testing. The approach taken here is of wide application and could be of value in other areas of microscopy such as scanning electron microscopy, microcomputerized tomography scan, and magnetic resonance imaging on cancellous bone structures. PMID:15000289
Mathematical modeling plasma transport in tokamaks
Quiang, Ji
1995-12-31
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 10{sup 20}/m{sup 3} 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%.
Mathematical modelling of animate and intentional motion.
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
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.
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.
Cocaine addiction and personality: a mathematical model.
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. PMID:20030966
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.
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
On Mathematical Modeling Of Quantum Systems
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.
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.
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Mathematical Modeling of Electrochemical Flow Capacitors
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.
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…
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 Council of Teachers of…
Mathematics Teacher TPACK Standards and Development Model
ERIC Educational Resources Information Center
Niess, Margaret L.; Ronau, Robert N.; Shafer, Kathryn G.; Driskell, Shannon O.; Harper, Suzanne R.; Johnston, Christopher; Browning, Christine; Ozgun-Koca, S. Asli; Kersaint, Gladis
2009-01-01
What knowledge is needed to teach mathematics with digital technologies? The overarching construct, called technology, pedagogy, and content knowledge (TPACK), has been proposed as the interconnection and intersection of technology, pedagogy, and content knowledge. Mathematics Teacher TPACK Standards offer guidelines for thinking about this…
Modelling Mathematical Argumentation: The Importance of Qualification
ERIC Educational Resources Information Center
Inglis, Matthew; Mejia-Ramos, Juan; Simpson, Adrian
2007-01-01
In recent years several mathematics education researchers have attempted to analyse students' arguments using a restricted form of Toulmina's ["The Uses of Argument," Cambridge University Press, UK, 1958] argumentation scheme. In this paper we report data from task-based interviews conducted with highly talented postgraduate mathematics students,…
Mathematical Models and the Experimental Analysis of Behavior
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 equally accurate predictions for a large body of data. In such cases, it is important to find and investigate situations for which the competing models make different predictions because, unless two models are actually mathematically equivalent, they are based on different assumptions about the psychological processes that underlie an observed behavior. Mathematical models developed in basic behavioral research have been used to predict and control behavior in applied settings, and they have guided research in other areas of psychology. A good mathematical model can provide a common framework for understanding what might otherwise appear to be diverse and unrelated behavioral phenomena. Because psychologists vary in their quantitative skills and in their tolerance for mathematical equations, it is important for those who develop mathematical models of behavior to find ways (such as verbal analogies, pictorial representations, or concrete examples) to communicate the key premises of their models to nonspecialists. PMID:16673829
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.
Analysis of Mathematical Modelling on Potentiometric Biosensors
Mehala, N.; Rajendran, L.
2014-01-01
A mathematical model of potentiometric enzyme electrodes for a nonsteady condition has been developed. The model is based on the system of two coupled nonlinear time-dependent reaction diffusion equations for Michaelis-Menten formalism that describes the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate and product and the corresponding flux response have been derived for all values of parameters using the new homotopy perturbation method. Furthermore, the complex inversion formula is employed in this work to solve the boundary value problem. The analytical solutions obtained allow a full description of the response curves for only two kinetic parameters (unsaturation/saturation parameter and reaction/diffusion parameter). Theoretical descriptions are given for the two limiting cases (zero and first order kinetics) and relatively simple approaches for general cases are presented. All the analytical results are compared with simulation results using Scilab/Matlab program. The numerical results agree with the appropriate theories. PMID:25969765
Analysis of mathematical modelling on potentiometric biosensors.
Mehala, N; Rajendran, L
2014-01-01
A mathematical model of potentiometric enzyme electrodes for a nonsteady condition has been developed. The model is based on the system of two coupled nonlinear time-dependent reaction diffusion equations for Michaelis-Menten formalism that describes the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate and product and the corresponding flux response have been derived for all values of parameters using the new homotopy perturbation method. Furthermore, the complex inversion formula is employed in this work to solve the boundary value problem. The analytical solutions obtained allow a full description of the response curves for only two kinetic parameters (unsaturation/saturation parameter and reaction/diffusion parameter). Theoretical descriptions are given for the two limiting cases (zero and first order kinetics) and relatively simple approaches for general cases are presented. All the analytical results are compared with simulation results using Scilab/Matlab program. The numerical results agree with the appropriate theories. PMID:25969765
Mathematical Modeling of Photochemical Air Pollution.
NASA Astrophysics Data System (ADS)
McRae, Gregory John
Air pollution is an environmental problem that is both pervasive and difficult to control. An important element of any rational control approach is a reliable means for evaluating the air quality impact of alternative abatement measures. This work presents such a capability, in the form of a mathematical description of the production and transport of photochemical oxidants within an urban airshed. The combined influences of advection, turbulent diffusion, chemical reaction, emissions and surface removal processes are all incorporated into a series of models that are based on the species continuity equations. A delineation of the essential assumptions underlying the formulation of a three-dimensional, a Lagrangian trajectory, a vertically integrated and single cell air quality model is presented. Since each model employs common components and input data the simpler forms can be used for rapid screening calculations and the more complex ones for detailed evaluations. The flow fields, needed for species transport, are constructed using inverse distance weighted polynomial interpolation techniques that map routine monitoring data onto a regular computational mesh. Variational analysis procedures are then employed to adjust the field so that mass is conserved. Initial concentration and mixing height distributions can be established with the same interpolation algorithms. Subgrid scale turbulent transport is characterized by a gradient diffusion hypothesis. Similarity solutions are used to model the surface layer fluxes. Above this layer different treatments of turbulent diffusivity are required to account for variations in atmospheric stability. Convective velocity scaling is utilized to develop eddy diffusivities for unstable conditions. The predicted mixing times are in accord with results obtained during sulfur hexafluoride (SF(,6)) tracer experiments. Conventional models are employed for neutral and stable conditions. A new formulation for gaseous deposition fluxes
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…
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.
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…
Teaching Modelling as an Alternative Approach to School Mathematics
ERIC Educational Resources Information Center
Yanagimoto, Tomoko
2005-01-01
Nowadays, mathematics has come to be increasingly put into practical use in various fields in society. However, Japanese students dislike mathematics. The purpose of this study is to consider the significance of teaching modelling. In this paper, I take up "Fuzzy modelling" as teaching material for senior high school students. As a result, it was…
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…
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…
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…
A mathematical model of biological evolution.
Ishii, K; Matsuda, H; Ogita, N
1982-01-01
In order to understand generally how the biological evolution rate depends on relevant parameters such as mutation rate, intensity of selection pressure and its persistence time, the following mathematical model is proposed: dNn(t)/dt = (mn(t) - mu)Nn(t) + muNn-1(t) (n = 0,1,2,3,...), where Nn(t) and mn(t) are respectively the number and Malthusian parameter of replicons with step number n in a population at time t and mean is the mutation rate, assumed to be a positive constant. The step number of each replicon is defined as either equal to or larger by one than that of its parent, the latter case occurring when and only when mutation has taken place. The average evolution rate defined by v infinity identical to lim t leads to infinity sigma infinity n = o nNn(t)/t sigma infinity n = o Nn(t) is rigorously obtained for the case (i) mn(t) = mn is independent of t (constant fitness model), where mn is essentially periodic with respect to n, and for the case (ii) mn(t) = s(-1) n+[t/tau] (periodic fitness model), together with the long time average -m infinity of the average Malthusian parameter -m identical to sigma infinity n = o mn(t)Nn(t)/sigma infinity n = o Nn(t). The biological meaning of the results is discussed, comparing them with the features of actual molecular evolution and with some results of computer simulation of the model for finite populations. PMID:7119589
Mathematical modeling of biomass fuels formation process
Gaska, Krzysztof Wandrasz, Andrzej J.
2008-07-01
The increasing demand for thermal and electric energy in many branches of industry and municipal management accounts for a drastic diminishing of natural resources (fossil fuels). Meanwhile, in numerous technical processes, a huge mass of wastes is produced. A segregated and converted combustible fraction of the wastes, with relatively high calorific value, may be used as a component of formed fuels. The utilization of the formed fuel components from segregated groups of waste in associated processes of co-combustion with conventional fuels causes significant savings resulting from partial replacement of fossil fuels, and reduction of environmental pollution resulting directly from the limitation of waste migration to the environment (soil, atmospheric air, surface and underground water). The realization of technological processes with the utilization of formed fuel in associated thermal systems should be qualified by technical criteria, which means that elementary processes as well as factors of sustainable development, from a global viewpoint, must not be disturbed. The utilization of post-process waste should be preceded by detailed technical, ecological and economic analyses. In order to optimize the mixing process of fuel components, a mathematical model of the forming process was created. The model is defined as a group of data structures which uniquely identify a real process and conversion of this data in algorithms based on a problem of linear programming. The paper also presents the optimization of parameters in the process of forming fuels using a modified simplex algorithm with a polynomial worktime. This model is a datum-point in the numerical modeling of real processes, allowing a precise determination of the optimal elementary composition of formed fuels components, with assumed constraints and decision variables of the task.
Nutritional Systems Biology Modeling: From Molecular Mechanisms to Physiology
de Graaf, Albert A.; Freidig, Andreas P.; De Roos, Baukje; Jamshidi, Neema; Heinemann, Matthias; Rullmann, Johan A.C.; Hall, Kevin D.; Adiels, Martin; van Ommen, Ben
2009-01-01
The use of computational modeling and simulation has increased in many biological fields, but despite their potential these techniques are only marginally applied in nutritional sciences. Nevertheless, recent applications of modeling have been instrumental in answering important nutritional questions from the cellular up to the physiological levels. Capturing the complexity of today's important nutritional research questions poses a challenge for modeling to become truly integrative in the consideration and interpretation of experimental data at widely differing scales of space and time. In this review, we discuss a selection of available modeling approaches and applications relevant for nutrition. We then put these models into perspective by categorizing them according to their space and time domain. Through this categorization process, we identified a dearth of models that consider processes occurring between the microscopic and macroscopic scale. We propose a “middle-out” strategy to develop the required full-scale, multilevel computational models. Exhaustive and accurate phenotyping, the use of the virtual patient concept, and the development of biomarkers from “-omics” signatures are identified as key elements of a successful systems biology modeling approach in nutrition research—one that integrates physiological mechanisms and data at multiple space and time scales. PMID:19956660
Is there Life after Modelling? Student conceptions of mathematics
NASA Astrophysics Data System (ADS)
Houston, Ken; Mather, Glyn; Wood, Leigh N.; Petocz, Peter; Reid, Anna; Harding, Ansie; Engelbrecht, Johann; Smith, Geoff H.
2010-09-01
We have been investigating university student conceptions of mathematics over a number of years, with the goal of enhancing student learning and professional development. We developed an open-ended survey of three questions, on "What is mathematics" and two questions about the role of mathematics in the students' future. This questionnaire was completed by 1,200 undergraduate students of mathematics in Australia, the UK, Canada, South Africa, and Brunei. The sample included students ranging from those majoring in mathematics to those taking only one or two modules in mathematics. Responses were analysed starting from a previously-developed phenomenographic framework that required only minor modification, leading to an outcome space of four levels of conceptions about mathematics. We found that for many students modelling is fundamental to their conception of "What is mathematics?". In a small number of students, we identified a broader conception of mathematics, that we have labelled Life. This describes a view of mathematics as a way of thinking about reality and as an integral part of life, and represents an ideal aim for university mathematics education.
A mathematical model of a computational problem solving system
NASA Astrophysics Data System (ADS)
Aris, Teh Noranis Mohd; Nazeer, Shahrin Azuan
2015-05-01
This paper presents a mathematical model based on fuzzy logic for a computational problem solving system. The fuzzy logic uses truth degrees as a mathematical model to represent vague algorithm. The fuzzy logic mathematical model consists of fuzzy solution and fuzzy optimization modules. The algorithm is evaluated based on a software metrics calculation that produces the fuzzy set membership. The fuzzy solution mathematical model is integrated in the fuzzy inference engine that predicts various solutions to computational problems. The solution is extracted from a fuzzy rule base. Then, the solutions are evaluated based on a software metrics calculation that produces the level of fuzzy set membership. The fuzzy optimization mathematical model is integrated in the recommendation generation engine that generate the optimize solution.
Mathematical model of electrical contact bouncing
NASA Astrophysics Data System (ADS)
Kharin, Stanislav
2015-09-01
Mathematical model of a contact bouncing takes into account elastic-plastic and electrodynamic forces, phase transformations during interaction of electrical arc with the contact surface as a result of increasing temperature. It is based on the integro-differential equations for the contact motion and Stefan problem for the temperature field. These equations describe four consecutive stages of the contact vibration from the impact at contact closing up to opening after bouncing including effects of penetration and restitution. The new method for the solution of the Stefan problem is elaborated, which enables us to get the information about dynamics of zones of elasticity, plasticity and phase transformations during contact vibration. It is shown that the decrement of damping depends on the coefficient of plasticity and the moment of inertia only, while the frequency of vibration depends also on the hardness of contact, its temperature, properties of contact spring, and geometry of rotational mechanism. It is found also from the solution of Stefan problem that the relationship between dynamical zones of plasticity and melting explains the decrease of current density and contact welding. The results of calculations are compared with the experimental data.
Mathematical models in biology: from molecules to life
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
ERIC Educational Resources Information Center
Saur, Susan
An elementary level nutrition unit provides teachers with student background information, suggested activities, and student worksheets. Part 1 focuses on the relationship of food to growth, health, and energy. In part 2, students learn about the four main food groups. Part 3 deals with nutrients and provides information about carbohydrates, fats,…
Retrospective Study on Mathematical Modeling Based on Computer Graphic Processing
NASA Astrophysics Data System (ADS)
Zhang, Kai Li
Graphics & image making is an important field in computer application, in which visualization software has been widely used with the characteristics of convenience and quick. However, it was thought by modeling designers that the software had been limited in it's function and flexibility because mathematics modeling platform was not built. A non-visualization graphics software appearing at this moment enabled the graphics & image design has a very good mathematics modeling platform. In the paper, a polished pyramid is established by multivariate spline function algorithm, and validate the non-visualization software is good in mathematical modeling.
Physical vs. Mathematical Models in Rock Mechanics
NASA Astrophysics Data System (ADS)
Morozov, I. B.; Deng, W.
2013-12-01
One of the less noted challenges in understanding the mechanical behavior of rocks at both in situ and lab conditions is the character of theoretical approaches being used. Currently, the emphasis is made on spatial averaging theories (homogenization and numerical models of microstructure), empirical models for temporal behavior (material memory, compliance functions and complex moduli), and mathematical transforms (Laplace and Fourier) used to infer the Q-factors and 'relaxation mechanisms'. In geophysical applications, we have to rely on such approaches for very broad spatial and temporal scales which are not available in experiments. However, the above models often make insufficient use of physics and utilize, for example, the simplified 'correspondence principle' instead of the laws of viscosity and friction. As a result, the commonly-used time- and frequency dependent (visco)elastic moduli represent apparent properties related to the measurement procedures and not necessarily to material properties. Predictions made from such models may therefore be inaccurate or incorrect when extrapolated beyond the lab scales. To overcome the above challenge, we need to utilize the methods of micro- and macroscopic mechanics and thermodynamics known in theoretical physics. This description is rigorous and accurate, uses only partial differential equations, and allows straightforward numerical implementations. One important observation from the physical approach is that the analysis should always be done for the specific geometry and parameters of the experiment. Here, we illustrate these methods on axial deformations of a cylindrical rock sample in the lab. A uniform, isotropic elastic rock with a thermoelastic effect is considered in four types of experiments: 1) axial extension with free transverse boundary, 2) pure axial extension with constrained transverse boundary, 3) pure bulk expansion, and 4) axial loading harmonically varying with time. In each of these cases, an
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…
Explorations in the Modeling of the Learning of Mathematics.
ERIC Educational Resources Information Center
Fuson, Karen C., Ed.; And Others
Eleven research reports in the area of models of learning mathematics are presented in this publication of the Mathematics Education Reports series. The papers represent a mixture of theories, viewpoints, and references to other areas. Content areas addressed range from preschool to college levels. All the papers are concerned with the learning of…
Mathematical Manipulative Models: In Defense of “Beanbag Biology”
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
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…
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…
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…
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)
Mathematical modeling of efficient protocols to control glioma growth.
Branco, J R; Ferreira, J A; de Oliveira, Paula
2014-09-01
In this paper we propose a mathematical model to describe the evolution of glioma cells taking into account the viscoelastic properties of brain tissue. The mathematical model is established considering that the glioma cells are of two phenotypes: migratory and proliferative. The evolution of the migratory cells is described by a diffusion-reaction equation of non Fickian type deduced considering a mass conservation law with a non Fickian migratory mass flux. The evolution of the proliferative cells is described by a reaction equation. A stability analysis that leads to the design of efficient protocols is presented. Numerical simulations that illustrate the behavior of the mathematical model are included. PMID:25057777
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
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.
A novel nutrition medicine education model: the Boston University experience.
Lenders, Carine; Gorman, Kathy; Milch, Hannah; Decker, Ashley; Harvey, Nanette; Stanfield, Lorraine; Lim-Miller, Aimee; Salge-Blake, Joan; Judd, Laura; Levine, Sharon
2013-01-01
Most deaths in the United States are preventable and related to nutrition. Although physicians are expected to counsel their patients about nutrition-related health conditions, a recent survey reported minimal improvements in nutrition medicine education in US medical schools in the past decade. Starting in 2006, we have developed an educational plan using a novel student-centered model of nutrition medicine education at Boston University School of Medicine that focuses on medical student-mentored extracurricular activities to develop, evaluate, and sustain nutrition medicine education. The medical school uses a team-based approach focusing on case-based learning in the classroom, practice-based learning in the clinical setting, extracurricular activities, and a virtual curriculum to improve medical students' knowledge, attitudes, and practice skills across their 4-y period of training. We have been using objectives from the NIH National Academy Awards guide and tools from the Association of American Medical Colleges to detect new areas of nutrition medicine taught at the medical school. Although we were only able to identify 20.5 h of teaching in the preclerkship years, we observed that most preclerkship nutrition medicine objectives were covered during the course of the 4-y teaching period, and extracurricular activities provided new opportunities for student leadership and partnership with other health professionals. These observations are very encouraging as new assessment tools are being developed. Future plans include further evaluation and dissemination of lessons learned using this model to improve public health wellness with support from academia, government, industry, and foundations. PMID:23319117
Computational and mathematical models of microstructural evolution
Bullard, J.W.; Chen, L.Q.; Kalia, R.K.; Stoneham, A.M.
1998-12-31
This symposium was designed to bring together the foremost materials theorists and applied mathematicians from around the world to share and discuss some of the newest and most promising mathematical and computational tools for simulating, understanding, and predicting the various complex processes that occur during the evolution of microstructures. Separate abstracts were prepared for 25 papers.
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,…
Mathematics and Science Integration: Models and Characterizations
ERIC Educational Resources Information Center
Stinson, Kevin; Harkness, Shelly Sheats; Meyer, Helen; Stallworth, James
2009-01-01
The squeeze on instructional time and other factors increasingly leads educators to consider mathematics and science integration in an effort to be more efficient and effective. Unfortunately, the need for common understandings for what it means to integrate these disciplines, as well as the need for improving disciplinary knowledge, appears to…
The Mathematical Modeling of Chaotic Social Structures.
ERIC Educational Resources Information Center
Marion, Russ; Richardson, Michael D.
Chaos theory describes the way systems change over time. It proposes that systems governed by physical laws can undergo transitions to a highly irregular form of behavior and that although chaotic behavior appears random, it is governed by strict mathematical conditions. This paper applies chaos theory to administrative and organizational issues.…
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…
A nutrition model for developing nations with special reference to Bangladesh.
Shams-ur-rahman; Clarke, H R
1991-09-01
A linear programming model of nutritional planning, applied to 3 nutrition problems of nutrition planning in 2 villages, Shitalpur and Kulia-Durgapur in southwest Bangladesh is described and results are discussed. The model takes into consideration features identified as affecting nutritional requirements: age and sex, recommended requirements by age and sex, activity level, proportion of lactating women, excess requirement for lactating and pregnant women, and proportion of women pregnant. Other important factors are production of nutrients in the region as affected by assimilable number of nutrients and net yield per acre and number of acres, net usage of nutrients in the region as affected by transfer of crops between regions, and net food import into the region as affected by aid import of food type and exports of food type. Total area of arable land is restriction on production. Consumption = production - net interregional transfers - net foreign trade exports and constraints. It is assumed that any shortfall in domestic production can be met in this supply side analysis. 2 types of policy objectives (self-sufficiency and surplus maximization) are also modeled. The applied model is simplified for the village analysis and the following assumptions are made: there is no trade between villages, transportation cost is not added, and crop yield depends only on land input used in production. The 3 types of nutritional planning problems are that 1) only calorie and protein are considered and arable lands are available year long; 2) calcium and vitamins A, B2, and C (multinutrients) must be met; and 3) inadequate irrigation and flood control technologies limit the amount of land available during the winter and summer months. The Mathematical Programming System and Extension Package (MPSX) was used to solve the simplified model. 8 crops are considered in 10 cropping patterns. The results are that both villages can be net food exporters if all land can be utilized and
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.
MATHEMATICAL MODEL FOR THE SELECTIVE DEPOSITION OF INHALED PHARMACEUTICALS
To accurately assess the potential therapeutic effects of airborne drugs, the deposition sites of inhaled particles must be known. erein, an original theory is presented for physiologically based pharmacokinetic modeling and related prophylaxis of airway diseases. he mathematical...
A MATHEMATICAL MODEL OF ELECTROSTATIC PRECIPITATION: REVISION 1
The computer program performs the calculations in the mathematical model of electrostatic precipitation and is documented in other publications. The program predicts collection efficiency in an electrostatic precipitator as a function of particle diameter, electrical operating co...
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)
Classical and Weak Solutions for Two Models in Mathematical Finance
NASA Astrophysics Data System (ADS)
Gyulov, Tihomir B.; Valkov, Radoslav L.
2011-12-01
We study two mathematical models, arising in financial mathematics. These models are one-dimensional analogues of the famous Black-Scholes equation on finite interval. The main difficulty is the degeneration at the both ends of the space interval. First, classical solutions are studied. Positivity and convexity properties of the solutions are discussed. Variational formulation in weighted Sobolev spaces is introduced and existence and uniqueness of the weak solution is proved. Maximum principle for weak solution is discussed.
Boullata, Joseph I; Holcombe, Beverly; Sacks, Gordon; Gervasio, Jane; Adams, Stephen C; Christensen, Michael; Durfee, Sharon; Ayers, Phil; Marshall, Neil; Guenter, Peggi
2016-08-01
Parenteral nutrition (PN) is a high-alert medication with a complex drug use process. Key steps in the process include the review of each PN prescription followed by the preparation of the formulation. The preparation step includes compounding the PN or activating a standardized commercially available PN product. The verification and review, as well as preparation of this complex therapy, require competency that may be determined by using a standardized process for pharmacists and for pharmacy technicians involved with PN. An American Society for Parenteral and Enteral Nutrition (ASPEN) standardized model for PN order review and PN preparation competencies is proposed based on a competency framework, the ASPEN-published interdisciplinary core competencies, safe practice recommendations, and clinical guidelines, and is intended for institutions and agencies to use with their staff. PMID:27317615
The Mathematical Models of the Periodical Literature Publishing Process.
ERIC Educational Resources Information Center
Guang, Yu; Daren, Yu; Yihong, Rong
2000-01-01
Describes two mathematical models of the periodical publishing process based on a theoretical analysis. Discusses the publishing process for periodical literature, explains the continuous model and the discrete model, presents partial differential equations, and demonstrates the adaptability and the validity of the models. (LRW)
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…
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…
Eating Competence: Nutrition Education with the Satter Eating Competence Model
ERIC Educational Resources Information Center
Satter, Ellyn
2007-01-01
The Satter Eating Competence Model (ecSatter) conceptualizes eating competence as having 4 components: eating attitudes, food acceptance, regulation of food intake and body weight, and management of the eating context (including family meals). According to ecSatter, supporting nutritional health requires establishing and maintaining positive…
Technology Transfer Automated Retrieval System (TEKTRAN)
The effects of eating or skipping breakfast on ERP correlates of mental arithmetic were studied in preadolescents differing in experience (age) and mathematical skills. Participants, randomly assigned to treatment [eat (B) or skip (SB) breakfast (each, n = 41)], were sub-grouped by age [8.8 yrs (B: ...
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…
Evaluation of Limb Load Asymmetry Using Two New Mathematical Models
Kumar, Senthil NS; Omar, Baharudin; Joseph, Leonard H.; Htwe, Ohnmar; Jagannathan, K.; Hamdan, Nor M Y; Rajalakshmi, D.
2015-01-01
Quantitative measurement of limb loading is important in orthopedic and neurological rehabilitation. In current practice, mathematical models such as Symmetry index (SI), Symmetry ratio (SR), and Symmetry angle (SA) are used to quantify limb loading asymmetry. Literatures have identified certain limitations with the above mathematical models. Hence this study presents two new mathematical models Modified symmetry index (MSI) and Limb loading error (LLE) that would address these limitations. Furthermore, the current mathematical models were compared against the new model with the goal of achieving a better model. This study uses hypothetical data to simulate an algorithmic preliminary computational measure to perform with all numerical possibilities of even and uneven limb loading that can occur in human legs. Descriptive statistics are used to interpret the limb loading patterns: symmetry, asymmetry and maximum asymmetry. The five mathematical models were similar in analyzing symmetry between limbs. However, for asymmetry and maximum asymmetry data, the SA and SR values do not give any meaningful interpretation, and SI gives an inflated value. The MSI and LLE are direct, easy to interpret and identify the loading patterns with the side of asymmetry. The new models are notable as they quantify the amount and side of asymmetry under different loading patterns. PMID:25716372
A Mathematical Model of Immune-System-Melanoma Competition
Pennisi, Marzio
2012-01-01
We present a mathematical model developed to reproduce the immune response entitled with the combined administration of activated OT1 cytotoxic T lymphocytes (CTLs) and Anti-CD137 monoclonal antibodies. The treatment is directed against melanoma in B16 OVA mouse models exposed to a specific immunotherapy strategy. We model two compartments: the injection point compartment where the treatment is administered and the skin compartment where melanoma tumor cells proliferate. To model the migration of OT1 CTLs and antibodies from the injection to the skin compartment, we use delay differential equations (DDEs). The outcomes of the mathematical model are in good agreement with the in vivo results. Moreover, sensitivity analysis of the mathematical model underlines the key role of OT1 CTLs and suggests that a possible reduction of the number of injected antibodies should not affect substantially the treatment efficacy. PMID:22701144
A Mathematical Model for Evolution and SETI
NASA Astrophysics Data System (ADS)
Maccone, Claudio
2011-12-01
Darwinian evolution theory may be regarded as a part of SETI theory in that the factor fl 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 fl 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.
A mathematical model for evolution and SETI.
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. PMID:22139521
Mathematical Modeling and the Redesign of a Teaching Ambulatory Clinic
ERIC Educational Resources Information Center
Baker, Duke H.; Mamlin, Joseph
1976-01-01
Mathematical modeling was utilized in the planning and decision-making process involved in reorganizing a teaching clinic to effect continuity of care. The model interrelated physicians, time, and space, facilitating value judgments and decisions. The reorganization was successful and the outcomes remarkably similar to model predictions.…
Learning and Teaching Mathematics through Real Life Models
ERIC Educational Resources Information Center
Takaci, Djurdjica; Budinski, Natalija
2011-01-01
This paper proposes modelling based learning as a tool for learning and teaching mathematics in high school. We report on an example of modelling real world problems in two high schools in Serbia where students were introduced for the first time to the basic concepts of modelling. Student use of computers and educational software, GeoGebra, was…
A Review on Mathematical Modeling for Textile Processes
NASA Astrophysics Data System (ADS)
Chattopadhyay, R.
2015-10-01
Mathematical model is a powerful tool in engineering for studying variety of problems related to design and development of products and processes, optimization of manufacturing process, understanding a phenomenon and predicting product's behaviour in actual use. An insight of the process and use of appropriate mathematical tools are necessary for developing models. In the present paper, a review of types of model, procedure followed in developing them and their limitations have been discussed. Modeling techniques being used in few textile processes available in the literature have been cited as examples.
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.
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).
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.