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

PubMed

Hoskinson, Anne-Marie

2010-01-01

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

Case Studies of the Urban Mathematics Collaborative Project: Program Report 91-3.

ERIC Educational Resources Information Center

Popkewitz, Thomas S.; Myrdal, Sigurjon

The Urban Mathematics Collaborative (UMC) project has the goal of contributing to the improvement of mathematics education in the inner-city schools by identifying models to enhance the professional lives of teachers and encouraging the entry of high school mathematics teachers into a larger mathematics community including mathematicians from…

Attitude determination of a high altitude balloon system. Part 1: Development of the mathematical model

NASA Technical Reports Server (NTRS)

Nigro, N. J.; Elkouh, A. F.; Shen, K. S.; Nimityongskul, P.; Jhaveri, V. N.; Sethi, A.

1975-01-01

A mathematical model for predicting the three dimensional motion of the balloon system is developed, which includes the effects of bounce, pendulation and spin of each subsystem. Boundary layer effects are also examined, along with the aerodynamic forces acting on the balloon. Various simplified forms of the system mathematical model were developed, based on an order of magnitude analysis.

Redundancy management of electrohydraulic servoactuators by mathematical model referencing

NASA Technical Reports Server (NTRS)

Campbell, R. A.

1971-01-01

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

Assessment and Learning of Mathematics.

ERIC Educational Resources Information Center

Leder, Gilah C., Ed.

This book addresses the link between student learning of mathematics, the teaching method adopted in the mathematics classroom, and the assessment procedures used to determine and measure student knowledge. Fifteen chapters address issues that include a review of different models of mathematics learning and assessment practices, three contrasting…

Modelling in Primary School: Constructing Conceptual Models and Making Sense of Fractions

ERIC Educational Resources Information Center

Shahbari, Juhaina Awawdeh; Peled, Irit

2017-01-01

This article describes sixth-grade students' engagement in two model-eliciting activities offering students the opportunity to construct mathematical models. The findings show that students utilized their knowledge of fractions including conceptual and procedural knowledge in constructing mathematical models for the given situations. Some students…

Public Views on the Gendering of Mathematics and Related Careers: International Comparisons

ERIC Educational Resources Information Center

Forgasz, Helen; Leder, Gilah; Tan, Hazel

2014-01-01

Mathematics continues to be an enabling discipline for Science, Technology, Engineering, and Mathematics (STEM)-based university studies and related careers. Explanatory models for females' underrepresentation in higher level mathematics and STEM-based courses comprise learner-related and environmental variables--including societal beliefs. Using…

Engaging Students in Mathematical Modeling through Service-Learning

ERIC Educational Resources Information Center

Carducci, Olivia M.

2014-01-01

I have included a service-learning project in my mathematical modeling course for the last 6 years. This article describes my experience with service-learning in this course. The article includes a description of the course and the service-learning projects. There is a discussion of how to connect with community partners and identify…

Goddard trajectory determination subsystem: Mathematical specifications

NASA Technical Reports Server (NTRS)

Wagner, W. E. (Editor); Velez, C. E. (Editor)

1972-01-01

The mathematical specifications of the Goddard trajectory determination subsystem of the flight dynamics system are presented. These specifications include the mathematical description of the coordinate systems, dynamic and measurement model, numerical integration techniques, and statistical estimation concepts.

A Mediation Model to Explain the Role of Mathematics Skills and Probabilistic Reasoning on Statistics Achievement

ERIC Educational Resources Information Center

Primi, Caterina; Donati, Maria Anna; Chiesi, Francesca

2016-01-01

Among the wide range of factors related to the acquisition of statistical knowledge, competence in basic mathematics, including basic probability, has received much attention. In this study, a mediation model was estimated to derive the total, direct, and indirect effects of mathematical competence on statistics achievement taking into account…

A Mathematical Model of a Simple Amplifier Using a Ferroelectric Transistor

NASA Technical Reports Server (NTRS)

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

2009-01-01

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

Model Of Bearing With Hydrostatic Damper

NASA Technical Reports Server (NTRS)

Goggin, David G.

1991-01-01

Improved mathematical model of rotational and vibrational dynamics of bearing package in turbopump incorporates effects of hydrostatic damper. Part of larger finite-element model representing rotational and vibrational dynamics of rotor and housing of pump. Includes representations of deadband and nonlinear stiffness and damping of ball bearings, nonlinear stiffness and damping of hydrostatic film, and stiffness of bearing support. Enables incorporation of effects of hydrostatic damper into overall rotor-dynamic mathematical model without addition of mathematical submodel of major substructure.

A Unified Mathematical Definition of Classical Information Retrieval.

ERIC Educational Resources Information Center

Dominich, Sandor

2000-01-01

Presents a unified mathematical definition for the classical models of information retrieval and identifies a mathematical structure behind relevance feedback. Highlights include vector information retrieval; probabilistic information retrieval; and similarity information retrieval. (Contains 118 references.) (Author/LRW)

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

PubMed

Campitelli, Guillermo; Gerrans, Paul

2014-04-01

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

A mathematical model of a large open fire

NASA Technical Reports Server (NTRS)

Harsha, P. T.; Bragg, W. N.; Edelman, R. B.

1981-01-01

A mathematical model capable of predicting the detailed characteristics of large, liquid fuel, axisymmetric, pool fires is described. The predicted characteristics include spatial distributions of flame gas velocity, soot concentration and chemical specie concentrations including carbon monoxide, carbon dioxide, water, unreacted oxygen, unreacted fuel and nitrogen. Comparisons of the predictions with experimental values are also given.

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

PubMed

Richards, D; Berry, S; Howard, M

2012-01-01

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

Early Math Trajectories: Low-Income Children's Mathematics Knowledge from Ages 4 to 11

ERIC Educational Resources Information Center

Rittle-Johnson, Bethany; Fyfe, Emily R.; Hofer, Kerry G.; Farran, Dale C.

2017-01-01

Early mathematics knowledge is a strong predictor of later academic achievement, but children from low-income families enter school with weak mathematics knowledge. An early math trajectories model is proposed and evaluated within a longitudinal study of 517 low-income American children from ages 4 to 11. This model includes a broad range of math…

Early Math Trajectories: Low-Income Children's Mathematics Knowledge from Age 4 to 11

ERIC Educational Resources Information Center

Rittle-Johnson, Bethany; Fyfe, Emily R.; Hofer, Kerry G.; Farran, Dale C.

2016-01-01

Early mathematics knowledge is a strong predictor of later academic achievement, but children from low-income families enter school with weak mathematics knowledge. An Early Math Trajectories model is proposed and evaluated within a longitudinal study of 517 low-income American children from age 4 to 11. This model includes a broad range of math…

Techtalk: Mobile Apps and College Mathematics

ERIC Educational Resources Information Center

Hoang, Theresa V.; Caverly, David C.

2013-01-01

In this column, the authors discuss apps useful in developing mathematical reasoning. They place these into a theoretical framework, suggesting how they could be used in an instructional model such as the Algorithmic Instructional Technique (AIT) developed by Vasquez (2003). This model includes four stages: modeling, practice, transition, and…

V/STOL tilt rotor aircraft study mathematical model for a real time simulation of a tilt rotor aircraft (Boeing Vertol Model 222), volume 8

NASA Technical Reports Server (NTRS)

Rosenstein, H.; Mcveigh, M. A.; Mollenkof, P. A.

1973-01-01

A mathematical model for a real time simulation of a tilt rotor aircraft was developed. The mathematical model is used for evaluating aircraft performance and handling qualities. The model is based on an eleven degree of freedom total force representation. The rotor is treated as a point source of forces and moments with appropriate response time lags and actuator dynamics. The aerodynamics of the wing, tail, rotors, landing gear, and fuselage are included.

ASTP ranging system mathematical model

NASA Technical Reports Server (NTRS)

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

1973-01-01

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

A model of a fishery with fish stock involving delay equations.

PubMed

Auger, P; Ducrot, Arnaud

2009-12-13

The aim of this paper is to provide a new mathematical model for a fishery by including a stock variable for the resource. This model takes the form of an infinite delay differential equation. It is mathematically studied and a bifurcation analysis of the steady states is fulfilled. Depending on the different parameters of the problem, we show that Hopf bifurcation may occur leading to oscillating behaviours of the system. The mathematical results are finally discussed.

Crazing in Polymeric and Composite Systems

DTIC Science & Technology

1990-04-23

these physical variations into consideration in any mathematical modeling and formulation in analyzing the stresses from the time when crazes incept to...as boundary tractions with great strength; any governing mathematical formulation must include this feature for any adequate analysis. Crazes of...constants the mathematical model describing the crazing mechanism have been successful [25-29]. References 1 J. A. Sauer, J. Marin and C. C. Hsiao, J. App

Towards a Dialogical Pedagogy: Some Characteristics of a Community of Mathematical Inquiry

ERIC Educational Resources Information Center

Kennedy, Nadia Stoyanova

2009-01-01

This paper discusses a teaching model called community of mathematical inquiry (CMI), characterized by dialogical and inquiry-driven communication and a dynamic structure of intertwined cognitive processes including distributed thinking, mathematical argumentation, integrated reasoning, conceptual transformation, internalization of critical…

Problems in Mathematics--Moving towards a Holistic Approach.

ERIC Educational Resources Information Center

Maree, J. G.

1992-01-01

Explanations for problems in mathematics are offered, and examples that may lead to a better understanding of problems in mathematics are discussed. Examples include the developmental, dyscalculia, dyspedagogia, behaviorist, medical, psychoanalytic, cultural, curricular, social, transactional, moral, and eclectic models. A case study exemplifies…

Mathematical formulation of the Applications Technology Satellite-F (ATS-F) orbital maneuver control program (CNTRLF)

NASA Technical Reports Server (NTRS)

Goorevich, C. E.

1975-01-01

The mathematical formulation is presented of CNTRLF, the maneuver control program for the Applications Technology Satellite-F (ATS-F). The purpose is to specify the mathematical models that are included in the design of CNTRLF.

Preliminary Evaluation Report on the Los Angeles City Schools, SB 28 Demonstration Program in Mathematics.

ERIC Educational Resources Information Center

Gordon, C. Wayne

The purpose of this preliminary report is to describe and evaluate the Los Angeles Model Mathematics Project (LAMMP). The objectives of this project include the improvement of mathematical skills and understanding of mathematical concepts, the improvement of students' self-image, the development of instructional materials and the assessment of…

Cooperative learning model with high order thinking skills questions: an understanding on geometry

NASA Astrophysics Data System (ADS)

Sari, P. P.; Budiyono; Slamet, I.

2018-05-01

Geometry, a branch of mathematics, has an important role in mathematics learning. This research aims to find out the effect of learning model, emotional intelligence, and the interaction between learning model and emotional intelligence toward students’ mathematics achievement. This research is quasi-experimental research with 2 × 3 factorial design. The sample in this research included 179 Senior High School students on 11th grade in Sukoharjo Regency, Central Java, Indonesia in academic year of 2016/2017. The sample was taken by using stratified cluster random sampling. The results showed that: the student are taught by Thinking Aloud Pairs Problem-Solving using HOTs questions provides better mathematics learning achievement than Make A Match using HOTs questions. High emotional intelligence students have better mathematics learning achievement than moderate and low emotional intelligence students, and moderate emotional intelligence students have better mathematics learning achievement than low emotional intelligence students. There is an interaction between learning model and emotional intelligence, and these affect mathematics learning achievement. We conclude that appropriate learning model can support learning activities become more meaningful and facilitate students to understand material. For further research, we suggest to explore the contribution of other aspects in cooperative learning modification to mathematics achievement.

Three dimensional thermal pollution models. Volume 1: Review of mathematical formulations. [waste heat discharge from power plants and effects on ecosystems

NASA Technical Reports Server (NTRS)

Lee, S. S.; Sengupta, S.

1978-01-01

A mathematical model package for thermal pollution analyses and prediction is presented. These models, intended as user's manuals, are three dimensional and time dependent using the primitive equation approach. Although they have sufficient generality for application at sites with diverse topographical features; they also present specific instructions regarding data preparation for program execution and sample problems. The mathematical formulation of these models is presented including assumptions, approximations, governing equations, boundary and initial conditions, numerical method of solution, and same results.

Experimenting with Mathematical Biology

ERIC Educational Resources Information Center

Sanft, Rebecca; Walter, Anne

2016-01-01

St. Olaf College recently added a Mathematical Biology concentration to its curriculum. The core course, Mathematics of Biology, was redesigned to include a wet laboratory. The lab classes required students to collect data and implement the essential modeling techniques of formulation, implementation, validation, and analysis. The four labs…

White House Suggests Model Used in Reading to Elevate Math Skills

ERIC Educational Resources Information Center

Cavanagh, Sean

2006-01-01

This article discusses the Bush administration's aim to improve mathematics education through a suggested reading model. The White House is focusing on research to shape how students across the country are taught the most basic mathematical concepts. This undertaking would be modeled on the government's action toward reading, which includes the…

Generalized Adaptive Artificial Neural Networks

NASA Technical Reports Server (NTRS)

Tawel, Raoul

1993-01-01

Mathematical model of supervised learning by artificial neural network provides for simultaneous adjustments of both temperatures of neurons and synaptic weights, and includes feedback as well as feedforward synaptic connections. Extension of mathematical model described in "Adaptive Neurons For Artificial Neural Networks" (NPO-17803). Dynamics of neural network represented in new model by less-restrictive continuous formalism.

Multiscale modeling of brain dynamics: from single neurons and networks to mathematical tools.

PubMed

Siettos, Constantinos; Starke, Jens

2016-09-01

The extreme complexity of the brain naturally requires mathematical modeling approaches on a large variety of scales; the spectrum ranges from single neuron dynamics over the behavior of groups of neurons to neuronal network activity. Thus, the connection between the microscopic scale (single neuron activity) to macroscopic behavior (emergent behavior of the collective dynamics) and vice versa is a key to understand the brain in its complexity. In this work, we attempt a review of a wide range of approaches, ranging from the modeling of single neuron dynamics to machine learning. The models include biophysical as well as data-driven phenomenological models. The discussed models include Hodgkin-Huxley, FitzHugh-Nagumo, coupled oscillators (Kuramoto oscillators, Rössler oscillators, and the Hindmarsh-Rose neuron), Integrate and Fire, networks of neurons, and neural field equations. In addition to the mathematical models, important mathematical methods in multiscale modeling and reconstruction of the causal connectivity are sketched. The methods include linear and nonlinear tools from statistics, data analysis, and time series analysis up to differential equations, dynamical systems, and bifurcation theory, including Granger causal connectivity analysis, phase synchronization connectivity analysis, principal component analysis (PCA), independent component analysis (ICA), and manifold learning algorithms such as ISOMAP, and diffusion maps and equation-free techniques. WIREs Syst Biol Med 2016, 8:438-458. doi: 10.1002/wsbm.1348 For further resources related to this article, please visit the WIREs website. © 2016 Wiley Periodicals, Inc.

Longitudinal associations between reading and mathematics achievement.

PubMed

Grimm, Kevin J

2008-01-01

The association between early reading skills and changes in mathematics was examined in a large, low-income sample to determine whether students who have a greater level of reading skills in early elementary school exhibit more rapid gains in tests of mathematics. The longitudinal associations between third grade reading comprehension and changes in three components of mathematics achievement (Problem Solving and Data Interpretation, Mathematical Concepts and Estimation, Mathematical Computation) from third through eighth grade were examined. Latent growth models were fit to the repeated assessments of each mathematics component and the students' third grade reading and global mathematics scores were included as predictors of the intercept and slope. Gender, poverty status, and ethnicity were included in the models as control variables. The results showed males and African-American students tended to have shallower rates of change than females and non-African-American/non-Hispanic students. In terms of the effect of reading on changes in mathematics, third grade reading comprehension was found to be a positive significant predictor of change for each component of mathematics, suggesting students with a greater level of reading achievement in early elementary school change more rapidly in mathematics skills controlling for prior mathematics skills and student characteristics. The largest effects were shown for the Problem Solving and Data Interpretation test, a test focused on the applications of mathematics knowledge, and the Mathematical Concepts and Estimation test. Negligible effects were found for changes in Mathematical Computation. Thus, early reading comprehension was shown to be related to a conceptual understanding of mathematics and the application of mathematics knowledge. These findings lend support for the notion that early reading skills are important for success in mathematics.

Economic Theory and Management Games II.

ERIC Educational Resources Information Center

Zernik, Wolfgang

1988-01-01

Description of management games continues a previous article's discussion of how mathematical modeling and microeconomic concepts can be used by players. Highlights include an initial condition simulating a profit-maximizing monopoly; simulating the transition from monopoly to oligopoly; and how mathematical properties of the model affect final…

Progress in Modeling Nonlinear Dendritic Evolution in Two and Three Dimensions, and Its Mathematical Justification

NASA Technical Reports Server (NTRS)

Tanveer, S.; Foster, M. R.

2002-01-01

We report progress in three areas of investigation related to dendritic crystal growth. Those items include: 1. Selection of tip features dendritic crystal growth; 2) Investigation of nonlinear evolution for two-sided model; and 3) Rigorous mathematical justification.

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.

Development of mathematical models of environmental physiology

NASA Technical Reports Server (NTRS)

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

1971-01-01

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

Terrestrial implications of mathematical modeling developed for space biomedical research

NASA Technical Reports Server (NTRS)

Lujan, Barbara F.; White, Ronald J.; Leonard, Joel I.; Srinivasan, R. Srini

1988-01-01

This paper summarizes several related research projects supported by NASA which seek to apply computer models to space medicine and physiology. These efforts span a wide range of activities, including mathematical models used for computer simulations of physiological control systems; power spectral analysis of physiological signals; pattern recognition models for detection of disease processes; and computer-aided diagnosis programs.

The enhancement of mathematical analogical reasoning ability of university students through concept attainment model

NASA Astrophysics Data System (ADS)

Angraini, L. M.; Kusumah, Y. S.; Dahlan, J. A.

2018-05-01

This study aims to see the enhancement of mathematical analogical reasoning ability of the university students through concept attainment model learning based on overall and Prior Mathematical Knowledge (PMK) and interaction of both. Quasi experiments with the design of this experimental-controlled equivalent group involved 54 of second semester students at the one of State Islamic University. The instrument used is pretest-postest. Kolmogorov-Smirnov test, Levene test, t test, two-way ANOVA test were used to analyse the data. The result of this study includes: (1) The enhancement of the mathematical analogical reasoning ability of the students who gets the learning of concept attainment model is better than the enhancement of the mathematical analogical reasoning ability of the students who gets the conventional learning as a whole and based on PMK; (2) There is no interaction between the learning that is used and PMK on enhancing mathematical analogical reasoning ability.

Early Math Trajectories: Low-Income Children's Mathematics Knowledge From Ages 4 to 11.

PubMed

Rittle-Johnson, Bethany; Fyfe, Emily R; Hofer, Kerry G; Farran, Dale C

2017-09-01

Early mathematics knowledge is a strong predictor of later academic achievement, but children from low-income families enter school with weak mathematics knowledge. An early math trajectories model is proposed and evaluated within a longitudinal study of 517 low-income American children from ages 4 to 11. This model includes a broad range of math topics, as well as potential pathways from preschool to middle grades mathematics achievement. In preschool, nonsymbolic quantity, counting, and patterning knowledge predicted fifth-grade mathematics achievement. By the end of first grade, symbolic mapping, calculation, and patterning knowledge were the important predictors. Furthermore, the first-grade predictors mediated the relation between preschool math knowledge and fifth-grade mathematics achievement. Findings support the early math trajectories model among low-income children. © 2016 The Authors. Child Development © 2016 Society for Research in Child Development, Inc.

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

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

PubMed

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

2014-12-11

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

Comparing functional responses in predator-infected eco-epidemics models.

PubMed

Haque, Mainul; Rahman, Md Sabiar; Venturino, Ezio

2013-11-01

The current paper deals with the mathematical models of predator-prey system where a transmissible disease spreads among the predator species only. Four mathematical models are proposed and analysed with several popular predator functional responses in order to show the influence of functional response on eco-epidemic models. The existence, boundedness, uniqueness of solutions of all the models are established. Mathematical analysis including stability and bifurcation are observed. Comparison among the results of these models allows the general conclusion that relevant behaviour of the eco-epidemic predator-prey system, including switching of stability, extinction, persistence and oscillations for any species depends on four important parameters viz. the rate of infection, predator interspecies competition and the attack rate on susceptible predator. The paper ends with a discussion of the biological implications of the analytical and numerical results. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

The Use of Technology in a Model of Formative Assessment

ERIC Educational Resources Information Center

García López, Alfonsa; García Mazarío, Francisco

2016-01-01

This work describes a formative assessment model for a Mathematical Analysis course taken by engineering students. It includes online quizzes with feedback, a portfolio with weekly assignments, exams involving the use of mathematical software and a project to be completed in small groups of two or three students. The model has been perfected since…

Mathematical estimation of the level of microbial contamination on spacecraft surfaces by volumetric air sampling

NASA Technical Reports Server (NTRS)

Oxborrow, G. S.; Roark, A. L.; Fields, N. D.; Puleo, J. R.

1974-01-01

Microbiological sampling methods presently used for enumeration of microorganisms on spacecraft surfaces require contact with easily damaged components. Estimation of viable particles on surfaces using air sampling methods in conjunction with a mathematical model would be desirable. Parameters necessary for the mathematical model are the effect of angled surfaces on viable particle collection and the number of viable cells per viable particle. Deposition of viable particles on angled surfaces closely followed a cosine function, and the number of viable cells per viable particle was consistent with a Poisson distribution. Other parameters considered by the mathematical model included deposition rate and fractional removal per unit time. A close nonlinear correlation between volumetric air sampling and airborne fallout on surfaces was established with all fallout data points falling within the 95% confidence limits as determined by the mathematical model.

Conformal mapping in optical biosensor applications.

PubMed

Zumbrum, Matthew E; Edwards, David A

2015-09-01

Optical biosensors are devices used to investigate surface-volume reaction kinetics. Current mathematical models for reaction dynamics rely on the assumption of unidirectional flow within these devices. However, new devices, such as the Flexchip, include a geometry that introduces two-dimensional flow, complicating the depletion of the volume reactant. To account for this, a previous mathematical model is extended to include two-dimensional flow, and the Schwarz-Christoffel mapping is used to relate the physical device geometry to that for a device with unidirectional flow. Mappings for several Flexchip dimensions are considered, and the ligand depletion effect is investigated for one of these mappings. Estimated rate constants are produced for simulated data to quantify the inclusion of two-dimensional flow in the mathematical model.

School Mathematics Study Group, Unit Number Two. Chapter 3 - Informal Algorithms and Flow Charts. Chapter 4 - Applications and Mathematics Models.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This is the second unit of a 15-unit School Mathematics Study Group (SMSG) mathematics text for high school students. Topics presented in the first chapter (Informal Algorithms and Flow Charts) include: changing a flat tire; algorithms, flow charts, and computers; assignment and variables; input and output; using a variable as a counter; decisions…

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

NASA Astrophysics Data System (ADS)

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

2008-02-01

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

The Use of Mathematical Models of Chlamydia Transmission to Address Public Health Policy Questions: A Systematic Review.

PubMed

Rönn, Minttu M; Wolf, Emory E; Chesson, Harrell; Menzies, Nicolas A; Galer, Kara; Gorwitz, Rachel; Gift, Thomas; Hsu, Katherine; Salomon, Joshua A

2017-05-01

Mathematical models of chlamydia transmission can help inform disease control policy decisions when direct empirical evaluation of alternatives is impractical. We reviewed published chlamydia models to understand the range of approaches used for policy analyses and how the studies have responded to developments in the field. We performed a literature review by searching Medline and Google Scholar (up to October 2015) to identify publications describing dynamic chlamydia transmission models used to address public health policy questions. We extracted information on modeling methodology, interventions, and key findings. We identified 47 publications (including two model comparison studies), which reported collectively on 29 distinct mathematical models. Nine models were individual-based, and 20 were deterministic compartmental models. The earliest studies evaluated the benefits of national-level screening programs and predicted potentially large benefits from increased screening. Subsequent trials and further modeling analyses suggested the impact might have been overestimated. Partner notification has been increasingly evaluated in mathematical modeling, whereas behavioral interventions have received relatively limited attention. Our review provides an overview of chlamydia transmission models and gives a perspective on how mathematical modeling has responded to increasing empirical evidence and addressed policy questions related to prevention of chlamydia infection and sequelae.

The Particle/Wave-in-a-Box Model in Dutch Secondary Schools

ERIC Educational Resources Information Center

Hoekzema, Dick; van den Berg, Ed; Schooten, Gert; van Dijk, Leo

2007-01-01

The combination of mathematical and conceptual difficulties makes teaching quantum physics at secondary schools a precarious undertaking. With many of the conceptual difficulties being unavoidable, simplifying the mathematics becomes top priority. The particle/wave-in-a-box provides a teaching model which includes many aspects of serious …

Faculty Sufficiency and AACSB Accreditation Compliance within a Global University: A Mathematical Modeling Approach

ERIC Educational Resources Information Center

Boronico, Jess; Murdy, Jim; Kong, Xinlu

2014-01-01

This manuscript proposes a mathematical model to address faculty sufficiency requirements towards assuring overall high quality management education at a global university. Constraining elements include full-time faculty coverage by discipline, location, and program, across multiple campus locations subject to stated service quality standards of…

Pathways to Mathematics: Longitudinal Predictors of Performance

ERIC Educational Resources Information Center

LeFevre, Jo-Anne; Fast, Lisa; Skwarchuk, Sheri-Lynn; Smith-Chant, Brenda L.; Bisanz, Jeffrey; Kamawar, Deepthi; Penner-Wilger, Marcie

2010-01-01

A model of the relations among cognitive precursors, early numeracy skill, and mathematical outcomes was tested for 182 children from 4.5 to 7.5 years of age. The model integrates research from neuroimaging, clinical populations, and normal development in children and adults. It includes 3 precursor pathways: quantitative, linguistic, and spatial…

Rationale and Resources for Teaching the Mathematical Modeling of Athletic Training and Performance

ERIC Educational Resources Information Center

Clarke, David C.; Skiba, Philip F.

2013-01-01

A number of professions rely on exercise prescription to improve health or athletic performance, including coaching, fitness/personal training, rehabilitation, and exercise physiology. It is therefore advisable that the professionals involved learn the various tools available for designing effective training programs. Mathematical modeling of…

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

ERIC Educational Resources Information Center

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

2016-01-01

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

Differential equations with applications in cancer diseases.

PubMed

Ilea, M; Turnea, M; Rotariu, M

2013-01-01

Mathematical modeling is a process by which a real world problem is described by a mathematical formulation. The cancer modeling is a highly challenging problem at the frontier of applied mathematics. A variety of modeling strategies have been developed, each focusing on one or more aspects of cancer. The vast majority of mathematical models in cancer diseases biology are formulated in terms of differential equations. We propose an original mathematical model with small parameter for the interactions between these two cancer cell sub-populations and the mathematical model of a vascular tumor. We work on the assumption that, the quiescent cells' nutrient consumption is long. One the equations system includes small parameter epsilon. The smallness of epsilon is relative to the size of the solution domain. MATLAB simulations obtained for transition rate from the quiescent cells' nutrient consumption is long, we show a similar asymptotic behavior for two solutions of the perturbed problem. In this system, the small parameter is an asymptotic variable, different from the independent variable. The graphical output for a mathematical model of a vascular tumor shows the differences in the evolution of the tumor populations of proliferating, quiescent and necrotic cells. The nutrient concentration decreases sharply through the viable rim and tends to a constant level in the core due to the nearly complete necrosis in this region. Many mathematical models can be quantitatively characterized by ordinary differential equations or partial differential equations. The use of MATLAB in this article illustrates the important role of informatics in research in mathematical modeling. The study of avascular tumor growth cells is an exciting and important topic in cancer research and will profit considerably from theoretical input. Interpret these results to be a permanent collaboration between math's and medical oncologists.

A Biologically Constrained, Mathematical Model of Cortical Wave Propagation Preceding Seizure Termination

PubMed Central

González-Ramírez, Laura R.; Ahmed, Omar J.; Cash, Sydney S.; Wayne, C. Eugene; Kramer, Mark A.

2015-01-01

Epilepsy—the condition of recurrent, unprovoked seizures—manifests in brain voltage activity with characteristic spatiotemporal patterns. These patterns include stereotyped semi-rhythmic activity produced by aggregate neuronal populations, and organized spatiotemporal phenomena, including waves. To assess these spatiotemporal patterns, we develop a mathematical model consistent with the observed neuronal population activity and determine analytically the parameter configurations that support traveling wave solutions. We then utilize high-density local field potential data recorded in vivo from human cortex preceding seizure termination from three patients to constrain the model parameters, and propose basic mechanisms that contribute to the observed traveling waves. We conclude that a relatively simple and abstract mathematical model consisting of localized interactions between excitatory cells with slow adaptation captures the quantitative features of wave propagation observed in the human local field potential preceding seizure termination. PMID:25689136

Mathematical modeling to predict residential solid waste generation.

PubMed

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

2008-01-01

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

Steps Forward and Back in Adult Numeracy Teacher Professional Development: A Reflection on a Teacher Workshop Experience

ERIC Educational Resources Information Center

Saliga, Linda Marie; Daviso, Al; Stuart, Denise; Pachnowski, Lynne

2015-01-01

In this project, a university team of teacher education and mathematics professors conducted eight professional development sessions for General Educational Development (GED) teachers in the area of mathematics teaching. Topics included concretely modeling mathematics concepts in algebra, number sense, geometry, and differentiating instruction in…

Response to Intervention: Using Single-Case Design to Examine the Impact of Tier 2 Mathematics Interventions

ERIC Educational Resources Information Center

Valenzuela, Vanessa V.; Gutierrez, Gabriel; Lambros, Katina M.

2014-01-01

An A-B single-case design assessed at-risk students' responsiveness to mathematics interventions. Four culturally and linguistically diverse second-grade students were given a Tier 2 standard protocol mathematics intervention that included number sense instruction, modeling procedures, guided math drill and practice of addition and subtraction…

Lesson Study with Mathematical Resources: A Sustainable Model for Locally-Led Teacher Professional Learning

ERIC Educational Resources Information Center

Lewis, Catherine; Perry, Rebecca

2014-01-01

Teams of educators conducted lesson study independently, supported by a resource kit that included mathematical tasks, curriculum materials, lesson videos and plans, and research articles, as well as protocols to support lesson study. The mathematical resources focused on linear measurement interpretation of fractions. This report examines the…

Applicability of mathematical modeling to problems of environmental physiology

NASA Technical Reports Server (NTRS)

White, Ronald J.; Lujan, Barbara F.; Leonard, Joel I.; Srinivasan, R. Srini

1988-01-01

The paper traces the evolution of mathematical modeling and systems analysis from terrestrial research to research related to space biomedicine and back again to terrestrial research. Topics covered include: power spectral analysis of physiological signals; pattern recognition models for detection of disease processes; and, computer-aided diagnosis programs used in conjunction with a special on-line biomedical computer library.

Remembering the hindu festivities mathematically by the balinese using integer operations and least common multiple

NASA Astrophysics Data System (ADS)

Budi Darmayasa, Jero; Wahyudin; Mulyana, Tatang; Subali Noto, Muchamad

2018-04-01

Ethnomathematicsis considered as a new study in mathematic education. As a study, numerous regions in this world starts to explore through ethnomathematics, including Indonesia. As the intersection between mathematics and mathematical modelling and culture, ethnomathematics exists in various society’s cultural elements, including in the Balinese Hindus’ festivities. To find the mathematical concept used in determining the festivity days, the researcher(s) conducted ethnographic research in Bali Mula society in Kintamani District, Bali. Participation observation, in-depth interview, and literature and documentation were used in collecting the data. As the result, the researcher(s) revealed that the mathematical concept used is integer operations, least common multiple, mixed fraction, and number sequences. Since it contains mathematical concept used in junior high, thus ethnomathematics of “4-hindu’s festivities” may be used as context in mathematics learning. By using ethnomathematics as the context, the researcher(s) expect that it will help teachers in motivation their students to learn mathematics.

How to Build a Course in Mathematical–Biological Modeling: Content and Processes for Knowledge and Skill

PubMed Central

2010-01-01

Biological problems in the twenty-first century are complex and require mathematical insight, often resulting in mathematical models of biological systems. Building mathematical–biological models requires cooperation among biologists and mathematicians, and mastery of building models. A new course in mathematical modeling presented the opportunity to build both content and process learning of mathematical models, the modeling process, and the cooperative process. There was little guidance from the literature on how to build such a course. Here, I describe the iterative process of developing such a course, beginning with objectives and choosing content and process competencies to fulfill the objectives. I include some inductive heuristics for instructors seeking guidance in planning and developing their own courses, and I illustrate with a description of one instructional model cycle. Students completing this class reported gains in learning of modeling content, the modeling process, and cooperative skills. Student content and process mastery increased, as assessed on several objective-driven metrics in many types of assessments. PMID:20810966

Modeling and simulation for fewer-axis grinding of complex surface

NASA Astrophysics Data System (ADS)

Li, Zhengjian; Peng, Xiaoqiang; Song, Ci

2017-10-01

As the basis of fewer-axis grinding of complex surface, the grinding mathematical model is of great importance. A mathematical model of the grinding wheel was established, and then coordinate and normal vector of the wheel profile could be calculated. Through normal vector matching at the cutter contact point and the coordinate system transformation, the grinding mathematical model was established to work out the coordinate of the cutter location point. Based on the model, interference analysis was simulated to find out the right position and posture of workpiece for grinding. Then positioning errors of the workpiece including the translation positioning error and the rotation positioning error were analyzed respectively, and the main locating datum was obtained. According to the analysis results, the grinding tool path was planned and generated to grind the complex surface, and good form accuracy was obtained. The grinding mathematical model is simple, feasible and can be widely applied.

Current advancements and challenges in soil-root interactions modelling

NASA Astrophysics Data System (ADS)

Schnepf, Andrea; Huber, Katrin; Abesha, Betiglu; Meunier, Felicien; Leitner, Daniel; Roose, Tiina; Javaux, Mathieu; Vanderborght, Jan; Vereecken, Harry

2015-04-01

Roots change their surrounding soil chemically, physically and biologically. This includes changes in soil moisture and solute concentration, the exudation of organic substances into the rhizosphere, increased growth of soil microorganisms, or changes in soil structure. The fate of water and solutes in the root zone is highly determined by these root-soil interactions. Mathematical models of soil-root systems in combination with non-invasive techniques able to characterize root systems are a promising tool to understand and predict the behaviour of water and solutes in the root zone. With respect to different fields of applications, predictive mathematical models can contribute to the solution of optimal control problems in plant recourse efficiency. This may result in significant gains in productivity, efficiency and environmental sustainability in various land use activities. Major challenges include the coupling of model parameters of the relevant processes with the surrounding environment such as temperature, nutrient concentration or soil water content. A further challenge is the mathematical description of the different spatial and temporal scales involved. This includes in particular the branched structures formed by root systems or the external mycelium of mycorrhizal fungi. Here, reducing complexity as well as bridging between spatial scales is required. Furthermore, the combination of experimental and mathematical techniques may advance the field enormously. Here, the use of root system, soil and rhizosphere models is presented through a number of modelling case studies, including image based modelling of phosphate uptake by a root with hairs, model-based optimization of root architecture for phosphate uptake from soil, upscaling of rhizosphere models, modelling root growth in structured soil, and the effect of root hydraulic architecture on plant water uptake efficiency and drought resistance.

Current Advancements and Challenges in Soil-Root Interactions Modelling

NASA Astrophysics Data System (ADS)

Schnepf, A.; Huber, K.; Abesha, B.; Meunier, F.; Leitner, D.; Roose, T.; Javaux, M.; Vanderborght, J.; Vereecken, H.

2014-12-01

Roots change their surrounding soil chemically, physically and biologically. This includes changes in soil moisture and solute concentration, the exudation of organic substances into the rhizosphere, increased growth of soil microorganisms, or changes in soil structure. The fate of water and solutes in the root zone is highly determined by these root-soil interactions. Mathematical models of soil-root systems in combination with non-invasive techniques able to characterize root systems are a promising tool to understand and predict the behaviour of water and solutes in the root zone. With respect to different fields of applications, predictive mathematical models can contribute to the solution of optimal control problems in plant recourse efficiency. This may result in significant gains in productivity, efficiency and environmental sustainability in various land use activities. Major challenges include the coupling of model parameters of the relevant processes with the surrounding environment such as temperature, nutrient concentration or soil water content. A further challenge is the mathematical description of the different spatial and temporal scales involved. This includes in particular the branched structures formed by root systems or the external mycelium of mycorrhizal fungi. Here, reducing complexity as well as bridging between spatial scales is required. Furthermore, the combination of experimental and mathematical techniques may advance the field enormously. Here, the use of root system, soil and rhizosphere models is presented through a number of modelling case studies, including image based modelling of phosphate uptake by a root with hairs, model-based optimization of root architecture for phosphate uptake from soil, upscaling of rhizosphere models, modelling root growth in structured soil, and the effect of root hydraulic architecture on plant water uptake efficiency and drought resistance.

Will big data yield new mathematics? An evolving synergy with neuroscience

PubMed Central

Feng, S.; Holmes, P.

2016-01-01

New mathematics has often been inspired by new insights into the natural world. Here we describe some ongoing and possible future interactions among the massive data sets being collected in neuroscience, methods for their analysis and mathematical models of the underlying, still largely uncharted neural substrates that generate these data. We start by recalling events that occurred in turbulence modelling when substantial space-time velocity field measurements and numerical simulations allowed a new perspective on the governing equations of fluid mechanics. While no analogous global mathematical model of neural processes exists, we argue that big data may enable validation or at least rejection of models at cellular to brain area scales and may illuminate connections among models. We give examples of such models and survey some relatively new experimental technologies, including optogenetics and functional imaging, that can report neural activity in live animals performing complex tasks. The search for analytical techniques for these data is already yielding new mathematics, and we believe their multi-scale nature may help relate well-established models, such as the Hodgkin–Huxley equations for single neurons, to more abstract models of neural circuits, brain areas and larger networks within the brain. In brief, we envisage a closer liaison, if not a marriage, between neuroscience and mathematics. PMID:27516705

Will big data yield new mathematics? An evolving synergy with neuroscience.

PubMed

Feng, S; Holmes, P

2016-06-01

New mathematics has often been inspired by new insights into the natural world. Here we describe some ongoing and possible future interactions among the massive data sets being collected in neuroscience, methods for their analysis and mathematical models of the underlying, still largely uncharted neural substrates that generate these data. We start by recalling events that occurred in turbulence modelling when substantial space-time velocity field measurements and numerical simulations allowed a new perspective on the governing equations of fluid mechanics. While no analogous global mathematical model of neural processes exists, we argue that big data may enable validation or at least rejection of models at cellular to brain area scales and may illuminate connections among models. We give examples of such models and survey some relatively new experimental technologies, including optogenetics and functional imaging, that can report neural activity in live animals performing complex tasks. The search for analytical techniques for these data is already yielding new mathematics, and we believe their multi-scale nature may help relate well-established models, such as the Hodgkin-Huxley equations for single neurons, to more abstract models of neural circuits, brain areas and larger networks within the brain. In brief, we envisage a closer liaison, if not a marriage, between neuroscience and mathematics.

Asymmetrical booster ascent guidance and control system design study. Volume 2: SSFS math models - Ascent. [space shuttle development

NASA Technical Reports Server (NTRS)

Williams, F. E.; Lemon, R. S.

1974-01-01

The engineering equations and mathematical models developed for use in the space shuttle functional simulator (SSFS) are presented, and include extensive revisions and additions to earlier documentation. Definitions of coordinate systems used by the SSFS models and coordinate tranformations are given, along with documentation of the flexible body mathematical models. The models were incorporated in the SSFS and are in the checkout stage.

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

ERIC Educational Resources Information Center

Fox, William

2012-01-01

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

Caring teaching practices in multiethnic mathematics classrooms: attending to health and well-being

NASA Astrophysics Data System (ADS)

Averill, Robin

2012-06-01

Factors that contribute to strong teacher-student relationships are vital to understand because of the influence these relationships have on achievement and motivation, particularly for minority group students. This article draws from a substantial quantity of empirical data, grounded in a wide theoretical and cultural base, regarding aspects of caring teacher practice to discuss mathematics teacher behaviours in relation to an existing model of health and well-being that encompasses cognitive, social, spiritual, and physical dimensions. Drawing from 100 Year 10 mathematics lesson observations involving six teachers and their classes across three urban schools, evidence emerged that for many indigenous (Māori), New Zealand Pacific, and New Zealand European students, caring teacher behaviours important for student engagement and achievement both include, and range beyond, traditional teaching practices. Examples include capitalising on student reactions and shared endeavours within the context of mathematics learning, expecting mathematical progress, showing respect for students and for their mathematics learning, being explicit about practice and expectations, incorporating one-to-one interactions, making opportunities within mathematics learning for sharing personal identities, and incorporating movement. This research illustrates how mathematics educators can attend to the specific and holistic mathematical learning needs of their students, including those often marginalised.

A Mathematical Model of the Great Solar Eclipse of 1991.

ERIC Educational Resources Information Center

Lamb, John Jr.

1991-01-01

An activity that shows how mathematics can be used to model events in the real world is described. A way to calculate the area of the sun covered by the moon during a partial eclipse is presented. A computer program that will determine the coverage percentage is also included. (KR)

Longitudinal Evaluation of a Scale-Up Model for Teaching Mathematics with Trajectories and Technologies: Mechanisms of Persistence of Effects

ERIC Educational Resources Information Center

Clements, Douglas H.

2011-01-01

The author and her colleagues' TRIAD model (Sarama, Clements, Starkey, Klein, & Wakeley, 2008), including the "Building Blocks" curriculum, have significantly and substantially increased preschooler's mathematical competence, both in previous studies (Clements & Sarama, 2008, g = 1.07) and in their present, largest implementation…

Explanatory model of emotional-cognitive variables in school mathematics performance: a longitudinal study in primary school.

PubMed

Cerda, Gamal; Pérez, Carlos; Navarro, José I; Aguilar, Manuel; Casas, José A; Aragón, Estíbaliz

2015-01-01

This study tested a structural model of cognitive-emotional explanatory variables to explain performance in mathematics. The predictor variables assessed were related to students' level of development of early mathematical competencies (EMCs), specifically, relational and numerical competencies, predisposition toward mathematics, and the level of logical intelligence in a population of primary school Chilean students (n = 634). This longitudinal study also included the academic performance of the students during a period of 4 years as a variable. The sampled students were initially assessed by means of an Early Numeracy Test, and, subsequently, they were administered a Likert-type scale to measure their predisposition toward mathematics (EPMAT) and a basic test of logical intelligence. The results of these tests were used to analyse the interaction of all the aforementioned variables by means of a structural equations model. This combined interaction model was able to predict 64.3% of the variability of observed performance. Preschool students' performance in EMCs was a strong predictor for achievement in mathematics for students between 8 and 11 years of age. Therefore, this paper highlights the importance of EMCs and the modulating role of predisposition toward mathematics. Also, this paper discusses the educational role of these findings, as well as possible ways to improve negative predispositions toward mathematical tasks in the school domain.

Analysis of critical thinking ability of VII grade students based on the mathematical anxiety level through learning cycle 7E model

NASA Astrophysics Data System (ADS)

Widyaningsih, E.; Waluya, S. B.; Kurniasih, A. W.

2018-03-01

This study aims to know mastery learning of students’ critical thinking ability with learning cycle 7E, determine whether the critical thinking ability of the students with learning cycle 7E is better than students’ critical thinking ability with expository model, and describe the students’ critical thinking phases based on the mathematical anxiety level. The method is mixed method with concurrent embedded. The population is VII grade students of SMP Negeri 3 Kebumen academic year 2016/2017. Subjects are determined by purposive sampling, selected two students from each level of mathematical anxiety. Data collection techniques include test, questionnaire, interview, and documentation. Quantitative data analysis techniques include mean test, proportion test, difference test of two means, difference test of two proportions and for qualitative data used Miles and Huberman model. The results show that: (1) students’ critical thinking ability with learning cycle 7E achieve mastery learning; (2) students’ critical thinking ability with learning cycle 7E is better than students’ critical thinking ability with expository model; (3) description of students’ critical thinking phases based on the mathematical anxiety level that is the lower the mathematical anxiety level, the subjects have been able to fulfil all of the indicators of clarification, assessment, inference, and strategies phases.

Models of Influence on Mathematics Instructional Coaches

ERIC Educational Resources Information Center

Brown, Sue; Harrell, Scott; Browning, Sandra

2017-01-01

In our study, we examine the factors influencing the implementation of a mathematics coaching initiative at four high schools including the assets an instructional coach brings to the position and the challenges unique to each school. In our case study we include data collected in individual interviews with instructional coaches, focus groups with…

Yeast for Mathematicians: A Ferment of Discovery and Model Competition to Describe Data.

PubMed

Lewis, Matthew; Powell, James

2017-02-01

In addition to the memorization, algorithmic skills and vocabulary which are the default focus in many mathematics classrooms, professional mathematicians are expected to creatively apply known techniques, construct new mathematical approaches and communicate with and about mathematics. We propose that students can learn these professional, higher-level skills through Laboratory Experiences in Mathematical Biology which put students in the role of mathematics researcher creating mathematics to describe and understand biological data. Here we introduce a laboratory experience centered on yeast (Saccharomyces cerevisiae) growing in a small capped flask with a jar to collect carbon dioxide created during yeast growth and respiration. The lab requires no specialized equipment and can easily be run in the context of a college math class. Students collect data and develop mathematical models to explain the data. To help place instructors in the role of mentor/collaborator (as opposed to jury/judge), we facilitate the lab using model competition judged via Bayesian Information Criterion. This article includes details about the class activity conducted, student examples and pedagogical strategies for success.

Using Formative Assessment and Self-Regulated Learning to Help Developmental Mathematics Students Achieve: A Multi-Campus Program

ERIC Educational Resources Information Center

Hudesman, John; Crosby, Sara; Ziehmke, Niesha; Everson, Howard; Issac, Sharlene; Flugman, Bert; Zimmerman, Barry; Moylan, Adam

2014-01-01

The authors describe an Enhanced Formative Assessment and Self-Regulated Learning (EFA-SRL) program designed to improve the achievement of community college students enrolled in developmental mathematics courses. Their model includes the use of specially formatted quizzes designed to assess both the students' mathematics and metacognitive skill…

Effectiveness of discovery learning model on mathematical problem solving

NASA Astrophysics Data System (ADS)

Herdiana, Yunita; Wahyudin, Sispiyati, Ririn

2017-08-01

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

The Dynamics of Drug Resistance: A Mathematical Perspective

PubMed Central

Lavi, Orit; Gottesman, Michael M.; Levy, Doron

2012-01-01

Resistance to chemotherapy is a key impediment to successful cancer treatment that has been intensively studied for the last three decades. Several central mechanisms have been identified as contributing to the resistance. In the case of multidrug resistance (MDR), the cell becomes resistant to a variety of structurally and mechanistically unrelated drugs in addition to the drug initially administered. Mathematical models of drug resistance have dealt with many of the known aspects of this field, such as pharmacologic sanctuary and location/diffusion resistance, intrinsic resistance that is therapy independent, therapy-dependent cellular alterations including induced resistance (dose-dependent) and acquired resistance (dose-independent). In addition, there are mathematical models that take into account the kinetic/phase resistance, and models that investigate intra-cellular mechanisms based on specific biological functions (such as ABC transporters, apoptosis and repair mechanisms). This review covers aspects of MDR that have been mathematically studied, and explains how, from a methodological perspective, mathematics can be used to study drug resistance. We discuss quantitative approaches of mathematical analysis, and demonstrate how mathematics can be used in combination with other experimental and clinical tools. We emphasize the potential benefits of integrating analytical and mathematical methods into future clinical and experimental studies of drug resistance. PMID:22387162

Mathematical modeling relevant to closed artificial ecosystems

USGS Publications Warehouse

DeAngelis, D.L.

2003-01-01

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

Automated method for the systematic interpretation of resonance peaks in spectrum data

DOEpatents

Damiano, B.; Wood, R.T.

1997-04-22

A method is described for spectral signature interpretation. The method includes the creation of a mathematical model of a system or process. A neural network training set is then developed based upon the mathematical model. The neural network training set is developed by using the mathematical model to generate measurable phenomena of the system or process based upon model input parameter that correspond to the physical condition of the system or process. The neural network training set is then used to adjust internal parameters of a neural network. The physical condition of an actual system or process represented by the mathematical model is then monitored by extracting spectral features from measured spectra of the actual process or system. The spectral features are then input into said neural network to determine the physical condition of the system or process represented by the mathematical model. More specifically, the neural network correlates the spectral features (i.e. measurable phenomena) of the actual process or system with the corresponding model input parameters. The model input parameters relate to specific components of the system or process, and, consequently, correspond to the physical condition of the process or system. 1 fig.

Dynamics of Zika virus outbreaks: an overview of mathematical modeling approaches.

PubMed

Wiratsudakul, Anuwat; Suparit, Parinya; Modchang, Charin

2018-01-01

The Zika virus was first discovered in 1947. It was neglected until a major outbreak occurred on Yap Island, Micronesia, in 2007. Teratogenic effects resulting in microcephaly in newborn infants is the greatest public health threat. In 2016, the Zika virus epidemic was declared as a Public Health Emergency of International Concern (PHEIC). Consequently, mathematical models were constructed to explicitly elucidate related transmission dynamics. In this review article, two steps of journal article searching were performed. First, we attempted to identify mathematical models previously applied to the study of vector-borne diseases using the search terms "dynamics," "mathematical model," "modeling," and "vector-borne" together with the names of vector-borne diseases including chikungunya, dengue, malaria, West Nile, and Zika. Then the identified types of model were further investigated. Second, we narrowed down our survey to focus on only Zika virus research. The terms we searched for were "compartmental," "spatial," "metapopulation," "network," "individual-based," "agent-based" AND "Zika." All relevant studies were included regardless of the year of publication. We have collected research articles that were published before August 2017 based on our search criteria. In this publication survey, we explored the Google Scholar and PubMed databases. We found five basic model architectures previously applied to vector-borne virus studies, particularly in Zika virus simulations. These include compartmental, spatial, metapopulation, network, and individual-based models. We found that Zika models carried out for early epidemics were mostly fit into compartmental structures and were less complicated compared to the more recent ones. Simple models are still commonly used for the timely assessment of epidemics. Nevertheless, due to the availability of large-scale real-world data and computational power, recently there has been growing interest in more complex modeling frameworks. Mathematical models are employed to explore and predict how an infectious disease spreads in the real world, evaluate the disease importation risk, and assess the effectiveness of intervention strategies. As the trends in modeling of infectious diseases have been shifting towards data-driven approaches, simple and complex models should be exploited differently. Simple models can be produced in a timely fashion to provide an estimation of the possible impacts. In contrast, complex models integrating real-world data require more time to develop but are far more realistic. The preparation of complicated modeling frameworks prior to the outbreaks is recommended, including the case of future Zika epidemic preparation.

Mathematical modelling as a proof of concept for MPNs as a human inflammation model for cancer development.

PubMed

Andersen, Morten; Sajid, Zamra; Pedersen, Rasmus K; Gudmand-Hoeyer, Johanne; Ellervik, Christina; Skov, Vibe; Kjær, Lasse; Pallisgaard, Niels; Kruse, Torben A; Thomassen, Mads; Troelsen, Jesper; Hasselbalch, Hans Carl; Ottesen, Johnny T

2017-01-01

The chronic Philadelphia-negative myeloproliferative neoplasms (MPNs) are acquired stem cell neoplasms which ultimately may transform to acute myelogenous leukemia. Most recently, chronic inflammation has been described as an important factor for the development and progression of MPNs in the biological continuum from early cancer stage to the advanced myelofibrosis stage, the MPNs being described as "A Human Inflammation Model for Cancer Development". This novel concept has been built upon clinical, experimental, genomic, immunological and not least epidemiological studies. Only a few studies have described the development of MPNs by mathematical models, and none have addressed the role of inflammation for clonal evolution and disease progression. Herein, we aim at using mathematical modelling to substantiate the concept of chronic inflammation as an important trigger and driver of MPNs.The basics of the model describe the proliferation from stem cells to mature cells including mutations of healthy stem cells to become malignant stem cells. We include a simple inflammatory coupling coping with cell death and affecting the basic model beneath. First, we describe the system without feedbacks or regulatory interactions. Next, we introduce inflammatory feedback into the system. Finally, we include other feedbacks and regulatory interactions forming the inflammatory-MPN model. Using mathematical modeling, we add further proof to the concept that chronic inflammation may be both a trigger of clonal evolution and an important driving force for MPN disease progression. Our findings support intervention at the earliest stage of cancer development to target the malignant clone and dampen concomitant inflammation.

Discrete Mathematical Models [and] Spreadsheets in the Classroom. Dissemination Packet--Summer 1989: Booklet #8.

ERIC Educational Resources Information Center

Knee, David; And Others

This booklet is the eighth in a series of nine from the Teacher Training Institute at Hofstra University (New York) and contains descriptive information about two courses included in the institute's program. The first course, by David Knee, William McKeough, and Robert Silverstone, is "Discrete Mathematical Models," which deals with…

Focusing on Interactions between Content and Cognition: A New Perspective on Gender Differences in Mathematical Sub-Competencies

ERIC Educational Resources Information Center

George, Ann Cathrice; Robitzsch, Alexander

2018-01-01

This article presents a new perspective on measuring gender differences in the large-scale assessment study Trends in International Science Study (TIMSS). The suggested empirical model is directly based on the theoretical competence model of the domain mathematics and thus includes the interaction between content and cognitive sub-competencies.…

Mathematical modeling of growth of non-O157 Shiga Toxin-producing Escherichia coli in raw ground beef

USDA-ARS?s Scientific Manuscript database

The objective of this study was to investigate the growth of Shiga toxin-producing Escherichia coli (STEC, including serogroups O45, O103, O111, O121, and O145) in raw ground beef and to develop mathematical models to describe the bacterial growth under different temperature conditions. Three prima...

Examples as an Instructional Tool in Mathematics and Science Classrooms: Teachers' Perceptions and Attitudes

ERIC Educational Resources Information Center

Huang, Xiaoxia; Cribbs, Jennifer

2017-01-01

This study examined mathematics and science teachers' perceptions and use of four types of examples, including typical textbook examples (standard worked examples) and erroneous worked examples in the written form as well as mastery modelling examples and peer modelling examples involving the verbalization of the problem-solving process. Data…

An Investigation of Learning Styles Influencing Mathematics Achievement of Seventh-Grade Students

ERIC Educational Resources Information Center

Sriphai, Sunan; Damrongpanit, Suntonrapot; Sakulku, Jaruwan

2011-01-01

This study aims to investigate the effect of learning styles, as well as compare the effect of two different variable structure models of learning styles on factors influencing mathematics achievement. The research sample was made up of 508 seventh-grade students. The findings were that the model including learning styles as factors influencing…

Mathematical psychology.

PubMed

Batchelder, William H

2010-09-01

Mathematical psychology is a sub-field of psychology that started in the 1950s and has continued to grow as an important contributor to formal psychological theory, especially in the cognitive areas of psychology such as learning, memory, classification, choice response time, decision making, attention, and problem solving. In addition, there are several scientific sub-areas that were originated by mathematical psychologists such as the foundations of measurement, stochastic memory models, and psychologically motivated reformulations of expected utility theory. Mathematical psychology does not include all uses of mathematics and statistics in psychology, and indeed there is a long history of such uses especially in the areas of perception and psychometrics. What is most unique about mathematical psychology is its approach to theory construction. While accepting the behaviorist dictum that the data in psychology must be observable and replicable, mathematical models are specified in terms of unobservable formal constructs that can predict detailed aspects of data across multiple experimental and natural settings. By now almost all the substantive areas of cognitive and experimental psychology have formal mathematical models and theories, and many of these are due to researchers that identify with mathematical psychology. Copyright © 2010 John Wiley & Sons, Ltd. For further resources related to this article, please visit the WIREs website. Copyright © 2010 John Wiley & Sons, Ltd.

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

NASA Astrophysics Data System (ADS)

Neves, Rui Gomes; Teodoro, Vítor Duarte

2012-09-01

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

Retrospective estimation of breeding phenology of American Goldfinch (Carduelis tristis) using pattern oriented modeling

EPA Science Inventory

Avian seasonal productivity is often modeled as a time-limited stochastic process. Many mathematical formulations have been proposed, including individual based models, continuous-time differential equations, and discrete Markov models. All such models typically include paramete...

A general consumer-resource population model

USGS Publications Warehouse

Lafferty, Kevin D.; DeLeo, Giulio; Briggs, Cheryl J.; Dobson, Andrew P.; Gross, Thilo; Kuris, Armand M.

2015-01-01

Food-web dynamics arise from predator-prey, parasite-host, and herbivore-plant interactions. Models for such interactions include up to three consumer activity states (questing, attacking, consuming) and up to four resource response states (susceptible, exposed, ingested, resistant). Articulating these states into a general model allows for dissecting, comparing, and deriving consumer-resource models. We specify this general model for 11 generic consumer strategies that group mathematically into predators, parasites, and micropredators and then derive conditions for consumer success, including a universal saturating functional response. We further show how to use this framework to create simple models with a common mathematical lineage and transparent assumptions. Underlying assumptions, missing elements, and composite parameters are revealed when classic consumer-resource models are derived from the general model.

Automated method for the systematic interpretation of resonance peaks in spectrum data

DOEpatents

Damiano, Brian; Wood, Richard T.

1997-01-01

A method for spectral signature interpretation. The method includes the creation of a mathematical model of a system or process. A neural network training set is then developed based upon the mathematical model. The neural network training set is developed by using the mathematical model to generate measurable phenomena of the system or process based upon model input parameter that correspond to the physical condition of the system or process. The neural network training set is then used to adjust internal parameters of a neural network. The physical condition of an actual system or process represented by the mathematical model is then monitored by extracting spectral features from measured spectra of the actual process or system. The spectral features are then input into said neural network to determine the physical condition of the system or process represented by the mathematical. More specifically, the neural network correlates the spectral features (i.e. measurable phenomena) of the actual process or system with the corresponding model input parameters. The model input parameters relate to specific components of the system or process, and, consequently, correspond to the physical condition of the process or system.

Mathematical model of compact type evaporator

NASA Astrophysics Data System (ADS)

Borovička, Martin; Hyhlík, Tomáš

2018-06-01

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

Mathematical models used to inform study design or surveillance systems in infectious diseases: a systematic review.

PubMed

Herzog, Sereina A; Blaizot, Stéphanie; Hens, Niel

2017-12-18

Mathematical models offer the possibility to investigate the infectious disease dynamics over time and may help in informing design of studies. A systematic review was performed in order to determine to what extent mathematical models have been incorporated into the process of planning studies and hence inform study design for infectious diseases transmitted between humans and/or animals. We searched Ovid Medline and two trial registry platforms (Cochrane, WHO) using search terms related to infection, mathematical model, and study design from the earliest dates to October 2016. Eligible publications and registered trials included mathematical models (compartmental, individual-based, or Markov) which were described and used to inform the design of infectious disease studies. We extracted information about the investigated infection, population, model characteristics, and study design. We identified 28 unique publications but no registered trials. Focusing on compartmental and individual-based models we found 12 observational/surveillance studies and 11 clinical trials. Infections studied were equally animal and human infectious diseases for the observational/surveillance studies, while all but one between humans for clinical trials. The mathematical models were used to inform, amongst other things, the required sample size (n = 16), the statistical power (n = 9), the frequency at which samples should be taken (n = 6), and from whom (n = 6). Despite the fact that mathematical models have been advocated to be used at the planning stage of studies or surveillance systems, they are used scarcely. With only one exception, the publications described theoretical studies, hence, not being utilised in real studies.

Developing calculus textbook model that supported with GeoGebra to enhancing students’ mathematical problem solving and mathematical representation

NASA Astrophysics Data System (ADS)

Dewi, N. R.; Arini, F. Y.

2018-03-01

The main purpose of this research is developing and produces a Calculus textbook model that supported with GeoGebra. This book was designed to enhancing students’ mathematical problem solving and mathematical representation. There were three stages in this research i.e. define, design, and develop. The textbooks consisted of 6 chapters which each chapter contains introduction, core materials and include examples and exercises. The textbook developed phase begins with the early stages of designed the book (draft 1) which then validated by experts. Revision of draft 1 produced draft 2. The data were analyzed with descriptive statistics. The analysis showed that the Calculus textbook model that supported with GeoGebra, valid and fill up the criteria of practicality.

Analysis, testing, and evaluation of faulted and unfaulted Wye, Delta, and open Delta connected electromechanical actuators

NASA Technical Reports Server (NTRS)

Nehl, T. W.; Demerdash, N. A.

1983-01-01

Mathematical models capable of simulating the transient, steady state, and faulted performance characteristics of various brushless dc machine-PSA (power switching assembly) configurations were developed. These systems are intended for possible future use as primemovers in EMAs (electromechanical actuators) for flight control applications. These machine-PSA configurations include wye, delta, and open-delta connected systems. The research performed under this contract was initially broken down into the following six tasks: development of mathematical models for various machine-PSA configurations; experimental validation of the model for failure modes; experimental validation of the mathematical model for shorted turn-failure modes; tradeoff study; and documentation of results and methodology.

An epidemiological model with vaccination strategies

NASA Astrophysics Data System (ADS)

Prates, Dérek B.; Silva, Jaqueline M.; Gomes, Jessica L.; Kritz, Maurício V.

2016-06-01

Mathematical models can be widely found in the literature describing epidemics. The epidemical models that use differential equations to represent mathematically such description are especially sensible to parameters. This work analyze a variation of the SIR model when applied to a epidemic scenario including several aspects, as constant vaccination, pulse vaccination, seasonality, cross-immunity factor, birth and dead rate. The analysis and results are performed through numerical solutions of the model and a special attention is given to the discussion generated by the paramenters variation.

Explanatory model of emotional-cognitive variables in school mathematics performance: a longitudinal study in primary school

PubMed Central

Cerda, Gamal; Pérez, Carlos; Navarro, José I.; Aguilar, Manuel; Casas, José A.; Aragón, Estíbaliz

2015-01-01

This study tested a structural model of cognitive-emotional explanatory variables to explain performance in mathematics. The predictor variables assessed were related to students’ level of development of early mathematical competencies (EMCs), specifically, relational and numerical competencies, predisposition toward mathematics, and the level of logical intelligence in a population of primary school Chilean students (n = 634). This longitudinal study also included the academic performance of the students during a period of 4 years as a variable. The sampled students were initially assessed by means of an Early Numeracy Test, and, subsequently, they were administered a Likert-type scale to measure their predisposition toward mathematics (EPMAT) and a basic test of logical intelligence. The results of these tests were used to analyse the interaction of all the aforementioned variables by means of a structural equations model. This combined interaction model was able to predict 64.3% of the variability of observed performance. Preschool students’ performance in EMCs was a strong predictor for achievement in mathematics for students between 8 and 11 years of age. Therefore, this paper highlights the importance of EMCs and the modulating role of predisposition toward mathematics. Also, this paper discusses the educational role of these findings, as well as possible ways to improve negative predispositions toward mathematical tasks in the school domain. PMID:26441739

Self-concept mediates the relation between achievement and emotions in mathematics.

PubMed

Van der Beek, Jojanneke P J; Van der Ven, Sanne H G; Kroesbergen, Evelyn H; Leseman, Paul P M

2017-09-01

Mathematics achievement is related to positive and negative emotions. Pekrun's control-value theory of achievement emotions suggests that students' self-concept (i.e., self-appraisal of ability) may be an important mediator of the relation between mathematics achievement and emotions. The aims were (1) to investigate the mediating role of mathematical self-concept in the relation between mathematics achievement and the achievement emotions of enjoyment and anxiety in a comprehensive model, and (2) to test possible differences in this mediating role between low-, average-, and high-achieving students. Participants were ninth-grade students (n = 1,014) from eight secondary schools in the Netherlands. Through an online survey including mathematical problems, students were asked to indicate their levels of mathematics enjoyment, anxiety, and self-concept. Structural equation modelling was used to test the mediating role of self-concept in the relation between mathematics achievement and emotions. Multigroup analyses were performed to compare these relations across the three achievement groups. Results confirmed full mediation of the relation between mathematics achievement and emotions by mathematical self-concept. Furthermore, we found higher self-concepts, more enjoyment and less math anxiety in high-achieving students compared to their average and low-achieving peers. No differences across these achievement groups were found in the relations in the mediational model. Mathematical self-concept plays a pivotal role in students' appraisal of mathematics. Mathematics achievement is only one factor explaining students' self-concept. Likely also classroom instruction and teachers' feedback strategies help to shape students' self-concept. © 2017 The British Psychological Society.

Integrated Technology Rotor Methodology Assessment Workshop

NASA Technical Reports Server (NTRS)

Mcnulty, Michael J. (Editor); Bousman, William G. (Editor)

1988-01-01

The conference proceedings contains 14 formal papers and the results of two panel discussions. In addition, a transcript of discussion that followed the paper presentations and panels is included. The papers are of two kinds. The first seven papers were directed specifically to the correlation of industry and government mathematical models with data for rotorcraft stability from six experiments. The remaining 7 papers dealt with related topics in the prediction of rotor aeroelastic or aeromechanical stability. The first of the panels provided an evaluation of the correlation that was shown between the mathematical models and the experimental data. The second panel addressed the general problems of the validation of mathematical models.

Mathematical and information-geometrical entropy for phenomenological Fourier and non-Fourier heat conduction

NASA Astrophysics Data System (ADS)

Li, Shu-Nan; Cao, Bing-Yang

2017-09-01

The second law of thermodynamics governs the direction of heat transport, which provides the foundational definition of thermodynamic Clausius entropy. The definitions of entropy are further generalized for the phenomenological heat transport models in the frameworks of classical irreversible thermodynamics and extended irreversible thermodynamics (EIT). In this work, entropic functions from mathematics are combined with phenomenological heat conduction models and connected to several information-geometrical conceptions. The long-time behaviors of these mathematical entropies exhibit a wide diversity and physical pictures in phenomenological heat conductions, including the tendency to thermal equilibrium, and exponential decay of nonequilibrium and asymptotics, which build a bridge between the macroscopic and microscopic modelings. In contrast with the EIT entropies, the mathematical entropies expressed in terms of the internal energy function can avoid singularity paired with nonpositive local absolute temperature caused by non-Fourier heat conduction models.

Mathematical model of an air-filled alpha stirling refrigerator

NASA Astrophysics Data System (ADS)

McFarlane, Patrick; Semperlotti, Fabio; Sen, Mihir

2013-10-01

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

Mathematical Model Of Variable-Polarity Plasma Arc Welding

NASA Technical Reports Server (NTRS)

Hung, R. J.

1996-01-01

Mathematical model of variable-polarity plasma arc (VPPA) welding process developed for use in predicting characteristics of welds and thus serves as guide for selection of process parameters. Parameters include welding electric currents in, and durations of, straight and reverse polarities; rates of flow of plasma and shielding gases; and sizes and relative positions of welding electrode, welding orifice, and workpiece.

A Mathematical Model for the Hippocampus: Towards the Understanding of Episodic Memory and Imagination

NASA Astrophysics Data System (ADS)

Tsuda, I.; Yamaguti, Y.; Kuroda, S.; Fukushima, Y.; Tsukada, M.

How does the brain encode episode? Based on the fact that the hippocampus is responsible for the formation of episodic memory, we have proposed a mathematical model for the hippocampus. Because episodic memory includes a time series of events, an underlying dynamics for the formation of episodic memory is considered to employ an association of memories. David Marr correctly pointed out in his theory of archecortex for a simple memory that the hippocampal CA3 is responsible for the formation of associative memories. However, a conventional mathematical model of associative memory simply guarantees a single association of memory unless a rule for an order of successive association of memories is given. The recent clinical studies in Maguire's group for the patients with the hippocampal lesion show that the patients cannot make a new story, because of the lack of ability of imagining new things. Both episodic memory and imagining things include various common characteristics: imagery, the sense of now, retrieval of semantic information, and narrative structures. Taking into account these findings, we propose a mathematical model of the hippocampus in order to understand the common mechanism of episodic memory and imagination.

Mathematics and Information Retrieval.

ERIC Educational Resources Information Center

Salton, Gerald

1979-01-01

Examines the main mathematical approaches to information retrieval, including both algebraic and probabilistic models, and describes difficulties which impede formalization of information retrieval processes. A number of developments are covered where new theoretical understandings have directly led to improved retrieval techniques and operations.…

QR-STEM: Energy and Environment as a Context for Improving QR and STEM Understandings of 6-12 Grade Teachers II. The Quantitative Reasoning

NASA Astrophysics Data System (ADS)

Mayes, R.; Lyford, M. E.; Myers, J. D.

2009-12-01

The Quantitative Reasoning in STEM (QR STEM) project is a state level Mathematics and Science Partnership Project (MSP) with a focus on the mathematics and statistics that underlies the understanding of complex global scientific issues. This session is a companion session to the QR STEM: The Science presentation. The focus of this session is the quantitative reasoning aspects of the project. As students move from understandings that range from local to global in perspective on issues of energy and environment, there is a significant increase in the need for mathematical and statistical conceptual understanding. These understandings must be accessible to the students within the scientific context, requiring the special understandings that are endemic within quantitative reasoning. The QR STEM project brings together interdisciplinary teams of higher education faculty and middle/high school teachers to explore complex problems in energy and environment. The disciplines include life sciences, physics, chemistry, earth science, statistics, and mathematics. These interdisciplinary teams develop open ended performance tasks to implement in the classroom, based on scientific concepts that underpin energy and environment. Quantitative reasoning is broken down into three components: Quantitative Literacy, Quantitative Interpretation, and Quantitative Modeling. Quantitative Literacy is composed of arithmetic concepts such as proportional reasoning, numeracy, and descriptive statistics. Quantitative Interpretation includes algebraic and geometric concepts that underlie the ability to interpret a model of natural phenomena which is provided for the student. This model may be a table, graph, or equation from which the student is to make predictions or identify trends, or from which they would use statistics to explore correlations or patterns in data. Quantitative modeling is the ability to develop the model from data, including the ability to test hypothesis using statistical procedures. We use the term model very broadly, so it includes visual models such as box models, as well as best fit equation models and hypothesis testing. One of the powerful outcomes of the project is the conversation which takes place between science teachers and mathematics teachers. First they realize that though they are teaching concepts that cross their disciplines, the barrier of scientific language within their subjects restricts students from applying the concepts across subjects. Second the mathematics teachers discover the context of science as a means of providing real world situations that engage students in the utility of mathematics as a tool for solving problems. Third the science teachers discover the barrier to understanding science that is presented by poor quantitative reasoning ability. Finally the students are engaged in exploring energy and environment in a manner which exposes the importance of seeing a problem from multiple interdisciplinary perspectives. The outcome is a democratic citizen capable of making informed decisions, and perhaps a future scientist.

Proceedings of the Annual Conference of the International Group for the Psychology of Mathematics Education (12th, Veszprem, Hungary, July 20-25, 1988), Volume 2.

ERIC Educational Resources Information Center

Borbas, Andrea, Ed.

The proceedings for the annual conference of the International Group for the Psychology of Mathematics Education (PME) include the following papers: "Intervention in a Mathematics Course at the College Level" (L. Gattuso & R. Lacasse); "The Education of Talented Children" (F. Genzwein); "The Development of a Model for Competence in Mathematical…

A mathematical simulation model of a 1985-era tilt-rotor passenger aircraft

NASA Technical Reports Server (NTRS)

Mcveigh, M. A.; Widdison, C. A.

1976-01-01

A mathematical model for use in real-time piloted simulation of a 1985-era tilt rotor passenger aircraft is presented. The model comprises the basic six degrees-of-freedom equations of motion, and a large angle of attack representation of the airframe and rotor aerodynamics, together with equations and functions used to model turbine engine performance, aircraft control system and stability augmentation system. A complete derivation of the primary equations is given together with a description of the modeling techniques used. Data for the model is included in an appendix.

Modeling Simple Telescope Optics in Secondary Mathematics Classrooms

NASA Astrophysics Data System (ADS)

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

2007-12-01

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

Mathematical modeling of silica deposition in Tongonan-I reinjection wells, Philippines

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

Malate, R.C.M.; O`Sullivan, M.J.

1993-10-01

Mathematical models of silica deposition are derived using the method of characteristics for the problem of variable rate injection into a well producing radially symmetric flow. Solutions are developed using the first order rate equation of silica deposition suggested by Rimstidt and Barnes (1980). The changes in porosity and permeability resulting from deposition are included in the models. The models developed are successfully applied in simulating the changes in injection capacity in some of the reinjection wells in Tongonan geothermal field, Philippines.

Nonconvex Model of Material Growth: Mathematical Theory

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

ECOLOGICAL THEORY. A general consumer-resource population model.

PubMed

Lafferty, Kevin D; DeLeo, Giulio; Briggs, Cheryl J; Dobson, Andrew P; Gross, Thilo; Kuris, Armand M

2015-08-21

Food-web dynamics arise from predator-prey, parasite-host, and herbivore-plant interactions. Models for such interactions include up to three consumer activity states (questing, attacking, consuming) and up to four resource response states (susceptible, exposed, ingested, resistant). Articulating these states into a general model allows for dissecting, comparing, and deriving consumer-resource models. We specify this general model for 11 generic consumer strategies that group mathematically into predators, parasites, and micropredators and then derive conditions for consumer success, including a universal saturating functional response. We further show how to use this framework to create simple models with a common mathematical lineage and transparent assumptions. Underlying assumptions, missing elements, and composite parameters are revealed when classic consumer-resource models are derived from the general model. Copyright © 2015, American Association for the Advancement of Science.

Mathematical models to characterize early epidemic growth: A Review

PubMed Central

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

2016-01-01

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

Mathematical models to characterize early epidemic growth: A review

NASA Astrophysics Data System (ADS)

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

2016-09-01

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

A Mathematical Model of Marine Diesel Engine Speed Control System

NASA Astrophysics Data System (ADS)

Sinha, Rajendra Prasad; Balaji, Rajoo

2018-02-01

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

Software and mathematical support of Kazakhstani star tracker

NASA Astrophysics Data System (ADS)

Akhmedov, D.; Yelubayev, S.; Ten, V.; Bopeyev, T.; Alipbayev, K.; Sukhenko, A.

2016-10-01

Currently the specialists of Kazakhstan have been developing the star tracker that is further planned to use on Kazakhstani satellites of various purposes. At the first stage it has been developed the experimental model of star tracker that has following characteristics: field of view 20°, update frequency 2 Hz, exclusion angle 40°, accuracy of attitude determination of optical axis/around optical axis 15/50 arcsec. Software and mathematical support are the most high technology parts of star tracker. The results of software and mathematical support development of experimental model of Kazakhstani star tracker are represented in this article. In particular, there are described the main mathematical models and algorithms that have been used as a basis for program units of preliminary image processing of starry sky, stars identification and star tracker attitude determination. The results of software and mathematical support testing with the help of program simulation complex using various configurations of defects including image sensor noises, point spread function modeling, optical system distortion up to 2% are presented. Analysis of testing results has shown that accuracy of attitude determination of star tracker is within the permissible range

Editorial: Mathematical Methods and Modeling in Machine Fault Diagnosis

DOE PAGES

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

2014-12-18

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

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

NASA Astrophysics Data System (ADS)

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

2017-08-01

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

Decision science and cervical cancer.

PubMed

Cantor, Scott B; Fahs, Marianne C; Mandelblatt, Jeanne S; Myers, Evan R; Sanders, Gillian D

2003-11-01

Mathematical modeling is an effective tool for guiding cervical cancer screening, diagnosis, and treatment decisions for patients and policymakers. This article describes the use of mathematical modeling as outlined in five presentations from the Decision Science and Cervical Cancer session of the Second International Conference on Cervical Cancer held at The University of Texas M. D. Anderson Cancer Center, April 11-14, 2002. The authors provide an overview of mathematical modeling, especially decision analysis and cost-effectiveness analysis, and examples of how it can be used for clinical decision making regarding the prevention, diagnosis, and treatment of cervical cancer. Included are applications as well as theory regarding decision science and cervical cancer. Mathematical modeling can answer such questions as the optimal frequency for screening, the optimal age to stop screening, and the optimal way to diagnose cervical cancer. Results from one mathematical model demonstrated that a vaccine against high-risk strains of human papillomavirus was a cost-effective use of resources, and discussion of another model demonstrated the importance of collecting direct non-health care costs and time costs for cost-effectiveness analysis. Research presented indicated that care must be taken when applying the results of population-wide, cost-effectiveness analyses to reduce health disparities. Mathematical modeling can encompass a variety of theoretical and applied issues regarding decision science and cervical cancer. The ultimate objective of using decision-analytic and cost-effectiveness models is to identify ways to improve women's health at an economically reasonable cost. Copyright 2003 American Cancer Society.

Students’ Mathematical Problem-Solving Abilities Through The Application of Learning Models Problem Based Learning

NASA Astrophysics Data System (ADS)

Nasution, M. L.; Yerizon, Y.; Gusmiyanti, R.

2018-04-01

One of the purpose mathematic learning is to develop problem solving abilities. Problem solving is obtained through experience in questioning non-routine. Improving students’ mathematical problem-solving abilities required an appropriate strategy in learning activities one of them is models problem based learning (PBL). Thus, the purpose of this research is to determine whether the problem solving abilities of mathematical students’ who learn to use PBL better than on the ability of students’ mathematical problem solving by applying conventional learning. This research included quasi experiment with static group design and population is students class XI MIA SMAN 1 Lubuk Alung. Class experiment in the class XI MIA 5 and class control in the class XI MIA 6. The instrument of final test students’ mathematical problem solving used essay form. The result of data final test in analyzed with t-test. The result is students’ mathematical problem solving abilities with PBL better then on the ability of students’ mathematical problem solving by applying conventional learning. It’s seen from the high percentage achieved by the group of students who learn to use PBL for each indicator of students’ mathematical problem solving.

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

M. A. Wasiolek

The purpose of this report is to document the biosphere model, the Environmental Radiation Model for Yucca Mountain, Nevada (ERMYN), which describes radionuclide transport processes in the biosphere and associated human exposure that may arise as the result of radionuclide release from the geologic repository at Yucca Mountain. The biosphere model is one of the process models that support the Yucca Mountain Project (YMP) Total System Performance Assessment (TSPA) for the license application (LA), the TSPA-LA. The ERMYN model provides the capability of performing human radiation dose assessments. This report documents the biosphere model, which includes: (1) Describing the referencemore » biosphere, human receptor, exposure scenarios, and primary radionuclides for each exposure scenario (Section 6.1); (2) Developing a biosphere conceptual model using site-specific features, events, and processes (FEPs), the reference biosphere, the human receptor, and assumptions (Section 6.2 and Section 6.3); (3) Building a mathematical model using the biosphere conceptual model and published biosphere models (Sections 6.4 and 6.5); (4) Summarizing input parameters for the mathematical model, including the uncertainty associated with input values (Section 6.6); (5) Identifying improvements in the ERMYN model compared with the model used in previous biosphere modeling (Section 6.7); (6) Constructing an ERMYN implementation tool (model) based on the biosphere mathematical model using GoldSim stochastic simulation software (Sections 6.8 and 6.9); (7) Verifying the ERMYN model by comparing output from the software with hand calculations to ensure that the GoldSim implementation is correct (Section 6.10); and (8) Validating the ERMYN model by corroborating it with published biosphere models; comparing conceptual models, mathematical models, and numerical results (Section 7).« less

Mathematical Model of Two Phase Flow in Natural Draft Wet-Cooling Tower Including Flue Gas Injection

NASA Astrophysics Data System (ADS)

Hyhlík, Tomáš

2016-03-01

The previously developed model of natural draft wet-cooling tower flow, heat and mass transfer is extended to be able to take into account the flow of supersaturated moist air. The two phase flow model is based on void fraction of gas phase which is included in the governing equations. Homogeneous equilibrium model, where the two phases are well mixed and have the same velocity, is used. The effect of flue gas injection is included into the developed mathematical model by using source terms in governing equations and by using momentum flux coefficient and kinetic energy flux coefficient. Heat and mass transfer in the fill zone is described by the system of ordinary differential equations, where the mass transfer is represented by measured fill Merkel number and heat transfer is calculated using prescribed Lewis factor.

Gender Gap in Mathematics and Physics in Chinese Middle Schools: A Case Study of A Beijing's District

ERIC Educational Resources Information Center

Li, Manli; Zhang, Yu; Wang, Yihan

2017-01-01

This study examines the gender gaps in mathematics and physics in Chinese middle schools. The data is from the Education Bureau management database which includes all middle school students who took high school entrance exam in a district of Beijing from 2006-2013. The ordinary least square model and quantile regression model are applied. This…

Dynamics of Zika virus outbreaks: an overview of mathematical modeling approaches

PubMed Central

Wiratsudakul, Anuwat; Suparit, Parinya

2018-01-01

Background The Zika virus was first discovered in 1947. It was neglected until a major outbreak occurred on Yap Island, Micronesia, in 2007. Teratogenic effects resulting in microcephaly in newborn infants is the greatest public health threat. In 2016, the Zika virus epidemic was declared as a Public Health Emergency of International Concern (PHEIC). Consequently, mathematical models were constructed to explicitly elucidate related transmission dynamics. Survey Methodology In this review article, two steps of journal article searching were performed. First, we attempted to identify mathematical models previously applied to the study of vector-borne diseases using the search terms “dynamics,” “mathematical model,” “modeling,” and “vector-borne” together with the names of vector-borne diseases including chikungunya, dengue, malaria, West Nile, and Zika. Then the identified types of model were further investigated. Second, we narrowed down our survey to focus on only Zika virus research. The terms we searched for were “compartmental,” “spatial,” “metapopulation,” “network,” “individual-based,” “agent-based” AND “Zika.” All relevant studies were included regardless of the year of publication. We have collected research articles that were published before August 2017 based on our search criteria. In this publication survey, we explored the Google Scholar and PubMed databases. Results We found five basic model architectures previously applied to vector-borne virus studies, particularly in Zika virus simulations. These include compartmental, spatial, metapopulation, network, and individual-based models. We found that Zika models carried out for early epidemics were mostly fit into compartmental structures and were less complicated compared to the more recent ones. Simple models are still commonly used for the timely assessment of epidemics. Nevertheless, due to the availability of large-scale real-world data and computational power, recently there has been growing interest in more complex modeling frameworks. Discussion Mathematical models are employed to explore and predict how an infectious disease spreads in the real world, evaluate the disease importation risk, and assess the effectiveness of intervention strategies. As the trends in modeling of infectious diseases have been shifting towards data-driven approaches, simple and complex models should be exploited differently. Simple models can be produced in a timely fashion to provide an estimation of the possible impacts. In contrast, complex models integrating real-world data require more time to develop but are far more realistic. The preparation of complicated modeling frameworks prior to the outbreaks is recommended, including the case of future Zika epidemic preparation. PMID:29593941

Mathematical Astronomy in India

NASA Astrophysics Data System (ADS)

Plofker, Kim

Astronomy in South Asia's Sanskrit tradition, apparently originating in simple calendric computations regulating the timing of ancient ritual practices, expanded over the course of two or three millennia to include detailed spherical models, an endless variety of astrological systems, and academic mathematics in general. Assimilating various technical models, methods, and genres from the astronomy of neighboring cultures, Indian astronomers created new forms that were in turn borrowed by their foreign counterparts. Always recognizably related to the main themes of Eurasian geocentric mathematical astronomy, Indian astral science nonetheless maintained its culturally distinct character until Keplerian heliocentrism and Newtonian mechanics replaced it in colonial South Asia's academic mainstream.

Mathematics Intervention for First- and Second-Grade Students with Mathematics Difficulties: The Effects of Tier 2 Intervention Delivered as Booster Lessons

ERIC Educational Resources Information Center

Bryant, Diane Pedrotty; Bryant, Brian R.; Gersten, Russell; Scammacca, Nancy; Chavez, Melissa M.

2008-01-01

This study sought to examine the effects of Tier 2 intervention in a multitiered model on the performance of first- and second-grade students who were identified as having mathematics difficulties. A regression discontinuity design was utilized. Participants included 126 (Tier 2, n = 26) first graders and 140 (Tier 2, n = 25) second graders. Tier…

Dynamic Analyses Including Joints Of Truss Structures

NASA Technical Reports Server (NTRS)

Belvin, W. Keith

1991-01-01

Method for mathematically modeling joints to assess influences of joints on dynamic response of truss structures developed in study. Only structures with low-frequency oscillations considered; only Coulomb friction and viscous damping included in analysis. Focus of effort to obtain finite-element mathematical models of joints exhibiting load-vs.-deflection behavior similar to measured load-vs.-deflection behavior of real joints. Experiments performed to determine stiffness and damping nonlinearities typical of joint hardware. Algorithm for computing coefficients of analytical joint models based on test data developed to enable study of linear and nonlinear effects of joints on global structural response. Besides intended application to large space structures, applications in nonaerospace community include ground-based antennas and earthquake-resistant steel-framed buildings.

Pathway Model of the Kinetics of the TGFbeta Antagonist Smad7 and Cross-Talk with the ATM and WNT Pathways

NASA Technical Reports Server (NTRS)

Carra, Claudio; Wang, Minli; Huff, Janice L.; Hada, Megumi; ONeill, Peter; Cucinotta, Francis A.

2010-01-01

Signal transduction controls cellular and tissue responses to radiation. Transforming growth factor beta (TGFbeta) is an important regulator of cell growth and differentiation and tissue homeostasis, and is often dis-regulated in tumor formation. Mathematical models of signal transduction pathways can be used to elucidate how signal transduction varies with radiation quality, and dose and dose-rate. Furthermore, modeling of tissue specific responses can be considered through mechanistic based modeling. We developed a mathematical model of the negative feedback regulation by Smad7 in TGFbeta-Smad signaling and are exploring possible connections to the WNT/beta -catenin, and ATM/ATF2 signaling pathways. A pathway model of TGFbeta-Smad signaling that includes Smad7 kinetics based on data in the scientific literature is described. Kinetic terms included are TGFbeta/Smad transcriptional regulation of Smad7 through the Smad3-Smad4 complex, Smad7-Smurf1 translocation from nucleus to cytoplasm, and Smad7 negative feedback regulation of the TGFO receptor through direct binding to the TGFO receptor complex. The negative feedback controls operating in this pathway suggests non-linear responses in signal transduction, which are described mathematically. We then explored possibilities for cross-talk mediated by Smad7 between DNA damage responses mediated by ATM, and with the WNT pathway and consider the design of experiments to test model driven hypothesis. Numerical comparisons of the mathematical model to experiments and representative predictions are described.

A Simple Mathematical Model for Standard Model of Elementary Particles and Extension Thereof

NASA Astrophysics Data System (ADS)

Sinha, Ashok

2016-03-01

An algebraically (and geometrically) simple model representing the masses of the elementary particles in terms of the interaction (strong, weak, electromagnetic) constants is developed, including the Higgs bosons. The predicted Higgs boson mass is identical to that discovered by LHC experimental programs; while possibility of additional Higgs bosons (and their masses) is indicated. The model can be analyzed to explain and resolve many puzzles of particle physics and cosmology including the neutrino masses and mixing; origin of the proton mass and the mass-difference between the proton and the neutron; the big bang and cosmological Inflation; the Hubble expansion; etc. A novel interpretation of the model in terms of quaternion and rotation in the six-dimensional space of the elementary particle interaction-space - or, equivalently, in six-dimensional spacetime - is presented. Interrelations among particle masses are derived theoretically. A new approach for defining the interaction parameters leading to an elegant and symmetrical diagram is delineated. Generalization of the model to include supersymmetry is illustrated without recourse to complex mathematical formulation and free from any ambiguity. This Abstract represents some results of the Author's Independent Theoretical Research in Particle Physics, with possible connection to the Superstring Theory. However, only very elementary mathematics and physics is used in my presentation.

Mathematics and Measurement.

PubMed

Boisvert, R F; Donahue, M J; Lozier, D W; McMichael, R; Rust, B W

2001-01-01

In this paper we describe the role that mathematics plays in measurement science at NIST. We first survey the history behind NIST's current work in this area, starting with the NBS Math Tables project of the 1930s. We then provide examples of more recent efforts in the application of mathematics to measurement science, including the solution of ill-posed inverse problems, characterization of the accuracy of software for micromagnetic modeling, and in the development and dissemination of mathematical reference data. Finally, we comment on emerging issues in measurement science to which mathematicians will devote their energies in coming years.

Instructional Aids in Mathematics: Using Models as Instructional Aids

ERIC Educational Resources Information Center

Johnson, Donovan A.; And Others

1973-01-01

Models are discussed both as concrete representations of mental constructs and as various manipulative devices. Illustrations of effective model use, suggestions for acquiring models, and lists of models for specific concepts are included. (LS)

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, and non-linear effects such as compression of response with stimulus level, two-tone suppression and the generation of harmonic and distortion products.

Time-Series INSAR: An Integer Least-Squares Approach For Distributed Scatterers

NASA Astrophysics Data System (ADS)

Samiei-Esfahany, Sami; Hanssen, Ramon F.

2012-01-01

The objective of this research is to extend the geode- tic mathematical model which was developed for persistent scatterers to a model which can exploit distributed scatterers (DS). The main focus is on the integer least- squares framework, and the main challenge is to include the decorrelation effect in the mathematical model. In order to adapt the integer least-squares mathematical model for DS we altered the model from a single master to a multi-master configuration and introduced the decorrelation effect stochastically. This effect is described in our model by a full covariance matrix. We propose to de- rive this covariance matrix by numerical integration of the (joint) probability distribution function (PDF) of interferometric phases. This PDF is a function of coherence values and can be directly computed from radar data. We show that the use of this model can improve the performance of temporal phase unwrapping of distributed scatterers.

Comparison of mathematical models of fibrosis. Comment on "Towards a unified approach in the modeling of fibrosis: A review with research perspectives" by M. Ben Amar and C. Bianca

NASA Astrophysics Data System (ADS)

Kachapova, Farida

2016-07-01

Mathematical and computational models in biology and medicine help to improve diagnostics and medical treatments. Modeling of pathological fibrosis is reviewed by M. Ben Amar and C. Bianca in [4]. Pathological fibrosis is the process when excessive fibrous tissue is deposited on an organ or tissue during a wound healing and can obliterate their normal function. In [4] the phenomena of fibrosis are briefly explained including the causes, mechanism and management; research models of pathological fibrosis are described, compared and critically analyzed. Different models are suitable at different levels: molecular, cellular and tissue. The main goal of mathematical modeling of fibrosis is to predict long term behavior of the system depending on bifurcation parameters; there are two main trends: inhibition of fibrosis due to an active immune system and swelling of fibrosis because of a weak immune system.

Are Three Sheets Enough? Using Toilet Paper to Teach Science and Mathematics

ERIC Educational Resources Information Center

Woolverton, Christopher J.; Woolverton, Lyssa N.

2006-01-01

Toilet paper (TP) composition and physical characteristics were used to model scientific investigations that combined several "National Science Education Standards." Experiments with TP permitted the integration of TP history, societal change resulting from invention, mathematics (including geometry and statistics), germ theory, and personal…

Ross, macdonald, and a theory for the dynamics and control of mosquito-transmitted pathogens.

PubMed

Smith, David L; Battle, Katherine E; Hay, Simon I; Barker, Christopher M; Scott, Thomas W; McKenzie, F Ellis

2012-01-01

Ronald Ross and George Macdonald are credited with developing a mathematical model of mosquito-borne pathogen transmission. A systematic historical review suggests that several mathematicians and scientists contributed to development of the Ross-Macdonald model over a period of 70 years. Ross developed two different mathematical models, Macdonald a third, and various "Ross-Macdonald" mathematical models exist. Ross-Macdonald models are best defined by a consensus set of assumptions. The mathematical model is just one part of a theory for the dynamics and control of mosquito-transmitted pathogens that also includes epidemiological and entomological concepts and metrics for measuring transmission. All the basic elements of the theory had fallen into place by the end of the Global Malaria Eradication Programme (GMEP, 1955-1969) with the concept of vectorial capacity, methods for measuring key components of transmission by mosquitoes, and a quantitative theory of vector control. The Ross-Macdonald theory has since played a central role in development of research on mosquito-borne pathogen transmission and the development of strategies for mosquito-borne disease prevention.

Ross, Macdonald, and a Theory for the Dynamics and Control of Mosquito-Transmitted Pathogens

PubMed Central

Smith, David L.; Battle, Katherine E.; Hay, Simon I.; Barker, Christopher M.; Scott, Thomas W.; McKenzie, F. Ellis

2012-01-01

Ronald Ross and George Macdonald are credited with developing a mathematical model of mosquito-borne pathogen transmission. A systematic historical review suggests that several mathematicians and scientists contributed to development of the Ross-Macdonald model over a period of 70 years. Ross developed two different mathematical models, Macdonald a third, and various “Ross-Macdonald” mathematical models exist. Ross-Macdonald models are best defined by a consensus set of assumptions. The mathematical model is just one part of a theory for the dynamics and control of mosquito-transmitted pathogens that also includes epidemiological and entomological concepts and metrics for measuring transmission. All the basic elements of the theory had fallen into place by the end of the Global Malaria Eradication Programme (GMEP, 1955–1969) with the concept of vectorial capacity, methods for measuring key components of transmission by mosquitoes, and a quantitative theory of vector control. The Ross-Macdonald theory has since played a central role in development of research on mosquito-borne pathogen transmission and the development of strategies for mosquito-borne disease prevention. PMID:22496640

Cognitive components of a mathematical processing network in 9-year-old children.

PubMed

Szűcs, Dénes; Devine, Amy; Soltesz, Fruzsina; Nobes, Alison; Gabriel, Florence

2014-07-01

We determined how various cognitive abilities, including several measures of a proposed domain-specific number sense, relate to mathematical competence in nearly 100 9-year-old children with normal reading skill. Results are consistent with an extended number processing network and suggest that important processing nodes of this network are phonological processing, verbal knowledge, visuo-spatial short-term and working memory, spatial ability and general executive functioning. The model was highly specific to predicting arithmetic performance. There were no strong relations between mathematical achievement and verbal short-term and working memory, sustained attention, response inhibition, finger knowledge and symbolic number comparison performance. Non-verbal intelligence measures were also non-significant predictors when added to our model. Number sense variables were non-significant predictors in the model and they were also non-significant predictors when entered into regression analysis with only a single visuo-spatial WM measure. Number sense variables were predicted by sustained attention. Results support a network theory of mathematical competence in primary school children and falsify the importance of a proposed modular 'number sense'. We suggest an 'executive memory function centric' model of mathematical processing. Mapping a complex processing network requires that studies consider the complex predictor space of mathematics rather than just focusing on a single or a few explanatory factors.

Cognitive components of a mathematical processing network in 9-year-old children

PubMed Central

Szűcs, Dénes; Devine, Amy; Soltesz, Fruzsina; Nobes, Alison; Gabriel, Florence

2014-01-01

We determined how various cognitive abilities, including several measures of a proposed domain-specific number sense, relate to mathematical competence in nearly 100 9-year-old children with normal reading skill. Results are consistent with an extended number processing network and suggest that important processing nodes of this network are phonological processing, verbal knowledge, visuo-spatial short-term and working memory, spatial ability and general executive functioning. The model was highly specific to predicting arithmetic performance. There were no strong relations between mathematical achievement and verbal short-term and working memory, sustained attention, response inhibition, finger knowledge and symbolic number comparison performance. Non-verbal intelligence measures were also non-significant predictors when added to our model. Number sense variables were non-significant predictors in the model and they were also non-significant predictors when entered into regression analysis with only a single visuo-spatial WM measure. Number sense variables were predicted by sustained attention. Results support a network theory of mathematical competence in primary school children and falsify the importance of a proposed modular ‘number sense’. We suggest an ‘executive memory function centric’ model of mathematical processing. Mapping a complex processing network requires that studies consider the complex predictor space of mathematics rather than just focusing on a single or a few explanatory factors. PMID:25089322

A Categorization Model for Educational Values of the History of Mathematics. An Empirical Study

NASA Astrophysics Data System (ADS)

Wang, Xiao-qin; Qi, Chun-yan; Wang, Ke

2017-11-01

There is not a clear consensus on the categorization framework of the educational values of the history of mathematics. By analyzing 20 Chinese teaching cases on integrating the history of mathematics into mathematics teaching based on the relevant literature, this study examined a new categorization framework of the educational values of the history of mathematics by combining the objectives of high school mathematics curriculum in China. This framework includes six dimensions: the harmony of knowledge, the beauty of ideas or methods, the pleasure of inquiries, the improvement of capabilities, the charm of cultures, and the availability of moral education. The results show that this framework better explained the all-educational values of the history of mathematics that all teaching cases showed. Therefore, the framework can guide teachers to better integrate the history of mathematics into teaching.

Aspects of job scheduling

NASA Technical Reports Server (NTRS)

Phillips, K.

1976-01-01

A mathematical model for job scheduling in a specified context is presented. The model uses both linear programming and combinatorial methods. While designed with a view toward optimization of scheduling of facility and plant operations at the Deep Space Communications Complex, the context is sufficiently general to be widely applicable. The general scheduling problem including options for scheduling objectives is discussed and fundamental parameters identified. Mathematical algorithms for partitioning problems germane to scheduling are presented.

The Poisson Random Process. Applications of Probability Theory to Operations Research. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Unit 340.

ERIC Educational Resources Information Center

Wilde, Carroll O.

The Poisson probability distribution is seen to provide a mathematical model from which useful information can be obtained in practical applications. The distribution and some situations to which it applies are studied, and ways to find answers to practical questions are noted. The unit includes exercises and a model exam, and provides answers to…

Mathematical modeling of a nickel-cadmium battery

NASA Technical Reports Server (NTRS)

Fan, Deyuan; White, Ralph E.

1991-01-01

Extensions are presented for a mathematical model of an Ni-CD cell (Fan and White, 1991). These extensions consist of intercalation thermodynamics for the nickel electrode and oxygen generation and reduction reactions during charge and overcharge. The simulated results indicate that intercalation may be important in the nickel electrode and that including the oxygen reactions provides a means of predicting the efficiency of the cell on charge and discharge.

Optimizing Marine Corps Pilot Conversion to the Joint Strike Fighter

DTIC Science & Technology

2010-06-01

Office of Civilian Manpower Management. Included are a summary of modeling efforts and the mathematics behind them, models for aggregate manpower...Vajda for the Admiralty of the Royal Navy. They also mention work by one of the first actuaries , John Rowe, who as early as 1779, conducted studies...idea of using mathematical and statistical techniques to obtain better information on the manpower requirements has its roots in personnel research

A mathematical model of an active control landing gear for load control during impact and roll-out

NASA Technical Reports Server (NTRS)

Mcgehee, J. R.; Carden, H. D.

1976-01-01

A mathematical model of an active control landing gear (ACOLAG) was developed and programmed for operation on a digital computer. The mathematical model includes theoretical subsonic aerodynamics; first-mode wing bending and torsional characteristics; oleo-pneumatic shock strut with fit and binding friction; closed-loop, series-hydraulic control; empirical tire force-deflection characteristics; antiskid braking; and sinusoidal or random runway roughness. The mathematical model was used to compute the loads and motions for a simulated vertical drop test and a simulated landing impact of a conventional (passive) main landing gear designed for a 2268-kg (5000-lbm) class airplane. Computations were also made for a simply modified version of the passive gear including a series-hydraulic active control system. Comparison of computed results for the passive gear with experimental data shows that the active control landing gear analysis is valid for predicting the loads and motions of an airplane during a symmetrical landing. Computed results for the series-hydraulic active control in conjunction with the simply modified passive gear show that 20- to 30-percent reductions in wing force, relative to those occurring with the modified passive gear, can be obtained during the impact phase of the landing. These reductions in wing force could result in substantial increases in fatigue life of the structure.

Introduction to a special section on ecohydrology of semiarid environments: Confronting mathematical models with ecosystem complexity

NASA Astrophysics Data System (ADS)

Svoray, Tal; Assouline, Shmuel; Katul, Gabriel

2015-11-01

Current literature provides large number of publications about ecohydrological processes and their effect on the biota in drylands. Given the limited laboratory and field experiments in such systems, many of these publications are based on mathematical models of varying complexity. The underlying implicit assumption is that the data set used to evaluate these models covers the parameter space of conditions that characterize drylands and that the models represent the actual processes with acceptable certainty. However, a question raised is to what extent these mathematical models are valid when confronted with observed ecosystem complexity? This Introduction reviews the 16 papers that comprise the Special Section on Eco-hydrology of Semiarid Environments: Confronting Mathematical Models with Ecosystem Complexity. The subjects studied in these papers include rainfall regime, infiltration and preferential flow, evaporation and evapotranspiration, annual net primary production, dispersal and invasion, and vegetation greening. The findings in the papers published in this Special Section show that innovative mathematical modeling approaches can represent actual field measurements. Hence, there are strong grounds for suggesting that mathematical models can contribute to greater understanding of ecosystem complexity through characterization of space-time dynamics of biomass and water storage as well as their multiscale interactions. However, the generality of the models and their low-dimensional representation of many processes may also be a "curse" that results in failures when particulars of an ecosystem are required. It is envisaged that the search for a unifying "general" model, while seductive, may remain elusive in the foreseeable future. It is for this reason that improving the merger between experiments and models of various degrees of complexity continues to shape the future research agenda.

Mathematical models of the simplest fuzzy PI/PD controllers with skewed input and output fuzzy sets.

PubMed

Mohan, B M; Sinha, Arpita

2008-07-01

This paper unveils mathematical models for fuzzy PI/PD controllers which employ two skewed fuzzy sets for each of the two-input variables and three skewed fuzzy sets for the output variable. The basic constituents of these models are Gamma-type and L-type membership functions for each input, trapezoidal/triangular membership functions for output, intersection/algebraic product triangular norm, maximum/drastic sum triangular conorm, Mamdani minimum/Larsen product/drastic product inference method, and center of sums defuzzification method. The existing simplest fuzzy PI/PD controller structures derived via symmetrical fuzzy sets become special cases of the mathematical models revealed in this paper. Finally, a numerical example along with its simulation results are included to demonstrate the effectiveness of the simplest fuzzy PI controllers.

[Stature estimation for Sichuan Han nationality female based on X-ray technology with measurement of lumbar vertebrae].

PubMed

Qing, Si-han; Chang, Yun-feng; Dong, Xiao-ai; Li, Yuan; Chen, Xiao-gang; Shu, Yong-kang; Deng, Zhen-hua

2013-10-01

To establish the mathematical models of stature estimation for Sichuan Han female with measurement of lumbar vertebrae by X-ray to provide essential data for forensic anthropology research. The samples, 206 Sichuan Han females, were divided into three groups including group A, B and C according to the ages. Group A (206 samples) consisted of all ages, group B (116 samples) were 20-45 years old and 90 samples over 45 years old were group C. All the samples were examined lumbar vertebrae through CR technology, including the parameters of five centrums (L1-L5) as anterior border, posterior border and central heights (x1-x15), total central height of lumbar spine (x16), and the real height of every sample. The linear regression analysis was produced using the parameters to establish the mathematical models of stature estimation. Sixty-two trained subjects were tested to verify the accuracy of the mathematical models. The established mathematical models by hypothesis test of linear regression equation model were statistically significant (P<0.05). The standard errors of the equation were 2.982-5.004 cm, while correlation coefficients were 0.370-0.779 and multiple correlation coefficients were 0.533-0.834. The return tests of the highest correlation coefficient and multiple correlation coefficient of each group showed that the highest accuracy of the multiple regression equation, y = 100.33 + 1.489 x3 - 0.548 x6 + 0.772 x9 + 0.058 x12 + 0.645 x15, in group A were 80.6% (+/- lSE) and 100% (+/- 2SE). The established mathematical models in this study could be applied for the stature estimation for Sichuan Han females.

MSaTERs: Mathematics, Science, and Technology Educators & Researchers of The Ohio State University. Proceedings of the Annual Spring Conference (5th, Columbus, Ohio, May 5, 2001).

ERIC Educational Resources Information Center

Herman, Marlena F., Ed.

The Mathematics, Science, and Technology Educators and Researchers of The Ohio State University (MSaTERs-OSU) is a student organization that grew out of the former Ohio State University Council of Teachers of Mathematics (OSU-CTM). Papers from the fifth annual conference include: (1) "Models of the Structure of Matter: Why Should We Care…

A mathematical model for predicting cyclic voltammograms of electronically conductive polypyrrole

NASA Technical Reports Server (NTRS)

Yeu, Taewhan; Nguyen, Trung V.; White, Ralph E.

1988-01-01

Polypyrrole is an attractive polymer for use as a high-energy-density secondary battery because of its potential as an inexpensive, lightweight, and noncorrosive electrode material. A mathematical model to simulate cyclic voltammograms for polypyrrole is presented. The model is for a conductive porous electrode film on a rotating disk electrode (RDE) and is used to predict the spatial and time dependence of concentration, overpotential, and stored charge profiles within a polypyrrole film. The model includes both faradic and capacitance charge components in the total current density expression.

A mathematical model for predicting cyclic voltammograms of electronically conductive polypyrrole

NASA Technical Reports Server (NTRS)

Yeu, Taewhan; Nguyen, Trung V.; White, Ralph E.

1987-01-01

Polypyrrole is an attractive polymer for use as a high-energy-density secondary battery because of its potential as an inexpensive, lightweight, and noncorrosive electrode material. A mathematical model to simulate cyclic voltammograms for polypyrrole is presented. The model is for a conductive porous electrode film on a rotating disk electrode (RDE) and is used to predict the spatial and time dependence of concentration, overpotential, and stored charge profiles within a polypyrrole film. The model includes both faradic and capacitance charge components in the total current density expression.

Categorical Working Memory Representations are used in Delayed Estimation of Continuous Colors

PubMed Central

Hardman, Kyle O; Vergauwe, Evie; Ricker, Timothy J

2016-01-01

In the last decade, major strides have been made in understanding visual working memory through mathematical modeling of color production responses. In the delayed color estimation task (Wilken & Ma, 2004), participants are given a set of colored squares to remember and a few seconds later asked to reproduce those colors by clicking on a color wheel. The degree of error in these responses is characterized with mathematical models that estimate working memory precision and the proportion of items remembered by participants. A standard mathematical model of color memory assumes that items maintained in memory are remembered through memory for precise details about the particular studied shade of color. We contend that this model is incomplete in its present form because no mechanism is provided for remembering the coarse category of a studied color. In the present work we remedy this omission and present a model of visual working memory that includes both continuous and categorical memory representations. In two experiments we show that our new model outperforms this standard modeling approach, which demonstrates that categorical representations should be accounted for by mathematical models of visual working memory. PMID:27797548

Categorical working memory representations are used in delayed estimation of continuous colors.

PubMed

Hardman, Kyle O; Vergauwe, Evie; Ricker, Timothy J

2017-01-01

In the last decade, major strides have been made in understanding visual working memory through mathematical modeling of color production responses. In the delayed color estimation task (Wilken & Ma, 2004), participants are given a set of colored squares to remember, and a few seconds later asked to reproduce those colors by clicking on a color wheel. The degree of error in these responses is characterized with mathematical models that estimate working memory precision and the proportion of items remembered by participants. A standard mathematical model of color memory assumes that items maintained in memory are remembered through memory for precise details about the particular studied shade of color. We contend that this model is incomplete in its present form because no mechanism is provided for remembering the coarse category of a studied color. In the present work, we remedy this omission and present a model of visual working memory that includes both continuous and categorical memory representations. In 2 experiments, we show that our new model outperforms this standard modeling approach, which demonstrates that categorical representations should be accounted for by mathematical models of visual working memory. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

Understanding the Problems of Learning Mathematics.

ERIC Educational Resources Information Center

Semilla-Dube, Lilia

1983-01-01

A model is being developed to categorize problems in teaching and learning mathematics. Categories include problems due to language difficulties, lack of prerequisite knowledge, and those related to the affective domain. This paper calls on individuals to share teaching and learning episodes; those submitted will then be compiled and categorized.…

STEAM by Another Name: Transdisciplinary Practice in Art and Design Education

ERIC Educational Resources Information Center

Costantino, Tracie

2018-01-01

The recent movement to include art and design in Science, Technology, Engineering, and Mathematics (STEM) education has made Science, Technology, Engineering, Arts, and Mathematics (STEAM) an increasingly common acronym in the education lexicon. The STEAM movement builds on existing models of interdisciplinary curriculum, but what makes the union…

Emotion Regulation in Mathematics Homework: An Empirical Study

ERIC Educational Resources Information Center

Xu, Jianzhong

2018-01-01

The author examined 2 distinctive aspects of emotion regulation in mathematics homework, including emotion management and cognitive reappraisal. Participants were 1,799 high school students from 46 classes in China. Two multilevel models were run, 1 with emotion management and another with cognitive reappraisal as the dependent variable. Both…

Modeling in the quality by design environment: Regulatory requirements and recommendations for design space and control strategy appointment.

PubMed

Djuris, Jelena; Djuric, Zorica

2017-11-30

Mathematical models can be used as an integral part of the quality by design (QbD) concept throughout the product lifecycle for variety of purposes, including appointment of the design space and control strategy, continual improvement and risk assessment. Examples of different mathematical modeling techniques (mechanistic, empirical and hybrid) in the pharmaceutical development and process monitoring or control are provided in the presented review. In the QbD context, mathematical models are predominantly used to support design space and/or control strategies. Considering their impact to the final product quality, models can be divided into the following categories: high, medium and low impact models. Although there are regulatory guidelines on the topic of modeling applications, review of QbD-based submission containing modeling elements revealed concerns regarding the scale-dependency of design spaces and verification of models predictions at commercial scale of manufacturing, especially regarding real-time release (RTR) models. Authors provide critical overview on the good modeling practices and introduce concepts of multiple-unit, adaptive and dynamic design space, multivariate specifications and methods for process uncertainty analysis. RTR specification with mathematical model and different approaches to multivariate statistical process control supporting process analytical technologies are also presented. Copyright © 2017 Elsevier B.V. All rights reserved.

Interdisciplinary education - a predator-prey model for developing a skill set in mathematics, biology and technology

NASA Astrophysics Data System (ADS)

van der Hoff, Quay

2017-08-01

The science of biology has been transforming dramatically and so the need for a stronger mathematical background for biology students has increased. Biological students reaching the senior or post-graduate level often come to realize that their mathematical background is insufficient. Similarly, students in a mathematics programme, interested in biological phenomena, find it difficult to master the complex systems encountered in biology. In short, the biologists do not have enough mathematics and the mathematicians are not being taught enough biology. The need for interdisciplinary curricula that includes disciplines such as biology, physical science, and mathematics is widely recognized, but has not been widely implemented. In this paper, it is suggested that students develop a skill set of ecology, mathematics and technology to encourage working across disciplinary boundaries. To illustrate such a skill set, a predator-prey model that contains self-limiting factors for both predator and prey is suggested. The general idea of dynamics, is introduced and students are encouraged to discover the applicability of this approach to more complex biological systems. The level of mathematics and technology required is not advanced; therefore, it is ideal for inclusion in a senior-level or introductory graduate-level course for students interested in mathematical biology.

Student and high-school characteristics related to completing a science, technology, engineering or mathematics (STEM) major in college

NASA Astrophysics Data System (ADS)

LeBeau, Brandon; Harwell, Michael; Monson, Debra; Dupuis, Danielle; Medhanie, Amanuel; Post, Thomas R.

2012-04-01

Background: The importance of increasing the number of US college students completing degrees in science, technology, engineering or mathematics (STEM) has prompted calls for research to provide a better understanding of factors related to student participation in these majors, including the impact of a student's high-school mathematics curriculum. Purpose: This study examines the relationship between various student and high-school characteristics and completion of a STEM major in college. Of specific interest is the influence of a student's high-school mathematics curriculum on the completion of a STEM major in college. Sample: The sample consisted of approximately 3500 students from 229 high schools. Students were predominantly Caucasian (80%), with slightly more males than females (52% vs 48%). Design and method: A quasi-experimental design with archival data was used for students who enrolled in, and graduated from, a post-secondary institution in the upper Midwest. To be included in the sample, students needed to have completed at least three years of high-school mathematics. A generalized linear mixed model was used with students nested within high schools. The data were cross-sectional. Results: High-school predictors were not found to have a significant impact on the completion of a STEM major. Significant student-level predictors included ACT mathematics score, gender and high-school mathematics GPA. Conclusions: The results provide evidence that on average students are equally prepared for the rigorous mathematics coursework regardless of the high-school mathematics curriculum they completed.

An integrative approach to space-flight physiology using systems analysis and mathematical simulation

NASA Technical Reports Server (NTRS)

Leonard, J. I.; White, R. J.; Rummel, J. A.

1980-01-01

An approach was developed to aid in the integration of many of the biomedical findings of space flight, using systems analysis. The mathematical tools used in accomplishing this task include an automated data base, a biostatistical and data analysis system, and a wide variety of mathematical simulation models of physiological systems. A keystone of this effort was the evaluation of physiological hypotheses using the simulation models and the prediction of the consequences of these hypotheses on many physiological quantities, some of which were not amenable to direct measurement. This approach led to improvements in the model, refinements of the hypotheses, a tentative integrated hypothesis for adaptation to weightlessness, and specific recommendations for new flight experiments.

Concentrator optical characterization using computer mathematical modelling and point source testing

NASA Technical Reports Server (NTRS)

Dennison, E. W.; John, S. L.; Trentelman, G. F.

1984-01-01

The optical characteristics of a paraboloidal solar concentrator are analyzed using the intercept factor curve (a format for image data) to describe the results of a mathematical model and to represent reduced data from experimental testing. This procedure makes it possible not only to test an assembled concentrator, but also to evaluate single optical panels or to conduct non-solar tests of an assembled concentrator. The use of three-dimensional ray tracing computer programs to calculate the mathematical model is described. These ray tracing programs can include any type of optical configuration from simple paraboloids to array of spherical facets and can be adapted to microcomputers or larger computers, which can graphically display real-time comparison of calculated and measured data.

Thermodynamic investigation of the interaction between cyclodextrins and preservatives - Application and verification in a mathematical model to determine the needed preservative surplus in aqueous cyclodextrin formulations.

PubMed

Holm, René; Olesen, Niels Erik; Alexandersen, Signe Dalgaard; Dahlgaard, Birgitte N; Westh, Peter; Mu, Huiling

2016-05-25

Preservatives are inactivated when added to conserve aqueous cyclodextrin (CD) formulations due to complex formation between CDs and the preservative. To maintain the desired conservation effect the preservative needs to be added in apparent surplus to account for this inactivation. The purpose of the present work was to establish a mathematical model, which defines this surplus based upon knowledge of stability constants and the minimal concentration of preservation to inhibit bacterial growth. The stability constants of benzoic acid, methyl- and propyl-paraben with different frequently used βCDs were determined by isothermal titration calorimetry. Based upon this knowledge mathematical models were constructed to account for the equilibrium systems and to calculate the required concentration of the preservations, which was evaluated experimentally based upon the USP/Ph. Eur./JP monograph. The mathematical calculations were able to predict the needed concentration of preservation in the presence of CDs; it clearly demonstrated the usefulness of including all underlying chemical equilibria in a mathematical model, such that the formulation design can be based on quantitative arguments. Copyright © 2015 Elsevier B.V. All rights reserved.

Support Center for Regulatory Atmospheric Modeling (SCRAM)

EPA Pesticide Factsheets

This technical site provides access to air quality models (including computer code, input data, and model processors) and other mathematical simulation techniques used in assessing air emissions control strategies and source impacts.

Theoretical studies in isoelectric focusing. [mathematical modeling and computer simulation for biologicals purification process

NASA Technical Reports Server (NTRS)

Mosher, R. A.; Palusinski, O. A.; Bier, M.

1982-01-01

A mathematical model has been developed which describes the steady state in an isoelectric focusing (IEF) system with ampholytes or monovalent buffers. The model is based on the fundamental equations describing the component dissociation equilibria, mass transport due to diffusion and electromigration, electroneutrality, and the conservation of charge. The validity and usefulness of the model has been confirmed by using it to formulate buffer systems in actual laboratory experiments. The model has been recently extended to include the evolution of transient states not only in IEF but also in other modes of electrophoresis.

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.

Current advances in mathematical modeling of anti-cancer drug penetration into tumor tissues.

PubMed

Kim, Munju; Gillies, Robert J; Rejniak, Katarzyna A

2013-11-18

Delivery of anti-cancer drugs to tumor tissues, including their interstitial transport and cellular uptake, is a complex process involving various biochemical, mechanical, and biophysical factors. Mathematical modeling provides a means through which to understand this complexity better, as well as to examine interactions between contributing components in a systematic way via computational simulations and quantitative analyses. In this review, we present the current state of mathematical modeling approaches that address phenomena related to drug delivery. We describe how various types of models were used to predict spatio-temporal distributions of drugs within the tumor tissue, to simulate different ways to overcome barriers to drug transport, or to optimize treatment schedules. Finally, we discuss how integration of mathematical modeling with experimental or clinical data can provide better tools to understand the drug delivery process, in particular to examine the specific tissue- or compound-related factors that limit drug penetration through tumors. Such tools will be important in designing new chemotherapy targets and optimal treatment strategies, as well as in developing non-invasive diagnosis to monitor treatment response and detect tumor recurrence.

Theoretical studies of solar lasers and converters

NASA Technical Reports Server (NTRS)

Heinbockel, John H.

1990-01-01

The research described consisted of developing and refining the continuous flow laser model program including the creation of a working model. The mathematical development of a two pass amplifier for an iodine laser is summarized. A computer program for the amplifier's simulation is included with output from the simulation model.

Mathematical models frame environmental dispute [Review of the article Useless arithmetic: Ten points to ponder when using mathematical models in environmental decision making

USGS Publications Warehouse

Lamb, Berton Lee; Burkardt, Nina

2008-01-01

When Linda Pilkey- Jarvis and Orrin Pilkey state in their article, "Useless Arithmetic," that "mathematical models are simplified, generalized representations of a process or system," they probably do not mean to imply that these models are simple. Rather, the models are simpler than nature and that is the heart of the problem with predictive models. We have had a long professional association with the developers and users of one of these simplifications of nature in the form of a mathematical model known as Physical Habitat Simulation (PHABSIM), which is part of the Instream Flow Incremental Methodology (IFIM). The IFIM is a suite of techniques, including PHABSIM, that allows the analyst to incorporate hydrology , hydraulics, habitat, water quality, stream temperature, and other variables into a tradeoff analysis that decision makers can use to design a flow regime to meet management objectives (Stalnaker et al. 1995). Although we are not the developers of the IFIM, we have worked with those who did design it, and we have tried to understand how the IFIM and PHABSIM are actually used in decision making (King, Burkardt, and Clark 2006; Lamb 1989).

Estimating the Uncertain Mathematical Structure of Hydrological Model via Bayesian Data Assimilation

NASA Astrophysics Data System (ADS)

Bulygina, N.; Gupta, H.; O'Donell, G.; Wheater, H.

2008-12-01

The structure of hydrological model at macro scale (e.g. watershed) is inherently uncertain due to many factors, including the lack of a robust hydrological theory at the macro scale. In this work, we assume that a suitable conceptual model for the hydrologic system has already been determined - i.e., the system boundaries have been specified, the important state variables and input and output fluxes to be included have been selected, and the major hydrological processes and geometries of their interconnections have been identified. The structural identification problem then is to specify the mathematical form of the relationships between the inputs, state variables and outputs, so that a computational model can be constructed for making simulations and/or predictions of system input-state-output behaviour. We show how Bayesian data assimilation can be used to merge both prior beliefs in the form of pre-assumed model equations with information derived from the data to construct a posterior model. The approach, entitled Bayesian Estimation of Structure (BESt), is used to estimate a hydrological model for a small basin in England, at hourly time scales, conditioned on the assumption of 3-dimensional state - soil moisture storage, fast and slow flow stores - conceptual model structure. Inputs to the system are precipitation and potential evapotranspiration, and outputs are actual evapotranspiration and streamflow discharge. Results show the difference between prior and posterior mathematical structures, as well as provide prediction confidence intervals that reflect three types of uncertainty: due to initial conditions, due to input and due to mathematical structure.

PASMet: a web-based platform for prediction, modelling and analyses of metabolic systems

PubMed Central

Sriyudthsak, Kansuporn; Mejia, Ramon Francisco; Arita, Masanori; Hirai, Masami Yokota

2016-01-01

PASMet (Prediction, Analysis and Simulation of Metabolic networks) is a web-based platform for proposing and verifying mathematical models to understand the dynamics of metabolism. The advantages of PASMet include user-friendliness and accessibility, which enable biologists and biochemists to easily perform mathematical modelling. PASMet offers a series of user-functions to handle the time-series data of metabolite concentrations. The functions are organised into four steps: (i) Prediction of a probable metabolic pathway and its regulation; (ii) Construction of mathematical models; (iii) Simulation of metabolic behaviours; and (iv) Analysis of metabolic system characteristics. Each function contains various statistical and mathematical methods that can be used independently. Users who may not have enough knowledge of computing or programming can easily and quickly analyse their local data without software downloads, updates or installations. Users only need to upload their files in comma-separated values (CSV) format or enter their model equations directly into the website. Once the time-series data or mathematical equations are uploaded, PASMet automatically performs computation on server-side. Then, users can interactively view their results and directly download them to their local computers. PASMet is freely available with no login requirement at http://pasmet.riken.jp/ from major web browsers on Windows, Mac and Linux operating systems. PMID:27174940

POEM: PESTICIDE ORCHARD ECOSYSTEM MODEL

EPA Science Inventory

The Pesticide Orchard Ecosystem Model (POEM) is a mathematical model of organophosphate pesticide movement in an apple orchard ecosystem. In addition submodels on invertebrate population dynamics are included. The fate model allows the user to select the pesticide, its applicatio...

Modeling Newspaper Advertising

ERIC Educational Resources Information Center

Harper, Joseph; And Others

1978-01-01

Presents a mathematical model for simulating a newspaper financial system. Includes the effects of advertising and circulation for predicting advertising linage as a function of population, income, and advertising rate. (RL)

Hispanic students' mathematics achievement in the context of their high school types as STEM and non-STEM schools

NASA Astrophysics Data System (ADS)

Bicer, Ali; Capraro, Robert M.; Capraro, Mary M.

2018-07-01

The purpose of this paper is to demonstrate Hispanic students' mathematics achievement growth rate in Inclusive science, technology, engineering, and mathematics (STEM) high schools compared to Hispanic students' mathematics achievement growth rate in traditional public schools. Twenty-eight schools, 14 of which were Texas STEM (T-STEM) academies and 14 of which were matched non-STEM schools, were included in this study. A hierarchical linear modelling method was conducted. The result of the present study revealed that there was no difference in Hispanic students' mathematics achievement growth rate in T-STEM academies compared to Hispanic students' mathematics achievement growth rate in comparison schools. However, in terms of gender, the results indicated that female Hispanic students in T-STEM academies outperformed female Hispanic students in comparison schools in their mathematics growth rate.

Mathematics and Measurement

PubMed Central

Boisvert, Ronald F.; Donahue, Michael J.; Lozier, Daniel W.; McMichael, Robert; Rust, Bert W.

2001-01-01

In this paper we describe the role that mathematics plays in measurement science at NIST. We first survey the history behind NIST’s current work in this area, starting with the NBS Math Tables project of the 1930s. We then provide examples of more recent efforts in the application of mathematics to measurement science, including the solution of ill-posed inverse problems, characterization of the accuracy of software for micromagnetic modeling, and in the development and dissemination of mathematical reference data. Finally, we comment on emerging issues in measurement science to which mathematicians will devote their energies in coming years. PMID:27500024

An overview of the mathematical and statistical analysis component of RICIS

NASA Technical Reports Server (NTRS)

Hallum, Cecil R.

1987-01-01

Mathematical and statistical analysis components of RICIS (Research Institute for Computing and Information Systems) can be used in the following problem areas: (1) quantification and measurement of software reliability; (2) assessment of changes in software reliability over time (reliability growth); (3) analysis of software-failure data; and (4) decision logic for whether to continue or stop testing software. Other areas of interest to NASA/JSC where mathematical and statistical analysis can be successfully employed include: math modeling of physical systems, simulation, statistical data reduction, evaluation methods, optimization, algorithm development, and mathematical methods in signal processing.

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

NASA Technical Reports Server (NTRS)

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

1992-01-01

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

Nonlinear-programming mathematical modeling of coal blending for power plant

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

Tang Longhua; Zhou Junhu; Yao Qiang

At present most of the blending works are guided by experience or linear-programming (LP) which can not reflect the coal complicated characteristics properly. Experimental and theoretical research work shows that most of the coal blend properties can not always be measured as a linear function of the properties of the individual coals in the blend. The authors introduced nonlinear functions or processes (including neural network and fuzzy mathematics), established on the experiments directed by the authors and other researchers, to quantitatively describe the complex coal blend parameters. Finally nonlinear-programming (NLP) mathematical modeling of coal blend is introduced and utilized inmore » the Hangzhou Coal Blending Center. Predictions based on the new method resulted in different results from the ones based on LP modeling. The authors concludes that it is very important to introduce NLP modeling, instead of NL modeling, into the work of coal blending.« less

Mathematical model for adaptive control system of ASEA robot at Kennedy Space Center

NASA Technical Reports Server (NTRS)

Zia, Omar

1989-01-01

The dynamic properties and the mathematical model for the adaptive control of the robotic system presently under investigation at Robotic Application and Development Laboratory at Kennedy Space Center are discussed. NASA is currently investigating the use of robotic manipulators for mating and demating of fuel lines to the Space Shuttle Vehicle prior to launch. The Robotic system used as a testbed for this purpose is an ASEA IRB-90 industrial robot with adaptive control capabilities. The system was tested and it's performance with respect to stability was improved by using an analogue force controller. The objective of this research project is to determine the mathematical model of the system operating under force feedback control with varying dynamic internal perturbation in order to provide continuous stable operation under variable load conditions. A series of lumped parameter models are developed. The models include some effects of robot structural dynamics, sensor compliance, and workpiece dynamics.

The HIV Cure Research Agenda: The Role of Mathematical Modelling and Cost-Effectiveness Analysis.

PubMed

Freedberg, Kenneth A; Possas, Cristina; Deeks, Steven; Ross, Anna Laura; Rosettie, Katherine L; Di Mascio, Michele; Collins, Chris; Walensky, Rochelle P; Yazdanpanah, Yazdan

The research agenda towards an HIV cure is building rapidly. In this article, we discuss the reasons for and methodological approach to using mathematical modeling and cost-effectiveness analysis in this agenda. We provide a brief description of the proof of concept for cure and the current directions of cure research. We then review the types of clinical economic evaluations, including cost analysis, cost-benefit analysis, and cost-effectiveness analysis. We describe the use of mathematical modeling and cost-effectiveness analysis early in the HIV epidemic as well as in the era of combination antiretroviral therapy. We then highlight the novel methodology of Value of Information analysis and its potential role in the planning of clinical trials. We close with recommendations for modeling and cost-effectiveness analysis in the HIV cure agenda.

Study on the tumor-induced angiogenesis using mathematical models.

PubMed

Suzuki, Takashi; Minerva, Dhisa; Nishiyama, Koichi; Koshikawa, Naohiko; Chaplain, Mark Andrew Joseph

2018-01-01

We studied angiogenesis using mathematical models describing the dynamics of tip cells. We reviewed the basic ideas of angiogenesis models and its numerical simulation technique to produce realistic computer graphics images of sprouting angiogenesis. We examined the classical model of Anderson-Chaplain using fundamental concepts of mass transport and chemical reaction with ECM degradation included. We then constructed two types of numerical schemes, model-faithful and model-driven ones, where new techniques of numerical simulation are introduced, such as transient probability, particle velocity, and Boolean variables. © 2017 The Authors. Cancer Science published by John Wiley & Sons Australia, Ltd on behalf of Japanese Cancer Association.

Relations among Brief Measures of Mathematics, Reading, and Processing Speed: A Construct Validity Study

ERIC Educational Resources Information Center

Maynard, Jennifer Leigh

2012-01-01

Emphasis on regular mathematics skill assessment, intervention, and progress monitoring under the RTI model has created a need for the development of assessment instruments that are psychometrically sound, reliable, universal, and brief. Important factors to consider when developing or selecting assessments for the school environment include what…

Trying Three-Act Tasks with Primary Students

ERIC Educational Resources Information Center

Lomax, Kendra; Alfonzo, Kristin; Dietz, Sarah; Kleyman, Ellen; Kazemi, Elham

2017-01-01

The goals of problem-solving activities in the elementary grades often include making sense of story problems, developing a range of strategies, and reaching accurate solutions. These are important mathematical aims, but they do not fully address the demands of modeling with mathematics as described in the fourth of the Common Core's eight…

Assisting Students with High-Incidence Disabilities to Pursue Careers in Science, Technology, Engineering, and Mathematics

ERIC Educational Resources Information Center

Dunn, Cari; Rabren, Karen S.; Taylor, Stephanie L.; Dotson, Courtney K.

2012-01-01

Persons with disabilities have been underrepresented in the science, technology, engineering, and mathematics (STEM) fields for many years. Reasons for this include low expectations for students with disabilities, limited exposure to prerequisite courses, lack of role models, and lack of access to individualized supports. This article identifies…

Preface.

PubMed

Friedman, Avner; Lachowicz, Mirosław; Ledzewicz, Urszula; Piotrowska, Monika Joanna; Szymanska, Zuzanna

2017-02-01

This volume was inspired by the topics presented at the international conference "Micro and Macro Systems in Life Sciences" which was held on Jun 8-12, 2015 in Będlewo, Poland. System biology is an approach which tries to understand how micro systems, at the molecular and cellular levels, affect macro systems such as organs, tissue and populations. Thus it is not surprising that a major theme of this volume evolves around cancer and its treatment. Articles on this topic include models for tumor induced angiogenesis, without and with delays, metastatic niche of the bone marrow, drug resistance and metronomic chemotherapy, and virotherapy of glioma. Methods range from dynamical systems to optimal control. Another well represented topic of this volume is mathematical modeling in epidemiology. Mathematical approaches to modeling and control of more specific diseases like malaria, Ebola or human papillomavirus are discussed as well as a more general approaches to the SEIR, and even more general class of models in epidemiology, by using the tools of optimal control and optimization. The volume also brings up challenges in mathematical modeling of other diseases such as tuberculosis. Partial differential equations combined with numerical approaches are becoming important tools in modeling not only tumor growth and treatment, but also other diseases, such as fibrosis of the liver, and atherosclerosis and its associated blood flow dynamics, and our volume presents a state of the art approach on these topics. Understanding mathematics behind the cell motion, appearance of the special patterns in various cell populations, and age structured mutations are among topics addressed inour volume. A spatio-temporal models of synthetic genetic oscillators brings the analysis to the gene level which is the focus of much of current biological research. Mathematics can help biologists to explain the collective behavior of bacterial, a topic that is also presented here. Finally some more across the discipline topics are being addresses, which can appear as a challenge in studying problems in systems biology on all, macro, meso and micro levels. They include numerical approaches to stochastic wave equation arising in modeling Brownian motion, discrete velocity models, many particle approximations as well as very important aspect on the connection between discrete measurement and the construction of the models for various phenomena, particularly the one involving delays. With the variety of biological topics and their mathematical approaches we very much hope that the reader of the Mathematical Biosciences and Engineering will find this volume interesting and inspirational for their own research.

Neurotech for Neuroscience: Unifying Concepts, Organizing Principles, and Emerging Tools

PubMed Central

Silver, Rae; Boahen, Kwabena; Grillner, Sten; Kopell, Nancy; Olsen, Kathie L.

2012-01-01

The ability to tackle analysis of the brain at multiple levels simultaneously is emerging from rapid methodological developments. The classical research strategies of “measure,” “model,” and “make” are being applied to the exploration of nervous system function. These include novel conceptual and theoretical approaches, creative use of mathematical modeling, and attempts to build brain-like devices and systems, as well as other developments including instrumentation and statistical modeling (not covered here). Increasingly, these efforts require teams of scientists from a variety of traditional scientific disciplines to work together. The potential of such efforts for understanding directed motor movement, emergence of cognitive function from neuronal activity, and development of neuromimetic computers are described by a team that includes individuals experienced in behavior and neuroscience, mathematics, and engineering. Funding agencies, including the National Science Foundation, explore the potential of these changing frontiers of research for developing research policies and long-term planning. PMID:17978017

Contributions of Motivation, Early Numeracy Skills, and Executive Functioning to Mathematical Performance. A Longitudinal Study.

PubMed

Mercader, Jessica; Miranda, Ana; Presentación, M Jesús; Siegenthaler, Rebeca; Rosel, Jesús F

2017-01-01

The main goal of this longitudinal study is to examine the power of different variables and its dynamic interactions in predicting mathematical performance. The model proposed in this study includes indicators of motivational constructs (learning motivation and attributions), executive functioning (inhibition and working memory), and early numeracy skills (logical operations, counting, and magnitude comparison abilities), assessed during kindergarten, and mathematical performance in the second year of Primary Education. The sample consisted of 180 subjects assessed in two moments (5-6 and 7-8 years old). The results showed an indirect effect of initial motivation on later mathematical performance. Executive functioning and early numeracy skills mediated the effect of motivation on later mathematic achievement. Practical implications of these findings for mathematics education are discussed.

Contributions of Motivation, Early Numeracy Skills, and Executive Functioning to Mathematical Performance. A Longitudinal Study

PubMed Central

Mercader, Jessica; Miranda, Ana; Presentación, M. Jesús; Siegenthaler, Rebeca; Rosel, Jesús F.

2018-01-01

The main goal of this longitudinal study is to examine the power of different variables and its dynamic interactions in predicting mathematical performance. The model proposed in this study includes indicators of motivational constructs (learning motivation and attributions), executive functioning (inhibition and working memory), and early numeracy skills (logical operations, counting, and magnitude comparison abilities), assessed during kindergarten, and mathematical performance in the second year of Primary Education. The sample consisted of 180 subjects assessed in two moments (5–6 and 7–8 years old). The results showed an indirect effect of initial motivation on later mathematical performance. Executive functioning and early numeracy skills mediated the effect of motivation on later mathematic achievement. Practical implications of these findings for mathematics education are discussed. PMID:29379462

New and practical mathematical model of membrane fouling in an aerobic submerged membrane bioreactor.

PubMed

Zuthi, Mst Fazana Rahman; Guo, Wenshan; Ngo, Huu Hao; Nghiem, Duc Long; Hai, Faisal I; Xia, Siqing; Li, Jianxin; Li, Jixiang; Liu, Yi

2017-08-01

This study aimed to develop a practical semi-empirical mathematical model of membrane fouling that accounts for cake formation on the membrane and its pore blocking as the major processes of membrane fouling. In the developed model, the concentration of mixed liquor suspended solid is used as a lumped parameter to describe the formation of cake layer including the biofilm. The new model considers the combined effect of aeration and backwash on the foulants' detachment from the membrane. New exponential coefficients are also included in the model to describe the exponential increase of transmembrane pressure that typically occurs after the initial stage of an MBR operation. The model was validated using experimental data obtained from a lab-scale aerobic sponge-submerged membrane bioreactor (MBR), and the simulation of the model agreed well with the experimental findings. Copyright © 2017 Elsevier Ltd. All rights reserved.

The Quark's Model and Confinement

ERIC Educational Resources Information Center

Novozhilov, Yuri V.

1977-01-01

Quarks are elementary particles considered to be components of the proton, the neutron, and others. This article presents the quark model as a mathematical concept. Also discussed are gluons and bag models. A bibliography is included. (MA)

Testing the World with Simulations.

ERIC Educational Resources Information Center

Roberts, Nancy

1983-01-01

Discusses steps involved in model building and simulation: understanding a problem, building a model, and simulation. Includes a mathematical model (focusing on a problem dealing with influenza) written in the DYNAMO computer language, developed specifically for writing simulation models. (Author/JN)

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.

Modeling and control of flexible space platforms with articulated payloads

NASA Technical Reports Server (NTRS)

Graves, Philip C.; Joshi, Suresh M.

1989-01-01

The first steps in developing a methodology for spacecraft control-structure interaction (CSI) optimization are identification and classification of anticipated missions, and the development of tractable mathematical models in each mission class. A mathematical model of a generic large flexible space platform (LFSP) with multiple independently pointed rigid payloads is considered. The objective is not to develop a general purpose numerical simulation, but rather to develop an analytically tractable mathematical model of such composite systems. The equations of motion for a single payload case are derived, and are linearized about zero steady-state. The resulting model is then extended to include multiple rigid payloads, yielding the desired analytical form. The mathematical models developed clearly show the internal inertial/elastic couplings, and are therefore suitable for analytical and numerical studies. A simple decentralized control law is proposed for fine pointing the payloads and LFSP attitude control, and simulation results are presented for an example problem. The decentralized controller is shown to be adequate for the example problem chosen, but does not, in general, guarantee stability. A centralized dissipative controller is then proposed, requiring a symmetric form of the composite system equations. Such a controller guarantees robust closed loop stability despite unmodeled elastic dynamics and parameter uncertainties.

Simplified mathematical model of losses in a centrifugal compressor stage

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

Seleznev, K.P.; Galerkin, Yu.B.; Popova, E.Yu.

1988-05-01

A mathematical model was developed for optimizing the parameters of the stage which does not require calculation of the flow around grids. The loss coefficients of the stage elements were considered as functions of the flow-through section, the angle of incidence, the compressibility criterion, and the Reynolds number. The relationships were used to calculate losses in all blade components, including blade diffusers, deflectors, and rotors. The model is implemented in a microcomputer and will compute the efficiency of one variant of the flow-through section of a stage in 60 minutes.

Self-charging of identical grains in the absence of an external field.

PubMed

Yoshimatsu, R; Araújo, N A M; Wurm, G; Herrmann, H J; Shinbrot, T

2017-01-06

We investigate the electrostatic charging of an agitated bed of identical grains using simulations, mathematical modeling, and experiments. We simulate charging with a discrete-element model including electrical multipoles and find that infinitesimally small initial charges can grow exponentially rapidly. We propose a mathematical Turing model that defines conditions for exponential charging to occur and provides insights into the mechanisms involved. Finally, we confirm the predicted exponential growth in experiments using vibrated grains under microgravity, and we describe novel predicted spatiotemporal states that merit further study.

Self-charging of identical grains in the absence of an external field

NASA Astrophysics Data System (ADS)

Yoshimatsu, R.; Araújo, N. A. M.; Wurm, G.; Herrmann, H. J.; Shinbrot, T.

2017-01-01

We investigate the electrostatic charging of an agitated bed of identical grains using simulations, mathematical modeling, and experiments. We simulate charging with a discrete-element model including electrical multipoles and find that infinitesimally small initial charges can grow exponentially rapidly. We propose a mathematical Turing model that defines conditions for exponential charging to occur and provides insights into the mechanisms involved. Finally, we confirm the predicted exponential growth in experiments using vibrated grains under microgravity, and we describe novel predicted spatiotemporal states that merit further study.

Something from nothing: self-charging of identical grains

NASA Astrophysics Data System (ADS)

Shinbrot, Troy; Yoshimatsu, Ryuta; Nuno Araujo, Nuno; Wurm, Gerhard; Herrmann, Hans

We investigate the electrostatic charging of an agitated bed of identical grains using simulations, mathematical modeling, and experiments. We simulate charging with a discrete-element model including electrical multipoles and find that infinitesimally small initial charges can grow exponentially rapidly. We propose a mathematical Turing model that defines conditions for exponential charging to occur and provides insights into the mechanisms involved. Finally, we confirm the predicted exponential growth in experiments using vibrated grains under microgravity, and we describe novel predicted spatiotemporal states that merit further study. I acknowledge support from NSF/DMR, award 1404792.

Mathematical and computational modelling of skin biophysics: a review

PubMed Central

2017-01-01

The objective of this paper is to provide a review on some aspects of the mathematical and computational modelling of skin biophysics, with special focus on constitutive theories based on nonlinear continuum mechanics from elasticity, through anelasticity, including growth, to thermoelasticity. Microstructural and phenomenological approaches combining imaging techniques are also discussed. Finally, recent research applications on skin wrinkles will be presented to highlight the potential of physics-based modelling of skin in tackling global challenges such as ageing of the population and the associated skin degradation, diseases and traumas. PMID:28804267

Mathematical and computational modelling of skin biophysics: a review

NASA Astrophysics Data System (ADS)

Limbert, Georges

2017-07-01

The objective of this paper is to provide a review on some aspects of the mathematical and computational modelling of skin biophysics, with special focus on constitutive theories based on nonlinear continuum mechanics from elasticity, through anelasticity, including growth, to thermoelasticity. Microstructural and phenomenological approaches combining imaging techniques are also discussed. Finally, recent research applications on skin wrinkles will be presented to highlight the potential of physics-based modelling of skin in tackling global challenges such as ageing of the population and the associated skin degradation, diseases and traumas.

The mathematical modeling of rapid solidification processing. Ph.D. Thesis. Final Report

NASA Technical Reports Server (NTRS)

Gutierrez-Miravete, E.

1986-01-01

The detailed formulation of and the results obtained from a continuum mechanics-based mathematical model of the planar flow melt spinning (PFMS) rapid solidification system are presented and discussed. The numerical algorithm proposed is capable of computing the cooling and freezing rates as well as the fluid flow and capillary phenomena which take place inside the molten puddle formed in the PFMS process. The FORTRAN listings of some of the most useful computer programs and a collection of appendices describing the basic equations used for the modeling are included.

Self-charging of identical grains in the absence of an external field

PubMed Central

Yoshimatsu, R.; Araújo, N. A. M.; Wurm, G.; Herrmann, H. J.; Shinbrot, T.

2017-01-01

We investigate the electrostatic charging of an agitated bed of identical grains using simulations, mathematical modeling, and experiments. We simulate charging with a discrete-element model including electrical multipoles and find that infinitesimally small initial charges can grow exponentially rapidly. We propose a mathematical Turing model that defines conditions for exponential charging to occur and provides insights into the mechanisms involved. Finally, we confirm the predicted exponential growth in experiments using vibrated grains under microgravity, and we describe novel predicted spatiotemporal states that merit further study. PMID:28059124

Computer modeling of heat pipe performance

NASA Technical Reports Server (NTRS)

Peterson, G. P.

1983-01-01

A parametric study of the defining equations which govern the steady state operational characteristics of the Grumman monogroove dual passage heat pipe is presented. These defining equations are combined to develop a mathematical model which describes and predicts the operational and performance capabilities of a specific heat pipe given the necessary physical characteristics and working fluid. Included is a brief review of the current literature, a discussion of the governing equations, and a description of both the mathematical and computer model. Final results of preliminary test runs of the model are presented and compared with experimental tests on actual prototypes.

A hybrid model of mathematics support for science students emphasizing basic skills and discipline relevance

NASA Astrophysics Data System (ADS)

Jackson, Deborah C.; Johnson, Elizabeth D.

2013-09-01

The problem of students entering university lacking basic mathematical skills is a critical issue in the Australian higher-education sector and relevant globally. The Maths Skills programme at La Trobe University has been developed to address under preparation in the first-year science cohort in the absence of an institutional mathematics support centre. The programme was delivered through first-year science and statistics subjects with large enrolments and focused on basic mathematical skills relevant to each science discipline. The programme offered a new approach to the traditional mathematical support centre or class. It was designed through close collaboration between science subject coordinators and the project leader, a mathematician, and includes resources relevant to science and mathematics questions written in context. Evaluation of the programme showed it improved the confidence of the participating students who found it helpful and relevant. The programme was delivered through three learning modes to allow students to select activities most suitable for them, which was appreciated by students. Mathematics skills appeared to increase following completion of the programme and student participation in the programme correlated positively and highly with academic grades in their relevant science subjects. This programme offers an alternative model for mathematics support tailored to science disciplines.

Vibration of rotating-shaft design spindles with flexible bases

NASA Astrophysics Data System (ADS)

Tseng, Chaw-Wu

The purpose of this study is to demonstrate an accurate mathematical model predicting forced vibration of rotating-shaft HDD spindle motors with flexible stationary parts. The mathematical model consists of three parts: a rotating part, a stationary part, and bearings. The rotating part includes a flexible hub, a flexible shaft press-fit into the hub, and N elastic disks mounted on the hub. The stationary part can include motor bracket (stator), base casting, and top cover. The bearings under consideration can be ball bearings or hydrodynamic bearings (HDB). The rotating disks are modelled through the classical plate theory. The rotating part (except the disks) and the stationary part are modelled through finite element analyses (FEA). With mode shapes and natural frequencies obtained from FEA, the kinetic and potential energies of the rotating and stationary parts are formulated and discretized to compensate for the gyroscopic effects from rotation. Finally, use of Lagrange equation results in the equations of motion. To verify the mathematical model, frequency response functions are measured experimentally for an HDB spindle carrying two identical disks at motor and drive levels. Experimental measurements agree very well with theoretical predictions not only in resonance frequency but also in resonance amplitude.

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

ERIC Educational Resources Information Center

Yilmaz, Suha; Tekin-Dede, Ayse

2016-01-01

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

Vistas in applied mathematics: Numerical analysis, atmospheric sciences, immunology

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

Balakrishnan, A.V.; Dorodnitsyn, A.A.; Lions, J.L.

1986-01-01

Advances in the theory and application of numerical modeling techniques are discussed in papers contributed, primarily by Soviet scientists, on the occasion of the 60th birthday of Gurii I. Marchuk. Topics examined include splitting techniques for computations of industrial flows, the mathematical foundations of the k-epsilon turbulence model, splitting methods for the solution of the incompressible Navier-Stokes equations, the approximation of inhomogeneous hyperbolic boundary-value problems, multigrid methods, and the finite-element approximation of minimal surfaces. Consideration is given to dynamic modeling of moist atmospheres, satellite observations of the earth radiation budget and the problem of energy-active ocean regions, a numerical modelmore » of the biosphere for use with GCMs, and large-scale modeling of ocean circulation. Also included are several papers on modeling problems in immunology.« less

MAESTRO: Mathematics and Earth Science Teachers' Resource Organization

NASA Astrophysics Data System (ADS)

Courtier, A. M.; Pyle, E. J.; Fichter, L.; Lucas, S.; Jackson, A.

2013-12-01

The Mathematics and Earth Science Teachers' Resource Organization (MAESTRO) partnership between James Madison University and Harrisonburg City and Page County Public Schools, funded through NSF-GEO. The partnership aims to transform mathematics and Earth science instruction in middle and high schools by developing an integrated mathematics and Earth systems science approach to instruction. This curricular integration is intended to enhance the mathematical skills and confidence of students through concrete, Earth systems-based examples, while increasing the relevance and rigor of Earth science instruction via quantification and mathematical modeling of Earth system phenomena. MAESTRO draws heavily from the Earth Science Literacy Initiative (2009) and is informed by criterion-level standardized test performance data in both mathematics and Earth science. The project has involved two summer professional development workshops, academic year Lesson Study (structured teacher observation and reflection), and will incorporate site-based case studies with direct student involvement. Participating teachers include Grade 6 Science and Mathematics teachers, and Grade 9 Earth Science and Algebra teachers. It is anticipated that the proposed integration across grade bands will first strengthen students' interests in mathematics and science (a problem in middle school) and subsequently reinforce the relevance of mathematics and other sciences (a problem in high school), both in support of Earth systems literacy. MAESTRO's approach to the integration of math and science focuses on using box models to emphasize the interconnections among the geo-, atmo-, bio-, and hydrospheres, and demonstrates the positive and negative feedback processes that connect their mutual evolution. Within this framework we explore specific relationships that can be described both qualitatively and mathematically, using mathematical operations appropriate for each grade level. Site-based case studies, developed in collaboration between teachers and JMU faculty members, provide a tangible, relevant setting in which students can apply and understand mathematical applications and scientific processes related to evolving Earth systems. Initial results from student questionnaires and teacher focus groups suggest that the anticipated impacts of MAESTRO on students are being realized, including increased valuing of mathematics and Earth science in society and transfer between mathematics and science courses. As a high percentage of students in the MAESTRO schools are of low socio-economic status, they also face the prospect of becoming first-generation college students, hopefully considering STEM academic pathways. MAESTRO will drive the development of challenging and engaging instruction designed to draw a larger pool of students into STEM career pathways.

From classroom environment to mathematics achievement: The mediating role of self-perceived ability and subject interest.

PubMed

Tosto, Maria G; Asbury, Kathryn; Mazzocco, Michèle M M; Petrill, Stephen A; Kovas, Yulia

2016-08-01

Drawing on Bandura's triadic reciprocal causation model, perceived classroom environment and three intrapersonal factors (mathematics self-efficacy, maths interest and academic self-concept) were considered as predictors of test performance in two correlated mathematics assessments: a public examination (GCSE) and an on-line test, both taken by UK pupils at age 16 (n = 6689). Intrapersonal factors were significantly associated with both test scores, even when the alternative score was taken into account. Classroom environment did not correlate with mathematics achievement once intrapersonal factors and alternative test performance were included in the model, but was associated with subject interest and academic self-concept. Perceptions of classroom environment may exercise an indirect influence on achievement by boosting interest and self-concept. In turn, these intrapersonal factors have direct relationships with achievement and were found to mediate the relationship between perceived classroom environment and maths performance. Findings and their implications for mathematics education are discussed.

Computer-Aided Geometry Modeling

NASA Technical Reports Server (NTRS)

Shoosmith, J. N. (Compiler); Fulton, R. E. (Compiler)

1984-01-01

Techniques in computer-aided geometry modeling and their application are addressed. Mathematical modeling, solid geometry models, management of geometric data, development of geometry standards, and interactive and graphic procedures are discussed. The applications include aeronautical and aerospace structures design, fluid flow modeling, and gas turbine design.

pyomocontrib_simplemodel v. 1.0

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

Hart, William

2017-03-02

Pyomo supports the formulation and analysis of mathematical models for complex optimization applications. This library extends the API of Pyomo to include a simple modeling representation: a list of objectives and constraints.

Mathematical modeling of vesicle drug delivery systems 2: targeted vesicle interactions with cells, tumors, and the body.

PubMed

Ying, Chong T; Wang, Juntian; Lamm, Robert J; Kamei, Daniel T

2013-02-01

Vesicles have been studied for several years in their ability to deliver drugs. Mathematical models have much potential in reducing time and resources required to engineer optimal vesicles, and this review article summarizes these models that aid in understanding the ability of targeted vesicles to bind and internalize into cancer cells, diffuse into tumors, and distribute in the body. With regard to binding and internalization, radiolabeling and surface plasmon resonance experiments can be performed to determine optimal vesicle size and the number and type of ligands conjugated. Binding and internalization properties are also inputs into a mathematical model of vesicle diffusion into tumor spheroids, which highlights the importance of the vesicle diffusion coefficient and the binding affinity of the targeting ligand. Biodistribution of vesicles in the body, along with their half-life, can be predicted with compartmental models for pharmacokinetics that include the effect of targeting ligands, and these predictions can be used in conjunction with in vivo models to aid in the design of drug carriers. Mathematical models can prove to be very useful in drug carrier design, and our hope is that this review will encourage more investigators to combine modeling with quantitative experimentation in the field of vesicle-based drug delivery.

Fluid mechanics of continuous flow electrophoresis

NASA Technical Reports Server (NTRS)

Saville, D. A.; Ostrach, S.

1978-01-01

The following aspects of continuous flow electrophoresis were studied: (1) flow and temperature fields; (2) hydrodynamic stability; (3) separation efficiency, and (4) characteristics of wide gap chambers (the SPAR apparatus). Simplified mathematical models were developed so as to furnish a basis for understanding the phenomena and comparison of different chambers and operating conditions. Studies of the hydrodynamic stability disclosed that a wide gap chamber may be particularly sensitive to axial temperature variations which could be due to uneven heating or cooling. The mathematical model of the separation process includes effects due to the axial velocity, electro-osmotic cross flow and electrophoretic migration, all including the effects of temperature dependent properties.

Mathematical model for the assessment of fracture risk associated with osteoporosis

NASA Astrophysics Data System (ADS)

Dinis, Jairson; Pereira, Ana I.; Fonseca, Elza M.

2012-09-01

Osteoporosis is a skeletal disease characterized by low bone mass. It is considered a worldwide public health problem that affects a large number of people, in particularly for women with more than 50 years old. The occurrence pattern of osteoporosis in a population may be related to several factors, including socio-economic factors such as income, educational attainment, and factors related to lifestyle such as diet and physical activity. These and other aspects have increasingly been identified as determining the occurrence of various diseases, including osteoporosis. This work proposes a mathematical model that provides the level of osteoporosis in the patient. Preliminary numerical results are presented.

Growth trajectories of mathematics achievement: Longitudinal tracking of student academic progress.

PubMed

Mok, Magdalena M C; McInerney, Dennis M; Zhu, Jinxin; Or, Anthony

2015-06-01

A number of methods to investigate growth have been reported in the literature, including hierarchical linear modelling (HLM), latent growth modelling (LGM), and multidimensional scaling applied to longitudinal profile analysis (LPAMS). This study aimed at modelling the mathematics growth of students over a span of 6 years from Grade 3 to Grade 9. The sample comprised secondary longitudinal data collected in three waves from n = 866 Hong Kong students when they were in Grade 3, Grade 6, and Grade 9. Mathematics achievement was measured thrice on a vertical scale linked with anchor items. Linear and nonlinear latent growth models were used to assess students' growth. Gender differences were also examined. A nonlinear latent growth curve with a decelerated rate had a good fit to the data. Initial achievement and growth rate were negatively correlated. No gender difference was found. Mathematics growth from Grade 6 to Grade 9 was slower than that from Grade 3 to Grade 6. Students with lower initial achievement improved at a faster rate than those who started at a higher level. Gender did not affect growth rate. © 2014 The British Psychological Society.

New techniques for the analysis of manual control systems. [mathematical models of human operator behavior

NASA Technical Reports Server (NTRS)

Bekey, G. A.

1971-01-01

Studies are summarized on the application of advanced analytical and computational methods to the development of mathematical models of human controllers in multiaxis manual control systems. Specific accomplishments include the following: (1) The development of analytical and computer methods for the measurement of random parameters in linear models of human operators. (2) Discrete models of human operator behavior in a multiple display situation were developed. (3) Sensitivity techniques were developed which make possible the identification of unknown sampling intervals in linear systems. (4) The adaptive behavior of human operators following particular classes of vehicle failures was studied and a model structure proposed.

Theoretical models for supercritical fluid extraction.

PubMed

Huang, Zhen; Shi, Xiao-Han; Jiang, Wei-Juan

2012-08-10

For the proper design of supercritical fluid extraction processes, it is essential to have a sound knowledge of the mass transfer mechanism of the extraction process and the appropriate mathematical representation. In this paper, the advances and applications of kinetic models for describing supercritical fluid extraction from various solid matrices have been presented. The theoretical models overviewed here include the hot ball diffusion, broken and intact cell, shrinking core and some relatively simple models. Mathematical representations of these models have been in detail interpreted as well as their assumptions, parameter identifications and application examples. Extraction process of the analyte solute from the solid matrix by means of supercritical fluid includes the dissolution of the analyte from the solid, the analyte diffusion in the matrix and its transport to the bulk supercritical fluid. Mechanisms involved in a mass transfer model are discussed in terms of external mass transfer resistance, internal mass transfer resistance, solute-solid interactions and axial dispersion. The correlations of the external mass transfer coefficient and axial dispersion coefficient with certain dimensionless numbers are also discussed. Among these models, the broken and intact cell model seems to be the most relevant mathematical model as it is able to provide realistic description of the plant material structure for better understanding the mass-transfer kinetics and thus it has been widely employed for modeling supercritical fluid extraction of natural matters. Copyright © 2012 Elsevier B.V. All rights reserved.

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…

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

ERIC Educational Resources Information Center

Schwerdtfeger, Sara

2017-01-01

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

Scripps Ocean Modeling and Remote Sensing (SOMARS)

DTIC Science & Technology

1988-09-20

Topics in this brief reports include: Kalman filtering of oceanographic data; Remote sensing of sea surface temperature; Altimetry and Surface heat fluxes; Ocean models of the marine mixed layer; Radar altimetry; Mathematical model of California current eddies.

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

ERIC Educational Resources Information Center

Stohlmann, Micah; Maiorca, Cathrine; Allen, Charlie

2017-01-01

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

Review: To be or not to be an identifiable model. Is this a relevant question in animal science modelling?

PubMed

Muñoz-Tamayo, R; Puillet, L; Daniel, J B; Sauvant, D; Martin, O; Taghipoor, M; Blavy, P

2018-04-01

What is a good (useful) mathematical model in animal science? For models constructed for prediction purposes, the question of model adequacy (usefulness) has been traditionally tackled by statistical analysis applied to observed experimental data relative to model-predicted variables. However, little attention has been paid to analytic tools that exploit the mathematical properties of the model equations. For example, in the context of model calibration, before attempting a numerical estimation of the model parameters, we might want to know if we have any chance of success in estimating a unique best value of the model parameters from available measurements. This question of uniqueness is referred to as structural identifiability; a mathematical property that is defined on the sole basis of the model structure within a hypothetical ideal experiment determined by a setting of model inputs (stimuli) and observable variables (measurements). Structural identifiability analysis applied to dynamic models described by ordinary differential equations (ODEs) is a common practice in control engineering and system identification. This analysis demands mathematical technicalities that are beyond the academic background of animal science, which might explain the lack of pervasiveness of identifiability analysis in animal science modelling. To fill this gap, in this paper we address the analysis of structural identifiability from a practitioner perspective by capitalizing on the use of dedicated software tools. Our objectives are (i) to provide a comprehensive explanation of the structural identifiability notion for the community of animal science modelling, (ii) to assess the relevance of identifiability analysis in animal science modelling and (iii) to motivate the community to use identifiability analysis in the modelling practice (when the identifiability question is relevant). We focus our study on ODE models. By using illustrative examples that include published mathematical models describing lactation in cattle, we show how structural identifiability analysis can contribute to advancing mathematical modelling in animal science towards the production of useful models and, moreover, highly informative experiments via optimal experiment design. Rather than attempting to impose a systematic identifiability analysis to the modelling community during model developments, we wish to open a window towards the discovery of a powerful tool for model construction and experiment design.

Dose- and time-dependence of the host-mediated response to paclitaxel therapy: a mathematical modeling approach.

PubMed

Benguigui, Madeleine; Alishekevitz, Dror; Timaner, Michael; Shechter, Dvir; Raviv, Ziv; Benzekry, Sebastien; Shaked, Yuval

2018-01-05

It has recently been suggested that pro-tumorigenic host-mediated processes induced in response to chemotherapy counteract the anti-tumor activity of therapy, and thereby decrease net therapeutic outcome. Here we use experimental data to formulate a mathematical model describing the host response to different doses of paclitaxel (PTX) chemotherapy as well as the duration of the response. Three previously described host-mediated effects are used as readouts for the host response to therapy. These include the levels of circulating endothelial progenitor cells in peripheral blood and the effect of plasma derived from PTX-treated mice on migratory and invasive properties of tumor cells in vitro . A first set of mathematical models, based on basic principles of pharmacokinetics/pharmacodynamics, did not appropriately describe the dose-dependence and duration of the host response regarding the effects on invasion. We therefore provide an alternative mathematical model with a dose-dependent threshold, instead of a concentration-dependent one, that describes better the data. This model is integrated into a global model defining all three host-mediated effects. It not only precisely describes the data, but also correctly predicts host-mediated effects at different doses as well as the duration of the host response. This mathematical model may serve as a tool to predict the host response to chemotherapy in cancer patients, and therefore may be used to design chemotherapy regimens with improved therapeutic outcome by minimizing host mediated effects.

Influence of drug-light-interval on photodynamic therapy of port wine stains--simulation and validation of mathematic models.

PubMed

Huang, Naiyan; Cheng, Gang; Li, Xiaosong; Gu, Ying; Liu, Fanguang; Zhong, Qiuhai; Wang, Ying; Zen, Jin; Qiu, Haixia; Chen, Hongxia

2008-06-01

We established mathematical models of photodynamic therapy (PDT) on port wine stains (PWS) to observe the effect of drug-light-interval (DLI) and optimize light dose. The mathematical simulations included determining (1) the distribution of laser light by Monte Carlo model, (2) the change of photosensitizer concentration in PWS vessels by a pharmacokinetics equation, (3) the change of photosensitizer distribution in tissue outside the vessels by a diffuse equation and photobleaching equation, and (4) the change of tissue oxygen concentration by the Fick's law with a consideration of the oxygen consumption during PDT. The concentration of singlet oxygen in the tissue model was calculated by the finite difference method. To validate those models, a PWS lesion of the same patient was divided into two areas and subjected to different DLIs and treated with different energy density. The color of lesion was assessed 8-12 weeks later. The simulation indicated the singlet oxygen concentration of the second treatment area (DLI=40 min) was lower than that of the first treatment area (DLI=0 min). However, it would be increased to a level similar to that of the first treatment area if the light irradiation time of the second treatment area was prolonged from 40 min to 55 min. Clinical results were consistent with the results predicted by the mathematical models. The mathematical models established in this study are helpful to optimize clinical protocol.

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…

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

NASA Astrophysics Data System (ADS)

Shahbari, Juhaina Awawdeh

2018-07-01

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

Development of a mathematical model of the human cardiovascular system: An educational perspective

NASA Astrophysics Data System (ADS)

Johnson, Bruce Allen

A mathematical model of the human cardiovascular system will be a useful educational tool in biological sciences and bioengineering classrooms. The goal of this project is to develop a mathematical model of the human cardiovascular system that responds appropriately to variations of significant physical variables. Model development is based on standard fluid statics and dynamics principles, pressure-volume characteristics of the cardiac cycle, and compliant behavior of blood vessels. Cardiac cycle phases provide the physical and logical model structure, and Boolean algebra links model sections. The model is implemented using VisSim, a highly intuitive and easily learned block diagram modeling software package. Comparisons of model predictions of key variables to published values suggest that the model reasonably approximates expected behavior of those variables. The model responds plausibly to variations of independent variables. Projected usefulness of the model as an educational tool is threefold: independent variables which determine heart function may be easily varied to observe cause and effect; the model is used in an interactive setting; and the relationship of governing equations to model behavior is readily viewable and intuitive. Future use of this model in classrooms may give a more reasonable indication of its value as an educational tool.* *This dissertation includes a CD that is multimedia (contains text and other applications that are not available in a printed format). The CD requires the following applications: CorelPhotoHouse, CorelWordPerfect, VisSinViewer (included on CD), Internet access.

Mathematics Difficulty with and without Reading Difficulty: Findings and Implications from a Four-Year Longitudinal Study

ERIC Educational Resources Information Center

Vukovic, Rose K.

2012-01-01

An overarching question guided this study:What is mathematics difficulty (MD) independent of reading difficulty (RD)? The sample included 203 children whom the researchers followed from kindergarten to third grade. The researchers used latent growth modeling to investigate the relationship between MD and measures of working memory, short-term…

Associations of Temperament Traits and Mathematics Grades in Adolescents Are Dependent on the Rater but Independent of Motivation and Cognitive Ability

ERIC Educational Resources Information Center

Hintsanen, Mirka; Alatupa, Saija; Jokela, Markus; Lipsanen, Jari; Hintsa, Taina; Leino, Mare

2012-01-01

The current study examines associations between self- and teacher-rated temperament traits (activity, inhibition, negative emotionality, persistence, distractibility, and mood) and mathematics grades. The sample includes 310 ninth grade students (mean age 15.0) from several schools in Finland. Analyses were conducted with multilevel modeling.…

Early Disparities in Mathematics Gains among Poor and Non-Poor Children: Examining the Role of Behavioral Engagement in Learning

ERIC Educational Resources Information Center

Robinson, Keith

2013-01-01

Multilevel modeling was used to investigate the relationship between poverty status, mathematics achievement gains, and behavioral engagement in learning over kindergarten. Data included information on 11,680 poor, low-income, and non-poor kindergartners from the Early Childhood Longitudinal Study-Kindergarten Cohort of 1998-1999 (ECLS-K). Results…

An Analysis of Mathematics Teacher Candidates' Critical Thinking Dispositions and Their Logical Thinking Skills

ERIC Educational Resources Information Center

Incikabi, Lutfi; Tuna, Abdulkadir; Biber, Abdullah Cagri

2013-01-01

This study aimed to investigate the existence of the relationship between mathematics teacher candidates' critical thinking skills and their logical thinking dispositions in terms of the variables of grade level in college, high school type, and gender. The current study utilized relational survey model and included a total of 99 mathematics…

Data-based mathematical modeling of vectorial transport across double-transfected polarized cells.

PubMed

Bartholomé, Kilian; Rius, Maria; Letschert, Katrin; Keller, Daniela; Timmer, Jens; Keppler, Dietrich

2007-09-01

Vectorial transport of endogenous small molecules, toxins, and drugs across polarized epithelial cells contributes to their half-life in the organism and to detoxification. To study vectorial transport in a quantitative manner, an in vitro model was used that includes polarized MDCKII cells stably expressing the recombinant human uptake transporter OATP1B3 in their basolateral membrane and the recombinant ATP-driven efflux pump ABCC2 in their apical membrane. These double-transfected cells enabled mathematical modeling of the vectorial transport of the anionic prototype substance bromosulfophthalein (BSP) that has frequently been used to examine hepatobiliary transport. Time-dependent analyses of (3)H-labeled BSP in the basolateral, intracellular, and apical compartments of cells cultured on filter membranes and efflux experiments in cells preloaded with BSP were performed. A mathematical model was fitted to the experimental data. Data-based modeling was optimized by including endogenous transport processes in addition to the recombinant transport proteins. The predominant contributions to the overall vectorial transport of BSP were mediated by OATP1B3 (44%) and ABCC2 (28%). Model comparison predicted a previously unrecognized endogenous basolateral efflux process as a negative contribution to total vectorial transport, amounting to 19%, which is in line with the detection of the basolateral efflux pump Abcc4 in MDCKII cells. Rate-determining steps in the vectorial transport were identified by calculating control coefficients. Data-based mathematical modeling of vectorial transport of BSP as a model substance resulted in a quantitative description of this process and its components. The same systems biology approach may be applied to other cellular systems and to different substances.

Fluorescence of bioaerosols: mathematical model including primary fluorescing and absorbing molecules in bacteria.

PubMed

Hill, Steven C; Pan, Yong-Le; Williamson, Chatt; Santarpia, Joshua L; Hill, Hanna H

2013-09-23

This paper describes a mathematical model of fluorescent biological particles composed of bacteria, viruses, or proteins. The fluorescent and/or light absorbing molecules included in the model are amino acids (tryptophan, etc.); nucleic acids (DNA, RNA, etc.); coenzymes (nicotinamide adenine dinucleotides, flavins, and vitamins B₆ and K and variants of these); and dipicolinates. The concentrations, absorptivities, and fluorescence quantum yields are estimated from the literature, often with large uncertainties. The bioparticles in the model are spherical and homogeneous. Calculated fluorescence cross sections for particles excited at 266, 280, and 355 nm are compared with measured values from the literature for several bacteria, bacterial spores and albumins. The calculated 266- and 280-nm excited fluorescence is within a factor of 3.2 of the measurements for the vegetative cells and proteins, but overestimates the fluorescence of spores by a factor of 10 or more. This is the first reported modeling of the fluorescence of bioaerosols in which the primary fluorophores and absorbing molecules are included.

Nitric oxide bioavailability in the microcirculation: insights from mathematical models.

PubMed

Tsoukias, Nikolaos M

2008-11-01

Over the last 30 years nitric oxide (NO) has emerged as a key signaling molecule involved in a number of physiological functions, including in the regulation of microcirculatory tone. Despite significant scientific contributions, fundamental questions about NO's role in the microcirculation remain unanswered. Mathematical modeling can assist in investigations of microcirculatory NO physiology and address experimental limitations in quantifying vascular NO concentrations. The number of mathematical models investigating the fate of NO in the vasculature has increased over the last few years, and new models are continuously emerging, incorporating an increasing level of complexity and detail. Models investigate mechanisms that affect NO availability in health and disease. They examine the significance of NO release from nonendothelial sources, the effect of transient release, and the complex interaction of NO with other substances, such as heme-containing proteins and reactive oxygen species. Models are utilized to test and generate hypotheses for the mechanisms that regulate NO-dependent signaling in the microcirculation.

Mathematical modeling in biological populations through branching processes. Application to salmonid populations.

PubMed

Molina, Manuel; Mota, Manuel; Ramos, Alfonso

2015-01-01

This work deals with mathematical modeling through branching processes. We consider sexually reproducing animal populations where, in each generation, the number of progenitor couples is determined in a non-predictable environment. By using a class of two-sex branching processes, we describe their demographic dynamics and provide several probabilistic and inferential contributions. They include results about the extinction of the population and the estimation of the offspring distribution and its main moments. We also present an application to salmonid populations.

Application of differential transformation method for solving dengue transmission mathematical model

NASA Astrophysics Data System (ADS)

Ndii, Meksianis Z.; Anggriani, Nursanti; Supriatna, Asep K.

2018-03-01

The differential transformation method (DTM) is a semi-analytical numerical technique which depends on Taylor series and has application in many areas including Biomathematics. The aim of this paper is to employ the differential transformation method (DTM) to solve system of non-linear differential equations for dengue transmission mathematical model. Analytical and numerical solutions are determined and the results are compared to that of Runge-Kutta method. We found a good agreement between DTM and Runge-Kutta method.

Mathematic Model of Digital Control System with PID Regulator and Regular Step of Quantization with Information Transfer via the Channel of Plural Access

NASA Astrophysics Data System (ADS)

Abramov, G. V.; Emeljanov, A. E.; Ivashin, A. L.

Theoretical bases for modeling a digital control system with information transfer via the channel of plural access and a regular quantization cycle are submitted. The theory of dynamic systems with random changes of the structure including elements of the Markov random processes theory is used for a mathematical description of a network control system. The characteristics of similar control systems are received. Experimental research of the given control systems is carried out.

Recent advances in mathematical modeling of nitrous oxides emissions from wastewater treatment processes.

PubMed

Ni, Bing-Jie; Yuan, Zhiguo

2015-12-15

Nitrous oxide (N2O) can be emitted from wastewater treatment contributing to its greenhouse gas footprint significantly. Mathematical modeling of N2O emissions is of great importance toward the understanding and reduction of the environmental impact of wastewater treatment systems. This article reviews the current status of the modeling of N2O emissions from wastewater treatment. The existing mathematical models describing all the known microbial pathways for N2O production are reviewed and discussed. These included N2O production by ammonia-oxidizing bacteria (AOB) through the hydroxylamine oxidation pathway and the AOB denitrification pathway, N2O production by heterotrophic denitrifiers through the denitrification pathway, and the integration of these pathways in single N2O models. The calibration and validation of these models using lab-scale and full-scale experimental data is also reviewed. We conclude that the mathematical modeling of N2O production, while is still being enhanced supported by new knowledge development, has reached a maturity that facilitates the estimation of site-specific N2O emissions and the development of mitigation strategies for a wastewater treatment plant taking into the specific design and operational conditions of the plant. Copyright © 2015 Elsevier Ltd. All rights reserved.

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…

EpiModel: An R Package for Mathematical Modeling of Infectious Disease over Networks.

PubMed

Jenness, Samuel M; Goodreau, Steven M; Morris, Martina

2018-04-01

Package EpiModel provides tools for building, simulating, and analyzing mathematical models for the population dynamics of infectious disease transmission in R. Several classes of models are included, but the unique contribution of this software package is a general stochastic framework for modeling the spread of epidemics on networks. EpiModel integrates recent advances in statistical methods for network analysis (temporal exponential random graph models) that allow the epidemic modeling to be grounded in empirical data on contacts that can spread infection. This article provides an overview of both the modeling tools built into EpiModel , designed to facilitate learning for students new to modeling, and the application programming interface for extending package EpiModel , designed to facilitate the exploration of novel research questions for advanced modelers.

EpiModel: An R Package for Mathematical Modeling of Infectious Disease over Networks

PubMed Central

Jenness, Samuel M.; Goodreau, Steven M.; Morris, Martina

2018-01-01

Package EpiModel provides tools for building, simulating, and analyzing mathematical models for the population dynamics of infectious disease transmission in R. Several classes of models are included, but the unique contribution of this software package is a general stochastic framework for modeling the spread of epidemics on networks. EpiModel integrates recent advances in statistical methods for network analysis (temporal exponential random graph models) that allow the epidemic modeling to be grounded in empirical data on contacts that can spread infection. This article provides an overview of both the modeling tools built into EpiModel, designed to facilitate learning for students new to modeling, and the application programming interface for extending package EpiModel, designed to facilitate the exploration of novel research questions for advanced modelers. PMID:29731699

Virtual Visualisation Laboratory for Science and Mathematics Content (Vlab-SMC) with Special Reference to Teaching and Learning of Chemistry

NASA Astrophysics Data System (ADS)

Badioze Zaman, Halimah; Bakar, Norashiken; Ahmad, Azlina; Sulaiman, Riza; Arshad, Haslina; Mohd. Yatim, Nor Faezah

Research on the teaching of science and mathematics in schools and universities have shown that available teaching models are not effective in instilling the understanding of scientific and mathematics concepts, and the right scientific and mathematics skills required for learners to become good future scientists (mathematicians included). The extensive development of new technologies has a marked influence on education, by facilitating the design of new learning and teaching materials, that can improve the attitude of learners towards Science and Mathematics and the plausibility of advanced interactive, personalised learning process. The usefulness of the computer in Science and Mathematics education; as an interactive communication medium that permits access to all types of information (texts, images, different types of data such as sound, graphics and perhaps haptics like smell and touch); as an instrument for problem solving through simulations of scientific and mathematics phenomenon and experiments; as well as measuring and monitoring scientific laboratory experiments. This paper will highlight on the design and development of the virtual Visualisation Laboratory for Science & Mathematics Content (VLab-SMC) based on the Cognitivist- Constructivist-Contextual development life cycle model as well as the Instructional Design (ID) model, in order to achieve its objectives in teaching and learning. However, this paper with only highlight one of the virtual labs within VLab-SMC that is, the Virtual Lab for teaching Chemistry (VLab- Chem). The development life cycle involves the educational media to be used, measurement of content, and the authoring and programming involved; whilst the ID model involves the application of the cognitivist, constructivist and contextual theories in the modeling of the modules of VLab-SMC generally and Vlab-Chem specifically, using concepts such as 'learning by doing', contextual learning, experimental simulations 3D and real-time animations to create a virtual laboratory based on a real laboratory. Initial preliminary study shows positive indicators of VLab-Chem for the teaching and learning of Chemistry on the topic of 'Salts and Acids'.

Developing workshop module of realistic mathematics education: Follow-up workshop

NASA Astrophysics Data System (ADS)

Palupi, E. L. W.; Khabibah, S.

2018-01-01

Realistic Mathematics Education (RME) is a learning approach which fits the aim of the curriculum. The success of RME in teaching mathematics concepts, triggering students’ interest in mathematics and teaching high order thinking skills to the students will make teachers start to learn RME. Hence, RME workshop is often offered and done. This study applied development model proposed by Plomp. Based on the study by RME team, there are three kinds of RME workshop: start-up workshop, follow-up workshop, and quality boost. However, there is no standardized or validated module which is used in that workshops. This study aims to develop a module of RME follow-up workshop which is valid and can be used. Plopm’s developmental model includes materials analysis, design, realization, implementation, and evaluation. Based on the validation, the developed module is valid. While field test shows that the module can be used effectively.

Computer Language For Optimization Of Design

NASA Technical Reports Server (NTRS)

Scotti, Stephen J.; Lucas, Stephen H.

1991-01-01

SOL is computer language geared to solution of design problems. Includes mathematical modeling and logical capabilities of computer language like FORTRAN; also includes additional power of nonlinear mathematical programming methods at language level. SOL compiler takes SOL-language statements and generates equivalent FORTRAN code and system calls. Provides syntactic and semantic checking for recovery from errors and provides detailed reports containing cross-references to show where each variable used. Implemented on VAX/VMS computer systems. Requires VAX FORTRAN compiler to produce executable program.

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

PubMed

Braatz, Elise M; Coleman, Randolph A

2015-06-01

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

A mathematical model for jet engine combustor pollutant emissions

NASA Technical Reports Server (NTRS)

Boccio, J. L.; Weilerstein, G.; Edelman, R. B.

1973-01-01

Mathematical modeling for the description of the origin and disposition of combustion-generated pollutants in gas turbines is presented. A unified model in modular form is proposed which includes kinetics, recirculation, turbulent mixing, multiphase flow effects, swirl and secondary air injection. Subelements of the overall model were applied to data relevant to laboratory reactors and practical combustor configurations. Comparisons between the theory and available data show excellent agreement for basic CO/H2/Air chemical systems. For hydrocarbons the trends are predicted well including higher-than-equilibrium NO levels within the fuel rich regime. Although the need for improved accuracy in fuel rich combustion is indicated, comparisons with actual jet engine data in terms of the effect of combustor-inlet temperature is excellent. In addition, excellent agreement with data is obtained regarding reduced NO emissions with water droplet and steam injection.

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

ERIC Educational Resources Information Center

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

2016-01-01

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

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…

Advances in multi-scale modeling of solidification and casting processes

NASA Astrophysics Data System (ADS)

Liu, Baicheng; Xu, Qingyan; Jing, Tao; Shen, Houfa; Han, Zhiqiang

2011-04-01

The development of the aviation, energy and automobile industries requires an advanced integrated product/process R&D systems which could optimize the product and the process design as well. Integrated computational materials engineering (ICME) is a promising approach to fulfill this requirement and make the product and process development efficient, economic, and environmentally friendly. Advances in multi-scale modeling of solidification and casting processes, including mathematical models as well as engineering applications are presented in the paper. Dendrite morphology of magnesium and aluminum alloy of solidification process by using phase field and cellular automaton methods, mathematical models of segregation of large steel ingot, and microstructure models of unidirectionally solidified turbine blade casting are studied and discussed. In addition, some engineering case studies, including microstructure simulation of aluminum casting for automobile industry, segregation of large steel ingot for energy industry, and microstructure simulation of unidirectionally solidified turbine blade castings for aviation industry are discussed.

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…

Design and Analysis of Precise Pointing Systems

NASA Technical Reports Server (NTRS)

Kim, Young K.

2000-01-01

The mathematical models of Glovebox Integrated Microgravity Isolation Technology (g- LIMIT) dynamics/control system, which include six degrees of freedom (DOF) equations of motion, mathematical models of position sensors, accelerometers and actuators, and acceleration and position controller, were developed using MATLAB and TREETOPS simulations. Optimal control parameters of G-LIMIT control system were determined through sensitivity studies and its performance were evaluated with the TREETOPS model of G-LIMIT dynamics and control system. The functional operation and performance of the Tektronix DTM920 digital thermometer were studied and the inputs to the crew procedures and training of the DTM920 were documented.

Evidence-based Controls for Epidemics Using Spatio-temporal Stochastic Model as a Bayesian Framwork

USDA-ARS?s Scientific Manuscript database

The control of highly infectious diseases of agricultural and plantation crops and livestock represents a key challenge in epidemiological and ecological modelling, with implemented control strategies often being controversial. Mathematical models, including the spatio-temporal stochastic models con...

A flight-dynamic helicopter mathematical model with a single flap-lag-torsion main rotor

NASA Technical Reports Server (NTRS)

Takahashi, Marc D.

1990-01-01

A mathematical model of a helicopter system with a single main rotor that includes rigid, hinge-restrained rotor blades with flap, lag, and torsion degrees of freedom is described. The model allows several hinge sequences and two offsets in the hinges. Quasi-steady Greenberg theory is used to calculate the blade-section aerodynamic forces, and inflow effects are accounted for by using three-state nonlinear dynamic inflow model. The motion of the rigid fuselage is defined by six degrees of freedom, and an optional rotor rpm degree of freedom is available. Empennage surfaces and the tail rotor are modeled, and the effect of main-rotor downwash on these elements is included. Model trim linearization, and time-integration operations are described and can be applied to a subset of the model in the rotating or nonrotating coordinate frame. A preliminary validation of the model is made by comparing its results with those of other analytical and experimental studies. This publication presents the results of research compiled in November 1989.

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

NASA Astrophysics Data System (ADS)

Khusna, H.; Heryaningsih, N. Y.

2018-01-01

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

WORKSHOP ON APPLICATION OF STATISTICAL METHODS TO BIOLOGICALLY-BASED PHARMACOKINETIC MODELING FOR RISK ASSESSMENT

EPA Science Inventory

Biologically-based pharmacokinetic models are being increasingly used in the risk assessment of environmental chemicals. These models are based on biological, mathematical, statistical and engineering principles. Their potential uses in risk assessment include extrapolation betwe...

Estimating Setup of Driven Piles into Louisiana Clayey Soils

DOT National Transportation Integrated Search

2009-11-15

Two types of mathematical models for pile setup prediction, the Skov-Denver model and the newly developed rate-based model, have been established from all the dynamic and static testing data, including restrikes of the production piles, restrikes, st...

Estimating setup of driven piles into Louisiana clayey soils.

DOT National Transportation Integrated Search

2010-11-15

Two types of mathematical models for pile setup prediction, the Skov-Denver model and the newly developed rate-based model, have been established from all the dynamic and static testing data, including restrikes of the production piles, restrikes, st...

Hydrogen production by the hyperthermophilic bacterium Thermotoga maritima Part II: modeling and experimental approaches for hydrogen production.

PubMed

Auria, Richard; Boileau, Céline; Davidson, Sylvain; Casalot, Laurence; Christen, Pierre; Liebgott, Pierre Pol; Combet-Blanc, Yannick

2016-01-01

Thermotoga maritima is a hyperthermophilic bacterium known to produce hydrogen from a large variety of substrates. The aim of the present study is to propose a mathematical model incorporating kinetics of growth, consumption of substrates, product formations, and inhibition by hydrogen in order to predict hydrogen production depending on defined culture conditions. Our mathematical model, incorporating data concerning growth, substrates, and products, was developed to predict hydrogen production from batch fermentations of the hyperthermophilic bacterium, T. maritima . It includes the inhibition by hydrogen and the liquid-to-gas mass transfer of H 2 , CO 2 , and H 2 S. Most kinetic parameters of the model were obtained from batch experiments without any fitting. The mathematical model is adequate for glucose, yeast extract, and thiosulfate concentrations ranging from 2.5 to 20 mmol/L, 0.2-0.5 g/L, or 0.01-0.06 mmol/L, respectively, corresponding to one of these compounds being the growth-limiting factor of T. maritima . When glucose, yeast extract, and thiosulfate concentrations are all higher than these ranges, the model overestimates all the variables. In the window of the model validity, predictions of the model show that the combination of both variables (increase in limiting factor concentration and in inlet gas stream) leads up to a twofold increase of the maximum H 2 -specific productivity with the lowest inhibition. A mathematical model predicting H 2 production in T. maritima was successfully designed and confirmed in this study. However, it shows the limit of validity of such mathematical models. Their limit of applicability must take into account the range of validity in which the parameters were established.

Problem Based Learning Technique and Its Effect on Acquisition of Linear Programming Skills by Secondary School Students in Kenya

ERIC Educational Resources Information Center

Nakhanu, Shikuku Beatrice; Musasia, Amadalo Maurice

2015-01-01

The topic Linear Programming is included in the compulsory Kenyan secondary school mathematics curriculum at form four. The topic provides skills for determining best outcomes in a given mathematical model involving some linear relationship. This technique has found application in business, economics as well as various engineering fields. Yet many…

Epistemological Beliefs of Prospective Preschool Teachers and Their Relation to Knowledge, Perception, and Planning Abilities in the Field of Mathematics: A Process Model

ERIC Educational Resources Information Center

Dunekacke, Simone; Jenßen, Lars; Eilerts, Katja; Blömeke, Sigrid

2016-01-01

Teacher competence is a multi-dimensional construct that includes beliefs as well as knowledge. The present study investigated the structure of prospective preschool teachers' mathematics-related beliefs and their relation to content knowledge and pedagogical content knowledge. In addition, prospective preschool teachers' perception and planning…

The Influence of the Pedagogical Content Knowledge Framework on Research in Mathematics Education: A Review across Grade Bands

ERIC Educational Resources Information Center

Matthews, Mary Elizabeth

2013-01-01

This literature review examines the models, theories, and research in mathematics education that are informed by Lee S. Shulman's construct, Pedagogical Content Knowledge. The application of the concept differs in nature and volume across levels of schooling. The research includes substantial work at the elementary level, fewer studies at the…

Guidelines for the use of mathematics in operational area-wide integrated pest management programs using the sterile insect technique with a special focus on Tephritid Fruit Flies

USDA-ARS?s Scientific Manuscript database

Pest control managers can benefit from using mathematical approaches, particularly models, when implementing area-wide pest control programs that include sterile insect technique (SIT), especially when these are used to calculate required rates of sterile releases to result in suppression or eradica...

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

ERIC Educational Resources Information Center

Zbiek, Rose Mary; Conner, Annamarie

2006-01-01

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

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

ERIC Educational Resources Information Center

Thrasher, Emily Plunkett

2016-01-01

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

Space physiology IV: mathematical modeling of the cardiovascular system in space exploration.

PubMed

Keith Sharp, M; Batzel, Jerry Joseph; Montani, Jean-Pierre

2013-08-01

Mathematical modeling represents an important tool for analyzing cardiovascular function during spaceflight. This review describes how modeling of the cardiovascular system can contribute to space life science research and illustrates this process via modeling efforts to study postflight orthostatic intolerance (POI), a key issue for spaceflight. Examining this application also provides a context for considering broader applications of modeling techniques to the challenges of bioastronautics. POI, which affects a large fraction of astronauts in stand tests upon return to Earth, presents as dizziness, fainting and other symptoms, which can diminish crew performance and cause safety hazards. POI on the Moon or Mars could be more critical. In the field of bioastronautics, POI has been the dominant application of cardiovascular modeling for more than a decade, and a number of mechanisms for POI have been investigated. Modeling approaches include computational models with a range of incorporated factors and hemodynamic sophistication, and also physical models tested in parabolic and orbital flight. Mathematical methods such as parameter sensitivity analysis can help identify key system mechanisms. In the case of POI, this could lead to more effective countermeasures. Validation is a persistent issue in modeling efforts, and key considerations and needs for experimental data to synergistically improve understanding of cardiovascular responses are outlined. Future directions in cardiovascular modeling include subject-specific assessment of system status, as well as research on integrated physiological responses, leading, for instance, to assessment of subject-specific susceptibility to POI or effects of cardiovascular alterations on muscular, vision and cognitive function.

Ordinary differential equations with applications in molecular biology.

PubMed

Ilea, M; Turnea, M; Rotariu, M

2012-01-01

Differential equations are of basic importance in molecular biology mathematics because many biological laws and relations appear mathematically in the form of a differential equation. In this article we presented some applications of mathematical models represented by ordinary differential equations in molecular biology. The vast majority of quantitative models in cell and molecular biology are formulated in terms of ordinary differential equations for the time evolution of concentrations of molecular species. Assuming that the diffusion in the cell is high enough to make the spatial distribution of molecules homogenous, these equations describe systems with many participating molecules of each kind. We propose an original mathematical model with small parameter for biological phospholipid pathway. All the equations system includes small parameter epsilon. The smallness of epsilon is relative to the size of the solution domain. If we reduce the size of the solution region the same small epsilon will result in a different condition number. It is clear that the solution for a smaller region is less difficult. We introduce the mathematical technique known as boundary function method for singular perturbation system. In this system, the small parameter is an asymptotic variable, different from the independent variable. In general, the solutions of such equations exhibit multiscale phenomena. Singularly perturbed problems form a special class of problems containing a small parameter which may tend to zero. Many molecular biology processes can be quantitatively characterized by ordinary differential equations. Mathematical cell biology is a very active and fast growing interdisciplinary area in which mathematical concepts, techniques, and models are applied to a variety of problems in developmental medicine and bioengineering. Among the different modeling approaches, ordinary differential equations (ODE) are particularly important and have led to significant advances. Ordinary differential equations are used to model biological processes on various levels ranging from DNA molecules or biosynthesis phospholipids on the cellular level.

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

PubMed

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

2008-01-01

There is a renewed interest in obtaining a systemic understanding of metabolism, gene expression and signal transduction processes, driven by the recent research focus on Systems Biology. From a biotechnological point of view, such a systemic understanding of how a biological system is designed to work can facilitate the rational manipulation of specific pathways in different cell types to achieve specific goals. Due to the intrinsic complexity of biological systems, mathematical models are a central tool for understanding and predicting the integrative behavior of those systems. Particularly, models are essential for a rational development of biotechnological applications and in understanding system's design from an evolutionary point of view. Mathematical models can be obtained using many different strategies. In each case, their utility will depend upon the properties of the mathematical representation and on the possibility of obtaining meaningful parameters from available data. In practice, there are several issues at stake when one has to decide which mathematical model is more appropriate for the study of a given problem. First, one needs a model that can represent the aspects of the system one wishes to study. Second, one must choose a mathematical representation that allows an accurate analysis of the system with respect to different aspects of interest (for example, robustness of the system, dynamical behavior, optimization of the system with respect to some production goal, parameter value determination, etc). Third, before choosing between alternative and equally appropriate mathematical representations for the system, one should compare representations with respect to easiness of automation for model set-up, simulation, and analysis of results. Fourth, one should also consider how to facilitate model transference and re-usability by other researchers and for distinct purposes. Finally, one factor that is important for all four aspects is the regularity in the mathematical structure of the equations because it facilitates computational manipulation. This regularity is a mark of kinetic representations based on approximation theory. The use of approximation theory to derive mathematical representations with regular structure for modeling purposes has a long tradition in science. In most applied fields, such as engineering and physics, those approximations are often required to obtain practical solutions to complex problems. In this paper we review some of the more popular mathematical representations that have been derived using approximation theory and are used for modeling in molecular systems biology. We will focus on formalisms that are theoretically supported by the Taylor Theorem. These include the Power-law formalism, the recently proposed (log)linear and Lin-log formalisms as well as some closely related alternatives. We will analyze the similarities and differences between these formalisms, discuss the advantages and limitations of each representation, and provide a tentative "road map" for their potential utilization for different problems.

Mathematical model of the heat transfer process taking into account the consequences of nonlocality in structurally sensitive materials

NASA Astrophysics Data System (ADS)

Kuvyrkin, G. N.; Savelyeva, I. Y.; Kuvshynnikova, D. A.

2018-04-01

Creation of new materials based on nanotechnology is an important direction of modern materials science development. Materials obtained using nanotechnology can possess unique physical-mechanical and thermophysical properties, allowing their effective use in structures exposed to high-intensity thermomechanical effects. An important step in creation and use of new materials is the construction of mathematical models to describe the behavior of these materials in a wide range of changes under external effects. The model of heat conduction of structural-sensitive materials is considered with regard to the medium nonlocality effects. The relations of the mathematical model include an integral term describing the spatial nonlocality of the medium. A difference scheme, which makes it possible to obtain a numerical solution of the problem of nonstationary heat conduction with regard to the influence of the medium nonlocality on space, has been developed. The influence of the model parameters on the temperature distributions is analyzed.

Use of open-ended problems as the basis for the mathematical creativity growth disclosure of student

NASA Astrophysics Data System (ADS)

Suyitno, A.; Suyitno, H.; Rochmad; Dwijanto

2018-03-01

Mathematical creativity is the essence of learning in mathematics. However, mathematical creativity had not yet grown among students. Means there was a gap between needs and reality. This gap must be bridged through by scientific studies, and there were novelty findings, namely the discovery of stages to cultivate of Mathematical Creativity. The problem formulation: How to use of open-ended problems as the basis for the mathematical creativity growth disclosure of student? The goal was to use of open issues as the basis for the mathematical creativity growth disclosure of student. Research method with a qualitative approach. After data was collected then activity in data analysis, include data reduction, data presentation, data interpretation, and conclusion/verification. The results of the research: After the learning by applying the modification of RTTW learning model, then the students were trained to do the open-ended problems and by looking at the UTS and UAS values then qualitatively the results: (1) There was a significant increase of the student's final score. (2) The category of the growth of mathematical creativity of students, the Very Good there were three students, the Good there were six students, There were 17 students, and there were six students. The validation of these results was reinforced by interviews and triangulation. (3) Stage to cultivate mathematical creativity: lecturers should need to provide inputs on student work; Apply an appropriate learning model, and train students to work on the continuing problems.

Reflective Modeling in Teacher Education.

ERIC Educational Resources Information Center

Shealy, Barry E.

This paper describes mathematical modeling activities from a secondary mathematics teacher education course taken by fourth-year university students. Experiences with mathematical modeling are viewed as important in helping teachers develop a more intuitive understanding of mathematics, generate and evaluate mathematical interpretations, and…

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…

Mathematical modeling and computational prediction of cancer drug resistance.

PubMed

Sun, Xiaoqiang; Hu, Bin

2017-06-23

Diverse forms of resistance to anticancer drugs can lead to the failure of chemotherapy. Drug resistance is one of the most intractable issues for successfully treating cancer in current clinical practice. Effective clinical approaches that could counter drug resistance by restoring the sensitivity of tumors to the targeted agents are urgently needed. As numerous experimental results on resistance mechanisms have been obtained and a mass of high-throughput data has been accumulated, mathematical modeling and computational predictions using systematic and quantitative approaches have become increasingly important, as they can potentially provide deeper insights into resistance mechanisms, generate novel hypotheses or suggest promising treatment strategies for future testing. In this review, we first briefly summarize the current progress of experimentally revealed resistance mechanisms of targeted therapy, including genetic mechanisms, epigenetic mechanisms, posttranslational mechanisms, cellular mechanisms, microenvironmental mechanisms and pharmacokinetic mechanisms. Subsequently, we list several currently available databases and Web-based tools related to drug sensitivity and resistance. Then, we focus primarily on introducing some state-of-the-art computational methods used in drug resistance studies, including mechanism-based mathematical modeling approaches (e.g. molecular dynamics simulation, kinetic model of molecular networks, ordinary differential equation model of cellular dynamics, stochastic model, partial differential equation model, agent-based model, pharmacokinetic-pharmacodynamic model, etc.) and data-driven prediction methods (e.g. omics data-based conventional screening approach for node biomarkers, static network approach for edge biomarkers and module biomarkers, dynamic network approach for dynamic network biomarkers and dynamic module network biomarkers, etc.). Finally, we discuss several further questions and future directions for the use of computational methods for studying drug resistance, including inferring drug-induced signaling networks, multiscale modeling, drug combinations and precision medicine. © The Author 2017. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

In-vitro development of vitrified-warmed bovine oocytes after activation may be predicted based on mathematical modelling of cooling and warming rates during vitrification, storage and sample removal.

PubMed

Sansinena, Marina; Santos, Maria Victoria; Chirife, Jorge; Zaritzky, Noemi

2018-05-01

Heat transfer during cooling and warming is difficult to measure in cryo-devices; mathematical modelling is an alternative method that can describe these processes. In this study, we tested the validity of one such model by assessing in-vitro development of vitrified and warmed bovine oocytes after parthenogenetic activation and culture. The viability of oocytes vitrified in four different cryo-devices was assessed. Consistent with modelling predictions, oocytes vitrified using cryo-devices with the highest modelled cooling rates had significantly (P < 0.05) better cleavage and blastocyst formation rates. We then evaluated a two-step sample removal process, in which oocytes were held in nitrogen vapour for 15 s to simulate sample identification during clinical application, before being removed completely and warmed. Oocytes exposed to this procedure showed reduced developmental potential, according to the model, owing to thermodynamic instability and devitrification at relatively low temperatures. These findings suggest that cryo-device selection and handling, including method of removal from nitrogen storage, are critical to survival of vitrified oocytes. Limitations of the study include use of parthenogenetically activated rather than fertilized ova and lack of physical measurement of recrystallization. We suggest mathematical modelling could be used to predict the effect of critical steps in cryopreservation. Copyright © 2018 Reproductive Healthcare Ltd. Published by Elsevier Ltd. All rights reserved.

Mathematical model to predict drivers' reaction speeds.

PubMed

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

2012-02-01

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

Perspectives for geographically oriented management of fusarium mycotoxins in the cereal supply chain.

PubMed

van der Fels-Klerx, H J; Booij, C J H

2010-06-01

This article provides an overview of available systems for management of Fusarium mycotoxins in the cereal grain supply chain, with an emphasis on the use of predictive mathematical modeling. From the state of the art, it proposes future developments in modeling and management and their challenges. Mycotoxin contamination in cereal grain-based feed and food products is currently managed and controlled by good agricultural practices, good manufacturing practices, hazard analysis critical control points, and by checking and more recently by notification systems and predictive mathematical models. Most of the predictive models for Fusarium mycotoxins in cereal grains focus on deoxynivalenol in wheat and aim to help growers make decisions about the application of fungicides during cultivation. Future developments in managing Fusarium mycotoxins should include the linkage between predictive mathematical models and geographical information systems, resulting into region-specific predictions for mycotoxin occurrence. The envisioned geographically oriented decision support system may incorporate various underlying models for specific users' demands and regions and various related databases to feed the particular models with (geographically oriented) input data. Depending on the user requirements, the system selects the best fitting model and available input information. Future research areas include organizing data management in the cereal grain supply chain, developing predictive models for other stakeholders (taking into account the period up to harvest), other Fusarium mycotoxins, and cereal grain types, and understanding the underlying effects of the regional component in the models.

West Nile Virus: Using Adapted Primary Literature in Mathematical Biology to Teach Scientific and Mathematical Reasoning in High School

NASA Astrophysics Data System (ADS)

Norris, Stephen P.; Macnab, John S.; Wonham, Marjorie; de Vries, Gerda

2009-05-01

This paper promotes the use of adapted primary literature as a curriculum and instruction innovation for use in high school. Adapted primary literature is useful for promoting an understanding of scientific and mathematical reasoning and argument and for introducing modern science into the schools. We describe a prototype adapted from a published article on a mathematical model of the spread of the West Nile virus in North America. The prototype is available as a web-based resource that includes supplemental pedagogical units. Preliminary feedback from use of the prototype in two classrooms is described and a sketch of an ongoing formal evaluation is provided.

The implementation of multiple intelligences based teaching model to improve mathematical problem solving ability for student of junior high school

NASA Astrophysics Data System (ADS)

Fasni, Nurli; Fatimah, Siti; Yulanda, Syerli

2017-05-01

This research aims to achieve some purposes such as: to know whether mathematical problem solving ability of students who have learned mathematics using Multiple Intelligences based teaching model is higher than the student who have learned mathematics using cooperative learning; to know the improvement of the mathematical problem solving ability of the student who have learned mathematics using Multiple Intelligences based teaching model., to know the improvement of the mathematical problem solving ability of the student who have learned mathematics using cooperative learning; to know the attitude of the students to Multiple Intelligences based teaching model. The method employed here is quasi-experiment which is controlled by pre-test and post-test. The population of this research is all of VII grade in SMP Negeri 14 Bandung even-term 2013/2014, later on two classes of it were taken for the samples of this research. A class was taught using Multiple Intelligences based teaching model and the other one was taught using cooperative learning. The data of this research were gotten from the test in mathematical problem solving, scale questionnaire of the student attitudes, and observation. The results show the mathematical problem solving of the students who have learned mathematics using Multiple Intelligences based teaching model learning is higher than the student who have learned mathematics using cooperative learning, the mathematical problem solving ability of the student who have learned mathematics using cooperative learning and Multiple Intelligences based teaching model are in intermediate level, and the students showed the positive attitude in learning mathematics using Multiple Intelligences based teaching model. As for the recommendation for next author, Multiple Intelligences based teaching model can be tested on other subject and other ability.

Predicting human chronically paralyzed muscle force: a comparison of three mathematical models.

PubMed

Frey Law, Laura A; Shields, Richard K

2006-03-01

Chronic spinal cord injury (SCI) induces detrimental musculoskeletal adaptations that adversely affect health status, ranging from muscle paralysis and skin ulcerations to osteoporosis. SCI rehabilitative efforts may increasingly focus on preserving the integrity of paralyzed extremities to maximize health quality using electrical stimulation for isometric training and/or functional activities. Subject-specific mathematical muscle models could prove valuable for predicting the forces necessary to achieve therapeutic loading conditions in individuals with paralyzed limbs. Although numerous muscle models are available, three modeling approaches were chosen that can accommodate a variety of stimulation input patterns. To our knowledge, no direct comparisons between models using paralyzed muscle have been reported. The three models include 1) a simple second-order linear model with three parameters and 2) two six-parameter nonlinear models (a second-order nonlinear model and a Hill-derived nonlinear model). Soleus muscle forces from four individuals with complete, chronic SCI were used to optimize each model's parameters (using an increasing and decreasing frequency ramp) and to assess the models' predictive accuracies for constant and variable (doublet) stimulation trains at 5, 10, and 20 Hz in each individual. Despite the large differences in modeling approaches, the mean predicted force errors differed only moderately (8-15% error; P=0.0042), suggesting physiological force can be adequately represented by multiple mathematical constructs. The two nonlinear models predicted specific force characteristics better than the linear model in nearly all stimulation conditions, with minimal differences between the two nonlinear models. Either nonlinear mathematical model can provide reasonable force estimates; individual application needs may dictate the preferred modeling strategy.

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

ERIC Educational Resources Information Center

Mumcu, Hayal Yavuz

2016-01-01

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

The impact of cell regeneration on the dynamics of viral coinfection

NASA Astrophysics Data System (ADS)

Pinky, Lubna; Dobrovolny, Hana M.

2017-06-01

Many mathematical models of respiratory viral infections do not include regeneration of cells within the respiratory tract, arguing that the infection is resolved before there is significant cellular regeneration. However, recent studies have found that ˜40% of patients hospitalized with influenza-like illness are infected with at least two different viruses, which could potentially lead to longer-lasting infections. In these longer infections, cell regeneration might affect the infection dynamics, in particular, allowing for the possibility of chronic coinfections. Several mathematical models have been used to describe cell regeneration in infection models, though the effect of model choice on the predicted time course of viral coinfections is not clear. We investigate four mathematical models incorporating different mechanisms of cell regeneration during respiratory viral coinfection to determine the effect of cell regeneration on infection dynamics. We perform linear stability analysis for each of the models and find the steady states analytically. The analysis suggests that chronic illness is possible but only with one viral species; chronic coexistence of two different viral species is not possible with the regeneration models considered here.

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

ERIC Educational Resources Information Center

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

2016-01-01

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

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

ERIC Educational Resources Information Center

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

2017-01-01

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

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

ERIC Educational Resources Information Center

Horton, Robert M.; Leonard, William H.

2005-01-01

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

Fortran Programs for Weapon Systems Analysis

DTIC Science & Technology

1990-06-01

interested in ballistics and related work. The programs include skeletal combat models , a set of discrete-event timing routines, mathematical and...32 4.3 LinEqs: Solve Linear Equations Like a Textbook ........................................................................... 34...military applications as it is of computer science. This crisis occurs in all fields, including the modeling of logistics, mobility, ballistics, and combat

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…

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

ERIC Educational Resources Information Center

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

2017-01-01

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

Software For Least-Squares And Robust Estimation

NASA Technical Reports Server (NTRS)

Jeffreys, William H.; Fitzpatrick, Michael J.; Mcarthur, Barbara E.; Mccartney, James

1990-01-01

GAUSSFIT computer program includes full-featured programming language facilitating creation of mathematical models solving least-squares and robust-estimation problems. Programming language designed to make it easy to specify complex reduction models. Written in 100 percent C language.

Exploring the Associations Among Nutrition, Science, and Mathematics Knowledge for an Integrative, Food-Based Curriculum.

PubMed

Stage, Virginia C; Kolasa, Kathryn M; Díaz, Sebastián R; Duffrin, Melani W

2018-01-01

Explore associations between nutrition, science, and mathematics knowledge to provide evidence that integrating food/nutrition education in the fourth-grade curriculum may support gains in academic knowledge. Secondary analysis of a quasi-experimental study. Sample included 438 students in 34 fourth-grade classrooms across North Carolina and Ohio; mean age 10 years old; gender (I = 53.2% female; C = 51.6% female). Dependent variable = post-test-nutrition knowledge; independent variables = baseline-nutrition knowledge, and post-test science and mathematics knowledge. Analyses included descriptive statistics and multiple linear regression. The hypothesized model predicted post-nutrition knowledge (F(437) = 149.4, p < .001; Adjusted R = .51). All independent variables were significant predictors with positive association. Science and mathematics knowledge were predictive of nutrition knowledge indicating use of an integrative science and mathematics curriculum to improve academic knowledge may also simultaneously improve nutrition knowledge among fourth-grade students. Teachers can benefit from integration by meeting multiple academic standards, efficiently using limited classroom time, and increasing nutrition education provided in the classroom. © 2018, American School Health Association.

Mathematical model for lift/cruise fan V/STOL aircraft simulator programming data

NASA Technical Reports Server (NTRS)

Bland, M. P.; Fajfar, B.; Konsewicz, R. K.

1976-01-01

Simulation data are reported for the purpose of programming the flight simulator for advanced aircraft for tests of the lift/cruise fan V/STOL Research Technology Aircraft. These simulation tests are to provide insight into problem areas which are encountered in operational use of the aircraft. A mathematical model is defined in sufficient detail to represent all the necessary pertinent aircraft and system characteristics. The model includes the capability to simulate two basic versions of an aircraft propulsion system: (1) the gas coupled configuration which uses insulated air ducts to transmit power between gas generators and fans in the form of high energy engine exhaust and (2) the mechanically coupled power system which uses shafts, clutches, and gearboxes for power transmittal. Both configurations are modeled such that the simulation can include vertical as well as rolling takeoff and landing, hover, powered lift flight, aerodynamic flight, and the transition between powered lift and aerodynamic flight.

Application of technology developed for flight simulation at NASA. Langley Research Center

NASA Technical Reports Server (NTRS)

Cleveland, Jeff I., II

1991-01-01

In order to meet the stringent time-critical requirements for real-time man-in-the-loop flight simulation, computer processing operations including mathematical model computation and data input/output to the simulators must be deterministic and be completed in as short a time as possible. Personnel at NASA's Langley Research Center are currently developing the use of supercomputers for simulation mathematical model computation for real-time simulation. This, coupled with the use of an open systems software architecture, will advance the state-of-the-art in real-time flight simulation.

Test-and-treat approach to HIV/AIDS: a primer for mathematical modeling.

PubMed

Nah, Kyeongah; Nishiura, Hiroshi; Tsuchiya, Naho; Sun, Xiaodan; Asai, Yusuke; Imamura, Akifumi

2017-09-05

The public benefit of test-and-treat has induced a need to justify goodness for the public, and mathematical modeling studies have played a key role in designing and evaluating the test-and-treat strategy for controlling HIV/AIDS. Here we briefly and comprehensively review the essence of contemporary understanding of the test-and-treat policy through mathematical modeling approaches and identify key pitfalls that have been identified to date. While the decrease in HIV incidence is achieved with certain coverages of diagnosis, care and continued treatment, HIV prevalence is not necessarily decreased and sometimes the test-and-treat is accompanied by increased long-term cost of antiretroviral therapy (ART). To confront with the complexity of assessment on this policy, the elimination threshold or the effective reproduction number has been proposed for its use in determining the overall success to anticipate the eventual elimination. Since the publication of original model in 2009, key issues of test-and-treat modeling studies have been identified, including theoretical problems surrounding the sexual partnership network, heterogeneities in the transmission dynamics, and realistic issues of achieving and maintaining high treatment coverage in the most hard-to-reach populations. To explicitly design country-specific control policy, quantitative modeling approaches to each single setting with differing epidemiological context would require multi-disciplinary collaborations among clinicians, public health practitioners, laboratory technologists, epidemiologists and mathematical modelers.

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

ERIC Educational Resources Information Center

Czocher, Jennifer A.

2016-01-01

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

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.…

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

ERIC Educational Resources Information Center

Stohlmann, Micah S.

2017-01-01

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

A Model for Math Modeling

ERIC Educational Resources Information Center

Lin, Tony; Erfan, Sasan

2016-01-01

Mathematical modeling is an open-ended research subject where no definite answers exist for any problem. Math modeling enables thinking outside the box to connect different fields of studies together including statistics, algebra, calculus, matrices, programming and scientific writing. As an integral part of society, it is the foundation for many…

Teaching Population Ecology Modeling by Means of the Hewlett-Packard 9100A.

ERIC Educational Resources Information Center

Tuinstra, Kenneth E.

The incorporation of mathematical modeling experiences into an undergraduate biology course is described. Detailed expositions of three models used to teach concepts of population ecology are presented, including introductions to major concepts, user instructions, trial data and problem sets. The models described are: 1) an exponential/logistic…

Simple Mathematical Models Do Not Accurately Predict Early SIV Dynamics

PubMed Central

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

2015-01-01

Upon infection of a new host, human immunodeficiency virus (HIV) replicates in the mucosal tissues and is generally undetectable in circulation for 1–2 weeks post-infection. Several interventions against HIV including vaccines and antiretroviral prophylaxis target virus replication at this earliest stage of infection. Mathematical models have been used to understand how HIV spreads from mucosal tissues systemically and what impact vaccination and/or antiretroviral prophylaxis has on viral eradication. Because predictions of such models have been rarely compared to experimental data, it remains unclear which processes included in these models are critical for predicting early HIV dynamics. Here we modified the “standard” mathematical model of HIV infection to include two populations of infected cells: cells that are actively producing the virus and cells that are transitioning into virus production mode. We evaluated the effects of several poorly known parameters on infection outcomes in this model and compared model predictions to experimental data on infection of non-human primates with variable doses of simian immunodifficiency virus (SIV). First, we found that the mode of virus production by infected cells (budding vs. bursting) has a minimal impact on the early virus dynamics for a wide range of model parameters, as long as the parameters are constrained to provide the observed rate of SIV load increase in the blood of infected animals. Interestingly and in contrast with previous results, we found that the bursting mode of virus production generally results in a higher probability of viral extinction than the budding mode of virus production. Second, this mathematical model was not able to accurately describe the change in experimentally determined probability of host infection with increasing viral doses. Third and finally, the model was also unable to accurately explain the decline in the time to virus detection with increasing viral dose. These results suggest that, in order to appropriately model early HIV/SIV dynamics, additional factors must be considered in the model development. These may include variability in monkey susceptibility to infection, within-host competition between different viruses for target cells at the initial site of virus replication in the mucosa, innate immune response, and possibly the inclusion of several different tissue compartments. The sobering news is that while an increase in model complexity is needed to explain the available experimental data, testing and rejection of more complex models may require more quantitative data than is currently available. PMID:25781919

Dialogic and Direct Instruction: Two Distinct Models of Mathematics Instruction and the Debate(s) Surrounding Them

ERIC Educational Resources Information Center

Munter, Charles; Stein, Mary Kay; Smith, Margaret Austin

2015-01-01

Background/Context: Which ideas should be included in the K-12 curriculum, how they are learned, and how they should be taught have been debated for decades in multiple subjects. In this article, we offer mathematics as a case in point of how new standards-related policies may offer an opportunity for reassessment and clarification of such…

Examining the Effects of the Flipped Model of Instruction on Student Engagement and Performance in the Secondary Mathematics Classroom: An Action Research Study

ERIC Educational Resources Information Center

Clark, Kevin R.

2013-01-01

In many of the secondary classrooms across the country, including the research site for this study, students are passively engaged in the mathematics content, and academic performance can be described, at best, as mediocre. This action research study sought to bring about improvements in student engagement and performance in the secondary…

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 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…

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

ERIC Educational Resources Information Center

Lingefjard, Thomas; Holmquist, Mikael

2005-01-01

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

Mathematical Modeling in the Undergraduate Curriculum

ERIC Educational Resources Information Center

Toews, Carl

2012-01-01

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

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…

Experimentation of cooperative learning model Numbered Heads Together (NHT) type by concept maps and Teams Games Tournament (TGT) by concept maps in terms of students logical mathematics intellegences

NASA Astrophysics Data System (ADS)

Irawan, Adi; Mardiyana; Retno Sari Saputro, Dewi

2017-06-01

This research is aimed to find out the effect of learning model towards learning achievement in terms of students’ logical mathematics intelligences. The learning models that were compared were NHT by Concept Maps, TGT by Concept Maps, and Direct Learning model. This research was pseudo experimental by factorial design 3×3. The population of this research was all of the students of class XI Natural Sciences of Senior High School in all regency of Karanganyar in academic year 2016/2017. The conclusions of this research were: 1) the students’ achievements with NHT learning model by Concept Maps were better than students’ achievements with TGT model by Concept Maps and Direct Learning model. The students’ achievements with TGT model by Concept Maps were better than the students’ achievements with Direct Learning model. 2) The students’ achievements that exposed high logical mathematics intelligences were better than students’ medium and low logical mathematics intelligences. The students’ achievements that exposed medium logical mathematics intelligences were better than the students’ low logical mathematics intelligences. 3) Each of student logical mathematics intelligences with NHT learning model by Concept Maps has better achievement than students with TGT learning model by Concept Maps, students with NHT learning model by Concept Maps have better achievement than students with the direct learning model, and the students with TGT by Concept Maps learning model have better achievement than students with Direct Learning model. 4) Each of learning model, students who have logical mathematics intelligences have better achievement then students who have medium logical mathematics intelligences, and students who have medium logical mathematics intelligences have better achievement than students who have low logical mathematics intelligences.

A tool for multi-scale modelling of the renal nephron

PubMed Central

Nickerson, David P.; Terkildsen, Jonna R.; Hamilton, Kirk L.; Hunter, Peter J.

2011-01-01

We present the development of a tool, which provides users with the ability to visualize and interact with a comprehensive description of a multi-scale model of the renal nephron. A one-dimensional anatomical model of the nephron has been created and is used for visualization and modelling of tubule transport in various nephron anatomical segments. Mathematical models of nephron segments are embedded in the one-dimensional model. At the cellular level, these segment models use models encoded in CellML to describe cellular and subcellular transport kinetics. A web-based presentation environment has been developed that allows the user to visualize and navigate through the multi-scale nephron model, including simulation results, at the different spatial scales encompassed by the model description. The Zinc extension to Firefox is used to provide an interactive three-dimensional view of the tubule model and the native Firefox rendering of scalable vector graphics is used to present schematic diagrams for cellular and subcellular scale models. The model viewer is embedded in a web page that dynamically presents content based on user input. For example, when viewing the whole nephron model, the user might be presented with information on the various embedded segment models as they select them in the three-dimensional model view. Alternatively, the user chooses to focus the model viewer on a cellular model located in a particular nephron segment in order to view the various membrane transport proteins. Selecting a specific protein may then present the user with a description of the mathematical model governing the behaviour of that protein—including the mathematical model itself and various simulation experiments used to validate the model against the literature. PMID:22670210

Pre-Service Teachers' Modelling Processes through Engagement with Model Eliciting Activities with a Technological Tool

ERIC Educational Resources Information Center

Daher, Wajeeh M.; Shahbari, Juhaina Awawdeh

2015-01-01

Engaging mathematics students with modelling activities helps them learn mathematics meaningfully. This engagement, in the case of model eliciting activities, helps the students elicit mathematical models by interpreting real-world situation in mathematical ways. This is especially true when the students utilize technology to build the models.…

The USC Faculty Planning Model: A History and Description.

ERIC Educational Resources Information Center

Bottomley, Wayne N.

A model for planning regarding college faculty is described. The USC Faculty Planning Model was developed by Robert Linnell and Paul Gray in 1974 at the University of Southern California as an interactive mathematical model to trace characteristics of faculty groups over time. Characteristics listed by the model include: faculty age distribution,…

System and method for anomaly detection

DOEpatents

Scherrer, Chad

2010-06-15

A system and method for detecting one or more anomalies in a plurality of observations is provided. In one illustrative embodiment, the observations are real-time network observations collected from a stream of network traffic. The method includes performing a discrete decomposition of the observations, and introducing derived variables to increase storage and query efficiencies. A mathematical model, such as a conditional independence model, is then generated from the formatted data. The formatted data is also used to construct frequency tables which maintain an accurate count of specific variable occurrence as indicated by the model generation process. The formatted data is then applied to the mathematical model to generate scored data. The scored data is then analyzed to detect anomalies.

Mathematical and Computational Modeling for Tumor Virotherapy with Mediated Immunity.

PubMed

Timalsina, Asim; Tian, Jianjun Paul; Wang, Jin

2017-08-01

We propose a new mathematical modeling framework based on partial differential equations to study tumor virotherapy with mediated immunity. The model incorporates both innate and adaptive immune responses and represents the complex interaction among tumor cells, oncolytic viruses, and immune systems on a domain with a moving boundary. Using carefully designed computational methods, we conduct extensive numerical simulation to the model. The results allow us to examine tumor development under a wide range of settings and provide insight into several important aspects of the virotherapy, including the dependence of the efficacy on a few key parameters and the delay in the adaptive immunity. Our findings also suggest possible ways to improve the virotherapy for tumor treatment.

The Integration of Mathematics in Middle School Science: Student and Teacher Impacts Related to Science Achievement and Attitudes Towards Integration

NASA Astrophysics Data System (ADS)

McHugh, Luisa

Contemporary research has suggested that in order for students to compete globally in the 21st century workplace, pedagogy must shift to include the integration of science and mathematics, where teachers effectively incorporate the two disciplines seamlessly. Mathematics facilitates a deeper understanding of science concepts and has been linked to improved student perception of the integration of science and mathematics. Although there is adequate literature to substantiate students' positive responses to integration in terms of attitudes, there has been little empirical data to support significant academic improvement when both disciplines are taught in an integrated method. This research study, conducted at several school districts on Long Island and New York City, New York, examined teachers' attitudes toward integration and students' attitudes about, and achievement on assessments in, an integrated 8th grade science classroom compared to students in a non-integrated classroom. An examination of these parameters was conducted to analyze the impact of the sizeable investment of time and resources needed to teach an integrated curriculum effectively. These resources included substantial teacher training, planning time, collaboration with colleagues, and administration of student assessments. The findings suggest that students had positive outcomes associated with experiencing an integrated science and mathematics curriculum, though these were only weakly correlated with teacher confidence in implementing the integrated model successfully. The positive outcomes included the ability of students to understand scientific concepts within a concrete mathematical framework, improved confidence in applying mathematics to scientific ideas, and increased agreement with the usefulness of mathematics in interpreting science concepts. Implications of these research findings may be of benefit to educators and policymakers looking to adapt integrated curricula in order to improve the preparation of students to learn and achieve in a global society.

Age-dependent Fourier model of the shape of the isolated ex vivo human crystalline lens.

PubMed

Urs, Raksha; Ho, Arthur; Manns, Fabrice; Parel, Jean-Marie

2010-06-01

To develop an age-dependent mathematical model of the zero-order shape of the isolated ex vivo human crystalline lens, using one mathematical function, that can be subsequently used to facilitate the development of other models for specific purposes such as optical modeling and analytical and numerical modeling of the lens. Profiles of whole isolated human lenses (n=30) aged 20-69, were measured from shadow-photogrammetric images. The profiles were fit to a 10th-order Fourier series consisting of cosine functions in polar-co-ordinate system that included terms for tilt and decentration. The profiles were corrected using these terms and processed in two ways. In the first, each lens was fit to a 10th-order Fourier series to obtain thickness and diameter, while in the second, all lenses were simultaneously fit to a Fourier series equation that explicitly include linear terms for age to develop an age-dependent mathematical model for the whole lens shape. Thickness and diameter obtained from Fourier series fits exhibited high correlation with manual measurements made from shadow-photogrammetric images. The root-mean-squared-error of the age-dependent fit was 205 microm. The age-dependent equations provide a reliable lens model for ages 20-60 years. The contour of the whole human crystalline lens can be modeled with a Fourier series. Shape obtained from the age-dependent model described in this paper can be used to facilitate the development of other models for specific purposes such as optical modeling and analytical and numerical modeling of the lens. Copyright (c) 2010 Elsevier Ltd. All rights reserved.

DigitalHuman (DH): An Integrative Mathematical Model ofHuman Physiology

NASA Technical Reports Server (NTRS)

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

2010-01-01

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

Mathematical modeling in realistic mathematics education

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Mathematical model for thermal and entropy analysis of thermal solar collectors by using Maxwell nanofluids with slip conditions, thermal radiation and variable thermal conductivity

NASA Astrophysics Data System (ADS)

Aziz, Asim; Jamshed, Wasim; Aziz, Taha

2018-04-01

In the present research a simplified mathematical model for the solar thermal collectors is considered in the form of non-uniform unsteady stretching surface. The non-Newtonian Maxwell nanofluid model is utilized for the working fluid along with slip and convective boundary conditions and comprehensive analysis of entropy generation in the system is also observed. The effect of thermal radiation and variable thermal conductivity are also included in the present model. The mathematical formulation is carried out through a boundary layer approach and the numerical computations are carried out for Cu-water and TiO2-water nanofluids. Results are presented for the velocity, temperature and entropy generation profiles, skin friction coefficient and Nusselt number. The discussion is concluded on the effect of various governing parameters on the motion, temperature variation, entropy generation, velocity gradient and the rate of heat transfer at the boundary.

Mathematical Modeling of Microbial Community Dynamics: A Methodological Review

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

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

Microorganisms in nature form diverse communities that dynamically change in structure and function in response to environmental variations. As a complex adaptive system, microbial communities show higher-order properties that are not present in individual microbes, but arise from their interactions. Predictive mathematical models not only help to understand the underlying principles of the dynamics and emergent properties of natural and synthetic microbial communities, but also provide key knowledge required for engineering them. In this article, we provide an overview of mathematical tools that include not only current mainstream approaches, but also less traditional approaches that, in our opinion, can bemore » potentially useful. We discuss a broad range of methods ranging from low-resolution supra-organismal to high-resolution individual-based modeling. Particularly, we highlight the integrative approaches that synergistically combine disparate methods. In conclusion, we provide our outlook for the key aspects that should be further developed to move microbial community modeling towards greater predictive power.« less

Zoonotic Transmission of Waterborne Disease: A Mathematical Model.

PubMed

Waters, Edward K; Hamilton, Andrew J; Sidhu, Harvinder S; Sidhu, Leesa A; Dunbar, Michelle

2016-01-01

Waterborne parasites that infect both humans and animals are common causes of diarrhoeal illness, but the relative importance of transmission between humans and animals and vice versa remains poorly understood. Transmission of infection from animals to humans via environmental reservoirs, such as water sources, has attracted attention as a potential source of endemic and epidemic infections, but existing mathematical models of waterborne disease transmission have limitations for studying this phenomenon, as they only consider contamination of environmental reservoirs by humans. This paper develops a mathematical model that represents the transmission of waterborne parasites within and between both animal and human populations. It also improves upon existing models by including animal contamination of water sources explicitly. Linear stability analysis and simulation results, using realistic parameter values to describe Giardia transmission in rural Australia, show that endemic infection of an animal host with zoonotic protozoa can result in endemic infection in human hosts, even in the absence of person-to-person transmission. These results imply that zoonotic transmission via environmental reservoirs is important.

Modeling and Analysis of Power Processing Systems (MAPPS). Volume 1: Technical report

NASA Technical Reports Server (NTRS)

Lee, F. C.; Rahman, S.; Carter, R. A.; Wu, C. H.; Yu, Y.; Chang, R.

1980-01-01

Computer aided design and analysis techniques were applied to power processing equipment. Topics covered include: (1) discrete time domain analysis of switching regulators for performance analysis; (2) design optimization of power converters using augmented Lagrangian penalty function technique; (3) investigation of current-injected multiloop controlled switching regulators; and (4) application of optimization for Navy VSTOL energy power system. The generation of the mathematical models and the development and application of computer aided design techniques to solve the different mathematical models are discussed. Recommendations are made for future work that would enhance the application of the computer aided design techniques for power processing systems.

Mathematical modeling of kidney transport.

PubMed

Layton, Anita T

2013-01-01

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

A systems analysis of the erythropoietic responses to weightlessness. Volume 1: Mathematical model simulations of the erythropoietic responses to weightlessness

NASA Technical Reports Server (NTRS)

Leonard, J. I.

1985-01-01

Theoretical responses to weightlessness are summarized. The studies include development and validation of a model of erythropoiesis regulation, analysis of the behavior of erythropoiesis under a variety of conditions, simulations of bed rest and space flight, and an evaluation of ground-based animal studies which were conducted as analogs of zero-g. A review of all relevant space flight findings and a set of testable hypotheses which attempt to explain how red cell mass decreases in space flight are presented. An additional document describes details of the mathematical model used in these studies.

Markov model of the loan portfolio dynamics considering influence of management and external economic factors

NASA Astrophysics Data System (ADS)

Bozhalkina, Yana; Timofeeva, Galina

2016-12-01

Mathematical model of loan portfolio in the form of a controlled Markov chain with discrete time is considered. It is assumed that coefficients of migration matrix depend on corrective actions and external factors. Corrective actions include process of receiving applications, interaction with existing solvent and insolvent clients. External factors are macroeconomic indicators, such as inflation and unemployment rates, exchange rates, consumer price indices, etc. Changes in corrective actions adjust the intensity of transitions in the migration matrix. The mathematical model for forecasting the credit portfolio structure taking into account a cumulative impact of internal and external changes is obtained.

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

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

Data Association Algorithms for Tracking Satellites

DTIC Science & Technology

2013-03-27

validation of the new tools. The description provided here includes the mathematical back ground and description of the models implemented, as well as a...simulation development. This work includes the addition of higher-fidelity models in CU-TurboProp and validation of the new tools. The description...ode45(), used in Ananke, and (3) provide the necessary inputs to the bidirectional reflectance distribution function ( BRDF ) model provided by Pacific

Model-Based Policymaking: A Framework to Promote Ethical "Good Practice" in Mathematical Modeling for Public Health Policymaking.

PubMed

Boden, Lisa A; McKendrick, Iain J

2017-01-01

Mathematical models are increasingly relied upon as decision support tools, which estimate risks and generate recommendations to underpin public health policies. However, there are no formal agreements about what constitutes professional competencies or duties in mathematical modeling for public health. In this article, we propose a framework to evaluate whether mathematical models that assess human and animal disease risks and control strategies meet standards consistent with ethical "good practice" and are thus "fit for purpose" as evidence in support of policy. This framework is derived from principles of biomedical ethics: independence, transparency (autonomy), beneficence/non-maleficence, and justice. We identify ethical risks associated with model development and implementation and consider the extent to which scientists are accountable for the translation and communication of model results to policymakers so that the strengths and weaknesses of the scientific evidence base and any socioeconomic and ethical impacts of biased or uncertain predictions are clearly understood. We propose principles to operationalize a framework for ethically sound model development and risk communication between scientists and policymakers. These include the creation of science-policy partnerships to mutually define policy questions and communicate results; development of harmonized international standards for model development; and data stewardship and improvement of the traceability and transparency of models via a searchable archive of policy-relevant models. Finally, we suggest that bespoke ethical advisory groups, with relevant expertise and access to these resources, would be beneficial as a bridge between science and policy, advising modelers of potential ethical risks and providing overview of the translation of modeling advice into policy.

Linking Preservice Teachers' Mathematics Self-Efficacy and Mathematics Teaching Efficacy to Their Mathematical Performance

ERIC Educational Resources Information Center

Bates, Alan B.; Latham, Nancy; Kim, Jin-ah

2011-01-01

This study examined preservice teachers' mathematics self-efficacy and mathematics teaching efficacy and compared them to their mathematical performance. Participants included 89 early childhood preservice teachers at a Midwestern university. Instruments included the Mathematics Self-Efficacy Scale (MSES), Mathematics Teaching Efficacy Beliefs…

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

ERIC Educational Resources Information Center

Mischo, Christoph; Maaß, Katja

2013-01-01

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

Leaning on Mathematical Habits of Mind

ERIC Educational Resources Information Center

Sword, Sarah; Matsuura, Ryota; Cuoco, Al; Kang, Jane; Gates, Miriam

2018-01-01

Mathematical modeling has taken on increasing curricular importance in the past decade due in no small measure to the Common Core State Standards in Mathematics (CCSSM) identifying modeling as one of the Standards for Mathematical Practice (SMP 4, CCSSI 2010, p. 7). Although researchers have worked on mathematical modeling (Lesh and Doerr 2003;…

Mathematical and Numerical Techniques in Energy and Environmental Modeling

NASA Astrophysics Data System (ADS)

Chen, Z.; Ewing, R. E.

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

Developing infrastructure for interconnecting transportation network and electric grid.

DOT National Transportation Integrated Search

2011-09-01

This report is primarily focused on the development of mathematical models that can be used to : support decisions regarding a charging station location and installation problem. The major parts : of developing the models included identification of t...

Proceedings of the 3rd Annual SCOLE Workshop

NASA Technical Reports Server (NTRS)

Taylor, Lawrence W., Jr. (Compiler)

1987-01-01

Topics addressed include: modeling and controlling the Spacecraft Control Laboratory Experiment (SCOLE) configurations; slewing maneuvers; mathematical models; vibration damping; gravitational effects; structural dynamics; finite element method; distributed parameter system; on-line pulse control; stability augmentation; and stochastic processes.

V/STOL tilt rotor study. Volume 5: A mathematical model for real time flight simulation of the Bell model 301 tilt rotor research aircraft

NASA Technical Reports Server (NTRS)

Harendra, P. B.; Joglekar, M. J.; Gaffey, T. M.; Marr, R. L.

1973-01-01

A mathematical model for real-time flight simulation of a tilt rotor research aircraft was developed. The mathematical model was used to support the aircraft design, pilot training, and proof-of-concept aspects of the development program. The structure of the mathematical model is indicated by a block diagram. The mathematical model differs from that for a conventional fixed wing aircraft principally in the added requirement to represent the dynamics and aerodynamics of the rotors, the interaction of the rotor wake with the airframe, and the rotor control and drive systems. The constraints imposed on the mathematical model are defined.

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

PubMed

Deng, Zhimin; Tian, Tianhai

2014-07-29

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

Logic integer programming models for signaling networks.

PubMed

Haus, Utz-Uwe; Niermann, Kathrin; Truemper, Klaus; Weismantel, Robert

2009-05-01

We propose a static and a dynamic approach to model biological signaling networks, and show how each can be used to answer relevant biological questions. For this, we use the two different mathematical tools of Propositional Logic and Integer Programming. The power of discrete mathematics for handling qualitative as well as quantitative data has so far not been exploited in molecular biology, which is mostly driven by experimental research, relying on first-order or statistical models. The arising logic statements and integer programs are analyzed and can be solved with standard software. For a restricted class of problems the logic models reduce to a polynomial-time solvable satisfiability algorithm. Additionally, a more dynamic model enables enumeration of possible time resolutions in poly-logarithmic time. Computational experiments are included.

Comment on “Mathematical modeling of unicellular microalgae and cyanobacteria metabolism for biofuel production” by Baroukh et al. [Curr Opin Biotechnol. 2015, 33:198–205

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

Song, Hyun-Seob; Ramkrishna, Doraiswami

This letter concerns an article recently published in Current Opinion in Biotechnology by Baroukh et al. entitled "Mathematical modeling of unicellular microalgae and cyanobacteria metabolism for biofuel production" (2015 Mar 26; 33:198-205). The issue we wish to bring to light is the authors’ claim that dynamic metabolic models including Hybrid Cybernetic Model (HCM) (Kim et al., 2008; Song et al., 2009) and Lumped HCM (L-HCM) (Song and Ramkrishna, 2010; 2011) are based on the balanced growth hypothesis so that they are unable to simulate the accumulation of intracellular metabolites. This is a misrepresentation of these models due to the followingmore » reasons.« less

Developing Students' Reflections on the Function and Status of Mathematical Modeling in Different Scientific Practices: History as a Provider of Cases

ERIC Educational Resources Information Center

Kjeldsen, Tinne Hoff; Blomhøj, Morten

2013-01-01

Mathematical models and mathematical modeling play different roles in the different areas and problems in which they are used. The function and status of mathematical modeling and models in the different areas depend on the scientific practice as well as the underlying philosophical and theoretical position held by the modeler(s) and the…

How Ordinary Meaning Underpins the Meaning of Mathematics.

ERIC Educational Resources Information Center

Ormell, Christopher

1991-01-01

Discusses the meaning of mathematics by looking at its uses in the real world. Offers mathematical modeling as a way to represent mathematical applications in real or potential situations. Presents levels of applicability, modus operandi, relationship to "pure mathematics," and consequences for education for mathematical modeling. (MDH)

Mathematical Modeling for Scrub Typhus and Its Implications for Disease Control.

PubMed

Min, Kyung Duk; Cho, Sung Il

2018-03-19

The incidence rate of scrub typhus has been increasing in the Republic of Korea. Previous studies have suggested that this trend may have resulted from the effects of climate change on the transmission dynamics among vectors and hosts, but a clear explanation of the process is still lacking. In this study, we applied mathematical models to explore the potential factors that influence the epidemiology of tsutsugamushi disease. We developed mathematical models of ordinary differential equations including human, rodent and mite groups. Two models, including simple and complex models, were developed, and all parameters employed in the models were adopted from previous articles that represent epidemiological situations in the Republic of Korea. The simulation results showed that the force of infection at the equilibrium state under the simple model was 0.236 (per 100,000 person-months), and that in the complex model was 26.796 (per 100,000 person-months). Sensitivity analyses indicated that the most influential parameters were rodent and mite populations and contact rate between them for the simple model, and trans-ovarian transmission for the complex model. In both models, contact rate between humans and mites is more influential than morality rate of rodent and mite group. The results indicate that the effect of controlling either rodents or mites could be limited, and reducing the contact rate between humans and mites is more practical and effective strategy. However, the current level of control would be insufficient relative to the growing mite population. © 2018 The Korean Academy of Medical Sciences.

Aids to determining fuel models for estimating fire behavior

Treesearch

Hal E. Anderson

1982-01-01

Presents photographs of wildland vegetation appropriate for the 13 fuel models used in mathematical models of fire behavior. Fuel model descriptions include fire behavior associated with each fuel and its physical characteristics. A similarity chart cross-references the 13 fire behavior fuel models to the 20 fuel models used in the National Fire Danger Rating System....

A review of methods for predicting air pollution dispersion

NASA Technical Reports Server (NTRS)

Mathis, J. J., Jr.; Grose, W. L.

1973-01-01

Air pollution modeling, and problem areas in air pollution dispersion modeling were surveyed. Emission source inventory, meteorological data, and turbulent diffusion are discussed in terms of developing a dispersion model. Existing mathematical models of urban air pollution, and highway and airport models are discussed along with their limitations. Recommendations for improving modeling capabilities are included.

THE LAKE MICHIGAN MASS BALANCE PROJECT: QUALITY ASSURANCE PLAN FOR MATHEMATICAL MODELLING

EPA Science Inventory

This report documents the quality assurance process for the development and application of the Lake Michigan Mass Balance Models. The scope includes the overall modeling framework as well as the specific submodels that are linked to form a comprehensive synthesis of physical, che...

MATHEMATICAL MODEL OF ELECTROSTATIC PRECIPITATION FOR THE TEXAS INSTRUMENTS PROGRAMMABLE 59 CALCULATOR

EPA Science Inventory

The report describes a version of EPA's electrostatic precipitator (ESP) model suitable for use on a Texas Instruments Programmable 59 (TI-59) hand-held calculator. This version of the model allows the calculation of ESP collection efficiency, including corrections for non-ideal ...

A MATHEMATICAL MODEL FOR THE KINETICS OF THE MALE REPRODUCTIVE ENDOCRINE SYSTEM

EPA Science Inventory

In this presentation a model for the hormonal regulation of the reproductive endocrine system in the adult male rat will be discussed. The model includes a description of the kinetics of the androgenic hormones testosterone and dihydrotestosterone, as well as the receptor-mediate...

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

PubMed

Ganusov, Vitaly V

2016-01-01

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

An Evolutionary Perspective on Learning Disability in Mathematics

PubMed Central

Geary, David C.

2015-01-01

A distinction between potentially evolved, or biologically-primary forms of cognition, and the culturally-specific, or biologically-secondary forms of cognition that are built from primary systems is used to explore mathematical learning disability (MLD). Using this model, MLD could result from deficits in the brain and cognitive systems that support biologically-primary mathematical competencies, or from the brain and cognitive systems that support the modification of primary systems for the creation of secondary knowledge and secondary cognitive competencies. The former include visuospatial long-term and working memory and the intraparietal sulcus, whereas the latter include the central executive component of working memory and the anterior cingulate cortex and lateral prefrontal cortex. Different forms of MLD are discussed as related to each of the cognitive and brain systems. PMID:17650991

A study of the continuum of integration of mathematics content with science concepts at the middle school level in West Virginia

NASA Astrophysics Data System (ADS)

Meisel, Edna Marie

The purpose of this study was to examine the practices and perceptions of regular education seventh grade middle school mathematics teachers in West Virginia concerning the integration of mathematics objectives with science concepts. In addition, this study also emphasized the use of integrated curriculum continuum models to study mathematics teachers' practices and perceptions for teaching mathematics objectives in connection with science concepts. It was argued that the integrated curriculum continuum model can be used to help educators begin to form a common definition of integrated curriculum. The population was described as the regular education seventh grade middle school mathematics teachers in West Virginia. The entire population (N = 173) was used as the participants in this study. Data was collected using an integrated curriculum practices and perceptions survey constructed by the researcher. This was a descriptive study that incorporated the Chi Square statistic to show trends in teacher practices and perceptions. Also, an ex post facto design, that incorporated the Mann-Whitney U statistic, was used to compare practices and perceptions between teachers grouped according to factors that influence teaching practices and perceptions. These factors included teaching certificate endorsement and teacher professional preparation. Results showed that the regular education seventh grade middle school mathematics teachers of West Virginia are teaching mathematics objectives mainly at a discipline-based level with no formal attempt for integration with science concepts. However, these teachers perceived that many of the mathematics objectives should be taught at varying levels of integration with science concepts. It was also shown that teachers who experienced professional preparation courses that emphasized integrated curriculum courses did teach many of the mathematics objectives at higher levels of integration with science than those teachers who did not experience integrated curriculum courses.

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

Yan, Ruqiang; Chen, Xuefeng; Li, Weihua

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

Mathematical Modeling of Protein Misfolding Mechanisms in Neurological Diseases: A Historical Overview.

PubMed

Carbonell, Felix; Iturria-Medina, Yasser; Evans, Alan C

2018-01-01

Protein misfolding refers to a process where proteins become structurally abnormal and lose their specific 3-dimensional spatial configuration. The histopathological presence of misfolded protein (MP) aggregates has been associated as the primary evidence of multiple neurological diseases, including Prion diseases, Alzheimer's disease, Parkinson's disease, and Creutzfeldt-Jacob disease. However, the exact mechanisms of MP aggregation and propagation, as well as their impact in the long-term patient's clinical condition are still not well understood. With this aim, a variety of mathematical models has been proposed for a better insight into the kinetic rate laws that govern the microscopic processes of protein aggregation. Complementary, another class of large-scale models rely on modern molecular imaging techniques for describing the phenomenological effects of MP propagation over the whole brain. Unfortunately, those neuroimaging-based studies do not take full advantage of the tremendous capabilities offered by the chemical kinetics modeling approach. Actually, it has been barely acknowledged that the vast majority of large-scale models have foundations on previous mathematical approaches that describe the chemical kinetics of protein replication and propagation. The purpose of the current manuscript is to present a historical review about the development of mathematical models for describing both microscopic processes that occur during the MP aggregation and large-scale events that characterize the progression of neurodegenerative MP-mediated diseases.

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…

Prospects of a mathematical theory of human behavior in complex man-machine systems tasks. [time sharing computer analogy of automobile driving

NASA Technical Reports Server (NTRS)

Johannsen, G.; Rouse, W. B.

1978-01-01

A hierarchy of human activities is derived by analyzing automobile driving in general terms. A structural description leads to a block diagram and a time-sharing computer analogy. The range of applicability of existing mathematical models is considered with respect to the hierarchy of human activities in actual complex tasks. Other mathematical tools so far not often applied to man machine systems are also discussed. The mathematical descriptions at least briefly considered here include utility, estimation, control, queueing, and fuzzy set theory as well as artificial intelligence techniques. Some thoughts are given as to how these methods might be integrated and how further work might be pursued.

Mathematical Modeling of Early Cellular Innate and Adaptive Immune Responses to Ischemia/Reperfusion Injury and Solid Organ Allotransplantation

PubMed Central

Day, Judy D.; Metes, Diana M.; Vodovotz, Yoram

2015-01-01

A mathematical model of the early inflammatory response in transplantation is formulated with ordinary differential equations. We first consider the inflammatory events associated only with the initial surgical procedure and the subsequent ischemia/reperfusion (I/R) events that cause tissue damage to the host as well as the donor graft. These events release damage-associated molecular pattern molecules (DAMPs), thereby initiating an acute inflammatory response. In simulations of this model, resolution of inflammation depends on the severity of the tissue damage caused by these events and the patient’s (co)-morbidities. We augment a portion of a previously published mathematical model of acute inflammation with the inflammatory effects of T cells in the absence of antigenic allograft mismatch (but with DAMP release proportional to the degree of graft damage prior to transplant). Finally, we include the antigenic mismatch of the graft, which leads to the stimulation of potent memory T cell responses, leading to further DAMP release from the graft and concomitant increase in allograft damage. Regulatory mechanisms are also included at the final stage. Our simulations suggest that surgical injury and I/R-induced graft damage can be well-tolerated by the recipient when each is present alone, but that their combination (along with antigenic mismatch) may lead to acute rejection, as seen clinically in a subset of patients. An emergent phenomenon from our simulations is that low-level DAMP release can tolerize the recipient to a mismatched allograft, whereas different restimulation regimens resulted in an exaggerated rejection response, in agreement with published studies. We suggest that mechanistic mathematical models might serve as an adjunct for patient- or sub-group-specific predictions, simulated clinical studies, and rational design of immunosuppression. PMID:26441988

A transformative model for undergraduate quantitative biology education.

PubMed

Usher, David C; Driscoll, Tobin A; Dhurjati, Prasad; Pelesko, John A; Rossi, Louis F; Schleiniger, Gilberto; Pusecker, Kathleen; White, Harold B

2010-01-01

The BIO2010 report recommended that students in the life sciences receive a more rigorous education in mathematics and physical sciences. The University of Delaware approached this problem by (1) developing a bio-calculus section of a standard calculus course, (2) embedding quantitative activities into existing biology courses, and (3) creating a new interdisciplinary major, quantitative biology, designed for students interested in solving complex biological problems using advanced mathematical approaches. To develop the bio-calculus sections, the Department of Mathematical Sciences revised its three-semester calculus sequence to include differential equations in the first semester and, rather than using examples traditionally drawn from application domains that are most relevant to engineers, drew models and examples heavily from the life sciences. The curriculum of the B.S. degree in Quantitative Biology was designed to provide students with a solid foundation in biology, chemistry, and mathematics, with an emphasis on preparation for research careers in life sciences. Students in the program take core courses from biology, chemistry, and physics, though mathematics, as the cornerstone of all quantitative sciences, is given particular prominence. Seminars and a capstone course stress how the interplay of mathematics and biology can be used to explain complex biological systems. To initiate these academic changes required the identification of barriers and the implementation of solutions.

A Transformative Model for Undergraduate Quantitative Biology Education

PubMed Central

Driscoll, Tobin A.; Dhurjati, Prasad; Pelesko, John A.; Rossi, Louis F.; Schleiniger, Gilberto; Pusecker, Kathleen; White, Harold B.

2010-01-01

The BIO2010 report recommended that students in the life sciences receive a more rigorous education in mathematics and physical sciences. The University of Delaware approached this problem by (1) developing a bio-calculus section of a standard calculus course, (2) embedding quantitative activities into existing biology courses, and (3) creating a new interdisciplinary major, quantitative biology, designed for students interested in solving complex biological problems using advanced mathematical approaches. To develop the bio-calculus sections, the Department of Mathematical Sciences revised its three-semester calculus sequence to include differential equations in the first semester and, rather than using examples traditionally drawn from application domains that are most relevant to engineers, drew models and examples heavily from the life sciences. The curriculum of the B.S. degree in Quantitative Biology was designed to provide students with a solid foundation in biology, chemistry, and mathematics, with an emphasis on preparation for research careers in life sciences. Students in the program take core courses from biology, chemistry, and physics, though mathematics, as the cornerstone of all quantitative sciences, is given particular prominence. Seminars and a capstone course stress how the interplay of mathematics and biology can be used to explain complex biological systems. To initiate these academic changes required the identification of barriers and the implementation of solutions. PMID:20810949

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

PubMed Central

Ganusov, Vitaly V.

2016-01-01

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

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 (Dis)abilities Within the Opportunity-Propensity Model: The Choice of Math Test Matters

PubMed Central

Baten, Elke; Desoete, Annemie

2018-01-01

This study examined individual differences in mathematics learning by combining antecedent (A), opportunity (O), and propensity (P) indicators within the Opportunity-Propensity Model. Although there is already some evidence for this model based on secondary datasets, there currently is no primary data available that simultaneously takes into account A, O, and P factors in children with and without Mathematical Learning Disabilities (MLD). Therefore, the mathematical abilities of 114 school-aged children (grade 3 till 6) with and without MLD were analyzed and combined with information retrieved from standardized tests and questionnaires. Results indicated significant differences in personality, motivation, temperament, subjective well-being, self-esteem, self-perceived competence, and parental aspirations when comparing children with and without MLD. In addition, A, O, and P factors were found to underlie mathematical abilities and disabilities. For the A factors, parental aspirations explained about half of the variance in fact retrieval speed in children without MLD, and SES was especially involved in the prediction of procedural accuracy in general. Teachers’ experience contributed as O factor and explained about 6% of the variance in mathematical abilities. P indicators explained between 52 and 69% of the variance, with especially intelligence as overall significant predictor. Indirect effects pointed towards the interrelatedness of the predictors and the value of including A, O, and P indicators in a comprehensive model. The role parental aspirations played in fact retrieval speed was partially mediated through the self-perceived competence of the children, whereas the effect of SES on procedural accuracy was partially mediated through intelligence in children of both groups and through working memory capacity in children with MLD. Moreover, in line with the componential structure of mathematics, our findings were dependent on the math task used. Different A, O, and P indicators seemed to be important for fact retrieval speed compared to procedural accuracy. Also, mathematical development type (MLD or typical development) mattered since some A, O, and P factors were predictive for MLD only and the other way around. Practical implications of these findings and recommendations for future research on MLD and on individual differences in mathematical abilities are provided. PMID:29867645

Mathematical (Dis)abilities Within the Opportunity-Propensity Model: The Choice of Math Test Matters.

PubMed

Baten, Elke; Desoete, Annemie

2018-01-01

This study examined individual differences in mathematics learning by combining antecedent (A), opportunity (O), and propensity (P) indicators within the Opportunity-Propensity Model. Although there is already some evidence for this model based on secondary datasets, there currently is no primary data available that simultaneously takes into account A, O, and P factors in children with and without Mathematical Learning Disabilities (MLD). Therefore, the mathematical abilities of 114 school-aged children (grade 3 till 6) with and without MLD were analyzed and combined with information retrieved from standardized tests and questionnaires. Results indicated significant differences in personality, motivation, temperament, subjective well-being, self-esteem, self-perceived competence, and parental aspirations when comparing children with and without MLD. In addition, A, O, and P factors were found to underlie mathematical abilities and disabilities. For the A factors, parental aspirations explained about half of the variance in fact retrieval speed in children without MLD, and SES was especially involved in the prediction of procedural accuracy in general. Teachers' experience contributed as O factor and explained about 6% of the variance in mathematical abilities. P indicators explained between 52 and 69% of the variance, with especially intelligence as overall significant predictor. Indirect effects pointed towards the interrelatedness of the predictors and the value of including A, O, and P indicators in a comprehensive model. The role parental aspirations played in fact retrieval speed was partially mediated through the self-perceived competence of the children, whereas the effect of SES on procedural accuracy was partially mediated through intelligence in children of both groups and through working memory capacity in children with MLD. Moreover, in line with the componential structure of mathematics, our findings were dependent on the math task used. Different A, O, and P indicators seemed to be important for fact retrieval speed compared to procedural accuracy. Also, mathematical development type (MLD or typical development) mattered since some A, O, and P factors were predictive for MLD only and the other way around. Practical implications of these findings and recommendations for future research on MLD and on individual differences in mathematical abilities are provided.

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

ERIC Educational Resources Information Center

Bukova-Guzel, Esra

2011-01-01

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

Towards A Complete Model Of Photopic Visual Threshold Performance

NASA Astrophysics Data System (ADS)

Overington, I.

1982-02-01

Based on a wide variety of fragmentary evidence taken from psycho-physics, neurophysiology and electron microscopy, it has been possible to put together a very widely applicable conceptual model of photopic visual threshold performance. Such a model is so complex that a single comprehensive mathematical version is excessively cumbersome. It is, however, possible to set up a suite of related mathematical models, each of limited application but strictly known envelope of usage. Such models may be used for assessment of a variety of facets of visual performance when using display imagery, including effects and interactions of image quality, random and discrete display noise, viewing distance, image motion, etc., both for foveal interrogation tasks and for visual search tasks. The specific model may be selected from the suite according to the assessment task in hand. The paper discusses in some depth the major facets of preperceptual visual processing and their interaction with instrumental image quality and noise. It then highlights the statistical nature of visual performance before going on to consider a number of specific mathematical models of partial visual function. Where appropriate, these are compared with widely popular empirical models of visual function.

Well test mathematical model for fractures network in tight oil reservoirs

NASA Astrophysics Data System (ADS)

Diwu, Pengxiang; Liu, Tongjing; Jiang, Baoyi; Wang, Rui; Yang, Peidie; Yang, Jiping; Wang, Zhaoming

2018-02-01

Well test, especially build-up test, has been applied widely in the development of tight oil reservoirs, since it is the only available low cost way to directly quantify flow ability and formation heterogeneity parameters. However, because of the fractures network near wellbore, generated from artificial fracturing linking up natural factures, traditional infinite and finite conductivity fracture models usually result in significantly deviation in field application. In this work, considering the random distribution of natural fractures, physical model of fractures network is proposed, and it shows a composite model feature in the large scale. Consequently, a nonhomogeneous composite mathematical model is established with threshold pressure gradient. To solve this model semi-analytically, we proposed a solution approach including Laplace transform and virtual argument Bessel function, and this method is verified by comparing with existing analytical solution. The matching data of typical type curves generated from semi-analytical solution indicates that the proposed physical and mathematical model can describe the type curves characteristic in typical tight oil reservoirs, which have up warping in late-term rather than parallel lines with slope 1/2 or 1/4. It means the composite model could be used into pressure interpretation of artificial fracturing wells in tight oil reservoir.

Predictors of early growth in academic achievement: the head-toes-knees-shoulders task

PubMed Central

McClelland, Megan M.; Cameron, Claire E.; Duncan, Robert; Bowles, Ryan P.; Acock, Alan C.; Miao, Alicia; Pratt, Megan E.

2014-01-01

Children's behavioral self-regulation and executive function (EF; including attentional or cognitive flexibility, working memory, and inhibitory control) are strong predictors of academic achievement. The present study examined the psychometric properties of a measure of behavioral self-regulation called the Head-Toes-Knees-Shoulders (HTKS) by assessing construct validity, including relations to EF measures, and predictive validity to academic achievement growth between prekindergarten and kindergarten. In the fall and spring of prekindergarten and kindergarten, 208 children (51% enrolled in Head Start) were assessed on the HTKS, measures of cognitive flexibility, working memory (WM), and inhibitory control, and measures of emergent literacy, mathematics, and vocabulary. For construct validity, the HTKS was significantly related to cognitive flexibility, working memory, and inhibitory control in prekindergarten and kindergarten. For predictive validity in prekindergarten, a random effects model indicated that the HTKS significantly predicted growth in mathematics, whereas a cognitive flexibility task significantly predicted growth in mathematics and vocabulary. In kindergarten, the HTKS was the only measure to significantly predict growth in all academic outcomes. An alternative conservative analytical approach, a fixed effects analysis (FEA) model, also indicated that growth in both the HTKS and measures of EF significantly predicted growth in mathematics over four time points between prekindergarten and kindergarten. Results demonstrate that the HTKS involves cognitive flexibility, working memory, and inhibitory control, and is substantively implicated in early achievement, with the strongest relations found for growth in achievement during kindergarten and associations with emergent mathematics. PMID:25071619

Proceedings of the Annual Conference of the International Group for the Psychology of Mathematics Education (13th, Paris, France, July 9-13, 1989), Volume 3.

ERIC Educational Resources Information Center

Vergnaud, Gerard, Ed.; Rogalski, Janine, Ed.; Artique, Michele, Ed.

This proceedings of the annual conference of the International Group for the Psychology of Mathematics Education (PME) includes the following research papers: "A Model of Understanding Two-Digit Numeration and Computation" (H. Murray & A. Olivier); "The Computer Produces a Special Graphic Situation of Learning the Change of Coordinate System" (S.…

Proceedings of the Conference of the International Group for the Psychology of Mathematics Education (22nd, Stellenbosch, South Africa, July 12-17, 1998). Volume 3.

ERIC Educational Resources Information Center

Olivier, Alwyn, Ed.; Newstead, Karen, Ed.

The third volume of this proceedings contains more of the research reports begun in Volume 2. Papers include: (1) "A Semiotic Model for Analyzing the Relationships between Thought, Language and Context in Mathematics Education" (Juan D. Godino and Angel M. Recio); (2) "Conceptions as Articulated in Different Microworlds Exploring Functions"…

An Evaluation Model Applied to a Mathematics-Methods Program Involving Three Characteristics of Teaching Style and Their Relationship to Pupil Achievement. Teacher Education Forum; Volume 3, Number 4.

ERIC Educational Resources Information Center

Dodd, Carol Ann

This study explores a technique for evaluating teacher education programs in terms of teaching competencies, as applied to the Indiana University Mathematics Methods Program (MMP). The evaluation procedures formulated for the study include a process product design in combination with a modification of Pophan's performance test paradigm and Gage's…

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

PubMed

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

2017-04-01

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

Mathematical Storage-Battery Models

NASA Technical Reports Server (NTRS)

Chapman, C. P.; Aston, M.

1985-01-01

Empirical formula represents performance of electrical storage batteries. Formula covers many battery types and includes numerous coefficients adjusted to fit peculiarities of each type. Battery and load parameters taken into account include power density in battery, discharge time, and electrolyte temperature. Applications include electric-vehicle "fuel" gages and powerline load leveling.

A mathematical representation of an advanced helicopter for piloted simulator investigations of control system and display variations

NASA Technical Reports Server (NTRS)

Aiken, E. W.

1980-01-01

A mathematical model of an advanced helicopter is described. The model is suitable for use in control/display research involving piloted simulation. The general design approach for the six degree of freedom equations of motion is to use the full set of nonlinear gravitational and inertial terms of the equations and to express the aerodynamic forces and moments as the reference values and first order terms of a Taylor series expansion about a reference trajectory defined as a function of longitudinal airspeed. Provisions for several different specific and generic flight control systems are included in the model. The logic required to drive various flight control and weapon delivery symbols on a pilot's electronic display is also provided. Finally, the model includes a simplified representation of low altitude wind and turbulence effects. This model was used in a piloted simulator investigation of the effects of control system and display variations for an attack helicopter mission.

Analyzing neuronal networks using discrete-time dynamics

NASA Astrophysics Data System (ADS)

Ahn, Sungwoo; Smith, Brian H.; Borisyuk, Alla; Terman, David

2010-05-01

We develop mathematical techniques for analyzing detailed Hodgkin-Huxley like models for excitatory-inhibitory neuronal networks. Our strategy for studying a given network is to first reduce it to a discrete-time dynamical system. The discrete model is considerably easier to analyze, both mathematically and computationally, and parameters in the discrete model correspond directly to parameters in the original system of differential equations. While these networks arise in many important applications, a primary focus of this paper is to better understand mechanisms that underlie temporally dynamic responses in early processing of olfactory sensory information. The models presented here exhibit several properties that have been described for olfactory codes in an insect’s Antennal Lobe. These include transient patterns of synchronization and decorrelation of sensory inputs. By reducing the model to a discrete system, we are able to systematically study how properties of the dynamics, including the complex structure of the transients and attractors, depend on factors related to connectivity and the intrinsic and synaptic properties of cells within the network.

Uncertainty and variability in computational and mathematical models of cardiac physiology.

PubMed

Mirams, Gary R; Pathmanathan, Pras; Gray, Richard A; Challenor, Peter; Clayton, Richard H

2016-12-01

Mathematical and computational models of cardiac physiology have been an integral component of cardiac electrophysiology since its inception, and are collectively known as the Cardiac Physiome. We identify and classify the numerous sources of variability and uncertainty in model formulation, parameters and other inputs that arise from both natural variation in experimental data and lack of knowledge. The impact of uncertainty on the outputs of Cardiac Physiome models is not well understood, and this limits their utility as clinical tools. We argue that incorporating variability and uncertainty should be a high priority for the future of the Cardiac Physiome. We suggest investigating the adoption of approaches developed in other areas of science and engineering while recognising unique challenges for the Cardiac Physiome; it is likely that novel methods will be necessary that require engagement with the mathematics and statistics community. The Cardiac Physiome effort is one of the most mature and successful applications of mathematical and computational modelling for describing and advancing the understanding of physiology. After five decades of development, physiological cardiac models are poised to realise the promise of translational research via clinical applications such as drug development and patient-specific approaches as well as ablation, cardiac resynchronisation and contractility modulation therapies. For models to be included as a vital component of the decision process in safety-critical applications, rigorous assessment of model credibility will be required. This White Paper describes one aspect of this process by identifying and classifying sources of variability and uncertainty in models as well as their implications for the application and development of cardiac models. We stress the need to understand and quantify the sources of variability and uncertainty in model inputs, and the impact of model structure and complexity and their consequences for predictive model outputs. We propose that the future of the Cardiac Physiome should include a probabilistic approach to quantify the relationship of variability and uncertainty of model inputs and outputs. © 2016 The Authors. The Journal of Physiology published by John Wiley & Sons Ltd on behalf of The Physiological Society.

Blood and small intestine cell kinetics under radiation exposures: Mathematical modeling

NASA Astrophysics Data System (ADS)

Smirnova, O. A.

2009-12-01

Mathematical models which describe the dynamics of two vital body systems (hematopoiesis and small intestinal epithelium) in mammals exposed to acute and chronic radiation are developed. These models, based on conventional biological theories, are implemented as systems of nonlinear differential equations. Their variables and constant parameters have clear biological meaning, that provides successful identification and verification of the models in hand. It is shown that the predictions of the models qualitatively and quantitatively agree with the respective experimental data for small laboratory animals (mice, rats) exposed to acute/chronic irradiation in wide ranges of doses and dose rates. The explanation of a number of radiobiological effects, including those of the low-level long-term exposures, is proposed proceeding from the modeling results. All this bears witness to the validity of employment of the developed models, after a proper identification, in investigation and prediction of radiation effects on the hematopoietic and small intestinal epithelium systems in various mammalian species, including humans. In particular, the models can be used for estimating effects of irradiation on astronauts in the long-term space missions, such as Lunar colonies and Mars voyages.

New Focus on Replacing Animals in the Lab.

ERIC Educational Resources Information Center

Holden, Constance

1982-01-01

Reviews the pros and cons of using animals or alternatives in scientific research. Such alternatives (as indicated in congressional bill HR 556) include mathematical models, isolated organs, tissue and cell cultures, computer simulations, mechanical models, and "lower" organisms among others. (SK)

Observables of QCD diffraction

NASA Astrophysics Data System (ADS)

Mieskolainen, Mikael; Orava, Risto

2017-03-01

A new combinatorial vector space measurement model is introduced for soft QCD diffraction. The model independent mathematical construction resolves experimental complications; the theoretical framework of the approach includes the Good-Walker view of diffraction, Regge phenomenology together with AGK cutting rules and random fluctuations.

Collaborative Understanding of Cyanobacteria in Lake Ecosystems

ERIC Educational Resources Information Center

Greer, Meredith L.; Ewing, Holly A.; Cottingham, Kathryn L.; Weathers, Kathleen C.

2013-01-01

We describe a collaboration between mathematicians and ecologists studying the cyanobacterium "Gloeotrichia echinulata" and its possible role in eutrophication of New England lakes. The mathematics includes compartmental modeling, differential equations, difference equations, and testing models against high-frequency data. The ecology…

A mathematical simulation model of the CH-47B helicopter, volume 2

NASA Technical Reports Server (NTRS)

Weber, J. M.; Liu, T. Y.; Chung, W.

1984-01-01

A nonlinear simulation model of the CH-47B helicopter, was adapted for use in a simulation facility. The model represents the specific configuration of the variable stability CH-47B helicopter. Modeling of the helicopter uses a total force approach in six rigid body degrees of freedom. Rotor dynamics are simulated using the Wheatley-Bailey equations, steady state flapping dynamics and included in the model of the option for simulation of external suspension, slung load equations of motion. Validation of the model was accomplished by static and dynamic data from the original Boeing Vertol mathematical model and flight test data. The model is appropriate for use in real time piloted simulation and is implemented on the ARC Sigma IX computer where it may be operated with a digital cycle time of 0.03 sec.

Learning to teach mathematical modelling in secondary and tertiary education

NASA Astrophysics Data System (ADS)

Ferri, Rita Borromeo

2017-07-01

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

The Routine Fitting of Kinetic Data to Models

PubMed Central

Berman, Mones; Shahn, Ezra; Weiss, Marjory F.

1962-01-01

A mathematical formalism is presented for use with digital computers to permit the routine fitting of data to physical and mathematical models. Given a set of data, the mathematical equations describing a model, initial conditions for an experiment, and initial estimates for the values of model parameters, the computer program automatically proceeds to obtain a least squares fit of the data by an iterative adjustment of the values of the parameters. When the experimental measures are linear combinations of functions, the linear coefficients for a least squares fit may also be calculated. The values of both the parameters of the model and the coefficients for the sum of functions may be unknown independent variables, unknown dependent variables, or known constants. In the case of dependence, only linear dependencies are provided for in routine use. The computer program includes a number of subroutines, each one of which performs a special task. This permits flexibility in choosing various types of solutions and procedures. One subroutine, for example, handles linear differential equations, another, special non-linear functions, etc. The use of analytic or numerical solutions of equations is possible. PMID:13867975

The (kinetic) theory of active particles applied to learning dynamics. Comment on "Collective learning modeling based on the kinetic theory of active particles" by D. Burini et al.

NASA Astrophysics Data System (ADS)

Nieto, J.

2016-03-01

The learning phenomena, their complexity, concepts, structure, suitable theories and models, have been extensively treated in the mathematical literature in the last century, and [4] contains a very good introduction to the literature describing the many approaches and lines of research developed about them. Two main schools have to be pointed out [5] in order to understand the two -not exclusive- kinds of existing models: the stimulus sampling models and the stochastic learning models. Also [6] should be mentioned as a survey where two methods of learning are pointed out, the cognitive and the social, and where the knowledge looks like a mathematical unknown. Finally, as the authors do, we refer to the works [9,10], where the concept of population thinking was introduced and which motivate the game theory rules as a tool (both included in [4] to develop their theory) and [7], where the ideas of developing a mathematical kinetic theory of perception and learning were proposed.

Mathematical Modeling of Dual Layer Shell Type Recuperation System for Biogas Dehumidification

NASA Astrophysics Data System (ADS)

Gendelis, S.; Timuhins, A.; Laizans, A.; Bandeniece, L.

2015-12-01

The main aim of the current paper is to create a mathematical model for dual layer shell type recuperation system, which allows reducing the heat losses from the biomass digester and water amount in the biogas without any additional mechanical or chemical components. The idea of this system is to reduce the temperature of the outflowing gas by creating two-layered counter-flow heat exchanger around the walls of biogas digester, thus increasing a thermal resistance and the gas temperature, resulting in a condensation on a colder surface. Complex mathematical model, including surface condensation, is developed for this type of biogas dehumidifier and the parameter study is carried out for a wide range of parameters. The model is reduced to 1D case to make numerical calculations faster. It is shown that latent heat of condensation is very important for the total heat balance and the condensation rate is highly dependent on insulation between layers and outside temperature. Modelling results allow finding optimal geometrical parameters for the known gas flow and predicting the condensation rate for different system setups and seasons.

The Effect of Math Modeling on Student's Emerging Understanding

ERIC Educational Resources Information Center

Sokolowski, Andrzej

2015-01-01

This study investigated the effects of applying mathematical modeling on revising students' preconception of the process of optimizing area enclosed by a string of a fixed length. A group of 28 high school pre-calculus students were immersed in modeling activity that included direct measurements, data collecting, and formulating algebraic…

A model for calculating expected performance of the Apollo unified S-band (USB) communication system

NASA Technical Reports Server (NTRS)

Schroeder, N. W.

1971-01-01

A model for calculating the expected performance of the Apollo unified S-band (USB) communication system is presented. The general organization of the Apollo USB is described. The mathematical model is reviewed and the computer program for implementation of the calculations is included.

SIMULATING RADIONUCLIDE FATE AND TRANSPORT IN THE UNSATURATED ZONE: EVALUATION AND SENSITIVITY ANALYSES OF SELECT COMPUTER MODELS

EPA Science Inventory

Numerical, mathematical models of water and chemical movement in soils are used as decision aids for determining soil screening levels (SSLs) of radionuclides in the unsaturated zone. Many models require extensive input parameters which include uncertainty due to soil variabil...

Online Testing: The Dog Sat on My Keyboard.

ERIC Educational Resources Information Center

White, Jacci

This paper will highlight some advantages and disadvantages of several online models for student assessment. These models will include: live exams, multiple choice tests, essay exams, and student projects. In addition, real student responses and "problems" will be used as prompts to improve models of authentic online assessment in mathematics.…

Mathematical optimization of high dose-rate brachytherapy—derivation of a linear penalty model from a dose-volume model

NASA Astrophysics Data System (ADS)

Morén, B.; Larsson, T.; Carlsson Tedgren, Å.

2018-03-01

High dose-rate brachytherapy is a method for cancer treatment where the radiation source is placed within the body, inside or close to a tumour. For dose planning, mathematical optimization techniques are being used in practice and the most common approach is to use a linear model which penalizes deviations from specified dose limits for the tumour and for nearby organs. This linear penalty model is easy to solve, but its weakness lies in the poor correlation of its objective value and the dose-volume objectives that are used clinically to evaluate dose distributions. Furthermore, the model contains parameters that have no clear clinical interpretation. Another approach for dose planning is to solve mixed-integer optimization models with explicit dose-volume constraints which include parameters that directly correspond to dose-volume objectives, and which are therefore tangible. The two mentioned models take the overall goals for dose planning into account in fundamentally different ways. We show that there is, however, a mathematical relationship between them by deriving a linear penalty model from a dose-volume model. This relationship has not been established before and improves the understanding of the linear penalty model. In particular, the parameters of the linear penalty model can be interpreted as dual variables in the dose-volume model.

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…

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

ERIC Educational Resources Information Center

Wright, Vince

2014-01-01

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

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

ERIC Educational Resources Information Center

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

2016-01-01

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

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…

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).

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

NASA Astrophysics Data System (ADS)

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

2016-02-01

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

GENASIS Mathematics : Object-oriented manifolds, operations, and solvers for large-scale physics simulations

NASA Astrophysics Data System (ADS)

Cardall, Christian Y.; Budiardja, Reuben D.

2018-01-01

The large-scale computer simulation of a system of physical fields governed by partial differential equations requires some means of approximating the mathematical limit of continuity. For example, conservation laws are often treated with a 'finite-volume' approach in which space is partitioned into a large number of small 'cells,' with fluxes through cell faces providing an intuitive discretization modeled on the mathematical definition of the divergence operator. Here we describe and make available Fortran 2003 classes furnishing extensible object-oriented implementations of simple meshes and the evolution of generic conserved currents thereon, along with individual 'unit test' programs and larger example problems demonstrating their use. These classes inaugurate the Mathematics division of our developing astrophysics simulation code GENASIS (Gen eral A strophysical Si mulation S ystem), which will be expanded over time to include additional meshing options, mathematical operations, solver types, and solver variations appropriate for many multiphysics applications.

Mathematical modeling of mutant transferrin-CRM107 molecular conjugates for cancer therapy.

PubMed

Yoon, Dennis J; Chen, Kevin Y; Lopes, André M; Pan, April A; Shiloach, Joseph; Mason, Anne B; Kamei, Daniel T

2017-03-07

The transferrin (Tf) trafficking pathway is a promising mechanism for use in targeted cancer therapy due to the overexpression of transferrin receptors (TfRs) on cancerous cells. We have previously developed a mathematical model of the Tf/TfR trafficking pathway to improve the efficiency of Tf as a drug carrier. By using diphtheria toxin (DT) as a model toxin, we found that mutating the Tf protein to change its iron release rate improves cellular association and efficacy of the drug. Though this is an improvement upon using wild-type Tf as the targeting ligand, conjugated toxins like DT are unfortunately still highly cytotoxic at off-target sites. In this work, we address this hurdle in cancer research by developing a mathematical model to predict the efficacy and selectivity of Tf conjugates that use an alternative toxin. For this purpose, we have chosen to study a mutant of DT, cross-reacting material 107 (CRM107). First, we developed a mathematical model of the Tf-DT trafficking pathway by extending our Tf/TfR model to include intracellular trafficking via DT and DT receptors. Using this mathematical model, we subsequently investigated the efficacy of several conjugates in cancer cells: DT and CRM107 conjugated to wild-type Tf, as well as to our engineered mutant Tf proteins (K206E/R632A Tf and K206E/R534A Tf). We also investigated the selectivity of mutant Tf-CRM107 against non-neoplastic cells. Through the use of our mathematical model, we predicted that (i) mutant Tf-CRM107 exhibits a greater cytotoxicity than wild-type Tf-CRM107 against cancerous cells, (ii) this improvement was more drastic with CRM107 conjugates than with DT conjugates, and (iii) mutant Tf-CRM107 conjugates were selective against non-neoplastic cells. These predictions were validated with in vitro cytotoxicity experiments, demonstrating that mutant Tf-CRM107 conjugates is indeed a more suitable therapeutic agent. Validation from in vitro experiments also confirmed that such whole-cell kinetic models can be useful in cancer therapeutic design. Copyright © 2017 Elsevier Ltd. All rights reserved.

Railway bogie vibration analysis by mathematical simulation model and a scaled four-wheel railway bogie set

NASA Astrophysics Data System (ADS)

Visayataksin, Noppharat; Sooklamai, Manon

2018-01-01

The bogie is the part that connects and transfers all the load from the vehicle body onto the railway track; interestingly the interaction between wheels and rails is the critical point for derailment of the rail vehicles. However, observing or experimenting with real bogies on rail vehicles is impossible due to the operational rules and safety concerns. Therefore, this research aimed to develop a vibration analysis set for a four-wheel railway bogie by constructing a four-wheel bogie with scale of 1:4.5. The bogie structures, including wheels and axles, were made from an aluminium alloy, equipped with springs and dampers. The bogie was driven by an electric motor using 4 round wheels instead of 2 straight rails, with linear velocity between 0 to 11.22 m/s. The data collected from the vibration analysis set was compared to the mathematical simulation model to investigate the vibration behavior of the bogie, especially the hunting motion. The results showed that vibration behavior from a scaled four-wheel railway bogie set significantly agreed with the mathematical simulation model in terms of displacement and hunting frequency. The critical speed of the wheelset was found by executing the mathematical simulation model at 13 m/s.

A Review of Mathematical Models for Leukemia and Lymphoma

PubMed Central

Clapp, Geoffrey; Levy, Doron

2014-01-01

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

Correlation of spacecraft thermal mathematical models to reference data

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Unresolved issues in theories of autoimmune disease using myocarditis as a framework

PubMed Central

Root-Bernstein, Robert; Fairweather, DeLisa

2014-01-01

Many theories of autoimmune disease have been proposed since the discovery that the immune system can attack the body. These theories include the hidden or cryptic antigen theory, modified antigen theory, T cell bypass, T cell-B cell mismatch, epitope spread or drift, the bystander effect, molecular mimicry, anti-idiotype theory, antigenic complementarity, and dual-affinity T cell receptors. We critically review these theories and relevant mathematical models as they apply to autoimmune myocarditis. All theories share the common assumption that autoimmune diseases are triggered by environmental factors such as infections or chemical exposure. Most, but not all, theories and mathematical models are unifactorial assuming single-agent causation of disease. Experimental and clinical evidence and mathematical models exist to support some aspects of most theories, but evidence/models that support one theory almost invariably supports other theories as well. More importantly, every theory (and every model) lacks the ability to account for some key autoimmune disease phenomena such as the fundamental roles of innate immunity, sex differences in disease susceptibility, the necessity for adjuvants in experimental animal models, and the often paradoxical effect of exposure timing and dose on disease induction. We argue that a more comprehensive and integrated theory of autoimmunity associated with new mathematical models is needed and suggest specific experimental and clinical tests for each major theory that might help to clarify how they relate to clinical disease and reveal how theories are related. PMID:25484004

Unresolved issues in theories of autoimmune disease using myocarditis as a framework.

PubMed

Root-Bernstein, Robert; Fairweather, DeLisa

2015-06-21

Many theories of autoimmune disease have been proposed since the discovery that the immune system can attack the body. These theories include the hidden or cryptic antigen theory, modified antigen theory, T cell bypass, T cell-B cell mismatch, epitope spread or drift, the bystander effect, molecular mimicry, anti-idiotype theory, antigenic complementarity, and dual-affinity T cell receptors. We critically review these theories and relevant mathematical models as they apply to autoimmune myocarditis. All theories share the common assumption that autoimmune diseases are triggered by environmental factors such as infections or chemical exposure. Most, but not all, theories and mathematical models are unifactorial assuming single-agent causation of disease. Experimental and clinical evidence and mathematical models exist to support some aspects of most theories, but evidence/models that support one theory almost invariably supports other theories as well. More importantly, every theory (and every model) lacks the ability to account for some key autoimmune disease phenomena such as the fundamental roles of innate immunity, sex differences in disease susceptibility, the necessity for adjuvants in experimental animal models, and the often paradoxical effect of exposure timing and dose on disease induction. We argue that a more comprehensive and integrated theory of autoimmunity associated with new mathematical models is needed and suggest specific experimental and clinical tests for each major theory that might help to clarify how they relate to clinical disease and reveal how theories are related. Copyright © 2014 Elsevier Ltd. All rights reserved.

The Mathematics of Navigating the Solar System

NASA Technical Reports Server (NTRS)

Hintz, Gerald

2000-01-01

In navigating spacecraft throughout the solar system, the space navigator relies on three academic disciplines - optimization, estimation, and control - that work on mathematical models of the real world. Thus, the navigator determines the flight path that will consume propellant and other resources in an efficient manner, determines where the craft is and predicts where it will go, and transfers it onto the optimal trajectory that meets operational and mission constraints. Mission requirements, for example, demand that observational measurements be made with sufficient precision that relativity must be modeled in collecting and fitting (the estimation process) the data, and propagating the trajectory. Thousands of parameters are now determined in near real-time to model the gravitational forces acting on a spacecraft in the vicinity of an irregularly shaped body. Completing these tasks requires mathematical models, analyses, and processing techniques. Newton, Gauss, Lambert, Legendre, and others are justly famous for their contributions to the mathematics of these tasks. More recently, graduate students participated in research to update the gravity model of the Saturnian system, including higher order gravity harmonics, tidal effects, and the influence of the rings. This investigation was conducted for the Cassini project to incorporate new trajectory modeling features in the navigation software. The resulting trajectory model will be used in navigating the 4-year tour of the Saturnian satellites. Also, undergraduate students are determining the ephemerides (locations versus time) of asteroids that will be used as reference objects in navigating the New Millennium's Deep Space 1 spacecraft autonomously.

Mathematical, numerical and experimental analysis of the swirling flow at a Kaplan runner outlet

NASA Astrophysics Data System (ADS)

Muntean, S.; Ciocan, T.; Susan-Resiga, R. F.; Cervantes, M.; Nilsson, H.

2012-11-01

The paper presents a novel mathematical model for a-priori computation of the swirling flow at Kaplan runners outlet. The model is an extension of the initial version developed by Susan-Resiga et al [1], to include the contributions of non-negligible radial velocity and of the variable rothalpy. Simple analytical expressions are derived for these additional data from three-dimensional numerical simulations of the Kaplan turbine. The final results, i.e. velocity components profiles, are validated against experimental data at two operating points, with the same Kaplan runner blades opening, but variable discharge.

Manpower Substitution and Productivity in Medical Practice

PubMed Central

Reinhardt, Uwe E.

1973-01-01

Probably in response to the often alleged physician shortage in this country, concerted research efforts are under way to identify technically feasible opportunities for manpower substitution in the production of ambulatory health care. The approaches range from descriptive studies of the effect of task delegation on output of medical services to rigorous mathematical modeling of health care production by means of linear or continuous production functions. In this article the distinct methodological approaches underlying mathematical models are presented in synopsis, and their inherent strengths and weaknesses are contrasted. The discussion includes suggestions for future research directions. Images Fig. 2 PMID:4586735

The application of virtual prototyping methods to determine the dynamic parameters of mobile robot

NASA Astrophysics Data System (ADS)

Kurc, Krzysztof; Szybicki, Dariusz; Burghardt, Andrzej; Muszyńska, Magdalena

2016-04-01

The paper presents methods used to determine the parameters necessary to build a mathematical model of an underwater robot with a crawler drive. The parameters present in the dynamics equation will be determined by means of advanced mechatronic design tools, including: CAD/CAE software andMES modules. The virtual prototyping process is described as well as the various possible uses (design adaptability) depending on the optional accessories added to the vehicle. A mathematical model is presented to show the kinematics and dynamics of the underwater crawler robot, essential for the design stage.

Choice of mathematical models for technological process of glass rod drawing

NASA Astrophysics Data System (ADS)

Alekseeva, L. B.

2017-10-01

The technological process of drawing glass rods (light guides) is considered. Automated control of the drawing process is reduced to the process of making decisions to ensure a given quality. The drawing process is considered as a control object, including the drawing device (control device) and the optical fiber forming zone (control object). To study the processes occurring in the formation zone, mathematical models are proposed, based on the continuum mechanics basics. To assess the influence of disturbances, a transfer function is obtained from the basis of the wave equation. Obtaining the regression equation also adequately describes the drawing process.

Mathematical Modeling in Systems for Operational Evaluation of the Stress-Strain State of the Arch-Gravity Dam at the Sayano-Shushenskaya Hydroelectric Power Plant

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

Bellendir, E. N.; Gordon, L. A., E-mail: lev-gordon@mail.ru; Khrapkov, A. A.

Current studies of the stress-strain state of the dam at the Sayano-Shushenskaya Hydroelectric Power Plant at VNIIG based on mathematical modeling including full scale and experimental data are described. Applications and programs intended for automatic operational evaluation of the stress-strain state of the dam for optimizing control of the upper race level in the course of the annual filling-drawdown cycle and during seismic events are examined. Improvements in systems for monitoring the stress-strain state of concrete dams are proposed.

A simplified rotor system mathematical model for piloted flight dynamics simulation

NASA Technical Reports Server (NTRS)

Chen, R. T. N.

1979-01-01

The model was developed for real-time pilot-in-the-loop investigation of helicopter flying qualities. The mathematical model included the tip-path plane dynamics and several primary rotor design parameters, such as flapping hinge restraint, flapping hinge offset, blade Lock number, and pitch-flap coupling. The model was used in several exploratory studies of the flying qualities of helicopters with a variety of rotor systems. The basic assumptions used and the major steps involved in the development of the set of equations listed are described. The equations consisted of the tip-path plane dynamic equation, the equations for the main rotor forces and moments, and the equation for control phasing required to achieve decoupling in pitch and roll due to cyclic inputs.

A mathematical model for CTL effect on a latently infected cell inclusive HIV dynamics and treatment

NASA Astrophysics Data System (ADS)

Tarfulea, N. E.

2017-10-01

This paper investigates theoretically and numerically the effect of immune effectors, such as the cytotoxic lymphocyte (CTL), in modeling HIV pathogenesis (via a newly developed mathematical model); our results suggest the significant impact of the immune response on the control of the virus during primary infection. Qualitative aspects (including positivity, boundedness, stability, uncertainty, and sensitivity analysis) are addressed. Additionally, by introducing drug therapy, we analyze numerically the model to assess the effect of treatment consisting of a combination of several antiretroviral drugs. Our results show that the inclusion of the CTL compartment produces a higher rebound for an individual's healthy helper T-cell compartment than drug therapy alone. Furthermore, we quantitatively characterize successful drugs or drug combination scenarios.

Algorithm for repairing the damaged images of grain structures obtained from the cellular automata and measurement of grain size

NASA Astrophysics Data System (ADS)

Ramírez-López, A.; Romero-Romo, M. A.; Muñoz-Negron, D.; López-Ramírez, S.; Escarela-Pérez, R.; Duran-Valencia, C.

2012-10-01

Computational models are developed to create grain structures using mathematical algorithms based on the chaos theory such as cellular automaton, geometrical models, fractals, and stochastic methods. Because of the chaotic nature of grain structures, some of the most popular routines are based on the Monte Carlo method, statistical distributions, and random walk methods, which can be easily programmed and included in nested loops. Nevertheless, grain structures are not well defined as the results of computational errors and numerical inconsistencies on mathematical methods. Due to the finite definition of numbers or the numerical restrictions during the simulation of solidification, damaged images appear on the screen. These images must be repaired to obtain a good measurement of grain geometrical properties. Some mathematical algorithms were developed to repair, measure, and characterize grain structures obtained from cellular automata in the present work. An appropriate measurement of grain size and the corrected identification of interfaces and length are very important topics in materials science because they are the representation and validation of mathematical models with real samples. As a result, the developed algorithms are tested and proved to be appropriate and efficient to eliminate the errors and characterize the grain structures.

Preservice Secondary Teachers' Conceptions from a Mathematical Modeling Activity and Connections to the Common Core State Standards

ERIC Educational Resources Information Center

Stohlmann, Micah; Maiorca, Cathrine; Olson, Travis A.

2015-01-01

Mathematical modeling is an essential integrated piece of the Common Core State Standards. However, researchers have shown that mathematical modeling activities can be difficult for teachers to implement. Teachers are more likely to implement mathematical modeling activities if they have their own successful experiences with such activities. This…

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

ERIC Educational Resources Information Center

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

2015-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2013-07-01

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

On an instability exhibited by the ballistic-diffusive heat conduction model of Xu and Hu

DOE PAGES

Christov, I. C.; Jordan, P. M.

2013-11-13

We show that the constitutive relation for the thermal flux proposed by Xu & Hu (2011) admits an unconditional instability. We also highlight the difference between mathematical models containing delay and those that include relaxation effects.

FILTRATION MODEL FOR COAL FLY ASH WITH GLASS FABRICS

EPA Science Inventory

The report describes a new mathematical model for predicting woven glass filter performance with coal fly ash aerosols from utility boilers. Its data base included: an extensive bench- and pilot-scale laboratory investigation of several dust/fabric combinations; field data from t...

Development of stable isotope mixing models in ecology - Dublin

EPA Science Inventory

More than 40 years ago, stable isotope analysis methods used in geochemistry began to be applied to ecological studies. One common application is using mathematical mixing models to sort out the proportional contributions of various sources to a mixture. Examples include contri...

Historical development of stable isotope mixing models in ecology

EPA Science Inventory

More than 40 years ago, stable isotope analysis methods used in geochemistry began to be applied to ecological studies. One common application is using mathematical mixing models to sort out the proportional contributions of various sources to a mixture. Examples include contri...

Development of stable isotope mixing models in ecology - Perth

EPA Science Inventory

More than 40 years ago, stable isotope analysis methods used in geochemistry began to be applied to ecological studies. One common application is using mathematical mixing models to sort out the proportional contributions of various sources to a mixture. Examples include contri...

Development of stable isotope mixing models in ecology - Fremantle

EPA Science Inventory

More than 40 years ago, stable isotope analysis methods used in geochemistry began to be applied to ecological studies. One common application is using mathematical mixing models to sort out the proportional contributions of various sources to a mixture. Examples include contri...

Development of stable isotope mixing models in ecology - Sydney

EPA Science Inventory

More than 40 years ago, stable isotope analysis methods used in geochemistry began to be applied to ecological studies. One common application is using mathematical mixing models to sort out the proportional contributions of various sources to a mixture. Examples include contri...

A novel energy recovery system for parallel hybrid hydraulic excavator.

PubMed

Li, Wei; Cao, Baoyu; Zhu, Zhencai; Chen, Guoan

2014-01-01

Hydraulic excavator energy saving is important to relieve source shortage and protect environment. This paper mainly discusses the energy saving for the hybrid hydraulic excavator. By analyzing the excess energy of three hydraulic cylinders in the conventional hydraulic excavator, a new boom potential energy recovery system is proposed. The mathematical models of the main components including boom cylinder, hydraulic motor, and hydraulic accumulator are built. The natural frequency of the proposed energy recovery system is calculated based on the mathematical models. Meanwhile, the simulation models of the proposed system and a conventional energy recovery system are built by AMESim software. The results show that the proposed system is more effective than the conventional energy saving system. At last, the main components of the proposed energy recovery system including accumulator and hydraulic motor are analyzed for improving the energy recovery efficiency. The measures to improve the energy recovery efficiency of the proposed system are presented.

A model for precalculus students to determine the resonance frequency of a trumpet mouthpiece

NASA Astrophysics Data System (ADS)

Chapman, Robert C.

2004-05-01

The trumpet mouthpiece as a Helmholtz resonator is used to show precalculus students a mathematical model for determining the approximate resonance frequency of the mouthpiece. The mathematics is limited to algebra and trigonometry. Using a system of mouthpieces that have interchangeable cups and backbores, students are introduced to the acoustics of this resonator. By gathering data on 51 different configurations of mouthpieces, the author modifies the existing Helmholtz resonator equation to account for both cup volumes and backbore configurations. Students then use this model for frequency predictions. Included are how to measure the different physical attributes of a trumpet mouthpiece at minimal cost. This includes methods for measuring cup volume, backbore volume, backbore length, throat area, etc. A portion of this phase is de-signed for students to become acquainted with some of the vocabulary of acoustics and the physics of sound.

Whole-body mathematical model for simulating intracranial pressure dynamics

NASA Technical Reports Server (NTRS)

Lakin, William D. (Inventor); Penar, Paul L. (Inventor); Stevens, Scott A. (Inventor); Tranmer, Bruce I. (Inventor)

2007-01-01

A whole-body mathematical model (10) for simulating intracranial pressure dynamics. In one embodiment, model (10) includes 17 interacting compartments, of which nine lie entirely outside of intracranial vault (14). Compartments (F) and (T) are defined to distinguish ventricular from extraventricular CSF. The vasculature of the intracranial system within cranial vault (14) is also subdivided into five compartments (A, C, P, V, and S, respectively) representing the intracranial arteries, capillaries, choroid plexus, veins, and venous sinus. The body's extracranial systemic vasculature is divided into six compartments (I, J, O, Z, D, and X, respectively) representing the arteries, capillaries, and veins of the central body and the lower body. Compartments (G) and (B) include tissue and the associated interstitial fluid in the intracranial and lower regions. Compartment (Y) is a composite involving the tissues, organs, and pulmonary circulation of the central body and compartment (M) represents the external environment.

A Novel Energy Recovery System for Parallel Hybrid Hydraulic Excavator

PubMed Central

Li, Wei; Cao, Baoyu; Zhu, Zhencai; Chen, Guoan

2014-01-01

Hydraulic excavator energy saving is important to relieve source shortage and protect environment. This paper mainly discusses the energy saving for the hybrid hydraulic excavator. By analyzing the excess energy of three hydraulic cylinders in the conventional hydraulic excavator, a new boom potential energy recovery system is proposed. The mathematical models of the main components including boom cylinder, hydraulic motor, and hydraulic accumulator are built. The natural frequency of the proposed energy recovery system is calculated based on the mathematical models. Meanwhile, the simulation models of the proposed system and a conventional energy recovery system are built by AMESim software. The results show that the proposed system is more effective than the conventional energy saving system. At last, the main components of the proposed energy recovery system including accumulator and hydraulic motor are analyzed for improving the energy recovery efficiency. The measures to improve the energy recovery efficiency of the proposed system are presented. PMID:25405215

Evolutionary game theory for physical and biological scientists. II. Population dynamics equations can be associated with interpretations

PubMed Central

Liao, David; Tlsty, Thea D.

2014-01-01

The use of mathematical equations to analyse population dynamics measurements is being increasingly applied to elucidate complex dynamic processes in biological systems, including cancer. Purely ‘empirical’ equations may provide sufficient accuracy to support predictions and therapy design. Nevertheless, interpretation of fitting equations in terms of physical and biological propositions can provide additional insights that can be used both to refine models that prove inconsistent with data and to understand the scope of applicability of models that validate. The purpose of this tutorial is to assist readers in mathematically associating interpretations with equations and to provide guidance in choosing interpretations and experimental systems to investigate based on currently available biological knowledge, techniques in mathematical and computational analysis and methods for in vitro and in vivo experiments. PMID:25097752

Transmission Dinamics Model Of Dengue Fever

NASA Astrophysics Data System (ADS)

Debora; Rendy; Rahmi

2018-01-01

Dengue fever is an endemic disease that is transmitted through the Aedes aegypti mosquito vector. The disease is present in more than 100 countries in America, Africa, and Asia, especially tropical countries. Differential equations can be used to represent the spread of dengue virus occurring in time intervals and model in the form of mathematical models. The mathematical model in this study tries to represent the spread of dengue fever based on the data obtained and the assumptions used. The mathematical model used is a mathematical model consisting of Susceptible (S), Infected (I), Viruses (V) subpopulations. The SIV mathematical model is then analyzed to see the solution behaviour of the system.

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…

Making the Most of Modeling Tasks

ERIC Educational Resources Information Center

Wernet, Jamie L.; Lawrence, Kevin A.; Gilbertson, Nicholas J.

2015-01-01

While there is disagreement among mathematics educators about some aspects of its meaning, mathematical modeling generally involves taking a real-world scenario and translating it into the mathematical world (Niss, Blum, and Galbraith 2007). The complete modeling process involves describing situations posed in problems with mathematical concepts,…

A mathematical model of physiological processes and its application to the study of aging

NASA Technical Reports Server (NTRS)

Hibbs, A. R.; Walford, R. L.

1989-01-01

The behavior of a physiological system which, after displacement, returns by homeostatic mechanisms to its original condition can be described by a simple differential equation in which the "recovery time" is a parameter. Two such systems, which influence one another, can be linked mathematically by the use of "coupling" or "feedback" coefficients. These concepts are the basis for many mathematical models of physiological behavior, and we describe the general nature of such models. Next, we introduce the concept of a "fatal limit" for the displacement of a physiological system, and show how measures of such limits can be included in mathematical models. We show how the numerical values of such limits depend on the values of other system parameters, i.e., recovery times and coupling coefficients, and suggest ways of measuring all these parameters experimentally, for example by monitoring changes induced by X-irradiation. Next, we discuss age-related changes in these parameters, and show how the parameters of mortality statistics, such as the famous Gompertz parameters, can be derived from experimentally measurable changes. Concepts of onset-of-aging, critical or fatal limits, equilibrium value (homeostasis), recovery times and coupling constants are involved. Illustrations are given using published data from mouse and rat populations. We believe that this method of deriving survival patterns from model that is experimentally testable is unique.

Advanced statistics: linear regression, part II: multiple linear regression.

PubMed

Marill, Keith A

2004-01-01

The applications of simple linear regression in medical research are limited, because in most situations, there are multiple relevant predictor variables. Univariate statistical techniques such as simple linear regression use a single predictor variable, and they often may be mathematically correct but clinically misleading. Multiple linear regression is a mathematical technique used to model the relationship between multiple independent predictor variables and a single dependent outcome variable. It is used in medical research to model observational data, as well as in diagnostic and therapeutic studies in which the outcome is dependent on more than one factor. Although the technique generally is limited to data that can be expressed with a linear function, it benefits from a well-developed mathematical framework that yields unique solutions and exact confidence intervals for regression coefficients. Building on Part I of this series, this article acquaints the reader with some of the important concepts in multiple regression analysis. These include multicollinearity, interaction effects, and an expansion of the discussion of inference testing, leverage, and variable transformations to multivariate models. Examples from the first article in this series are expanded on using a primarily graphic, rather than mathematical, approach. The importance of the relationships among the predictor variables and the dependence of the multivariate model coefficients on the choice of these variables are stressed. Finally, concepts in regression model building are discussed.

Model-Based Policymaking: A Framework to Promote Ethical “Good Practice” in Mathematical Modeling for Public Health Policymaking

PubMed Central

Boden, Lisa A.; McKendrick, Iain J.

2017-01-01

Mathematical models are increasingly relied upon as decision support tools, which estimate risks and generate recommendations to underpin public health policies. However, there are no formal agreements about what constitutes professional competencies or duties in mathematical modeling for public health. In this article, we propose a framework to evaluate whether mathematical models that assess human and animal disease risks and control strategies meet standards consistent with ethical “good practice” and are thus “fit for purpose” as evidence in support of policy. This framework is derived from principles of biomedical ethics: independence, transparency (autonomy), beneficence/non-maleficence, and justice. We identify ethical risks associated with model development and implementation and consider the extent to which scientists are accountable for the translation and communication of model results to policymakers so that the strengths and weaknesses of the scientific evidence base and any socioeconomic and ethical impacts of biased or uncertain predictions are clearly understood. We propose principles to operationalize a framework for ethically sound model development and risk communication between scientists and policymakers. These include the creation of science–policy partnerships to mutually define policy questions and communicate results; development of harmonized international standards for model development; and data stewardship and improvement of the traceability and transparency of models via a searchable archive of policy-relevant models. Finally, we suggest that bespoke ethical advisory groups, with relevant expertise and access to these resources, would be beneficial as a bridge between science and policy, advising modelers of potential ethical risks and providing overview of the translation of modeling advice into policy. PMID:28424768

A systematic review of mathematical models of mosquito-borne pathogen transmission: 1970–2010

PubMed Central

Reiner, Robert C.; Perkins, T. Alex; Barker, Christopher M.; Niu, Tianchan; Chaves, Luis Fernando; Ellis, Alicia M.; George, Dylan B.; Le Menach, Arnaud; Pulliam, Juliet R. C.; Bisanzio, Donal; Buckee, Caroline; Chiyaka, Christinah; Cummings, Derek A. T.; Garcia, Andres J.; Gatton, Michelle L.; Gething, Peter W.; Hartley, David M.; Johnston, Geoffrey; Klein, Eili Y.; Michael, Edwin; Lindsay, Steven W.; Lloyd, Alun L.; Pigott, David M.; Reisen, William K.; Ruktanonchai, Nick; Singh, Brajendra K.; Tatem, Andrew J.; Kitron, Uriel; Hay, Simon I.; Scott, Thomas W.; Smith, David L.

2013-01-01

Mathematical models of mosquito-borne pathogen transmission originated in the early twentieth century to provide insights into how to most effectively combat malaria. The foundations of the Ross–Macdonald theory were established by 1970. Since then, there has been a growing interest in reducing the public health burden of mosquito-borne pathogens and an expanding use of models to guide their control. To assess how theory has changed to confront evolving public health challenges, we compiled a bibliography of 325 publications from 1970 through 2010 that included at least one mathematical model of mosquito-borne pathogen transmission and then used a 79-part questionnaire to classify each of 388 associated models according to its biological assumptions. As a composite measure to interpret the multidimensional results of our survey, we assigned a numerical value to each model that measured its similarity to 15 core assumptions of the Ross–Macdonald model. Although the analysis illustrated a growing acknowledgement of geographical, ecological and epidemiological complexities in modelling transmission, most models during the past 40 years closely resemble the Ross–Macdonald model. Modern theory would benefit from an expansion around the concepts of heterogeneous mosquito biting, poorly mixed mosquito-host encounters, spatial heterogeneity and temporal variation in the transmission process. PMID:23407571

Understanding apparently non-exponential outbreaks Comment on "Mathematical models to characterize early epidemic growth: A review" by Gerardo Chowell et al.

NASA Astrophysics Data System (ADS)

Champredon, David; Earn, David J. D.

2016-09-01

Mechanistic mathematical modelling of the population dynamics of infectious diseases has advanced tremendously over the last few decades [1-6]. Transmission models have been applied to countless diseases of public health importance, including seasonal and pandemic influenza [7], childhood diseases such as measles [8,9] and whooping cough [10], vector transmitted diseases such as malaria [11] and dengue [12], and waterborne diseases such as cholera [13-15]. Much attention in recent years has been directed to emergent diseases such as SARS [16], new subtypes of influenza [17,18], Ebola [19,20], and Zika [21], for which an understanding of early outbreak dynamics is critical.

Available clinical markers of treatment outcome integrated in mathematical models to guide therapy in HIV infection.

PubMed

Vergu, Elisabeta; Mallet, Alain; Golmard, Jean-Louis

2004-02-01

Because treatment failure in many HIV-infected persons may be due to multiple causes, including resistance to antiretroviral agents, it is important to better tailor drug therapy to individual patients. This improvement requires the prediction of treatment outcome from baseline immunological or virological factors, and from results of resistance tests. Here, we review briefly the available clinical factors that have an impact on therapy outcome, and discuss the role of a predictive modelling approach integrating these factors proposed in a previous work. Mathematical and statistical models could become essential tools to address questions that are difficult to study clinically and experimentally, thereby guiding decisions in the choice of individualized drug regimens.

Improving mathematical problem solving ability through problem-based learning and authentic assessment for the students of Bali State Polytechnic

NASA Astrophysics Data System (ADS)

Darma, I. K.

2018-01-01

This research is aimed at determining: 1) the differences of mathematical problem solving ability between the students facilitated with problem-based learning model and conventional learning model, 2) the differences of mathematical problem solving ability between the students facilitated with authentic and conventional assessment model, and 3) interaction effect between learning and assessment model on mathematical problem solving. The research was conducted in Bali State Polytechnic, using the 2x2 experiment factorial design. The samples of this research were 110 students. The data were collected using a theoretically and empirically-validated test. Instruments were validated by using Aiken’s approach of technique content validity and item analysis, and then analyzed using anova stylistic. The result of the analysis shows that the students facilitated with problem-based learning and authentic assessment models get the highest score average compared to the other students, both in the concept understanding and mathematical problem solving. The result of hypothesis test shows that, significantly: 1) there is difference of mathematical problem solving ability between the students facilitated with problem-based learning model and conventional learning model, 2) there is difference of mathematical problem solving ability between the students facilitated with authentic assessment model and conventional assessment model, and 3) there is interaction effect between learning model and assessment model on mathematical problem solving. In order to improve the effectiveness of mathematics learning, collaboration between problem-based learning model and authentic assessment model can be considered as one of learning models in class.

Influence of Problem-Based Learning Model of Learning to the Mathematical Communication Ability of Students of Grade XI IPA SMAN 14 Padang

NASA Astrophysics Data System (ADS)

Nisa, I. M.

2018-04-01

The ability of mathematical communication is one of the goals of learning mathematics expected to be mastered by students. However, reality in the field found that the ability of mathematical communication the students of grade XI IPA SMA Negeri 14 Padang have not developed optimally. This is evident from the low test results of communication skills mathematically done. One of the factors that causes this happens is learning that has not been fully able to facilitate students to develop mathematical communication skills well. By therefore, to improve students' mathematical communication skills required a model in the learning activities. One of the models learning that can be used is Problem Based learning model Learning (PBL). The purpose of this study is to see whether the ability the students' mathematical communication using the PBL model better than the students' mathematical communication skills of the learning using conventional learning in Class XI IPA SMAN 14 Padang. This research type is quasi experiment with design Randomized Group Only Design. Population in this research that is student of class XI IPA SMAN 14 Padang with sample class XI IPA 3 and class XI IPA 4. Data retrieval is done by using communication skill test mathematically shaped essay. To test the hypothesis used U-Mann test Whitney. Based on the results of data analysis, it can be concluded that the ability mathematical communication of students whose learning apply more PBL model better than the students' mathematical communication skills of their learning apply conventional learning in class XI IPA SMA 14 Padang at α = 0.05. This indicates that the PBL learning model effect on students' mathematical communication ability.

Proceedings of the 27th International Group for the Psychology of Mathematics Education Conference Held Jointly with the 25th PME-NA Conference (Honolulu, Hawaii, July 13-18, 2003). Volume 3

ERIC Educational Resources Information Center

Pateman, Neil A., Ed; Dougherty, Barbara J., Ed.; Zilliox, Joseph T., Ed.

2003-01-01

This volume of the 27th International Group for the Psychology of Mathematics Education Conference includes the following research reports: (1) The Affective Views of Primary School Children (Peter Grootenboer); (2) Theoretical Model of Analysis of Rate Problems in Algebra (Jose Guzman, Nadine Bednarz and Fernando Hitt); (3) Locating Fractions on…

A lumped parameter mathematical model for simulation of subsonic wind tunnels

NASA Technical Reports Server (NTRS)

Krosel, S. M.; Cole, G. L.; Bruton, W. M.; Szuch, J. R.

1986-01-01

Equations for a lumped parameter mathematical model of a subsonic wind tunnel circuit are presented. The equation state variables are internal energy, density, and mass flow rate. The circuit model is structured to allow for integration and analysis of tunnel subsystem models which provide functions such as control of altitude pressure and temperature. Thus the model provides a useful tool for investigating the transient behavior of the tunnel and control requirements. The model was applied to the proposed NASA Lewis Altitude Wind Tunnel (AWT) circuit and included transfer function representations of the tunnel supply/exhaust air and refrigeration subsystems. Both steady state and frequency response data are presented for the circuit model indicating the type of results and accuracy that can be expected from the model. Transient data for closed loop control of the tunnel and its subsystems are also presented, demonstrating the model's use as a control analysis tool.

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

NASA Astrophysics Data System (ADS)

Plotnitsky, Arkady

2017-06-01

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

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 of fluid-electrolyte alterations during weightlessness

NASA Technical Reports Server (NTRS)

Leonard, J. I.

1984-01-01

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

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…

Mathematical Modeling in the High School Curriculum

ERIC Educational Resources Information Center

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

2016-01-01

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

Current status and future needs of the BehavePlus Fire Modeling System

Treesearch

Patricia L. Andrews

2014-01-01

The BehavePlus Fire Modeling System is among the most widely used systems for wildland fire prediction. It is designed for use in a range of tasks including wildfire behaviour prediction, prescribed fire planning, fire investigation, fuel hazard assessment, fire model understanding, communication and research. BehavePlus is based on mathematical models for fire...

A Model of E-Learning Uptake and Continued Use in Higher Education Institutions

ERIC Educational Resources Information Center

Pinpathomrat, Nakarin; Gilbert, Lester; Wills, Gary B.

2013-01-01

This research investigates the factors that affect a students' take-up and continued use of E-learning. A mathematical model was constructed by applying three grounded theories; Unified Theory of Acceptance and Use of Technology, Keller's ARCS model, and Expectancy Disconfirm Theory. The learning preference factor was included in the model.…

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

ERIC Educational Resources Information Center

Ciltas, Alper; Isik, Ahmet

2013-01-01

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

Iontophoretic transdermal drug delivery: a multi-layered approach.

PubMed

Pontrelli, Giuseppe; Lauricella, Marco; Ferreira, José A; Pena, Gonçalo

2017-12-11

We present a multi-layer mathematical model to describe the transdermal drug release from an iontophoretic system. The Nernst-Planck equation describes the basic convection-diffusion process, with the electric potential obtained by solving the Laplace's equation. These equations are complemented with suitable interface and boundary conditions in a multi-domain. The stability of the mathematical problem is discussed in different scenarios and a finite-difference method is used to solve the coupled system. Numerical experiments are included to illustrate the drug dynamics under different conditions. © The authors 2016. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Undergraduate Students' Perceptions of the Mathematics Courses Included in the Primary School Teacher Education Program

ERIC Educational Resources Information Center

Serin, Mehmet Koray; Incikabi, Semahat

2017-01-01

Mathematics educators have reported on many issues regarding students' mathematical education, particularly students who received mathematics education at different departments such as engineering, science or primary school, including their difficulties with mathematical concepts, their understanding of and preferences for mathematical concepts.…

Mathematical Modeling: Challenging the Figured Worlds of Elementary Mathematics

ERIC Educational Resources Information Center

Wickstrom, Megan H.

2017-01-01

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

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

ERIC Educational Resources Information Center

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

2013-01-01

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

Ocular hemodynamics and glaucoma: the role of mathematical modeling.

PubMed

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

2013-01-01

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

Multiscale Mathematics for Biomass Conversion to Renewable Hydrogen

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

Plechac, Petr; Vlachos, Dionisios; Katsoulakis, Markos

2013-09-05

The overall objective of this project is to develop multiscale models for understanding and eventually designing complex processes for renewables. To the best of our knowledge, our work is the first attempt at modeling complex reacting systems, whose performance relies on underlying multiscale mathematics. Our specific application lies at the heart of biofuels initiatives of DOE and entails modeling of catalytic systems, to enable economic, environmentally benign, and efficient conversion of biomass into either hydrogen or valuable chemicals. Specific goals include: (i) Development of rigorous spatio-temporal coarse-grained kinetic Monte Carlo (KMC) mathematics and simulation for microscopic processes encountered in biomassmore » transformation. (ii) Development of hybrid multiscale simulation that links stochastic simulation to a deterministic partial differential equation (PDE) model for an entire reactor. (iii) Development of hybrid multiscale simulation that links KMC simulation with quantum density functional theory (DFT) calculations. (iv) Development of parallelization of models of (i)-(iii) to take advantage of Petaflop computing and enable real world applications of complex, multiscale models. In this NCE period, we continued addressing these objectives and completed the proposed work. Main initiatives, key results, and activities are outlined.« less

A Multiphase Flow in the Antroduodenal Portion of the Gastrointestinal Tract: A Mathematical Model

PubMed Central

Trusov, P. V.

2016-01-01

A group of authors has developed a multilevel mathematical model that focuses on functional disorders in a human body associated with various chemical, physical, social, and other factors. At this point, the researchers have come up with structure, basic definitions and concepts of a mathematical model at the “macrolevel” that allow describing processes in a human body as a whole. Currently we are working at the “mesolevel” of organs and systems. Due to complexity of the tasks, this paper deals with only one meso-fragment of a digestive system model. It describes some aspects related to modeling multiphase flow in the antroduodenal portion of the gastrointestinal tract. Biochemical reactions, dissolution of food particles, and motor, secretory, and absorbing functions of the tract are taken into consideration. The paper outlines some results concerning influence of secretory function disorders on food dissolution rate and tract contents acidity. The effect which food density has on inflow of food masses from a stomach to a bowel is analyzed. We assume that the future development of the model will include digestive enzymes and related reactions of lipolysis, proteolysis, and carbohydrates breakdown. PMID:27413393

A mathematical function for the description of nutrient-response curve

PubMed Central

Ahmadi, Hamed

2017-01-01

Several mathematical equations have been proposed to modeling nutrient-response curve for animal and human justified on the goodness of fit and/or on the biological mechanism. In this paper, a functional form of a generalized quantitative model based on Rayleigh distribution principle for description of nutrient-response phenomena is derived. The three parameters governing the curve a) has biological interpretation, b) may be used to calculate reliable estimates of nutrient response relationships, and c) provide the basis for deriving relationships between nutrient and physiological responses. The new function was successfully applied to fit the nutritional data obtained from 6 experiments including a wide range of nutrients and responses. An evaluation and comparison were also done based simulated data sets to check the suitability of new model and four-parameter logistic model for describing nutrient responses. This study indicates the usefulness and wide applicability of the new introduced, simple and flexible model when applied as a quantitative approach to characterizing nutrient-response curve. This new mathematical way to describe nutritional-response data, with some useful biological interpretations, has potential to be used as an alternative approach in modeling nutritional responses curve to estimate nutrient efficiency and requirements. PMID:29161271

Basic research for the geodynamics program

NASA Technical Reports Server (NTRS)

1991-01-01

The mathematical models of space very long base interferometry (VLBI) observables suitable for least squares covariance analysis were derived and estimatability problems inherent in the space VLBI system were explored, including a detailed rank defect analysis and sensitivity analysis. An important aim is to carry out a comparative analysis of the mathematical models of the ground-based VLBI and space VLBI observables in order to describe the background in detail. Computer programs were developed in order to check the relations, assess errors, and analyze sensitivity. In order to investigate the estimatability of different geodetic and geodynamic parameters from the space VLBI observables, the mathematical models for time delay and time delay rate observables of space VLBI were analytically derived along with the partial derivatives with respect to the parameters. Rank defect analysis was carried out both by analytical and numerical testing of linear dependencies between the columns of the normal matrix thus formed. Definite conclusions were formed about the rank defects in the system.

The Sizing and Optimization Language, (SOL): Computer language for design problems

NASA Technical Reports Server (NTRS)

Lucas, Stephen H.; Scotti, Stephen J.

1988-01-01

The Sizing and Optimization Language, (SOL), a new high level, special purpose computer language was developed to expedite application of numerical optimization to design problems and to make the process less error prone. SOL utilizes the ADS optimization software and provides a clear, concise syntax for describing an optimization problem, the OPTIMIZE description, which closely parallels the mathematical description of the problem. SOL offers language statements which can be used to model a design mathematically, with subroutines or code logic, and with existing FORTRAN routines. In addition, SOL provides error checking and clear output of the optimization results. Because of these language features, SOL is best suited to model and optimize a design concept when the model consits of mathematical expressions written in SOL. For such cases, SOL's unique syntax and error checking can be fully utilized. SOL is presently available for DEC VAX/VMS systems. A SOL package is available which includes the SOL compiler, runtime library routines, and a SOL reference manual.

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

NASA Astrophysics Data System (ADS)

Widayanto, Arif; Pratiwi, Hasih; Mardiyana

2018-04-01

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

Evaluating AIDS Prevention: Contributions of Multiple Disciplines.

ERIC Educational Resources Information Center

Leviton, Laura C., Ed.; And Others

1990-01-01

Seven essays on efforts of evaluate prevention programs aimed at the acquired immune deficiency syndrome (AIDS) are presented. Topics include public health psychology, mathematical models of epidemiology, estimates of incubation periods, ethnographic evaluations of AIDS prevention programs, an AIDS education model, theory-based evaluation, and…

A mathematical model of a lithium/thionyl chloride primary cell

NASA Technical Reports Server (NTRS)

Evans, T. I.; Nguyen, T. V.; White, R. E.

1987-01-01

A 1-D mathematical model for the lithium/thionyl chloride primary cell was developed to investigate methods of improving its performance and safety. The model includes many of the components of a typical lithium/thionyl chloride cell such as the porous lithium chloride film which forms on the lithium anode surface. The governing equations are formulated from fundamental conservation laws using porous electrode theory and concentrated solution theory. The model is used to predict 1-D, time dependent profiles of concentration, porosity, current, and potential as well as cell temperature and voltage. When a certain discharge rate is required, the model can be used to determine the design criteria and operating variables which yield high cell capacities. Model predictions can be used to establish operational and design limits within which the thermal runaway problem, inherent in these cells, can be avoided.

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

NASA Astrophysics Data System (ADS)

Afrizal, Irfan Mufti; Dachlan, Jarnawi Afghani

2017-05-01

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

Mathematical modelling in developmental biology.

PubMed

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

2013-06-01

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

A cardiovascular system model for lower-body negative pressure response

NASA Technical Reports Server (NTRS)

Mitchell, B. A., Jr.; Giese, R. P.

1971-01-01

Mathematical models used to study complex physiological control systems are discussed. Efforts were made to modify a model of the cardiovascular system for use in studying lower body negative pressure. A computer program was written which allows orderly, straightforward expansion to include exercise, metabolism (thermal stress), respiration, and other body functions.

BehavePlus fire modeling system: Past, present, and future

Treesearch

Patricia L. Andrews

2007-01-01

Use of mathematical fire models to predict fire behavior and fire effects plays an important supporting role in wildland fire management. When used in conjunction with personal fire experience and a basic understanding of the fire models, predictions can be successfully applied to a range of fire management activities including wildfire behavior prediction, prescribed...

A NONSTEADY-STATE ANALYTICAL MODEL TO PREDICT GASEOUS EMISSIONS OF VOLATILE ORGANIC COMPOUNDS FROM LANDFILLS. (R825689C072)

EPA Science Inventory

Abstract

A general mathematical model is developed to predict emissions of volatile organic compounds (VOCs) from hazardous or sanitary landfills. The model is analytical in nature and includes important mechanisms occurring in unsaturated subsurface landfill environme...

Modeling crustal deformation near active faults and volcanic centers: a catalog of deformation models and modeling approaches

USGS Publications Warehouse

Battaglia, Maurizio; ,; Peter, F.; Murray, Jessica R.

2013-01-01

This manual provides the physical and mathematical concepts for selected models used to interpret deformation measurements near active faults and volcanic centers. The emphasis is on analytical models of deformation that can be compared with data from the Global Positioning System (GPS) receivers, Interferometric synthetic aperture radar (InSAR), leveling surveys, tiltmeters and strainmeters. Source models include pressurized spherical, ellipsoidal, and horizontal penny-shaped geometries in an elastic, homogeneous, flat half-space. Vertical dikes and faults are described following the mathematical notation for rectangular dislocations in an elastic, homogeneous, flat half-space. All the analytical expressions were verified against numerical models developed by use of COMSOL Multyphics, a Finite Element Analysis software (http://www.comsol.com). In this way, typographical errors present were identified and corrected. Matlab scripts are also provided to facilitate the application of these models.

Improving Odometric Accuracy for an Autonomous Electric Cart.

PubMed

Toledo, Jonay; Piñeiro, Jose D; Arnay, Rafael; Acosta, Daniel; Acosta, Leopoldo

2018-01-12

In this paper, a study of the odometric system for the autonomous cart Verdino, which is an electric vehicle based on a golf cart, is presented. A mathematical model of the odometric system is derived from cart movement equations, and is used to compute the vehicle position and orientation. The inputs of the system are the odometry encoders, and the model uses the wheels diameter and distance between wheels as parameters. With this model, a least square minimization is made in order to get the nominal best parameters. This model is updated, including a real time wheel diameter measurement improving the accuracy of the results. A neural network model is used in order to learn the odometric model from data. Tests are made using this neural network in several configurations and the results are compared to the mathematical model, showing that the neural network can outperform the first proposed model.

Mathematical modeling of bone marrow--peripheral blood dynamics in the disease state based on current emerging paradigms, part I.

PubMed

Afenya, Evans K; Ouifki, Rachid; Camara, Baba I; Mundle, Suneel D

2016-04-01

Stemming from current emerging paradigms related to the cancer stem cell hypothesis, an existing mathematical model is expanded and used to study cell interaction dynamics in the bone marrow and peripheral blood. The proposed mathematical model is described by a system of nonlinear differential equations with delay, to quantify the dynamics in abnormal hematopoiesis. The steady states of the model are analytically and numerically obtained. Some conditions for the local asymptotic stability of such states are investigated. Model analyses suggest that malignancy may be irreversible once it evolves from a nonmalignant state into a malignant one and no intervention takes place. This leads to the proposition that a great deal of emphasis be placed on cancer prevention. Nevertheless, should malignancy arise, treatment programs for its containment or curtailment may have to include a maximum and extensive level of effort to protect normal cells from eventual destruction. Further model analyses and simulations predict that in the untreated disease state, there is an evolution towards a situation in which malignant cells dominate the entire bone marrow - peripheral blood system. Arguments are then advanced regarding requirements for quantitatively understanding cancer stem cell behavior. Among the suggested requirements are, mathematical frameworks for describing the dynamics of cancer initiation and progression, the response to treatment, the evolution of resistance, and malignancy prevention dynamics within the bone marrow - peripheral blood architecture. Copyright © 2016 Elsevier Inc. All rights reserved.

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Integrative approaches for modeling regulation and function of the respiratory system.

PubMed

Ben-Tal, Alona; Tawhai, Merryn H

2013-01-01

Mathematical models have been central to understanding the interaction between neural control and breathing. Models of the entire respiratory system-which comprises the lungs and the neural circuitry that controls their ventilation-have been derived using simplifying assumptions to compartmentalize each component of the system and to define the interactions between components. These full system models often rely-through necessity-on empirically derived relationships or parameters, in addition to physiological values. In parallel with the development of whole respiratory system models are mathematical models that focus on furthering a detailed understanding of the neural control network, or of the several functions that contribute to gas exchange within the lung. These models are biophysically based, and rely on physiological parameters. They include single-unit models for a breathing lung or neural circuit, through to spatially distributed models of ventilation and perfusion, or multicircuit models for neural control. The challenge is to bring together these more recent advances in models of neural control with models of lung function, into a full simulation for the respiratory system that builds upon the more detailed models but remains computationally tractable. This requires first understanding the mathematical models that have been developed for the respiratory system at different levels, and which could be used to study how physiological levels of O2 and CO2 in the blood are maintained. Copyright © 2013 Wiley Periodicals, Inc.

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

ERIC Educational Resources Information Center

Gould, Heather; Wasserman, Nicholas H.

2014-01-01

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

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

ERIC Educational Resources Information Center

Jacobs, Gerrie J.; Durandt, Rina

2017-01-01

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

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

PubMed

Gilbert, Scott F

2018-01-31

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

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

NASA Technical Reports Server (NTRS)

Wang, Caroline; Purinton, Steve

1989-01-01

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

Full-scale flammability test data for validation of aircraft fire mathematical models

NASA Technical Reports Server (NTRS)

Kuminecz, J. F.; Bricker, R. W.

1982-01-01

Twenty-five large scale aircraft flammability tests were conducted in a Boeing 737 fuselage at the NASA Johnson Space Center (JSC). The objective of this test program was to provide a data base on the propagation of large scale aircraft fires to support the validation of aircraft fire mathematical models. Variables in the test program included cabin volume, amount of fuel, fuel pan area, fire location, airflow rate, and cabin materials. A number of tests were conducted with jet A-1 fuel only, while others were conducted with various Boeing 747 type cabin materials. These included urethane foam seats, passenger service units, stowage bins, and wall and ceiling panels. Two tests were also included using special urethane foam and polyimide foam seats. Tests were conducted with each cabin material individually, with various combinations of these materials, and finally, with all materials in the cabin. The data include information obtained from approximately 160 locations inside the fuselage.

Mathematical modelling of skeletal repair.

PubMed

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

2004-01-23

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

Theory, Modeling, Software and Hardware Development for Analytical and Computational Materials Science

NASA Technical Reports Server (NTRS)

Young, Gerald W.; Clemons, Curtis B.

2004-01-01

The focus of this Cooperative Agreement between the Computational Materials Laboratory (CML) of the Processing Science and Technology Branch of the NASA Glenn Research Center (GRC) and the Department of Theoretical and Applied Mathematics at The University of Akron was in the areas of system development of the CML workstation environment, modeling of microgravity and earth-based material processing systems, and joint activities in laboratory projects. These efforts complement each other as the majority of the modeling work involves numerical computations to support laboratory investigations. Coordination and interaction between the modelers, system analysts, and laboratory personnel are essential toward providing the most effective simulations and communication of the simulation results. Toward these means, The University of Akron personnel involved in the agreement worked at the Applied Mathematics Research Laboratory (AMRL) in the Department of Theoretical and Applied Mathematics while maintaining a close relationship with the personnel of the Computational Materials Laboratory at GRC. Network communication between both sites has been established. A summary of the projects we undertook during the time period 9/1/03 - 6/30/04 is included.

Applying mathematical models to predict resident physician performance and alertness on traditional and novel work schedules.

PubMed

Klerman, Elizabeth B; Beckett, Scott A; Landrigan, Christopher P

2016-09-13

In 2011 the U.S. Accreditation Council for Graduate Medical Education began limiting first year resident physicians (interns) to shifts of ≤16 consecutive hours. Controversy persists regarding the effectiveness of this policy for reducing errors and accidents while promoting education and patient care. Using a mathematical model of the effects of circadian rhythms and length of time awake on objective performance and subjective alertness, we quantitatively compared predictions for traditional intern schedules to those that limit work to ≤ 16 consecutive hours. We simulated two traditional schedules and three novel schedules using the mathematical model. The traditional schedules had extended duration work shifts (≥24 h) with overnight work shifts every second shift (including every third night, Q3) or every third shift (including every fourth night, Q4) night; the novel schedules had two different cross-cover (XC) night team schedules (XC-V1 and XC-V2) and a Rapid Cycle Rotation (RCR) schedule. Predicted objective performance and subjective alertness for each work shift were computed for each individual's schedule within a team and then combined for the team as a whole. Our primary outcome was the amount of time within a work shift during which a team's model-predicted objective performance and subjective alertness were lower than that expected after 16 or 24 h of continuous wake in an otherwise rested individual. The model predicted fewer hours with poor performance and alertness, especially during night-time work hours, for all three novel schedules than for either the traditional Q3 or Q4 schedules. Three proposed schedules that eliminate extended shifts may improve performance and alertness compared with traditional Q3 or Q4 schedules. Predicted times of worse performance and alertness were at night, which is also a time when supervision of trainees is lower. Mathematical modeling provides a quantitative comparison approach with potential to aid residency programs in schedule analysis and redesign.

BioModels: expanding horizons to include more modelling approaches and formats

PubMed Central

Nguyen, Tung V N; Graesslin, Martin; Hälke, Robert; Ali, Raza; Schramm, Jochen; Wimalaratne, Sarala M; Kothamachu, Varun B; Rodriguez, Nicolas; Swat, Maciej J; Eils, Jurgen; Eils, Roland; Laibe, Camille; Chelliah, Vijayalakshmi

2018-01-01

Abstract BioModels serves as a central repository of mathematical models representing biological processes. It offers a platform to make mathematical models easily shareable across the systems modelling community, thereby supporting model reuse. To facilitate hosting a broader range of model formats derived from diverse modelling approaches and tools, a new infrastructure for BioModels has been developed that is available at http://www.ebi.ac.uk/biomodels. This new system allows submitting and sharing of a wide range of models with improved support for formats other than SBML. It also offers a version-control backed environment in which authors and curators can work collaboratively to curate models. This article summarises the features available in the current system and discusses the potential benefit they offer to the users over the previous system. In summary, the new portal broadens the scope of models accepted in BioModels and supports collaborative model curation which is crucial for model reproducibility and sharing. PMID:29106614

Think Pair Share Using Realistic Mathematics Education Approach in Geometry Learning

NASA Astrophysics Data System (ADS)

Afthina, H.; Mardiyana; Pramudya, I.

2017-09-01

This research aims to determine the impact of mathematics learning applying Think Pair Share (TPS) using Realistic Mathematics Education (RME) viewed from mathematical-logical intelligence in geometry learning. Method that used in this research is quasi experimental research The result of this research shows that (1) mathematics achievement applying TPS using RME approach gives a better result than those applying direct learning model; (2) students with high mathematical-logical intelligence can reach a better mathematics achievement than those with average and low one, whereas students with average mathematical-logical intelligence can reach a better achievement than those with low one; (3) there is no interaction between learning model and the level of students’ mathematical-logical intelligence in giving a mathematics achievement. The impact of this research is that TPS model using RME approach can be applied in mathematics learning so that students can learn more actively and understand the material more, and mathematics learning become more meaningful. On the other hand, internal factors of students must become a consideration toward the success of students’ mathematical achievement particularly in geometry material.

Comparing the cognitive differences resulting from modeling instruction: Using computer microworld and physical object instruction to model real world problems

NASA Astrophysics Data System (ADS)

Oursland, Mark David

This study compared the modeling achievement of students receiving mathematical modeling instruction using the computer microworld, Interactive Physics, and students receiving instruction using physical objects. Modeling instruction included activities where students applied the (a) linear model to a variety of situations, (b) linear model to two-rate situations with a constant rate, (c) quadratic model to familiar geometric figures. Both quantitative and qualitative methods were used to analyze achievement differences between students (a) receiving different methods of modeling instruction, (b) with different levels of beginning modeling ability, or (c) with different levels of computer literacy. Student achievement was analyzed quantitatively through a three-factor analysis of variance where modeling instruction, beginning modeling ability, and computer literacy were used as the three independent factors. The SOLO (Structure of the Observed Learning Outcome) assessment framework was used to design written modeling assessment instruments to measure the students' modeling achievement. The same three independent factors were used to collect and analyze the interviews and observations of student behaviors. Both methods of modeling instruction used the data analysis approach to mathematical modeling. The instructional lessons presented problem situations where students were asked to collect data, analyze the data, write a symbolic mathematical equation, and use equation to solve the problem. The researcher recommends the following practice for modeling instruction based on the conclusions of this study. A variety of activities with a common structure are needed to make explicit the modeling process of applying a standard mathematical model. The modeling process is influenced strongly by prior knowledge of the problem context and previous modeling experiences. The conclusions of this study imply that knowledge of the properties about squares improved the students' ability to model a geometric problem more than instruction in data analysis modeling. The uses of computer microworlds such as Interactive Physics in conjunction with cooperative groups are a viable method of modeling instruction.

Preserving Pelicans with Models That Make Sense

ERIC Educational Resources Information Center

Moore, Tamara J.; Doerr, Helen M.; Glancy, Aran W.; Ntow, Forster D.

2015-01-01

Getting students to think deeply about mathematical concepts is not an easy job, which is why we often use problem-solving tasks to engage students in higher-level mathematical thinking. Mathematical modeling, one of the mathematical practices found in the Common Core State Standards for Mathematics (CCSSM), is a type of problem solving that can…

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

ERIC Educational Resources Information Center

Ludwig, Patrice; Tongen, Anthony; Walton, Brian

2018-01-01

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

Mathematical model for HIV dynamics in HIV-specific helper cells

NASA Astrophysics Data System (ADS)

Pinto, Carla M. A.; Carvalho, Ana

2014-03-01

In this paper we study a delay mathematical model for the dynamics of HIV in HIV-specific CD4 + T helper cells. We modify the model presented by Roy and Wodarz in 2012, where the HIV dynamics is studied, considering a single CD4 + T cell population. Non-specific helper cells are included as alternative target cell population, to account for macrophages and dendritic cells. In this paper, we include two types of delay: (1) a latent period between the time target cells are contacted by the virus particles and the time the virions enter the cells and; (2) virus production period for new virions to be produced within and released from the infected cells. We compute the reproduction number of the model, R0, and the local stability of the disease free equilibrium and of the endemic equilibrium. We find that for values of R0<1, the model approaches asymptotically the disease free equilibrium. For values of R0>1, the model approximates asymptotically the endemic equilibrium. We observe numerically the phenomenon of backward bifurcation for values of R0⪅1. This statement will be proved in future work. We also vary the values of the latent period and the production period of infected cells and free virus. We conclude that increasing these values translates in a decrease of the reproduction number. Thus, a good strategy to control the HIV virus should focus on drugs to prolong the latent period and/or slow down the virus production. These results suggest that the model is mathematically and epidemiologically well-posed.

Mathematical models of behavior of individual animals.

PubMed

Tsibulsky, Vladimir L; Norman, Andrew B

2007-01-01

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