Mathematical Modeling of Loop Heat Pipes

NASA Technical Reports Server (NTRS)

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

1998-01-01

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

Mathematical modelling of an electromagnetics automobile suspension

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

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…

Establishing Validity of the Thai Mathematics Teaching Efficacy Beliefs Instrument

ERIC Educational Resources Information Center

Matney, Gabriel; Jackson, Jack L., II.; Panarach, Yupadee

2016-01-01

This article presents our work in translating the Mathematics Teaching Efficacy Beliefs Instrument (MTEBI) from English to Thai and our resulting investigation of validity with Thai preservice teachers. The translation process occurred over several meetings between two U.S. mathematics educators and one Thai mathematics educator. To check for…

An instrument measuring prospective mathematics teacher self-regulated learning: validity and reliability

NASA Astrophysics Data System (ADS)

Nugroho, A. A.; Juniati, D.; Siswono, T. Y. E.

2018-03-01

Self Regulated Learning (SRL) is an individual's ability to achieve academic goals by controlling behavior, motivate yourself and use cognitive in learning, so it is important for a teacher especially teachers of mathematics related to the ability of management, design, implementation of learning and evaluation of learning outcomes. The purpose of the research is to develop an instrument to describe the SRL of a prospective mathematics teacher. Data were collected by (1) the study of the theory of SRL produced the indicator SRL used to design the questionnaire SRL; (2) analysis of the questionnaire SRL obtained from several References; and (3) development stage of the SRL questionnaire through validity test of content and empirical validation. The study involved 2 content experts in mathematics, 1 linguist, and 92 prospective mathematics teachers. The results of the research on content validity test based on Indonesian expert and 2 content experts indicate that the content can assess the indicator of the SRL and feasible to be used, in the test of legibility of two prospective mathematics teacher concluded that the instrument has a language that can be understood by the prospective teacher of mathematics and on empirical validation involving 92 prospective mathematics teacher generate data that of 65 statements there are 3 invalid statements. Reliability calculation shows high category that values 0,93. The conclusion is the SRL instrument developed for the prospective mathematics teacher.

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.

Development and Validation of a Mathematics Anxiety Scale for Students

ERIC Educational Resources Information Center

Ko, Ho Kyoung; Yi, Hyun Sook

2011-01-01

This study developed and validated a Mathematics Anxiety Scale for Students (MASS) that can be used to measure the level of mathematics anxiety that students experience in school settings and help them overcome anxiety and perform better in mathematics achievement. We conducted a series of preliminary analyses and panel reviews to evaluate quality…

Mathematical Model Formulation And Validation Of Water And Solute Transport In Whole Hamster Pancreatic Islets

PubMed Central

Benson, Charles T.; Critser, John K.

2014-01-01

Optimization of cryopreservation protocols for cells and tissues requires accurate models of heat and mass transport. Model selection often depends on the configuration of the tissue. Here, a mathematical and conceptual model of water and solute transport for whole hamster pancreatic islets has been developed and experimentally validated incorporating fundamental biophysical data from previous studies on individual hamster islet cells while retaining whole-islet structural information. It describes coupled transport of water and solutes through the islet by three methods: intracellularly, intercellularly, and in combination. In particular we use domain decomposition techniques to couple a transmembrane flux model with an interstitial mass transfer model. The only significant undetermined variable is the cellular surface area which is in contact with the intercellularly transported solutes, Ais. The model was validated and Ais determined using a 3 × 3 factorial experimental design blocked for experimental day. Whole islet physical experiments were compared with model predictions at three temperatures, three perfusing solutions, and three islet size groups. A mean of 4.4 islets were compared at each of the 27 experimental conditions and found to correlate with a coefficient of determination of 0.87 ± 0.06 (mean ± S.D.). Only the treatment variable of perfusing solution was found to be significant (p < 0.05). We have devised a model that retains much of the intrinsic geometric configuration of the system, and thus fewer laboratory experiments are needed to determine model parameters and thus to develop new optimized cryopreservation protocols. Additionally, extensions to ovarian follicles and other concentric tissue structures may be made. PMID:24950195

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…

Student mathematical imagination instruments: construction, cultural adaptation and validity

NASA Astrophysics Data System (ADS)

Dwijayanti, I.; Budayasa, I. K.; Siswono, T. Y. E.

2018-03-01

Imagination has an important role as the center of sensorimotor activity of the students. The purpose of this research is to construct the instrument of students’ mathematical imagination in understanding concept of algebraic expression. The researcher performs validity using questionnaire and test technique and data analysis using descriptive method. Stages performed include: 1) the construction of the embodiment of the imagination; 2) determine the learning style questionnaire; 3) construct instruments; 4) translate to Indonesian as well as adaptation of learning style questionnaire content to student culture; 5) perform content validation. The results stated that the constructed instrument is valid by content validation and empirical validation so that it can be used with revisions. Content validation involves Indonesian linguists, english linguists and mathematics material experts. Empirical validation is done through a legibility test (10 students) and shows that in general the language used can be understood. In addition, a questionnaire test (86 students) was analyzed using a biserial point correlation technique resulting in 16 valid items with a reliability test using KR 20 with medium reability criteria. While the test instrument test (32 students) to find all items are valid and reliability test using KR 21 with reability is 0,62.

The development of a valid discovery-based learning module to improve students' mathematical connection

NASA Astrophysics Data System (ADS)

Kuneni, Erna; Mardiyana, Pramudya, Ikrar

2017-08-01

Geometry is the most important branch in mathematics. The purpose of teaching this material is to develop students' level of thinking for a better understanding. Otherwise, geometry in particular, has contributed students' failure in mathematics examinations. This problem occurs due to special feature in geometry which has complexity of correlation among its concept. This relates to mathematical connection. It is still difficult for students to improve this ability. This is because teachers' lack in facilitating students towards it. Eventhough, facilitating students can be in the form of teaching material. A learning module can be a solution because it consists of series activities that should be taken by students to achieve a certain goal. A series activities in this case is adopted by the phases of discovery-based learning model. Through this module, students are facilitated to discover concept by deep instruction and guidance. It can build the mathematical habits of mind and also strengthen the mathematical connection. Method used in this research was ten stages of research and development proposed by Bord and Gall. The research purpose is to create a valid learning module to improve students' mathematical connection in teaching quadrilateral. The retrieved valid module based on media expert judgment is 2,43 for eligibility chart aspect, 2,60 for eligibility presentation aspect, and 3,00 for eligibility contents aspect. Then the retrieved valid module based on material expert judgment is 3,10 for eligibility content aspect, 2,87 for eligibility presentation aspect, and 2,80 for eligibility language and legibility aspect.

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.

Mathematical model formulation and validation of water and solute transport in whole hamster pancreatic islets.

PubMed

Benson, James D; Benson, Charles T; Critser, John K

2014-08-01

Optimization of cryopreservation protocols for cells and tissues requires accurate models of heat and mass transport. Model selection often depends on the configuration of the tissue. Here, a mathematical and conceptual model of water and solute transport for whole hamster pancreatic islets has been developed and experimentally validated incorporating fundamental biophysical data from previous studies on individual hamster islet cells while retaining whole-islet structural information. It describes coupled transport of water and solutes through the islet by three methods: intracellularly, intercellularly, and in combination. In particular we use domain decomposition techniques to couple a transmembrane flux model with an interstitial mass transfer model. The only significant undetermined variable is the cellular surface area which is in contact with the intercellularly transported solutes, Ais. The model was validated and Ais determined using a 3×3 factorial experimental design blocked for experimental day. Whole islet physical experiments were compared with model predictions at three temperatures, three perfusing solutions, and three islet size groups. A mean of 4.4 islets were compared at each of the 27 experimental conditions and found to correlate with a coefficient of determination of 0.87±0.06 (mean ± SD). Only the treatment variable of perfusing solution was found to be significant (p<0.05). We have devised a model that retains much of the intrinsic geometric configuration of the system, and thus fewer laboratory experiments are needed to determine model parameters and thus to develop new optimized cryopreservation protocols. Additionally, extensions to ovarian follicles and other concentric tissue structures may be made. Copyright © 2014 Elsevier Inc. All rights reserved.

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.

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

ERIC Educational Resources Information Center

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

2016-01-01

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

Mathematical modeling for novel cancer drug discovery and development.

PubMed

Zhang, Ping; Brusic, Vladimir

2014-10-01

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

Mathematical model of the SH-3G helicopter

NASA Technical Reports Server (NTRS)

Phillips, J. D.

1982-01-01

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

A Mathematical Model for Reactions During Top-Blowing in the AOD Process: Validation and Results

NASA Astrophysics Data System (ADS)

Visuri, Ville-Valtteri; Järvinen, Mika; Kärnä, Aki; Sulasalmi, Petri; Heikkinen, Eetu-Pekka; Kupari, Pentti; Fabritius, Timo

2017-06-01

In earlier work, a fundamental mathematical model was proposed for side-blowing operation in the argon oxygen decarburization (AOD) process. In the preceding part "Derivation of the Model," a new mathematical model was proposed for reactions during top-blowing in the AOD process. In this model it was assumed that reactions occur simultaneously at the surface of the cavity caused by the gas jet and at the surface of the metal droplets ejected from the metal bath. This paper presents validation and preliminary results with twelve industrial heats. In the studied heats, the last combined-blowing stage was altered so that oxygen was introduced from the top lance only. Four heats were conducted using an oxygen-nitrogen mixture (1:1), while eight heats were conducted with pure oxygen. Simultaneously, nitrogen or argon gas was blown via tuyères in order to provide mixing that is comparable to regular practice. The measured carbon content varied from 0.4 to 0.5 wt pct before the studied stage to 0.1 to 0.2 wt pct after the studied stage. The results suggest that the model is capable of predicting changes in metal bath composition and temperature with a reasonably high degree of accuracy. The calculations indicate that the top slag may supply oxygen for decarburization during top-blowing. Furthermore, it is postulated that the metal droplets generated by the shear stress of top-blowing create a large mass exchange area, which plays an important role in enabling the high decarburization rates observed during top-blowing in the AOD process. The overall rate of decarburization attributable to top-blowing in the last combined-blowing stage was found to be limited by the mass transfer of dissolved carbon.

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…

Validation of an integrative mathematical model of dehydration and rehydration in virtual humans.

PubMed

Pruett, W Andrew; Clemmer, John S; Hester, Robert L

2016-11-01

Water homeostasis is one of the body's most critical tasks. Physical challenges to the body, including exercise and surgery, almost always coordinate with some change in water handling reflecting the changing needs of the body. Vasopressin is the most important hormone that contributes to short-term water homeostasis. By manipulating vascular tone and regulating water reabsorption in the collecting duct of the kidneys, vasopressin can mediate the retention or loss of fluids quickly. In this study, we validated HumMod, an integrative mathematical model of human physiology, against six different challenges to water homeostasis with special attention to the secretion of vasopressin and maintenance of electrolyte balance. The studies chosen were performed in normal men and women, and represent a broad spectrum of perturbations. HumMod successfully replicated the experimental results, remaining within 1 standard deviation of the experimental means in 138 of 161 measurements. Only three measurements lay outside of the second standard deviation. Observations were made on serum osmolarity, serum vasopressin concentration, serum sodium concentration, urine osmolarity, serum protein concentration, hematocrit, and cumulative water intake following dehydration. This validation suggests that HumMod can be used to understand water homeostasis under a variety of conditions. © 2016 The Authors. Physiological Reports published by Wiley Periodicals, Inc. on behalf of The Physiological Society and the American Physiological Society.

Development and external validation of new ultrasound-based mathematical models for preoperative prediction of high-risk endometrial cancer.

PubMed

Van Holsbeke, C; Ameye, L; Testa, A C; Mascilini, F; Lindqvist, P; Fischerova, D; Frühauf, F; Fransis, S; de Jonge, E; Timmerman, D; Epstein, E

2014-05-01

To develop and validate strategies, using new ultrasound-based mathematical models, for the prediction of high-risk endometrial cancer and compare them with strategies using previously developed models or the use of preoperative grading only. Women with endometrial cancer were prospectively examined using two-dimensional (2D) and three-dimensional (3D) gray-scale and color Doppler ultrasound imaging. More than 25 ultrasound, demographic and histological variables were analyzed. Two logistic regression models were developed: one 'objective' model using mainly objective variables; and one 'subjective' model including subjective variables (i.e. subjective impression of myometrial and cervical invasion, preoperative grade and demographic variables). The following strategies were validated: a one-step strategy using only preoperative grading and two-step strategies using preoperative grading as the first step and one of the new models, subjective assessment or previously developed models as a second step. One-hundred and twenty-five patients were included in the development set and 211 were included in the validation set. The 'objective' model retained preoperative grade and minimal tumor-free myometrium as variables. The 'subjective' model retained preoperative grade and subjective assessment of myometrial invasion. On external validation, the performance of the new models was similar to that on the development set. Sensitivity for the two-step strategy with the 'objective' model was 78% (95% CI, 69-84%) at a cut-off of 0.50, 82% (95% CI, 74-88%) for the strategy with the 'subjective' model and 83% (95% CI, 75-88%) for that with subjective assessment. Specificity was 68% (95% CI, 58-77%), 72% (95% CI, 62-80%) and 71% (95% CI, 61-79%) respectively. The two-step strategies detected up to twice as many high-risk cases as preoperative grading only. The new models had a significantly higher sensitivity than did previously developed models, at the same specificity. Two

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…

What Is Measured in Mathematics Tests? Construct Validity of Curriculum-Based Mathematics Measures.

ERIC Educational Resources Information Center

Thurber, Robin Schul; Shinn, Mark R.; Smolkowski, Keith

2002-01-01

Mathematics curriculum-based measurement (M-CBM) is one tool that has been developed for formative evaluation in mathematics. This study examines what constructs M-CBM actually measures in the context of a range of other mathematics measures. Results indicated that a two-factor model of mathematics where Computation and Applications were distinct…

Generalizability and Validity of a Mathematics Performance Assessment.

ERIC Educational Resources Information Center

Lane, Suzanne; And Others

1996-01-01

Evidence from test results of 3,604 sixth and seventh graders is provided for the generalizability and validity of the Quantitative Understanding: Amplifying Student Achievement and Reasoning (QUASAR) Cognitive Assessment Instrument, which is designed to measure program outcomes and growth in mathematics. (SLD)

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…

Development of Mathematics Course Attitude Scale: A Preliminary Study of Validity & Reliability

ERIC Educational Resources Information Center

Eskici, Menekse; Ilgaz, Gökhan; Aricak, Osman Tolga

2017-01-01

The aim of this research is to develop a Mathematics Course Attitude Scale to measure high school students' attitudes towards mathematics and to test the validity and reliability of this scale. It is also aimed to reveal whether there are significant differences in school students' attitudes towards mathematics according to their gender and…

Mathematical models for principles of gyroscope theory

NASA Astrophysics Data System (ADS)

Usubamatov, Ryspek

2017-01-01

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

A Scale for Measuring Teachers' Mathematics-Related Beliefs: A Validity and Reliability Study

ERIC Educational Resources Information Center

Purnomo,Yoppy Wahyu

2017-01-01

The purpose of this study was to develop and validate a scale of teacher beliefs related to mathematics, namely, beliefs about the nature of mathematics, mathematics teaching, and assessment in mathematics learning. A scale development study was used to achieve it. The draft scale consisted of 54 items in which 16 items related to beliefs about…

Mathematical models of ABE fermentation: review and analysis.

PubMed

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

2013-12-01

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

Grip Forces During Object Manipulation: Experiment, Mathematical Model & Validation

PubMed Central

Slota, Gregory P.; Latash, Mark L.; Zatsiorsky, Vladimir M.

2011-01-01

When people transport handheld objects, they change the grip force with the object movement. Circular movement patterns were tested within three planes at two different rates (1.0, 1.5 Hz), and two diameters (20, 40 cm). Subjects performed the task reasonably well, matching frequencies and dynamic ranges of accelerations within expectations. A mathematical model was designed to predict the applied normal forces from kinematic data. The model is based on two hypotheses: (a) the grip force changes during movements along complex trajectories can be represented as the sum of effects of two basic commands associated with the parallel and orthogonal manipulation, respectively; (b) different central commands are sent to the thumb and virtual finger (Vf- four fingers combined). The model predicted the actual normal forces with a total variance accounted for of better than 98%. The effects of the two components of acceleration—along the normal axis and the resultant acceleration within the shear plane—on the digit normal forces are additive. PMID:21735245

Mathematical Models of Breast and Ovarian Cancers

PubMed Central

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

2016-01-01

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

Validity-Supporting Evidence of the Self-Efficacy for Teaching Mathematics Instrument

ERIC Educational Resources Information Center

McGee, Jennifer R.; Wang, Chuang

2014-01-01

The purpose of this study is to provide evidence of reliability and validity of the Self-Efficacy for Teaching Mathematics Instrument (SETMI). Self-efficacy, as defined by Bandura, was the theoretical framework for the development of the instrument. The complex belief systems of mathematics teachers, as touted by Ernest provided insights into the…

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…

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

Investigating the incremental validity of cognitive variables in early mathematics screening.

PubMed

Clarke, Ben; Shanley, Lina; Kosty, Derek; Baker, Scott K; Cary, Mari Strand; Fien, Hank; Smolkowski, Keith

2018-03-26

The purpose of this study was to investigate the incremental validity of a set of domain general cognitive measures added to a traditional screening battery of early numeracy measures. The sample consisted of 458 kindergarten students of whom 285 were designated as severely at-risk for mathematics difficulty. Hierarchical multiple regression results indicated that Wechsler Abbreviated Scales of Intelligence (WASI) Matrix Reasoning and Vocabulary subtests, and Digit Span Forward and Backward measures explained a small, but unique portion of the variance in kindergarten students' mathematics performance on the Test of Early Mathematics Ability-Third Edition (TEMA-3) when controlling for Early Numeracy Curriculum Based Measurement (EN-CBM) screening measures (R² change = .01). Furthermore, the incremental validity of the domain general cognitive measures was relatively stronger for the severely at-risk sample. We discuss results from the study in light of instructional decision-making and note the findings do not justify adding domain general cognitive assessments to mathematics screening batteries. (PsycINFO Database Record (c) 2018 APA, all rights reserved).

Reactant conversion in homogeneous turbulence: Mathematical modeling, computational validations and practical applications

NASA Technical Reports Server (NTRS)

Madnia, C. K.; Frankel, S. H.; Givi, P.

1992-01-01

Closed form analytical expressions are obtained for predicting the limited rate of reactant conversion in a binary reaction of the type F + rO yields (1 + r) Product in unpremixed homogeneous turbulence. These relations are obtained by means of a single point Probability Density Function (PDF) method based on the Amplitude Mapping Closure. It is demonstrated that with this model, the maximum rate of the reactants' decay can be conveniently expressed in terms of definite integrals of the Parabolic Cylinder Functions. For the cases with complete initial segregation, it is shown that the results agree very closely with those predicted by employing a Beta density of the first kind for an appropriately defined Shvab-Zeldovich scalar variable. With this assumption, the final results can also be expressed in terms of closed form analytical expressions which are based on the Incomplete Beta Functions. With both models, the dependence of the results on the stoichiometric coefficient and the equivalence ratio can be expressed in an explicit manner. For a stoichiometric mixture, the analytical results simplify significantly. In the mapping closure, these results are expressed in terms of simple trigonometric functions. For the Beta density model, they are in the form of Gamma Functions. In all the cases considered, the results are shown to agree well with data generated by Direct Numerical Simulations (DNS). Due to the simplicity of these expressions and because of nice mathematical features of the Parabolic Cylinder and the Incomplete Beta Functions, these models are recommended for estimating the limiting rate of reactant conversion in homogeneous reacting flows. These results also provide useful insights in assessing the extent of validity of turbulence closures in the modeling of unpremixed reacting flows. Some discussions are provided on the extension of the model for treating more complicated reacting systems including realistic kinetics schemes and multi-scalar mixing

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

PubMed Central

Ay, Ahmet; Arnosti, David N.

2011-01-01

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

Comparative Validity of the Descriptive Tests of Mathematical Skills (DTMS) and SAT-Mathematics (SAT-M) for Predicting Performance in Freshman College Mathematics Courses: Prefatory Report

ERIC Educational Resources Information Center

McLoughlin, M. Padraig M. M.; Bluford, Dontrell A.

2004-01-01

This study investigated the predictive validity of the Descriptive Tests of Mathematical Skills (DTMS) and the SAT-Mathematics (SAT-M) tests as placement tools for entering students in a small, liberal arts, historically black institution (HBI) using regression analysis. The placement schema is four-tiered: for a remedial algebra course, college…

Mathematical model of glucose-insulin homeostasis in healthy rats.

PubMed

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

2013-10-01

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

Validation of the replica trick for simple models

NASA Astrophysics Data System (ADS)

Shinzato, Takashi

2018-04-01

We discuss the replica analytic continuation using several simple models in order to prove mathematically the validity of the replica analysis, which is used in a wide range of fields related to large-scale complex systems. While replica analysis consists of two analytical techniques—the replica trick (or replica analytic continuation) and the thermodynamical limit (and/or order parameter expansion)—we focus our study on replica analytic continuation, which is the mathematical basis of the replica trick. We apply replica analysis to solve a variety of analytical models, and examine the properties of replica analytic continuation. Based on the positive results for these models we propose that replica analytic continuation is a robust procedure in replica analysis.

Economic analysis of model validation for a challenge problem

DOE PAGES

Paez, Paul J.; Paez, Thomas L.; Hasselman, Timothy K.

2016-02-19

It is now commonplace for engineers to build mathematical models of the systems they are designing, building, or testing. And, it is nearly universally accepted that phenomenological models of physical systems must be validated prior to use for prediction in consequential scenarios. Yet, there are certain situations in which testing only or no testing and no modeling may be economically viable alternatives to modeling and its associated testing. This paper develops an economic framework within which benefit–cost can be evaluated for modeling and model validation relative to other options. The development is presented in terms of a challenge problem. Asmore » a result, we provide a numerical example that quantifies when modeling, calibration, and validation yield higher benefit–cost than a testing only or no modeling and no testing option.« less

Beliefs and Gender Differences: A New Model for Research in Mathematics Education

ERIC Educational Resources Information Center

Li, Qing

2004-01-01

The major focus of this study is to propose a new research model, namely the Modified CGI gender model, for the study of gender differences in mathematics. This model is developed based on Fennema, Carpenter, and Peterson's (1989) CGI model. To examine the validity of this new model, this study also examines the gender differences in teacher and…

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…

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…

Structural equation modeling assessing relationship between mathematics beliefs, teachers' attitudes and teaching practices among novice teachers in Malaysia

NASA Astrophysics Data System (ADS)

Borhan, Noziati; Zakaria, Effandi

2017-05-01

This quantitative study was conducted to investigate the perception level of novice teachers about mathematics belief, teachers' attitude towards mathematics and teaching practices of mathematics in the classroom. In addition, it also aims to identify whether there is a correspondence model with the data obtained and to identify the relationship between the variables of beliefs, attitudes and practices among novice teachers in Malaysia. A total of 263 primary novice teachers throughout the country were involved in this study were selected randomly. Respondents are required to provide a response to the questionnaire of 66 items related to mathematics beliefs, attitudes and practices of the teaching mathematics. There are ten sub-factors which have been established in this instrument for three major constructs using a Likert scale rating of five points. The items of the constructs undergo the exploratory factor analysis (EFA) and confirmatory factor analysis (CFA) procedure involve of unidimensionality test, convergent validity, construct validity and discriminant validity. Descriptive statistics were used to describe the frequency, percentage, the mean and standard deviation for completing some research questions that have been expressed. As for inferential statistical analysis, the researchers used structural equation modeling (SEM) to answer the question of correspondents model and the relationship between these three variables. The results of the study were found that there exist a correspondence measurement and structural model with the data obtained. While the relationship between variable found that mathematics beliefs have a significant influence on teachers' attitudes towards mathematics as well as the relationship between the attitudes with teaching practices. Meanwhile, mathematics belief had no significant relationship with mathematics teaching practices among novice teachers in Malaysia.

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…

Numerical modeling and preliminary validation of drag-based vertical axis wind turbine

NASA Astrophysics Data System (ADS)

Krysiński, Tomasz; Buliński, Zbigniew; Nowak, Andrzej J.

2015-03-01

The main purpose of this article is to verify and validate the mathematical description of the airflow around a wind turbine with vertical axis of rotation, which could be considered as representative for this type of devices. Mathematical modeling of the airflow around wind turbines in particular those with the vertical axis is a problematic matter due to the complex nature of this highly swirled flow. Moreover, it is turbulent flow accompanied by a rotation of the rotor and the dynamic boundary layer separation. In such conditions, the key aspects of the mathematical model are accurate turbulence description, definition of circular motion as well as accompanying effects like centrifugal force or the Coriolis force and parameters of spatial and temporal discretization. The paper presents the impact of the different simulation parameters on the obtained results of the wind turbine simulation. Analysed models have been validated against experimental data published in the literature.

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.

The 24-Hour Mathematical Modeling Challenge

ERIC Educational Resources Information Center

Galluzzo, Benjamin J.; Wendt, Theodore J.

2015-01-01

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

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

ERIC Educational Resources Information Center

Suppes, Patrick

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

Mathematical 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.

Mathematical Modeling and Experimental Validation of Nanoemulsion-Based Drug Transport across Cellular Barriers.

PubMed

Kadakia, Ekta; Shah, Lipa; Amiji, Mansoor M

2017-07-01

Nanoemulsions have shown potential in delivering drug across epithelial and endothelial cell barriers, which express efflux transporters. However, their transport mechanisms are not entirely understood. Our goal was to investigate the cellular permeability of nanoemulsion-encapsulated drugs and apply mathematical modeling to elucidate transport mechanisms and sensitive nanoemulsion attributes. Transport studies were performed in Caco-2 cells, using fish oil nanoemulsions and a model substrate, rhodamine-123. Permeability data was modeled using a semi-mechanistic approach, capturing the following cellular processes: endocytotic uptake of the nanoemulsion, release of rhodamine-123 from the nanoemulsion, efflux and passive permeability of rhodamine-123 in aqueous solution. Nanoemulsions not only improved the permeability of rhodamine-123, but were also less sensitive to efflux transporters. The model captured bidirectional permeability results and identified sensitive processes, such as the release of the nanoemulsion-encapsulated drug and cellular uptake of the nanoemulsion. Mathematical description of cellular processes, improved our understanding of transport mechanisms, such as nanoemulsions don't inhibit efflux to improve drug permeability. Instead, their endocytotic uptake, results in higher intracellular drug concentrations, thereby increasing the concentration gradient and transcellular permeability across biological barriers. Modeling results indicated optimizing nanoemulsion attributes like the droplet size and intracellular drug release rate, may further improve drug permeability.

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…

Development and validation of a mathematical model for growth of pathogens in cut melons.

PubMed

Li, Di; Friedrich, Loretta M; Danyluk, Michelle D; Harris, Linda J; Schaffner, Donald W

2013-06-01

Many outbreaks of foodborne illness associated with the consumption of fresh-cut melons have been reported. The objective of our research was to develop a mathematical model that predicts the growth rate of Salmonella on fresh-cut cantaloupe over a range of storage temperatures and to validate that model by using Salmonella and Escherichia coli O157:H7 on cantaloupe, honeydew, and watermelon, using both new data and data from the published studies. The growth of Salmonella on honeydew and watermelon and E. coli O157:H7 on cantaloupe, honeydew, and watermelon was monitored at temperatures of 4 to 25°C. The Ratkowsky (or square-root model) was used to describe Salmonella growth on cantaloupe as a function of storage temperature. Our results show that the levels of Salmonella on fresh-cut cantaloupe with an initial load of 3 log CFU/g can reach over 7 log CFU/g at 25°C within 24 h. No growth was observed at 4°C. A linear correlation was observed between the square root of Salmonella growth rate and temperature, such that √growth rate = 0.026 × (T - 5.613), R(2) = 0.9779. The model was generally suitable for predicting the growth of both Salmonella and E. coli O157:H7 on cantaloupe, honeydew, and watermelon, for both new data and data from the published literature. When compared with existing models for growth of Salmonella, the new model predicts a theoretic minimum growth temperature similar to the ComBase Predictive Models and Pathogen Modeling Program models but lower than other food-specific models. The ComBase Prediction Models results are very similar to the model developed in this study. Our research confirms that Salmonella can grow quickly and reach high concentrations when cut cantaloupe is stored at ambient temperatures, without visual signs of spoilage. Our model provides a fast and cost-effective method to estimate the effects of storage temperature on fresh-cut melon safety and could also be used in subsequent quantitative microbial risk

Developing and Validating Proof Comprehension Tests in Undergraduate Mathematics

ERIC Educational Resources Information Center

Mejía-Ramos, Juan Pablo; Lew, Kristen; de la Torre, Jimmy; Weber, Keith

2017-01-01

In this article, we describe and illustrate the process by which we developed and validated short, multiple-choice, reliable tests to assess undergraduate students' comprehension of three mathematical proofs. We discuss the purpose for each stage and how it benefited the design of our instruments. We also suggest ways in which this process could…

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…

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

ERIC Educational Resources Information Center

Lowe, James; Carter, Merilyn; Cooper, Tom

2018-01-01

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

Mathematical Modeling: Convoying Merchant Ships

ERIC Educational Resources Information Center

Mathews, Susann M.

2004-01-01

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

A Primer for Mathematical Modeling

ERIC Educational Resources Information Center

Sole, Marla

2013-01-01

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

A model of professional competences in mathematics to update mathematical and didactic knowledge of teachers

NASA Astrophysics Data System (ADS)

Díaz, Verónica; Poblete, Alvaro

2017-07-01

This paper describes part of a research and development project carried out in public elementary schools. Its objective was to update the mathematical and didactic knowledge of teachers in two consecutive levels in urban and rural public schools of Region de Los Lagos and Region de Los Rios of southern Chile. To that effect, and by means of an advanced training project based on a professional competences model, didactic interventions based on types of problems and types of mathematical competences with analysis of contents and learning assessment were designed. The teachers' competence regarding the didactic strategy used and its results, as well as the students' learning achievements are specified. The project made possible to validate a strategy of lifelong improvement in mathematics, based on the professional competences of teachers and their didactic transposition in the classroom, as an alternative to consolidate learning in areas considered vulnerable in two regions of the country.

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…

A Mathematical Diet Model

ERIC Educational Resources Information Center

Toumasis, Charalampos

2004-01-01

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

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

PubMed

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

2018-01-01

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

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…

Development and Validation of an Instrument for Assessing Mathematics Classroom Environment in Tertiary Institutions

ERIC Educational Resources Information Center

Yin, Hongbiao; Lu, Genshu

2014-01-01

This report describes the development and validation of an instrument, the University Mathematics Classroom Environment Questionnaire (UMCEQ), for assessing the mathematics classroom environment in tertiary institutions in China. Through the use of multiple methods, including exploratory and confirmatory factor analyses, on two independent samples…

Mathematical model of the metabolism of 123I-16-iodo-9-hexadecenoic acid in an isolated rat heart. Validation by comparison with experimental measurements.

PubMed

Dubois, F; Depresseux, J C; Bontemps, L; Demaison, L; Keriel, C; Mathieu, J P; Pernin, C; Marti-Batlle, D; Vidal, M; Cuchet, P

1986-01-01

The aim of the present study was to demonstrate that it is possible to estimate the intracellular metabolism of a fatty acid labelled with iodine using external radioactivity measurements. 123I-16-iodo-9-hexadecenoic acid (IHA) was injected close to the coronary arteries of isolated rat hearts perfused according to the Langendorff technique. The time course of the cardiac radioactivity was measured using an INa crystal coupled to an analyser. The obtained curves were analysed using a four-compartment mathematical model, with the compartments corresponding to the vascular-IHA (O), intramyocardial free-IHA (1), esterified-IHA (2) and iodide (3) pools. Curve analysis using this model demonstrated that, as compared to substrate-free perfusion, the presence of glucose (11 mM) increased IHA storage and decreased its oxidation. These changes were enhanced by the presence of insulin. A comparison of these results with measurements of the radioactivity levels within the various cellular fractions validated our proposed mathematical model. Thus, using only a mathematical analysis of a cardiac time-activity curve, it is possible to obtain quantitative information about IHA distribution in the different intracellular metabolic pathways. This technique is potentially useful for the study of metabolic effects of ischaemia or anoxia, as well as for the study of the influence of various substrates or drugs on IHA metabolism in isolated rat hearts.

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…

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

PubMed Central

Gupta, Raj K.; Przekwas, Andrzej

2013-01-01

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

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

NASA Astrophysics Data System (ADS)

Pyt'ev, Yu. P.

2018-01-01

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

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

NASA Astrophysics Data System (ADS)

Sokolowski, Andrzej; Yalvac, Bugrahan; Loving, Cathleen

2011-04-01

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

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…

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

Mathematical Modeling of Rotary Blood Pumps in a Pulsatile In Vitro Flow Environment.

PubMed

Pirbodaghi, Tohid

2017-08-01

Nowadays, sacrificing animals to develop medical devices and receive regulatory approval has become more common, which increases ethical concerns. Although in vivo tests are necessary for development and evaluation of new devices, nonetheless, with appropriate in vitro setups and mathematical models, a part of the validation process can be performed using these models to reduce the number of sacrificed animals. The main aim of this study is to present a mathematical model simulating the hydrodynamic function of a rotary blood pump (RBP) in a pulsatile in vitro flow environment. This model relates the pressure head of the RBP to the flow rate, rotational speed, and time derivatives of flow rate and rotational speed. To identify the model parameters, an in vitro setup was constructed consisting of a piston pump, a compliance chamber, a throttle, a buffer reservoir, and the CentriMag RBP. A 40% glycerin-water mixture as a blood analog fluid and deionized water were used in the hydraulic circuit to investigate the effect of viscosity and density of the working fluid on the model parameters. First, model variables were physically measured and digitally acquired. Second, an identification algorithm based on regression analysis was used to derive the model parameters. Third, the completed model was validated with a totally different set of in vitro data. The model is usable for both mathematical simulations of the interaction between the pump and heart and indirect pressure measurement in a clinical context. © 2017 International Center for Artificial Organs and Transplantation and Wiley Periodicals, Inc.

Mathematical models for plant-herbivore interactions

USGS Publications Warehouse

Feng, Zhilan; DeAngelis, Donald L.

2017-01-01

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

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.

Mathematical modeling analysis of intratumoral disposition of anticancer agents and drug delivery systems.

PubMed

Popilski, Hen; Stepensky, David

2015-05-01

Solid tumors are characterized by complex morphology. Numerous factors relating to the composition of the cells and tumor stroma, vascularization and drainage of fluids affect the local microenvironment within a specific location inside the tumor. As a result, the intratumoral drug/drug delivery system (DDS) disposition following systemic or local administration is non-homogeneous and its complexity reflects the differences in the local microenvironment. Mathematical models can be used to analyze the intratumoral drug/DDS disposition and pharmacological effects and to assist in choice of optimal anticancer treatment strategies. The mathematical models that have been applied by different research groups to describe the intratumoral disposition of anticancer drugs/DDSs are summarized in this article. The properties of these models and of their suitability for prediction of the drug/DDS intratumoral disposition and pharmacological effects are reviewed. Currently available mathematical models appear to neglect some of the major factors that govern the drug/DDS intratumoral disposition, and apparently possess limited prediction capabilities. More sophisticated and detailed mathematical models and their extensive validation are needed for reliable prediction of different treatment scenarios and for optimization of drug treatment in the individual cancer patients.

Genetic programming-based mathematical modeling of influence of weather parameters in BOD5 removal by Lemna minor.

PubMed

Chandrasekaran, Sivapragasam; Sankararajan, Vanitha; Neelakandhan, Nampoothiri; Ram Kumar, Mahalakshmi

2017-11-04

This study, through extensive experiments and mathematical modeling, reveals that other than retention time and wastewater temperature (T w ), atmospheric parameters also play important role in the effective functioning of aquatic macrophyte-based treatment system. Duckweed species Lemna minor is considered in this study. It is observed that the combined effect of atmospheric temperature (T atm ), wind speed (U w ), and relative humidity (RH) can be reflected through one parameter, namely the "apparent temperature" (T a ). A total of eight different models are considered based on the combination of input parameters and the best mathematical model is arrived at which is validated through a new experimental set-up outside the modeling period. The validation results are highly encouraging. Genetic programming (GP)-based models are found to reveal deeper understandings of the wetland process.

Developing CORE model-based worksheet with recitation task to facilitate students’ mathematical communication skills in linear algebra course

NASA Astrophysics Data System (ADS)

Risnawati; Khairinnisa, S.; Darwis, A. H.

2018-01-01

The purpose of this study was to develop a CORE model-based worksheet with recitation task that were valid and practical and could facilitate students’ communication skills in Linear Algebra course. This study was conducted in mathematics education department of one public university in Riau, Indonesia. Participants of the study were media and subject matter experts as validators as well as students from mathematics education department. The objects of this study are students’ worksheet and students’ mathematical communication skills. The results of study showed that: (1) based on validation of the experts, the developed students’ worksheet was valid and could be applied for students in Linear Algebra courses; (2) based on the group trial, the practicality percentage was 92.14% in small group and 90.19% in large group, so the worksheet was very practical and could attract students to learn; and (3) based on the post test, the average percentage of ideals was 87.83%. In addition, the results showed that the students’ worksheet was able to facilitate students’ mathematical communication skills in linear algebra course.

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…

Developing the Irrational Beliefs in Mathematics Scale (IBIMS): A Validity and Reliability Study

ERIC Educational Resources Information Center

Kaya, Deniz

2017-01-01

The purpose of this study is developing a valid and reliable scale intended to determine the irrational beliefs of students in mathematics. The study was conducted with a study group consisting of 700 students in 2015-2016 academic year. Expert opinions were received for the content and face validity of the scale, and the Exploratory Factor…

Mathematical model of water transport in Bacon and alkaline matrix-type hydrogen-oxygen fuel cells

NASA Technical Reports Server (NTRS)

Prokopius, P. R.; Easter, R. W.

1972-01-01

Based on general mass continuity and diffusive transport equations, a mathematical model was developed that simulates the transport of water in Bacon and alkaline-matrix fuel cells. The derived model was validated by using it to analytically reproduce various Bacon and matrix-cell experimental water transport transients.

Comprehensive mathematical model of oxidative phosphorylation valid for physiological and pathological conditions.

PubMed

Heiske, Margit; Letellier, Thierry; Klipp, Edda

2017-09-01

We developed a mathematical model of oxidative phosphorylation (OXPHOS) that allows for a precise description of mitochondrial function with respect to the respiratory flux and the ATP production. The model reproduced flux-force relationships under various experimental conditions (state 3 and 4, uncoupling, and shortage of respiratory substrate) as well as time courses, exhibiting correct P/O ratios. The model was able to reproduce experimental threshold curves for perturbations of the respiratory chain complexes, the F 1 F 0 -ATP synthase, the ADP/ATP carrier, the phosphate/OH carrier, and the proton leak. Thus, the model is well suited to study complex interactions within the OXPHOS system, especially with respect to physiological adaptations or pathological modifications, influencing substrate and product affinities or maximal catalytic rates. Moreover, it could be a useful tool to study the role of OXPHOS and its capacity to compensate or enhance physiopathologies of the mitochondrial and cellular energy metabolism. © 2017 Federation of European Biochemical Societies.

Examining Validity of Sources of Mathematics Self-Efficacy Scale in Turkey

ERIC Educational Resources Information Center

Kandemir, Mehmet Ali; Akbas-Perkmen, Rahile

2017-01-01

The main purpose of the current study is to examine the construct, convergent and discriminant validity of the Sources of Mathematics Self-Efficacy Scale (Usher & Pajares, 2009) in a Turkish sample. Bandura's Social Cognitive Theory (1986) served as the theoretical framework for the current study. According to Bandura (1986), people's…

Investigating the Incremental Validity of Cognitive Variables in Early Mathematics Screening

ERIC Educational Resources Information Center

Clarke, Ben; Shanley, Lina; Kosty, Derek; Baker, Scott K.; Cary, Mari Strand; Fien, Hank; Smolkowski, Keith

2018-01-01

The purpose of this study was to investigate the incremental validity of a set of domain general cognitive measures added to a traditional screening battery of early numeracy measures. The sample consisted of 458 kindergarten students of whom 285 were designated as severely at-risk for mathematics difficulty. Hierarchical multiple regression…

Predictive modeling of infrared radiative heating in tomato dry-peeling process: Part II. Model validation and sensitivity analysis

USDA-ARS?s Scientific Manuscript database

A predictive mathematical model was developed to simulate heat transfer in a tomato undergoing double sided infrared (IR) heating in a dry-peeling process. The aims of this study were to validate the developed model using experimental data and to investigate different engineering parameters that mos...

Mathematical Modeling and Computational Thinking

ERIC Educational Resources Information Center

Sanford, John F.; Naidu, Jaideep T.

2017-01-01

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

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…

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…

Internal consistency reliability and validity of the Arabic translation of the Mathematics Teaching Efficacy Beliefs Instrument.

PubMed

Alkhateeb, Haitham M

2004-06-01

The Arabic translation of the Mathematics Teaching Efficacy Beliefs was completed by 144 undergraduate students (M age=20.6) in Jordan. The findings support the internal reliability of the Arabic translation of the Mathematics Teaching Efficacy Beliefs as well as its construct validity.

Explorations in Elementary Mathematical Modeling

ERIC Educational Resources Information Center

Shahin, Mazen

2010-01-01

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

Mathematical models of cell motility.

PubMed

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

2007-01-01

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

A mathematical model for ethanol fermentation from oil palm trunk sap using Saccharomyces cerevisiae

NASA Astrophysics Data System (ADS)

Sultana, S.; Jamil, Norazaliza Mohd; Saleh, E. A. M.; Yousuf, A.; Faizal, Che Ku M.

2017-09-01

This paper presents a mathematical model and solution strategy of ethanol fermentation for oil palm trunk (OPT) sap by considering the effect of substrate limitation, substrate inhibition product inhibition and cell death. To investigate the effect of cell death rate on the fermentation process we extended and improved the current mathematical model. The kinetic parameters of the model were determined by nonlinear regression using maximum likelihood function. The temporal profiles of sugar, cell and ethanol concentrations were modelled by a set of ordinary differential equations, which were solved numerically by the 4th order Runge-Kutta method. The model was validated by the experimental data and the agreement between the model and experimental results demonstrates that the model is reasonable for prediction of the dynamic behaviour of the fermentation process.

Mathematical Modeling of Diverse Phenomena

NASA Technical Reports Server (NTRS)

Howard, J. C.

1979-01-01

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

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…

Experimentally validated mathematical model of analyte uptake by permeation passive samplers.

PubMed

Salim, F; Ioannidis, M; Górecki, T

2017-11-15

A mathematical model describing the sampling process in a permeation-based passive sampler was developed and evaluated numerically. The model was applied to the Waterloo Membrane Sampler (WMS), which employs a polydimethylsiloxane (PDMS) membrane as a permeation barrier, and an adsorbent as a receiving phase. Samplers of this kind are used for sampling volatile organic compounds (VOC) from air and soil gas. The model predicts the spatio-temporal variation of sorbed and free analyte concentrations within the sampler components (membrane, sorbent bed and dead volume), from which the uptake rate throughout the sampling process can be determined. A gradual decline in the uptake rate during the sampling process is predicted, which is more pronounced when sampling higher concentrations. Decline of the uptake rate can be attributed to diminishing analyte concentration gradient within the membrane, which results from resistance to mass transfer and the development of analyte concentration gradients within the sorbent bed. The effects of changing the sampler component dimensions on the rate of this decline in the uptake rate can be predicted from the model. Performance of the model was evaluated experimentally for sampling of toluene vapors under controlled conditions. The model predictions proved close to the experimental values. The model provides a valuable tool to predict changes in the uptake rate during sampling, to assign suitable exposure times at different analyte concentration levels, and to optimize the dimensions of the sampler in a manner that minimizes these changes during the sampling period.

An integrated mathematical model of the human cardiopulmonary system: model development.

PubMed

Albanese, Antonio; Cheng, Limei; Ursino, Mauro; Chbat, Nicolas W

2016-04-01

Several cardiovascular and pulmonary models have been proposed in the last few decades. However, very few have addressed the interactions between these two systems. Our group has developed an integrated cardiopulmonary model (CP Model) that mathematically describes the interactions between the cardiovascular and respiratory systems, along with their main short-term control mechanisms. The model has been compared with human and animal data taken from published literature. Due to the volume of the work, the paper is divided in two parts. The present paper is on model development and normophysiology, whereas the second is on the model's validation on hypoxic and hypercapnic conditions. The CP Model incorporates cardiovascular circulation, respiratory mechanics, tissue and alveolar gas exchange, as well as short-term neural control mechanisms acting on both the cardiovascular and the respiratory functions. The model is able to simulate physiological variables typically observed in adult humans under normal and pathological conditions and to explain the underlying mechanisms and dynamics. Copyright © 2016 the American Physiological Society.

Improvement of mathematical models for simulation of vehicle handling : volume 7 : technical manual for the general simulation

DOT National Transportation Integrated Search

1980-03-01

This volume is the technical manual for the general simulation. Mathematical modelling of the vehicle and of the human driver is presented in detail, as are differences between the APL simulation and the current one. Information on model validation a...

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

PubMed

Umulis, David M; Othmer, Hans G

2015-05-01

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

Mathematical modeling of fluid flow in aluminum ladles for degasification with impeller - injector

NASA Astrophysics Data System (ADS)

Ramos-Gómez, E.; González-Rivera, C.; Ramírez-Argáez, M. A.

2012-09-01

In this work a fundamental Eulerian mathematical model was developed to simulate fluid flow in a water physical model of an aluminum ladle equipped with impeller for degassing treatment. The effect of critical process parameters such as rotor speed, gas flow rate on the fluid flow and vortex formation was analyzed with this model. Commercial CFD code PHOENICS 3.4 was used to solve all conservation equations governing the process for this twophase fluid flow system. The mathematical model was successfully validated against experimentally measured liquid velocity and turbulent profiles in a physical model. From the results it was concluded that the angular speed of the impeller is the most important parameter promoting better stirred baths. Pumping effect of the impeller is increased as impeller rotation speed increases. Gas flow rate is detrimental on bath stirring and diminishes pumping effect of impeller.

Incorporating neurophysiological concepts in mathematical thermoregulation models

NASA Astrophysics Data System (ADS)

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

2014-01-01

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

Validation of Fatigue Modeling Predictions in Aviation Operations

NASA Technical Reports Server (NTRS)

Gregory, Kevin; Martinez, Siera; Flynn-Evans, Erin

2017-01-01

Bio-mathematical fatigue models that predict levels of alertness and performance are one potential tool for use within integrated fatigue risk management approaches. A number of models have been developed that provide predictions based on acute and chronic sleep loss, circadian desynchronization, and sleep inertia. Some are publicly available and gaining traction in settings such as commercial aviation as a means of evaluating flight crew schedules for potential fatigue-related risks. Yet, most models have not been rigorously evaluated and independently validated for the operations to which they are being applied and many users are not fully aware of the limitations in which model results should be interpreted and applied.

Mathematical modeling of fluxgate magnetic gradiometers

NASA Astrophysics Data System (ADS)

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

2017-07-01

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

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.

Validation the use of refractometer and mathematic equations to measure dietary formula contents for clinical application.

PubMed

Chang, W-K; Chao, Y-C; Mcclave, S-A; Yeh, M-K

2005-10-01

Gastric residual volumes are widely used to evaluate gastric emptying for patients receiving enteral feeding, but controversy exists about what constitutes gastric residual volume. We have developed a method by using refractometer and derived mathematical equations to calculate the formula concentration, total residual volume (TRV), and formula volume. In this study, we like to validate these mathematical equations before they can be implemented for clinical patient care. Four dietary formulas were evaluated in two consecutive validation experiments. Firstly, dietary formula volume of 50, 100, 200, and 400 ml were diluted with 50 ml water, and then the Brix value (BV) was measured by the refractometer. Secondly, 50 ml of water, then 100 ml of dietary formula were infused into a beaker, and followed by the BV measurement. After this, 50 ml of water was infused and followed by the second BV measurement. The entire procedure of infusing of dietary formula (100 ml) and waster (50 ml) was repeated twice and followed by the BV measurement. The formula contents (formula concentration, TRV, and formula volume) were calculated by mathematical equations. The calculated formula concentrations, TRVs, and formula volumes measured from mathematic equations were strongly close to the true values in the first and second validation experiments (R2>0.98, P<0.001). Refractometer and the derived mathematical equations may be used to accurately measure the formula concentration, TRV, and formula volume and served as a tool to monitor gastric emptying for patients receiving enteral feeding.

Opinions of Secondary School Mathematics Teachers on Mathematical Modelling

ERIC Educational Resources Information Center

Tutak, Tayfun; Güder, Yunus

2013-01-01

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

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…

A mathematical model for simulating noise suppression of lined ejectors

NASA Technical Reports Server (NTRS)

Watson, Willie R.

1994-01-01

A mathematical model containing the essential features embodied in the noise suppression of lined ejectors is presented. Although some simplification of the physics is necessary to render the model mathematically tractable, the current model is the most versatile and technologically advanced at the current time. A system of linearized equations and the boundary conditions governing the sound field are derived starting from the equations of fluid dynamics. A nonreflecting boundary condition is developed. In view of the complex nature of the equations, a parametric study requires the use of numerical techniques and modern computers. A finite element algorithm that solves the differential equations coupled with the boundary condition is then introduced. The numerical method results in a matrix equation with several hundred thousand degrees of freedom that is solved efficiently on a supercomputer. The model is validated by comparing results either with exact solutions or with approximate solutions from other works. In each case, excellent correlations are obtained. The usefulness of the model as an optimization tool and the importance of variable impedance liners as a mechanism for achieving broadband suppression within a lined ejector are demonstrated.

Current problems in applied mathematics and mathematical modeling

NASA Astrophysics Data System (ADS)

Alekseev, A. S.

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

Mathematical Models for Doppler Measurements

NASA Technical Reports Server (NTRS)

Lear, William M.

1987-01-01

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

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.…

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…

Mathematical form models of tree trunks

Treesearch

Rudolfs Ozolins

2000-01-01

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

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.

Mathematical Modelling as a Professional Task

ERIC Educational Resources Information Center

Frejd, Peter; Bergsten, Christer

2016-01-01

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

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…

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…

The Role of Mathematical Models in Understanding Pattern Formation in Developmental Biology

PubMed Central

Umulis, David M.

2016-01-01

In a Wall Street Journal article published on April 5, 2013, E. O. Wilson attempted to make the case that biologists do not really need to learn any mathematics—whenever they run into difficulty with numerical issues, they can find a technician (aka mathematician) to help them out of their difficulty. He formalizes this in Wilsons Principle No. 1: “It is far easier for scientists to acquire needed collaboration from mathematicians and statisticians than it is for mathematicians and statisticians to find scientists able to make use of their equations.” This reflects a complete misunderstanding of the role of mathematics in all sciences throughout history. To Wilson, mathematics is mere number crunching, but as Galileo said long ago, “The laws of Nature are written in the language of mathematics…the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word.” Mathematics has moved beyond the geometry-based model of Galileo’s time, and in a rebuttal to Wilson, E. Frenkel has pointed out the role of mathematics in synthesizing the general principles in science (Both point and counter-point are available in Wilson and Frenkel in Notices Am Math Soc 60(7):837–838, 2013). We will take this a step further and show how mathematics has been used to make new and experimentally verified discoveries in developmental biology and how mathematics is essential for understanding a problem that has puzzled experimentalists for decades—that of how organisms can scale in size. Mathematical analysis alone cannot “solve” these problems since the validation lies at the molecular level, but conversely, a growing number of questions in biology cannot be solved without mathematical analysis and modeling. Herein, we discuss a few examples of the productive intercourse between mathematics and biology. PMID:25280665

Automatic mathematical modeling for space application

NASA Technical Reports Server (NTRS)

Wang, Caroline K.

1987-01-01

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

On Fences, Forms and Mathematical Modeling

ERIC Educational Resources Information Center

Lege, Jerry

2009-01-01

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

A qualitatively validated mathematical-computational model of the immune response to the yellow fever vaccine.

PubMed

Bonin, Carla R B; Fernandes, Guilherme C; Dos Santos, Rodrigo W; Lobosco, Marcelo

2018-05-25

Although a safe and effective yellow fever vaccine was developed more than 80 years ago, several issues regarding its use remain unclear. For example, what is the minimum dose that can provide immunity against the disease? A useful tool that can help researchers answer this and other related questions is a computational simulator that implements a mathematical model describing the human immune response to vaccination against yellow fever. This work uses a system of ten ordinary differential equations to represent a few important populations in the response process generated by the body after vaccination. The main populations include viruses, APCs, CD8+ T cells, short-lived and long-lived plasma cells, B cells and antibodies. In order to qualitatively validate our model, four experiments were carried out, and their computational results were compared to experimental data obtained from the literature. The four experiments were: a) simulation of a scenario in which an individual was vaccinated against yellow fever for the first time; b) simulation of a booster dose ten years after the first dose; c) simulation of the immune response to the yellow fever vaccine in individuals with different levels of naïve CD8+ T cells; and d) simulation of the immune response to distinct doses of the yellow fever vaccine. This work shows that the simulator was able to qualitatively reproduce some of the experimental results reported in the literature, such as the amount of antibodies and viremia throughout time, as well as to reproduce other behaviors of the immune response reported in the literature, such as those that occur after a booster dose of the vaccine.

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.

A Study of the Validity and Reliability of a Mathematics Lesson Attitude Scale and Student Attitudes

ERIC Educational Resources Information Center

Tezer, Murat; Ozcan, Deniz

2015-01-01

Attitudes of the students towards mathematics lessons are very important in terms of their success and motivation. The purpose of this study is to develop a scale for the assessment of primary school students' attitudes towards mathematics courses in the 2nd and 3rd grades, to analyse its validity-reliability structure and to determine the…

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…

Students' Mathematical Modeling of Motion

ERIC Educational Resources Information Center

Marshall, Jill A.; Carrejo, David J.

2008-01-01

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

Mathematical Modeling Approaches in Plant Metabolomics.

PubMed

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

2018-01-01

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

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…

Accounting for Test Variability through Sizing Local Domains in Sequential Design Optimization with Concurrent Calibration-Based Model Validation

DTIC Science & Technology

2013-08-01

in Sequential Design Optimization with Concurrent Calibration-Based Model Validation Dorin Drignei 1 Mathematics and Statistics Department...Validation 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) Dorin Drignei; Zissimos Mourelatos; Vijitashwa Pandey

Problem Posing and Solving with Mathematical Modeling

ERIC Educational Resources Information Center

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

2005-01-01

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

Mathematical Capture of Human Crowd Behavioral Data for Computational Model Building, Verification, and Validation

DTIC Science & Technology

2011-03-21

throughout the experimental runs. Reliable and validated measures of anxiety ( Spielberger , 1983), as well as custom-constructed questionnaires about...Crowd modeling and simulation technologies. Transactions on modeling and computer simulation, 20(4). Spielberger , C. D. (1983

Examples of Mathematical Modeling

PubMed Central

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

2008-01-01

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

Mathematical modeling of laser lipolysis

PubMed Central

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

2008-01-01

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

[Mathematical model of technical equipment of a clinical-diagnostic laboratory].

PubMed

Bukin, S I; Busygin, D V; Tilevich, M E

1990-01-01

The paper is concerned with the problems of technical equipment of standard clinico-diagnostic laboratories (CDL) in this country. The authors suggest a mathematic model that may minimize expenditures for laboratory studies. The model enables the following problems to be solved: to issue scientifically-based recommendations for technical equipment of CDL; to validate the medico-technical requirements for newly devised items; to select the optimum types of uniform items; to define optimal technical decisions at the stage of the design; to determine the lab assistant's labour productivity and the cost of some investigations; to compute the medical laboratory engineering requirement for treatment and prophylactic institutions of this country.

Exploring Yellowstone National Park with Mathematical Modeling

ERIC Educational Resources Information Center

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

2017-01-01

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

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…

Validation and calibration of structural models that combine information from multiple sources.

PubMed

Dahabreh, Issa J; Wong, John B; Trikalinos, Thomas A

2017-02-01

Mathematical models that attempt to capture structural relationships between their components and combine information from multiple sources are increasingly used in medicine. Areas covered: We provide an overview of methods for model validation and calibration and survey studies comparing alternative approaches. Expert commentary: Model validation entails a confrontation of models with data, background knowledge, and other models, and can inform judgments about model credibility. Calibration involves selecting parameter values to improve the agreement of model outputs with data. When the goal of modeling is quantitative inference on the effects of interventions or forecasting, calibration can be viewed as estimation. This view clarifies issues related to parameter identifiability and facilitates formal model validation and the examination of consistency among different sources of information. In contrast, when the goal of modeling is the generation of qualitative insights about the modeled phenomenon, calibration is a rather informal process for selecting inputs that result in model behavior that roughly reproduces select aspects of the modeled phenomenon and cannot be equated to an estimation procedure. Current empirical research on validation and calibration methods consists primarily of methodological appraisals or case-studies of alternative techniques and cannot address the numerous complex and multifaceted methodological decisions that modelers must make. Further research is needed on different approaches for developing and validating complex models that combine evidence from multiple sources.

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).

Rival approaches to mathematical modelling in immunology

NASA Astrophysics Data System (ADS)

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

2007-08-01

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

Mathematical modeling of ethanol production in solid-state fermentation based on solid medium' dry weight variation.

PubMed

Mazaheri, Davood; Shojaosadati, Seyed Abbas; Zamir, Seyed Morteza; Mousavi, Seyyed Mohammad

2018-04-21

In this work, mathematical modeling of ethanol production in solid-state fermentation (SSF) has been done based on the variation in the dry weight of solid medium. This method was previously used for mathematical modeling of enzyme production; however, the model should be modified to predict the production of a volatile compound like ethanol. The experimental results of bioethanol production from the mixture of carob pods and wheat bran by Zymomonas mobilis in SSF were used for the model validation. Exponential and logistic kinetic models were used for modeling the growth of microorganism. In both cases, the model predictions matched well with the experimental results during the exponential growth phase, indicating the good ability of solid medium weight variation method for modeling a volatile product formation in solid-state fermentation. In addition, using logistic model, better predictions were obtained.

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

PubMed

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

2010-01-01

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

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…

Mathematical modeling of a single stage ultrasonically assisted distillation process.

PubMed

Mahdi, Taha; Ahmad, Arshad; Ripin, Adnan; Abdullah, Tuan Amran Tuan; Nasef, Mohamed M; Ali, Mohamad W

2015-05-01

The ability of sonication phenomena in facilitating separation of azeotropic mixtures presents a promising approach for the development of more intensified and efficient distillation systems than conventional ones. To expedite the much-needed development, a mathematical model of the system based on conservation principles, vapor-liquid equilibrium and sonochemistry was developed in this study. The model that was founded on a single stage vapor-liquid equilibrium system and enhanced with ultrasonic waves was coded using MATLAB simulator and validated with experimental data for ethanol-ethyl acetate mixture. The effects of both ultrasonic frequency and intensity on the relative volatility and azeotropic point were examined, and the optimal conditions were obtained using genetic algorithm. The experimental data validated the model with a reasonable accuracy. The results of this study revealed that the azeotropic point of the mixture can be totally eliminated with the right combination of sonication parameters and this can be utilized in facilitating design efforts towards establishing a workable ultrasonically intensified distillation system. Copyright © 2014 Elsevier B.V. All rights reserved.

Sewer solids separation by sedimentation--the problem of modeling, validation and transferability.

PubMed

Kutzner, R; Brombach, H; Geiger, W F

2007-01-01

Sedimentation of sewer solids in tanks, ponds and similar devices is the most relevant process for the treatment of stormwater and combined sewer overflows in urban collecting systems. In the past a lot of research work was done to develop deterministic models for the description of this separation process. But these modern models are not commonly accepted in Germany until today. Water Authorities are sceptical with regard to model validation and transferability. Within this paper it is checked whether this scepticism is reasonable. A framework-proposal for the validation of mathematical models with zero or one dimensional spatial resolution for particle separation processes for stormwater and combined sewer overflow treatment is presented. This proposal was applied to publications of repute on sewer solids separation by sedimentation. The result was that none of the investigated models described in literature passed the validation entirely. There is an urgent need for future research in sewer solids sedimentation and remobilization!

Mathematical modeling of urea transport in the kidney.

PubMed

Layton, Anita T

2014-01-01

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

On Mathematical Modeling Of Quantum Systems

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

Achuthan, P.; Dept. of Mathematics, Indian Institute of Technology, Madras, 600 036; Narayanankutty, Karuppath

2009-07-02

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

The (Mathematical) Modeling Process in Biosciences

PubMed Central

Torres, Nestor V.; Santos, Guido

2015-01-01

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

The (Mathematical) Modeling Process in Biosciences.

PubMed

Torres, Nestor V; Santos, Guido

2015-01-01

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

Establishing an Explanatory Model for Mathematics Identity.

PubMed

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

2015-04-01

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

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.

Software Validation via Model Animation

NASA Technical Reports Server (NTRS)

Dutle, Aaron M.; Munoz, Cesar A.; Narkawicz, Anthony J.; Butler, Ricky W.

2015-01-01

This paper explores a new approach to validating software implementations that have been produced from formally-verified algorithms. Although visual inspection gives some confidence that the implementations faithfully reflect the formal models, it does not provide complete assurance that the software is correct. The proposed approach, which is based on animation of formal specifications, compares the outputs computed by the software implementations on a given suite of input values to the outputs computed by the formal models on the same inputs, and determines if they are equal up to a given tolerance. The approach is illustrated on a prototype air traffic management system that computes simple kinematic trajectories for aircraft. Proofs for the mathematical models of the system's algorithms are carried out in the Prototype Verification System (PVS). The animation tool PVSio is used to evaluate the formal models on a set of randomly generated test cases. Output values computed by PVSio are compared against output values computed by the actual software. This comparison improves the assurance that the translation from formal models to code is faithful and that, for example, floating point errors do not greatly affect correctness and safety properties.

Development of Mathematics Learning Strategy Module, Based on Higher Order Thinking Skill (Hots) To Improve Mathematic Communication And Self Efficacy On Students Mathematics Department

NASA Astrophysics Data System (ADS)

Andriani, Ade; Dewi, Izwita; Halomoan, Budi

2018-03-01

In general, this research is conducted to improve the quality of lectures on mathematics learning strategy in Mathematics Department. The specific objective of this research is to develop learning instrument of mathematics learning strategy based on Higher Order Thinking Skill (HOTS) that can be used to improve mathematical communication and self efficacy of mathematics education students. The type of research is development research (Research & Development), where this research aims to develop a new product or improve the product that has been made. This development research refers to the four-D Model, which consists of four stages: defining, designing, developing, and disseminating. The instrument of this research is the validation sheet and the student response sheet of the instrument.

Mathematical model for dynamic cell formation in fast fashion apparel manufacturing stage

NASA Astrophysics Data System (ADS)

Perera, Gayathri; Ratnayake, Vijitha

2018-05-01

This paper presents a mathematical programming model for dynamic cell formation to minimize changeover-related costs (i.e., machine relocation costs and machine setup cost) and inter-cell material handling cost to cope with the volatile production environments in apparel manufacturing industry. The model is formulated through findings of a comprehensive literature review. Developed model is validated based on data collected from three different factories in apparel industry, manufacturing fast fashion products. A program code is developed using Lingo 16.0 software package to generate optimal cells for developed model and to determine the possible cost-saving percentage when the existing layouts used in three factories are replaced by generated optimal cells. The optimal cells generated by developed mathematical model result in significant cost saving when compared with existing product layouts used in production/assembly department of selected factories in apparel industry. The developed model can be considered as effective in minimizing the considered cost terms in dynamic production environment of fast fashion apparel manufacturing industry. Findings of this paper can be used for further researches on minimizing the changeover-related costs in fast fashion apparel production stage.

Mathematical modelling of intra-aortic balloon pump.

PubMed

Abdolrazaghi, Mona; Navidbakhsh, Mahdi; Hassani, Kamran

2010-10-01

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

Mathematical modeling of aeroelastic systems

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Numerical Validation of Chemical Compositional Model for Wettability Alteration Processes

NASA Astrophysics Data System (ADS)

Bekbauov, Bakhbergen; Berdyshev, Abdumauvlen; Baishemirov, Zharasbek; Bau, Domenico

2017-12-01

Chemical compositional simulation of enhanced oil recovery and surfactant enhanced aquifer remediation processes is a complex task that involves solving dozens of equations for all grid blocks representing a reservoir. In the present work, we perform a numerical validation of the newly developed mathematical formulation which satisfies the conservation laws of mass and energy and allows applying a sequential solution approach to solve the governing equations separately and implicitly. Through its application to the numerical experiment using a wettability alteration model and comparisons with existing chemical compositional model's numerical results, the new model has proven to be practical, reliable and stable.

Modelling and Optimizing Mathematics Learning in Children

ERIC Educational Resources Information Center

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

2013-01-01

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

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

Mathematical modeling of a process the rolling delivery

NASA Astrophysics Data System (ADS)

Stepanov, Mikhail A.; Korolev, Andrey A.

2018-03-01

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

Mathematical Modeling in the Secondary School Curriculum.

ERIC Educational Resources Information Center

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

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

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.

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.

Student engagement in mathematics: Development of instrument and validation of construct

NASA Astrophysics Data System (ADS)

Kong, Qi-Ping; Wong, Ngai-Ying; Lam, Chi-Chung

2003-05-01

Universal education has aggravated the problems of students' disengagement in learning, highlighting in particular, a greater range of motivations to learn and wider diversification in students' interests. Students' engagement with curriculum has become a crucial element in classroom learning. How we cultivate their involvement in the curriculum may be seen as being far more important than the epistemological consideration in the design of the school curriculum. Though aspects of behavioural, affective and cognitive engagements have been revealed in literature, we are still in need of a validated instrument that measures student engagement for further research. In the present study, an instrument of student engagement in the subject area of mathematics was developed through grounded research. Its validity was established by statistical methods

Quantitative model validation of manipulative robot systems

NASA Astrophysics Data System (ADS)

Kartowisastro, Iman Herwidiana

This thesis is concerned with applying the distortion quantitative validation technique to a robot manipulative system with revolute joints. Using the distortion technique to validate a model quantitatively, the model parameter uncertainties are taken into account in assessing the faithfulness of the model and this approach is relatively more objective than the commonly visual comparison method. The industrial robot is represented by the TQ MA2000 robot arm. Details of the mathematical derivation of the distortion technique are given which explains the required distortion of the constant parameters within the model and the assessment of model adequacy. Due to the complexity of a robot model, only the first three degrees of freedom are considered where all links are assumed rigid. The modelling involves the Newton-Euler approach to obtain the dynamics model, and the Denavit-Hartenberg convention is used throughout the work. The conventional feedback control system is used in developing the model. The system behavior to parameter changes is investigated as some parameters are redundant. This work is important so that the most important parameters to be distorted can be selected and this leads to a new term called the fundamental parameters. The transfer function approach has been chosen to validate an industrial robot quantitatively against the measured data due to its practicality. Initially, the assessment of the model fidelity criterion indicated that the model was not capable of explaining the transient record in term of the model parameter uncertainties. Further investigations led to significant improvements of the model and better understanding of the model properties. After several improvements in the model, the fidelity criterion obtained was almost satisfied. Although the fidelity criterion is slightly less than unity, it has been shown that the distortion technique can be applied in a robot manipulative system. Using the validated model, the importance of

A new mathematical model of bacterial interactions in two-species oral biofilms

PubMed Central

Martin, Bénédicte; Tamanai-Shacoori, Zohreh; Bronsard, Julie; Ginguené, Franck; Meuric, Vincent

2017-01-01

Periodontitis are bacterial inflammatory diseases, where the bacterial biofilms present on the tooth-supporting tissues switch from a healthy state towards a pathogenic state. Among bacterial species involved in the disease, Porphyromonas gingivalis has been shown to induce dysbiosis, and to induce virulence of otherwise healthy bacteria like Streptococcus gordonii. During biofilm development, primary colonizers such as S. gordonii first attach to the surface and allow the subsequent adhesion of periodontal pathogens such as P. gingivalis. Interactions between those two bacteria have been extensively studied during the adhesion step of the biofilm. The aim of the study was to understand interactions of both species during the growing phase of the biofilm, for which little knowledge is available, using a mathematical model. This two-species biofilm model was based on a substrate-dependent growth, implemented with damage parameters, and validated thanks to data obtained on experimental biofilms. Three different hypothesis of interactions were proposed and assayed using this model: independence, competition between both bacteria species, or induction of toxicity by one species for the other species. Adequacy between experimental and simulated biofilms were found with the last hypothetic mathematical model. This new mathematical model of two species bacteria biofilms, dependent on different substrates for growing, can be applied to any bacteria species, environmental conditions, or steps of biofilm development. It will be of great interest for exploring bacterial interactions in biofilm conditions. PMID:28253369

Modelling Mathematical Reasoning in Physics Education

NASA Astrophysics Data System (ADS)

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

2012-04-01

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

Scaffolding Mathematical Modelling with a Solution Plan

ERIC Educational Resources Information Center

Schukajlow, Stanislaw; Kolter, Jana; Blum, Werner

2015-01-01

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

Leading Undergraduate Research Projects in Mathematical Modeling

ERIC Educational Resources Information Center

Seshaiyer, Padmanabhan

2017-01-01

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

Facultative Stabilization Pond: Measuring Biological Oxygen Demand using Mathematical Approaches

NASA Astrophysics Data System (ADS)

Wira S, Ihsan; Sunarsih, Sunarsih

2018-02-01

Pollution is a man-made phenomenon. Some pollutants which discharged directly to the environment could create serious pollution problems. Untreated wastewater will cause contamination and even pollution on the water body. Biological Oxygen Demand (BOD) is the amount of oxygen required for the oxidation by bacteria. The higher the BOD concentration, the greater the organic matter would be. The purpose of this study was to predict the value of BOD contained in wastewater. Mathematical modeling methods were chosen in this study to depict and predict the BOD values contained in facultative wastewater stabilization ponds. Measurements of sampling data were carried out to validate the model. The results of this study indicated that a mathematical approach can be applied to predict the BOD contained in the facultative wastewater stabilization ponds. The model was validated using Absolute Means Error with 10% tolerance limit, and AME for model was 7.38% (< 10%), so the model is valid. Furthermore, a mathematical approach can also be applied to illustrate and predict the contents of wastewater.

The Spectrum of Mathematical Models.

ERIC Educational Resources Information Center

Karplus, Walter J.

1983-01-01

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

Validation of a "Kane's Dynamics" Model for the Active Rack Isolation System

NASA Technical Reports Server (NTRS)

Beech, Geoffrey S.; Hampton, R. David

2000-01-01

Many microgravity space-science experiments require vibratory acceleration levels unachievable without active isolation. The Boeing Corporation's Active Rack Isolation System (ARIS) employs a novel combination of magnetic actuation and mechanical linkages, to address these isolation requirements on the International Space Station (ISS). ARIS provides isolation at the rack (international Standard Payload Rack, or ISPR) level. Effective model-based vibration isolation requires (1) an isolation device, (2) an adequate dynamic (i.e., mathematical) model of that isolator, and (3) a suitable, corresponding controller, ARIS provides the ISS response to the first requirement. In November 1999, the authors presented a response to the second ("A 'Kane's Dynamics' model for the Active Rack Isolation System", Hampton and Beech) intended to facilitate an optimal-controls approach to the third. This paper documents the validation of that high-fidelity dynamic model of ARIS. As before, this model contains the full actuator dynamics, however, the umbilical models are not included in this presentation. The validation of this dynamics model was achieved by utilizing two Commercial Off the Shelf (COTS) software tools: Deneb's ENVISION, and Online Dynamics' AUTOLEV. ENVISION is a robotics software package developed for the automotive industry that employs 3-dimensional (3-D) Computer Aided Design (CAD) models to facilitate both forward and inverse kinematics analyses. AUTOLEV is a DOS based interpreter that is designed in general to solve vector based mathematical problems and specifically to solve Dynamics problems using Kane's method.

Design and validation of diffusion MRI models of white matter

NASA Astrophysics Data System (ADS)

Jelescu, Ileana O.; Budde, Matthew D.

2017-11-01

Diffusion MRI is arguably the method of choice for characterizing white matter microstructure in vivo. Over the typical duration of diffusion encoding, the displacement of water molecules is conveniently on a length scale similar to that of the underlying cellular structures. Moreover, water molecules in white matter are largely compartmentalized which enables biologically-inspired compartmental diffusion models to characterize and quantify the true biological microstructure. A plethora of white matter models have been proposed. However, overparameterization and mathematical fitting complications encourage the introduction of simplifying assumptions that vary between different approaches. These choices impact the quantitative estimation of model parameters with potential detriments to their biological accuracy and promised specificity. First, we review biophysical white matter models in use and recapitulate their underlying assumptions and realms of applicability. Second, we present up-to-date efforts to validate parameters estimated from biophysical models. Simulations and dedicated phantoms are useful in assessing the performance of models when the ground truth is known. However, the biggest challenge remains the validation of the “biological accuracy” of estimated parameters. Complementary techniques such as microscopy of fixed tissue specimens have facilitated direct comparisons of estimates of white matter fiber orientation and densities. However, validation of compartmental diffusivities remains challenging, and complementary MRI-based techniques such as alternative diffusion encodings, compartment-specific contrast agents and metabolites have been used to validate diffusion models. Finally, white matter injury and disease pose additional challenges to modeling, which are also discussed. This review aims to provide an overview of the current state of models and their validation and to stimulate further research in the field to solve the remaining open

Design and validation of diffusion MRI models of white matter

PubMed Central

Jelescu, Ileana O.; Budde, Matthew D.

2018-01-01

Diffusion MRI is arguably the method of choice for characterizing white matter microstructure in vivo. Over the typical duration of diffusion encoding, the displacement of water molecules is conveniently on a length scale similar to that of the underlying cellular structures. Moreover, water molecules in white matter are largely compartmentalized which enables biologically-inspired compartmental diffusion models to characterize and quantify the true biological microstructure. A plethora of white matter models have been proposed. However, overparameterization and mathematical fitting complications encourage the introduction of simplifying assumptions that vary between different approaches. These choices impact the quantitative estimation of model parameters with potential detriments to their biological accuracy and promised specificity. First, we review biophysical white matter models in use and recapitulate their underlying assumptions and realms of applicability. Second, we present up-to-date efforts to validate parameters estimated from biophysical models. Simulations and dedicated phantoms are useful in assessing the performance of models when the ground truth is known. However, the biggest challenge remains the validation of the “biological accuracy” of estimated parameters. Complementary techniques such as microscopy of fixed tissue specimens have facilitated direct comparisons of estimates of white matter fiber orientation and densities. However, validation of compartmental diffusivities remains challenging, and complementary MRI-based techniques such as alternative diffusion encodings, compartment-specific contrast agents and metabolites have been used to validate diffusion models. Finally, white matter injury and disease pose additional challenges to modeling, which are also discussed. This review aims to provide an overview of the current state of models and their validation and to stimulate further research in the field to solve the remaining open

Developing Contextual Mathematical Thinking Learning Model to Enhance Higher-Order Thinking Ability for Middle School Students

ERIC Educational Resources Information Center

Samo, Damianus D.; Darhim; Kartasasmita, Bana

2017-01-01

The purpose of this research is to develop contextual mathematical thinking learning model which is valid, practical and effective based on the theoretical reviews and its support to enhance higher-order thinking ability. This study is a research and development (R & D) with three main phases: investigation, development, and implementation.…

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…

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.

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.

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.

Mathematics, Modelling and Students in Transition

ERIC Educational Resources Information Center

Wake, Geoff

2016-01-01

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

a Discrete Mathematical Model to Simulate Malware Spreading

NASA Astrophysics Data System (ADS)

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

2012-10-01

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

Mathematic models for a ray tracing method and its applications in wireless optical communications.

PubMed

Zhang, Minglun; Zhang, Yangan; Yuan, Xueguang; Zhang, Jinnan

2010-08-16

This paper presents a new ray tracing method, which contains a whole set of mathematic models, and its validity is verified by simulations. In addition, both theoretical analysis and simulation results show that the computational complexity of the method is much lower than that of previous ones. Therefore, the method can be used to rapidly calculate the impulse response of wireless optical channels for complicated systems.

Mathematical modeling of metabolism and hemodynamics.

PubMed

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

2012-06-01

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

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

ERIC Educational Resources Information Center

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

2008-01-01

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

Mathematical modeling of electrical activity of uterine muscle cells.

PubMed

Rihana, Sandy; Terrien, Jeremy; Germain, Guy; Marque, Catherine

2009-06-01

The uterine electrical activity is an efficient parameter to study the uterine contractility. In order to understand the ionic mechanisms responsible for its generation, we aimed at building a mathematical model of the uterine cell electrical activity based upon the physiological mechanisms. First, based on the voltage clamp experiments found in the literature, we focus on the principal ionic channels and their cognate currents involved in the generation of this electrical activity. Second, we provide the methodology of formulations of uterine ionic currents derived from a wide range of electrophysiological data. The model is validated step by step by comparing simulated voltage-clamp results with the experimental ones. The model reproduces successfully the generation of single spikes or trains of action potentials that fit with the experimental data. It allows analyzing ionic channels implications. Likewise, the calcium-dependent conductance influences significantly the cellular oscillatory behavior.

SU-E-T-17: A Mathematical Model for PinPoint Chamber Correction in Measuring Small Fields

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

Li, T; Zhang, Y; Li, X

2014-06-01

Purpose: For small field dosimetry, such as measuring the cone output factor for stereotactic radiosurgery, ion chambers often result in underestimation of the dose, due to both the volume averaging effect and the lack of electron equilibrium. The purpose of this work is to develop a mathematical model, specifically for the pinpoint chamber, to calculate the correction factors corresponding to different type of small fields, including single cone-based circular field and non-standard composite fields. Methods: A PTW 0.015cc PinPoint chamber was used in the study. Its response in a certain field was modeled as the total contribution of many smallmore » beamlets, each with different response factor depending on the relative strength, radial distance to the chamber axis, and the beam angle. To get these factors, 12 cone-shaped circular fields (5mm,7.5mm, 10mm, 12.5mm, 15mm, 20mm, 25mm, 30mm, 35mm, 40mm, 50mm, 60mm) were irradiated and measured with the PinPoint chamber. For each field size, hundreds of readings were recorded for every 2mm chamber shift in the horizontal plane. These readings were then compared with the theoretical doses as obtained with Monte Carlo calculation. A penalized-least-square optimization algorithm was developed to find out the beamlet response factors. After the parameter fitting, the established mathematical model was validated with the same MC code for other non-circular fields. Results: The optimization algorithm used for parameter fitting was stable and the resulted response factors were smooth in spatial domain. After correction with the mathematical model, the chamber reading matched with the Monte Carlo calculation for all the tested fields to within 2%. Conclusion: A novel mathematical model has been developed for the PinPoint chamber for dosimetric measurement of small fields. The current model is applicable only when the beam axis is perpendicular to the chamber axis. It can be applied to non-standard composite fields. Further

A new prospect in magnetic nanoparticle-based cancer therapy: Taking credit from mathematical tissue-mimicking phantom brain models.

PubMed

Saeedi, Mostafa; Vahidi, Omid; Goodarzi, Vahabodin; Saeb, Mohammad Reza; Izadi, Leila; Mozafari, Masoud

2017-11-01

Distribution patterns/performance of magnetic nanoparticles (MNPs) was visualized by computer simulation and experimental validation on agarose gel tissue-mimicking phantom (AGTMP) models. The geometry of a complex three-dimensional mathematical phantom model of a cancer tumor was examined by tomography imaging. The capability of mathematical model to predict distribution patterns/performance in AGTMP model was captured. The temperature profile vs. hyperthermia duration was obtained by solving bio-heat equations for four different MNPs distribution patterns and correlated with cell death rate. The outcomes indicated that bio-heat model was able to predict temperature profile throughout the tissue model with a reasonable precision, to be applied for complex tissue geometries. The simulation results on the cancer tumor model shed light on the effectiveness of the studied parameters. Copyright © 2017 Elsevier Inc. All rights reserved.

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

Modelling and validation of Proton exchange membrane fuel cell (PEMFC)

NASA Astrophysics Data System (ADS)

Mohiuddin, A. K. M.; Basran, N.; Khan, A. A.

2018-01-01

This paper is the outcome of a small scale fuel cell project. Fuel cell is an electrochemical device that converts energy from chemical reaction to electrical work. Proton Exchange Membrane Fuel Cell (PEMFC) is one of the different types of fuel cell, which is more efficient, having low operational temperature and fast start up capability results in high energy density. In this study, a mathematical model of 1.2 W PEMFC is developed and simulated using MATLAB software. This model describes the PEMFC behaviour under steady-state condition. This mathematical modeling of PEMFC determines the polarization curve, power generated, and the efficiency of the fuel cell. Simulation results were validated by comparing with experimental results obtained from the test of a single PEMFC with a 3 V motor. The performance of experimental PEMFC is little lower compared to simulated PEMFC, however both results were found in good agreement. Experiments on hydrogen flow rate also been conducted to obtain the amount of hydrogen consumed to produce electrical work on PEMFC.

Some Reflections on the Teaching of Mathematical Modeling

ERIC Educational Resources Information Center

Warwick, Jon

2007-01-01

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

Mathematical Manipulative Models: In Defense of “Beanbag Biology”

PubMed Central

Gaff, Holly; Weisstein, Anton E.

2010-01-01

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

Mathematical modeling of simultaneous carbon-nitrogen-sulfur removal from industrial wastewater.

PubMed

Xu, Xi-Jun; Chen, Chuan; Wang, Ai-Jie; Ni, Bing-Jie; Guo, Wan-Qian; Yuan, Ye; Huang, Cong; Zhou, Xu; Wu, Dong-Hai; Lee, Duu-Jong; Ren, Nan-Qi

2017-01-05

A mathematical model of carbon, nitrogen and sulfur removal (C-N-S) from industrial wastewater was constructed considering the interactions of sulfate-reducing bacteria (SRB), sulfide-oxidizing bacteria (SOB), nitrate-reducing bacteria (NRB), facultative bacteria (FB), and methane producing archaea (MPA). For the kinetic network, the bioconversion of C-N by heterotrophic denitrifiers (NO 3 - →NO 2 - →N 2 ), and that of C-S by SRB (SO 4 2- →S 2- ) and SOB (S 2- →S 0 ) was proposed and calibrated based on batch experimental data. The model closely predicted the profiles of nitrate, nitrite, sulfate, sulfide, lactate, acetate, methane and oxygen under both anaerobic and micro-aerobic conditions. The best-fit kinetic parameters had small 95% confidence regions with mean values approximately at the center. The model was further validated using independent data sets generated under different operating conditions. This work was the first successful mathematical modeling of simultaneous C-N-S removal from industrial wastewater and more importantly, the proposed model was proven feasible to simulate other relevant processes, such as sulfate-reducing, sulfide-oxidizing process (SR-SO) and denitrifying sulfide removal (DSR) process. The model developed is expected to enhance our ability to predict the treatment of carbon-nitrogen-sulfur contaminated industrial wastewater. Copyright © 2016 Elsevier B.V. All rights reserved.

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…

Validity issues in the evaluation of a measure of science and mathematics teacher knowledge

NASA Astrophysics Data System (ADS)

Talbot, Robert M., III

2011-12-01

This study investigates the reliability and validity of an instrument designed to measure science and mathematics teachers' strategic knowledge . Strategic knowledge is conceptualized as a construct that is related to pedagogical knowledge and is comprised of two dimensions: Flexible Application (FA) and Student Centered Instruction (SCI). The FA dimension describes how a science teacher invokes, applies and modifies her instructional repertoire in a given teaching context. The SCI dimension describes how a science teacher conceives of a given situation as an opportunity for active engagement with the students. The Flexible Application of Student-Centered Instruction (FASCI) survey instrument was designed to measure science teachers' strategic knowledge by eliciting open-ended responses to scenario-based items. This study addresses the following overarching question: What are some potential issues pertaining to the validity of measures of science and mathematics teacher knowledge? Using a validity argument framework, different sources of evidence are identified, collected, and evaluated to examine support for a set or propositions related to the intended score interpretation and instrument use: FASCI scores can be used to compare and distinguish the strategic knowledge of novice science and mathematics teachers in the evaluation of teacher education programs. Three separate but related studies are presented and discussed. These studies focus on the reliability of FASCI scores, the effect of adding specific science content to the scenario-based items, and the observation of strategic knowledge in teaching practice. Serious issues were found with the reliability of scores from the FASCI instrument. It was also found that adding science content to the scenario-based items has an effect on FASCI scores, but not for the reason hypothesized. Finally, it was found that more evidence is needed to make stronger claims about the relationship between FASCI scores and novice

A new simple local muscle recovery model and its theoretical and experimental validation.

PubMed

Ma, Liang; Zhang, Wei; Wu, Su; Zhang, Zhanwu

2015-01-01

This study was conducted to provide theoretical and experimental validation of a local muscle recovery model. Muscle recovery has been modeled in different empirical and theoretical approaches to determine work-rest allowance for musculoskeletal disorder (MSD) prevention. However, time-related parameters and individual attributes have not been sufficiently considered in conventional approaches. A new muscle recovery model was proposed by integrating time-related task parameters and individual attributes. Theoretically, this muscle recovery model was compared to other theoretical models mathematically. Experimentally, a total of 20 subjects participated in the experimental validation. Hand grip force recovery and shoulder joint strength recovery were measured after a fatiguing operation. The recovery profile was fitted by using the recovery model, and individual recovery rates were calculated as well after fitting. Good fitting values (r(2) > .8) were found for all the subjects. Significant differences in recovery rates were found among different muscle groups (p < .05). The theoretical muscle recovery model was primarily validated by characterization of the recovery process after fatiguing operation. The determined recovery rate may be useful to represent individual recovery attribute.

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.

Groundwater Model Validation

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

Ahmed E. Hassan

2006-01-24

Models have an inherent uncertainty. The difficulty in fully characterizing the subsurface environment makes uncertainty an integral component of groundwater flow and transport models, which dictates the need for continuous monitoring and improvement. Building and sustaining confidence in closure decisions and monitoring networks based on models of subsurface conditions require developing confidence in the models through an iterative process. The definition of model validation is postulated as a confidence building and long-term iterative process (Hassan, 2004a). Model validation should be viewed as a process not an end result. Following Hassan (2004b), an approach is proposed for the validation process ofmore » stochastic groundwater models. The approach is briefly summarized herein and detailed analyses of acceptance criteria for stochastic realizations and of using validation data to reduce input parameter uncertainty are presented and applied to two case studies. During the validation process for stochastic models, a question arises as to the sufficiency of the number of acceptable model realizations (in terms of conformity with validation data). Using a hierarchical approach to make this determination is proposed. This approach is based on computing five measures or metrics and following a decision tree to determine if a sufficient number of realizations attain satisfactory scores regarding how they represent the field data used for calibration (old) and used for validation (new). The first two of these measures are applied to hypothetical scenarios using the first case study and assuming field data consistent with the model or significantly different from the model results. In both cases it is shown how the two measures would lead to the appropriate decision about the model performance. Standard statistical tests are used to evaluate these measures with the results indicating they are appropriate measures for evaluating model realizations. The use of

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.

Modellus: Learning Physics with Mathematical Modelling

NASA Astrophysics Data System (ADS)

Teodoro, Vitor

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

Genetic demographic networks: Mathematical model and applications.

PubMed

Kimmel, Marek; Wojdyła, Tomasz

2016-10-01

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

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.

Mathematical Manipulative Models: In Defense of "Beanbag Biology"

ERIC Educational Resources Information Center

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

2010-01-01

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

Mathematical modeling of microstructural development in hypoeutectic cast iron

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

Maijer, D.; Cockcroft, S.L.; Patt, W.

A mathematical heat-transfer/microstructural model has been developed to predict the evolution of proeutectic austenite, white iron eutectic, and gray iron eutectic during solidification of hypoeutectic cast iron, based on the commercial finite-element code ABAQUS. Specialized routines which employ relationships describing nucleation and growth of equiaxed primary austenite, gray iron eutectic, and white iron eutectic have been formulated and incorporated into ABAQUS through user-specified subroutines. The relationships used in the model to describe microstructural evolution have been adapted from relationships describing equiaxed growth in the literature. The model has been validated/fine tuned against temperature data collected from a QuiK-Cup sample, whichmore » contained a thermocouple embedded approximately in the center of the casting. The phase distribution predicted with the model has been compared to the measured phase distribution inferred from the variation in hardness within the QuiK-Cup sample and from image analysis of photomicrographs of the polished and etched microstructure. Overall, the model results were found to agree well with the measured distribution of the microstructure.« less

Building Mathematical Models of Simple Harmonic and Damped Motion.

ERIC Educational Resources Information Center

Edwards, Thomas

1995-01-01

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

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.

Mathematical model of organic substrate degradation in solid waste windrow composting.

PubMed

Seng, Bunrith; Kristanti, Risky Ayu; Hadibarata, Tony; Hirayama, Kimiaki; Katayama-Hirayama, Keiko; Kaneko, Hidehiro

2016-01-01

Organic solid waste composting is a complex process that involves many coupled physical, chemical and biological mechanisms. To understand this complexity and to ease in planning, design and management of the composting plant, mathematical model for simulation is usually applied. The aim of this paper is to develop a mathematical model of organic substrate degradation and its performance evaluation in solid waste windrow composting system. The present model is a biomass-dependent model, considering biological growth processes under the limitation of moisture, oxygen and substrate contents, and temperature. The main output of this model is substrate content which was divided into two categories: slowly and rapidly degradable substrates. To validate the model, it was applied to a laboratory scale windrow composting of a mixture of wood chips and dog food. The wastes were filled into a cylindrical reactor of 6 cm diameter and 1 m height. The simulation program was run for 3 weeks with 1 s stepwise. The simulated results were in reasonably good agreement with the experimental results. The MC and temperature of model simulation were found to be matched with those of experiment, but limited for rapidly degradable substrates. Under anaerobic zone, the degradation of rapidly degradable substrate needs to be incorporated into the model to achieve full simulation of a long period static pile composting. This model is a useful tool to estimate the changes of substrate content during composting period, and acts as a basic model for further development of a sophisticated model.

Mathematical modelling and quantitative methods.

PubMed

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

2002-01-01

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

A Seminar in Mathematical Model-Building.

ERIC Educational Resources Information Center

Smith, David A.

1979-01-01

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

A mathematical model for the deformation of the eyeball by an elastic band.

PubMed

Keeling, Stephen L; Propst, Georg; Stadler, Georg; Wackernagel, Werner

2009-06-01

In a certain kind of eye surgery, the human eyeball is deformed sustainably by the application of an elastic band. This article presents a mathematical model for the mechanics of the combined eye/band structure along with an algorithm to compute the model solutions. These predict the immediate and the lasting indentation of the eyeball. The model is derived from basic physical principles by minimizing a potential energy subject to a volume constraint. Assuming spherical symmetry, this leads to a two-point boundary-value problem for a non-linear second-order ordinary differential equation that describes the minimizing static equilibrium. By comparison with laboratory data, a preliminary validation of the model is given.

Model Validation Status Review

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

E.L. Hardin

The primary objective for the Model Validation Status Review was to perform a one-time evaluation of model validation associated with the analysis/model reports (AMRs) containing model input to total-system performance assessment (TSPA) for the Yucca Mountain site recommendation (SR). This review was performed in response to Corrective Action Request BSC-01-C-01 (Clark 2001, Krisha 2001) pursuant to Quality Assurance review findings of an adverse trend in model validation deficiency. The review findings in this report provide the following information which defines the extent of model validation deficiency and the corrective action needed: (1) AMRs that contain or support models are identified,more » and conversely, for each model the supporting documentation is identified. (2) The use for each model is determined based on whether the output is used directly for TSPA-SR, or for screening (exclusion) of features, events, and processes (FEPs), and the nature of the model output. (3) Two approaches are used to evaluate the extent to which the validation for each model is compliant with AP-3.10Q (Analyses and Models). The approaches differ in regard to whether model validation is achieved within individual AMRs as originally intended, or whether model validation could be readily achieved by incorporating information from other sources. (4) Recommendations are presented for changes to the AMRs, and additional model development activities or data collection, that will remedy model validation review findings, in support of licensing activities. The Model Validation Status Review emphasized those AMRs that support TSPA-SR (CRWMS M&O 2000bl and 2000bm). A series of workshops and teleconferences was held to discuss and integrate the review findings. The review encompassed 125 AMRs (Table 1) plus certain other supporting documents and data needed to assess model validity. The AMRs were grouped in 21 model areas representing the modeling of processes affecting the natural

iSTEM: Promoting Fifth Graders' Mathematical Modeling

ERIC Educational Resources Information Center

Yanik, H. Bahadir; Karabas, Celil

2014-01-01

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

Investigating the Knowledge Needed for Teaching Mathematics: An Exploratory Validation Study Focusing on Teaching Practices

ERIC Educational Resources Information Center

Charalambous, Charalambos Y.

2016-01-01

Central in the frameworks proposed to capture the knowledge needed for teaching mathematics is the assumption that teachers need more than pure subject-matter knowledge. Validation studies exploring this assumption by recruiting contrasting populations are relatively scarce. Drawing on a sample of 644 Greek-Cypriots preservice and inservice…

Model-Based Method for Sensor Validation

NASA Technical Reports Server (NTRS)

Vatan, Farrokh

2012-01-01

Fault detection, diagnosis, and prognosis are essential tasks in the operation of autonomous spacecraft, instruments, and in situ platforms. One of NASA s key mission requirements is robust state estimation. Sensing, using a wide range of sensors and sensor fusion approaches, plays a central role in robust state estimation, and there is a need to diagnose sensor failure as well as component failure. Sensor validation can be considered to be part of the larger effort of improving reliability and safety. The standard methods for solving the sensor validation problem are based on probabilistic analysis of the system, from which the method based on Bayesian networks is most popular. Therefore, these methods can only predict the most probable faulty sensors, which are subject to the initial probabilities defined for the failures. The method developed in this work is based on a model-based approach and provides the faulty sensors (if any), which can be logically inferred from the model of the system and the sensor readings (observations). The method is also more suitable for the systems when it is hard, or even impossible, to find the probability functions of the system. The method starts by a new mathematical description of the problem and develops a very efficient and systematic algorithm for its solution. The method builds on the concepts of analytical redundant relations (ARRs).

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

ERIC Educational Resources Information Center

Dalla Vecchia, Rodrigo

2015-01-01

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

Validation of the Domains of Creativity Scale for Nigerian Preservice Science, Technology, and Mathematics Teachers

ERIC Educational Resources Information Center

Awofala, Adeneye O. A.; Fatade, Alfred O.

2015-01-01

Introduction: Investigation into the factor structure of Domains of Creativity Scale has been on for sometimes now. The purpose of this study was to test the validity of the Kaufman Domains of Creativity Scale on Nigerian preservice science, technology, and mathematics teachers. Method: Exploratory and confirmatory factor analyses were performed…

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

ERIC Educational Resources Information Center

Akgün, Levent

2015-01-01

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

Developing Understanding of Mathematical Modeling in Secondary Teacher Preparation

ERIC Educational Resources Information Center

Anhalt, Cynthia Oropesa; Cortez, Ricardo

2016-01-01

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

Propriomuscular coding of kinaesthetic sensation. Experimental approach and mathematical modelling.

PubMed

Gilhodes, J C; Coiton, Y; Roll, J P; Ans, B

1993-01-01

The role of propriomuscular information in kinaesthetic sensation was studied. Experiments were carried out on human subjects in whom kinaesthetic illusions were induced by applying tendon vibration with a variable frequency. Six patterns of frequency modulation were used, four of which had an arbitrary form and the other two mimicked natural Ia discharges. The results show that the shape of the illusory movements recorded depended on the type of vibratory pattern used. A mathematical model for the propriomuscular information decoding process is proposed. It takes into account both the agonist and antagonist muscle spindle populations as sources of kinaesthetic information and is based on the assumption that position and velocity information are additively combined. The experimental data show a good fit with the theoretical data obtained by means of model simulation, thus validating our initial hypothesis. Various aspects of the experimental results and the hypotheses involved in the model are discussed.

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

NASA Astrophysics Data System (ADS)

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

2007-02-01

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

Using a Functional Model to Develop a Mathematical Formula

ERIC Educational Resources Information Center

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

2008-01-01

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

Molecular modeling: An open invitation for applied mathematics

NASA Astrophysics Data System (ADS)

Mezey, Paul G.

2013-10-01

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

Application of mathematical modeling in sustained release delivery systems.

PubMed

Grassi, Mario; Grassi, Gabriele

2014-08-01

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

Understanding electricity generation in osmotic microbial fuel cells through integrated experimental investigation and mathematical modeling.

PubMed

Qin, Mohan; Ping, Qingyun; Lu, Yaobin; Abu-Reesh, Ibrahim M; He, Zhen

2015-11-01

Osmotic microbial fuel cells (OsMFCs) are a new type of MFCs with integrating forward osmosis (FO). However, it is not well understood why electricity generation is improved in OsMFCs compared to regular MFCs. Herein, an approach integrating experimental investigation and mathematical model was adopted to address the question. Both an OsMFC and an MFC achieved similar organic removal efficiency, but the OsMFC generated higher current than the MFC with or without water flux, resulting from the lower resistance of FO membrane. Combining NaCl and glucose as a catholyte demonstrated that the catholyte conductivity affected the electricity generation in the OsMFC. A mathematical model of OsMFCs was developed and validated with the experimental data. The model predicated the variation of internal resistance with increasing water flux, and confirmed the importance of membrane resistance. Increasing water flux with higher catholyte conductivity could decrease the membrane resistance. Copyright © 2015 Elsevier Ltd. All rights reserved.

The use of mathematical models in teaching wastewater treatment engineering.

PubMed

Morgenroth, E; Arvin, E; Vanrolleghem, P

2002-01-01

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

Mathematical modeling of swirled flows in industrial applications

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

A Mathematical Evaluation of the Core Conductor Model

PubMed Central

Clark, John; Plonsey, Robert

1966-01-01

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

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.

Mathematical modelling of clostridial acetone-butanol-ethanol fermentation.

PubMed

Millat, Thomas; Winzer, Klaus

2017-03-01

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

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 the Early School Years

ERIC Educational Resources Information Center

English, Lyn D.; Watters, James J.

2005-01-01

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

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

ERIC Educational Resources Information Center

Rash, Agnes M.; Zurbach, E. Peter

2004-01-01

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

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.

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

ERIC Educational Resources Information Center

Michelsen, Claus

2015-01-01

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

Applying an alternative mathematics pedagogy for students with weak mathematics: meta-analysis of alternative pedagogies

NASA Astrophysics Data System (ADS)

Lake, Warren; Wallin, Margie; Woolcott, Geoff; Boyd, Wendy; Foster, Alan; Markopoulos, Christos; Boyd, William

2017-02-01

Student mathematics performance and the need for work-ready graduates to be mathematics-competent is a core issue for many universities. While both student and teacher are responsible for learning outcomes, there is a need to explicitly acknowledge the weak mathematics foundation of many university students. A systematic literature review was undertaken of identified innovations and/or interventions that may lead to improvement in student outcomes for university mathematics-based units of study. The review revealed the importance of understanding the foundations of student performance in higher education mathematics learning, especially in first year. Pre-university mathematics skills were identified as significant in student retention and mathematics success at university, and a specific focus on student pre-university mathematics skill level was found to be more effective in providing help, rather than simply focusing on a particular at-risk group. Diagnostics tools were found to be important in identifying (1) student background and (2) appropriate intervention. The studies highlighted the importance of appropriate and validated interventions in mathematics teaching and learning, and the need to improve the learning model for mathematics-based subjects, communication and technology innovations.

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.

A Mathematical Model for the Middle Ear Ventilation

NASA Astrophysics Data System (ADS)

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

2008-09-01

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

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

ERIC Educational Resources Information Center

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

2017-01-01

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

Mathematical modeling of inhalation exposure

NASA Technical Reports Server (NTRS)

Fiserova-Bergerova, V.

1976-01-01

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

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…

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

ERIC Educational Resources Information Center

Karatas, Ilhan

2014-01-01

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

Authenticity of Mathematical Modeling

ERIC Educational Resources Information Center

Tran, Dung; Dougherty, Barbara J.

2014-01-01

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

Mathematical modeling of a Ti:sapphire solid-state laser

NASA Technical Reports Server (NTRS)

Swetits, John J.

1987-01-01

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

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…

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 modeling and validation of growth of Salmonella Enteritidis and background microorganisms in potato salad – one-step kinetic analysis and model development

USDA-ARS?s Scientific Manuscript database

This study was conducted to examine the growth of Salmonella Enteritidis (SE) in potato salad caused by cross-contamination and temperature abuse, and develop mathematical models to predict its growth. The growth of SE was investigated under constant temperature conditions (8, 10, 15, 20, 25, 30, a...

Evaluation of leaf litter leaching kinetics through commonly-used mathematical models

NASA Astrophysics Data System (ADS)

Montoya, J. V.; Bastianoni, A.; Mendez, C.; Paolini, J.

2012-04-01

distribution. Higher Adj-R2 were obtained for the power and the rational-type models. However, when AIC and residuals distribution were used, the only model that could satisfactory predict the behavior of our dataset was the rational-type. Even if the Adj-R2 was higher for some species when using the power model compared to the rational-type; our results showed that this criterion alone cannot demonstrate the predicting performance of any model. Usually Adj-R2 is used when assessing the goodness of fit for any mathematical model disregarding the fact that a good Adj-R2 could be obtained even when statistical assumptions required for the validity of the model are not satisfied. Our results showed that sampling at the initial stages of leaching is necessary to adequately describe this process. We also provided evidence that using traditional mathematical models is not the best option to evaluate leaching kinetics because of its mathematical inability to properly describe the abrupt changes that occur during the early stages of leaching. We also found useful applying different criteria to evaluate the goodness-of-fit and performance of any model considered taking into account both statistical and biological meaning of the results.

The mathematical and computer modeling of the worm tool shaping

NASA Astrophysics Data System (ADS)

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

2017-06-01

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

A Mathematical Model Development for the Lateral Collapse of Octagonal Tubes

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Antecedents of Mathematics Self-Efficacy Beliefs for Middle and High School Students: An Instrument Validation Study

ERIC Educational Resources Information Center

Freed, Mark R.

2013-01-01

There were three primary purposes for this study. First, I investigated the psychometric properties of the Sources of Middle School Mathematics Self-Efficacy (SMMSE) scale (Usher, 2007; Usher & Pajares, 2009) with high school students. Validation for expanded use of the SMMSE scale was achieved by assessing the instrument's psychometric…

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.

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

PubMed

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

2016-01-01

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

An Integrated Approach to Mathematical Modeling: A Classroom Study.

ERIC Educational Resources Information Center

Doerr, Helen M.

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

Evaluation of Limb Load Asymmetry Using Two New Mathematical Models

PubMed Central

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

2015-01-01

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

Mathematical modeling of molecular diffusion through mucus

PubMed Central

Cu, Yen; Saltzman, W. Mark

2008-01-01

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

Developing self-concept instrument for pre-service mathematics teachers

NASA Astrophysics Data System (ADS)

Afgani, M. W.; Suryadi, D.; Dahlan, J. A.

2018-01-01

This study aimed to develop self-concept instrument for undergraduate students of mathematics education in Palembang, Indonesia. Type of this study was development research of non-test instrument in questionnaire form. A Validity test of the instrument was performed with construct validity test by using Pearson product moment and factor analysis, while reliability test used Cronbach’s alpha. The instrument was tested by 65 undergraduate students of mathematics education in one of the universities at Palembang, Indonesia. The instrument consisted of 43 items with 7 aspects of self-concept, that were the individual concern, social identity, individual personality, view of the future, the influence of others who become role models, the influence of the environment inside or outside the classroom, and view of the mathematics. The result of validity test showed there was one invalid item because the value of Pearson’s r was 0.107 less than the critical value (0.244; α = 0.05). The item was included in social identity aspect. After the invalid item was removed, Construct validity test with factor analysis generated only one factor. The Kaiser-Meyer-Olkin (KMO) coefficient was 0.846 and reliability coefficient was 0.91. From that result, we concluded that the self-concept instrument for undergraduate students of mathematics education in Palembang, Indonesia was valid and reliable with 42 items.

Development and Validation of a New Measure of Teacher Perceptions of Science and Mathematics Learning Environments

ERIC Educational Resources Information Center

Ellett, Chad D.; Monsaas, Judy

2011-01-01

This article describes the development and validation of the Inventory of Teaching and Learning (ITAL) as a new measure of teacher perceptions of science and mathematics learning environments. The ITAL was initially developed and administered in 2004 and has subsequently been revised annually. The ITAL is administered using a confidential…

Mathematical modeling of nitrous oxide (N2O) emissions from full-scale wastewater treatment plants.

PubMed

Ni, Bing-Jie; Ye, Liu; Law, Yingyu; Byers, Craig; Yuan, Zhiguo

2013-07-16

Mathematical modeling of N2O emissions is of great importance toward understanding the whole environmental impact of wastewater treatment systems. However, information on modeling of N2O emissions from full-scale wastewater treatment plants (WWTP) is still sparse. In this work, a mathematical model based on currently known or hypothesized metabolic pathways for N2O productions by heterotrophic denitrifiers and ammonia-oxidizing bacteria (AOB) is developed and calibrated to describe the N2O emissions from full-scale WWTPs. The model described well the dynamic ammonium, nitrite, nitrate, dissolved oxygen (DO) and N2O data collected from both an open oxidation ditch (OD) system with surface aerators and a sequencing batch reactor (SBR) system with bubbling aeration. The obtained kinetic parameters for N2O production are found to be reasonable as the 95% confidence regions of the estimates are all small with mean values approximately at the center. The model is further validated with independent data sets collected from the same two WWTPs. This is the first time that mathematical modeling of N2O emissions is conducted successfully for full-scale WWTPs. While clearly showing that the NH2OH related pathways could well explain N2O production and emission in the two full-scale plants studied, the modeling results do not prove the dominance of the NH2OH pathways in these plants, nor rule out the possibility of AOB denitrification being a potentially dominating pathway in other WWTPs that are designed or operated differently.

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

PubMed

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

2014-08-28

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

Biomass viability: An experimental study and the development of an empirical mathematical model for submerged membrane bioreactor.

PubMed

Zuthi, M F R; Ngo, H H; Guo, W S; Nghiem, L D; Hai, F I; Xia, S Q; Zhang, Z Q; Li, J X

2015-08-01

This study investigates the influence of key biomass parameters on specific oxygen uptake rate (SOUR) in a sponge submerged membrane bioreactor (SSMBR) to develop mathematical models of biomass viability. Extra-cellular polymeric substances (EPS) were considered as a lumped parameter of bound EPS (bEPS) and soluble microbial products (SMP). Statistical analyses of experimental results indicate that the bEPS, SMP, mixed liquor suspended solids and volatile suspended solids (MLSS and MLVSS) have functional relationships with SOUR and their relative influence on SOUR was in the order of EPS>bEPS>SMP>MLVSS/MLSS. Based on correlations among biomass parameters and SOUR, two independent empirical models of biomass viability were developed. The models were validated using results of the SSMBR. However, further validation of the models for different operating conditions is suggested. Copyright © 2015 Elsevier Ltd. All rights reserved.

Mathematical model for gyroscope effects

NASA Astrophysics Data System (ADS)

Usubamatov, Ryspek

2015-05-01

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

Mathematical Modelling Research in Turkey: A Content Analysis Study

ERIC Educational Resources Information Center

Çelik, H. Coskun

2017-01-01

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

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

PubMed

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

2016-11-01

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

Enhancing dendritic cell immunotherapy for melanoma using a simple mathematical model.

PubMed

Castillo-Montiel, E; Chimal-Eguía, J C; Tello, J Ignacio; Piñon-Zaráte, G; Herrera-Enríquez, M; Castell-Rodríguez, A E

2015-06-09

The immunotherapy using dendritic cells (DCs) against different varieties of cancer is an approach that has been previously explored which induces a specific immune response. This work presents a mathematical model of DCs immunotherapy for melanoma in mice based on work by Experimental Immunotherapy Laboratory of the Medicine Faculty in the Universidad Autonoma de Mexico (UNAM). The model is a five delay differential equation (DDEs) which represents a simplified view of the immunotherapy mechanisms. The mathematical model takes into account the interactions between tumor cells, dendritic cells, naive cytotoxic T lymphocytes cells (inactivated cytotoxic cells), effector cells (cytotoxic T activated cytotoxic cells) and transforming growth factor β cytokine (T G F-β). The model is validated comparing the computer simulation results with biological trial results of the immunotherapy developed by the research group of UNAM. The results of the growth of tumor cells obtained by the control immunotherapy simulation show a similar amount of tumor cell population than the biological data of the control immunotherapy. Moreover, comparing the increase of tumor cells obtained from the immunotherapy simulation and the biological data of the immunotherapy applied by the UNAM researchers obtained errors of approximately 10 %. This allowed us to use the model as a framework to test hypothetical treatments. The numerical simulations suggest that by using more doses of DCs and changing the infusion time, the tumor growth decays compared with the current immunotherapy. In addition, a local sensitivity analysis is performed; the results show that the delay in time " τ", the maximal growth rate of tumor "r" and the maximal efficiency of tumor cytotoxic cells rate "aT" are the most sensitive model parameters. By using this mathematical model it is possible to simulate the growth of the tumor cells with or without immunotherapy using the infusion protocol of the UNAM researchers, to

Decompression models: review, relevance and validation capabilities.

PubMed

Hugon, J

2014-01-01

For more than a century, several types of mathematical models have been proposed to describe tissue desaturation mechanisms in order to limit decompression sickness. These models are statistically assessed by DCS cases, and, over time, have gradually included bubble formation biophysics. This paper proposes to review this evolution and discuss its limitations. This review is organized around the comparison of decompression model biophysical criteria and theoretical foundations. Then, the DCS-predictive capability was analyzed to assess whether it could be improved by combining different approaches. Most of the operational decompression models have a neo-Haldanian form. Nevertheless, bubble modeling has been gaining popularity, and the circulating bubble amount has become a major output. By merging both views, it seems possible to build a relevant global decompression model that intends to simulate bubble production while predicting DCS risks for all types of exposures and decompression profiles. A statistical approach combining both DCS and bubble detection databases has to be developed to calibrate a global decompression model. Doppler ultrasound and DCS data are essential: i. to make correlation and validation phases reliable; ii. to adjust biophysical criteria to fit at best the observed bubble kinetics; and iii. to build a relevant risk function.

A physiologically based mathematical model of dermal absorption in man.

PubMed

Auton, T R; Westhead, D R; Woollen, B H; Scott, R C; Wilks, M F

1994-01-01

A sound understanding of the mechanisms determining percutaneous absorption is necessary for toxicological risk assessment of chemicals contacting the skin. As part of a programme investigating these mechanisms we have developed a physiologically based mathematical model. The structure of the model parallels the multi-layer structure of the skin, with separate surface, stratum corneum and viable tissue layers. It simulates the effects of partitioning and diffusive transport between the sub-layers, and metabolism in the viable epidermis. In addition the model describes removal processes on the surface of the skin, including the effects of washing and desquamation, and rubbing off onto clothing. This model is applied to data on the penetration of the herbicide fluazifop-butyl through human skin in vivo and in vitro. Part of this dataset is used to estimate unknown model parameter values and the remainder is used to provide a partial validation of the model. Only a small fraction of the applied dose was absorbed through the skin; most of it was removed by washing or onto clothing. The model provides a quantitative description of these loss processes on the skin surface.

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

PubMed Central

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

2016-01-01

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

Systematized water content calculation in cartilage using T1-mapping MR estimations: design and validation of a mathematical model.

PubMed

Shiguetomi-Medina, J M; Ramirez-Gl, J L; Stødkilde-Jørgensen, H; Møller-Madsen, B

2017-09-01

Up to 80 % of cartilage is water; the rest is collagen fibers and proteoglycans. Magnetic resonance (MR) T1-weighted measurements can be employed to calculate the water content of a tissue using T1 mapping. In this study, a method that translates T1 values into water content data was tested statistically. To develop a predictive equation, T1 values were obtained for tissue-mimicking gelatin samples. 1.5 T MRI was performed using inverse angle phase and an inverse sequence at 37 (±0.5) °C. Regions of interest were manually delineated and the mean T1 value was estimated in arbitrary units. Data were collected and modeled using linear regression. To validate the method, articular cartilage from six healthy pigs was used. The experiment was conducted in accordance with the Danish Animal Experiment Committee. Double measurements were performed for each animal. Ex vivo, all water in the tissue was extracted by lyophilization, thus allowing the volume of water to be measured. This was then compared with the predicted water content via Lin's concordance correlation coefficient at the 95 % confidence level. The mathematical model was highly significant when compared to a null model (p < 0.0001). 97.3 % of the variation in water content can be explained by absolute T1 values. Percentage water content could be predicted as 0.476 + (T1 value) × 0.000193 × 100 %. We found that there was 98 % concordance between the actual and predicted water contents. The results of this study demonstrate that MR data can be used to predict percentage water contents of cartilage samples. 3 (case-control study).

Be-CoDiS: A Mathematical Model to Predict the Risk of Human Diseases Spread Between Countries--Validation and Application to the 2014-2015 Ebola Virus Disease Epidemic.

PubMed

Ivorra, Benjamin; Ngom, Diène; Ramos, Ángel M

2015-09-01

Ebola virus disease is a lethal human and primate disease that currently requires a particular attention from the international health authorities due to important outbreaks in some Western African countries and isolated cases in the UK, the USA and Spain. Regarding the emergency of this situation, there is a need for the development of decision tools, such as mathematical models, to assist the authorities to focus their efforts in important factors to eradicate Ebola. In this work, we propose a novel deterministic spatial-temporal model, called Between-Countries Disease Spread (Be-CoDiS), to study the evolution of human diseases within and between countries. The main interesting characteristics of Be-CoDiS are the consideration of the movement of people between countries, the control measure effects and the use of time-dependent coefficients adapted to each country. First, we focus on the mathematical formulation of each component of the model and explain how its parameters and inputs are obtained. Then, in order to validate our approach, we consider two numerical experiments regarding the 2014-2015 Ebola epidemic. The first one studies the ability of the model in predicting the EVD evolution between countries starting from the index cases in Guinea in December 2013. The second one consists of forecasting the evolution of the epidemic by using some recent data. The results obtained with Be-CoDiS are compared to real data and other model outputs found in the literature. Finally, a brief parameter sensitivity analysis is done. A free MATLAB version of Be-CoDiS is available at: http://www.mat.ucm.es/momat/software.htm.

Predicting Drug Combination Index and Simulating the Network-Regulation Dynamics by Mathematical Modeling of Drug-Targeted EGFR-ERK Signaling Pathway

NASA Astrophysics Data System (ADS)

Huang, Lu; Jiang, Yuyang; Chen, Yuzong

2017-01-01

Synergistic drug combinations enable enhanced therapeutics. Their discovery typically involves the measurement and assessment of drug combination index (CI), which can be facilitated by the development and applications of in-silico CI predictive tools. In this work, we developed and tested the ability of a mathematical model of drug-targeted EGFR-ERK pathway in predicting CIs and in analyzing multiple synergistic drug combinations against observations. Our mathematical model was validated against the literature reported signaling, drug response dynamics, and EGFR-MEK drug combination effect. The predicted CIs and combination therapeutic effects of the EGFR-BRaf, BRaf-MEK, FTI-MEK, and FTI-BRaf inhibitor combinations showed consistent synergism. Our results suggest that existing pathway models may be potentially extended for developing drug-targeted pathway models to predict drug combination CI values, isobolograms, and drug-response surfaces as well as to analyze the dynamics of individual and combinations of drugs. With our model, the efficacy of potential drug combinations can be predicted. Our method complements the developed in-silico methods (e.g. the chemogenomic profile and the statistically-inferenced network models) by predicting drug combination effects from the perspectives of pathway dynamics using experimental or validated molecular kinetic constants, thereby facilitating the collective prediction of drug combination effects in diverse ranges of disease systems.

A clinical data validated mathematical model of prostate cancer growth under intermittent androgen suppression therapy

NASA Astrophysics Data System (ADS)

Portz, Travis; Kuang, Yang; Nagy, John D.

2012-03-01

Prostate cancer is commonly treated by a form of hormone therapy called androgen suppression. This form of treatment, while successful at reducing the cancer cell population, adversely affects quality of life and typically leads to a recurrence of the cancer in an androgen-independent form. Intermittent androgen suppression aims to alleviate some of these adverse affects by cycling the patient on and off treatment. Clinical studies have suggested that intermittent therapy is capable of maintaining androgen dependence over multiple treatment cycles while increasing quality of life during off-treatment periods. This paper presents a mathematical model of prostate cancer to study the dynamics of androgen suppression therapy and the production of prostate-specific antigen (PSA), a clinical marker for prostate cancer. Preliminary models were based on the assumption of an androgen-independent (AI) cell population with constant net growth rate. These models gave poor accuracy when fitting clinical data during simulation. The final model presented hypothesizes an AI population with increased sensitivity to low levels of androgen. It also hypothesizes that PSA production is heavily dependent on androgen. The high level of accuracy in fitting clinical data with this model appears to confirm these hypotheses, which are also consistent with biological evidence.

Mathematical modeling of cancer metabolism.

PubMed

Medina, Miguel Ángel

2018-04-01

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

A mathematical model for expected time to extinction of pathogenic bacteria through antibiotic

NASA Astrophysics Data System (ADS)

Ghosh, M. K.; Nandi, S.; Roy, P. K.

2016-04-01

Application of antibiotics in human system to prevent bacterial diseases like Gastritis, Ulcers, Meningitis, Pneumonia and Gonorrhea are indispensable. Antibiotics saved innumerable lives and continue to be a strong support for therapeutic application against pathogenic bacteria. In human system, bacterial diseases occur when pathogenic bacteria gets into the body and begin to reproduce and crowd out healthy bacteria. In this process, immature bacteria releases enzyme which is essential for bacterial cell-wall biosynthesis. After complete formation of cell wall, immature bacteria are converted to mature or virulent bacteria which are harmful to us during bacterial infections. Use of antibiotics as drug inhibits the bacterial cell wall formation. After application of antibiotics within body, the released bacterial enzyme binds with antibiotic molecule instead of its functional site during the cell wall synthesis in a competitive inhibition approach. As a consequence, the bacterial cell-wall formation as well as maturation process of pathogenic bacteria is halted and the disease is cured with lysis of bacterial cells. With this idea, a mathematical model has been developed in the present research investigation to review the inhibition of biosynthesis of bacterial cell wall by the application of antibiotics as drug in the light of enzyme kinetics. This approach helps to estimate the expected time to extinction of the pathogenic bacteria. Our mathematical approach based on the enzyme kinetic model for finding out expected time to extinction contributes favorable results for understanding of disease dynamics. Analytical and numerical results based on simulated findings validate our mathematical model.

Mathematical model of polyethylene pipe bending stress state

NASA Astrophysics Data System (ADS)

Serebrennikov, Anatoly; Serebrennikov, Daniil

2018-03-01

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

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.

Mathematical model comparing of the multi-level economics systems

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Thermal mathematical modeling and system simulation of Space Shuttle less subsystem

NASA Technical Reports Server (NTRS)

Chao, D. C.; Battley, H. H.; Gallegos, J. J.; Curry, D. M.

1984-01-01

Applications, validation tests, and upgrades of the two- and three-dimensional system level thermal mathematical system simulation models (TMSSM) used for thermal protection system (TPS) analyses are described. The TMSSM were developed as an aid to predicting the performance requirements and configurations of the Shuttle wing leading edge (WLE) and nose cone (NC) TPS tiles. The WLE and its structure were subjected to acoustic, thermal/vacuum, and air loads tests to simulate launch, on-orbit, and re-entry behavior. STS-1, -2 and -5 flight data led to recalibration of on-board instruments and raised estimates of the thermal shock at the NC and WLE. Baseline heating data are now available for the design of future TPS.

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…

The Incidence Patterns Model to Estimate the Distribution of New HIV Infections in Sub-Saharan Africa: Development and Validation of a Mathematical Model

PubMed Central

Cori, Anne; Pufall, Erica L.; Price, Alison; Elmes, Jocelyn; Zaba, Basia; Crampin, Amelia C.; Lutalo, Tom; Gregson, Simon; Hallett, Timothy B.

2016-01-01

Background Programmatic planning in HIV requires estimates of the distribution of new HIV infections according to identifiable characteristics of individuals. In sub-Saharan Africa, robust routine data sources and historical epidemiological observations are available to inform and validate such estimates. Methods and Findings We developed a predictive model, the Incidence Patterns Model (IPM), representing populations according to factors that have been demonstrated to be strongly associated with HIV acquisition risk: gender, marital/sexual activity status, geographic location, “key populations” based on risk behaviours (sex work, injecting drug use, and male-to-male sex), HIV and ART status within married or cohabiting unions, and circumcision status. The IPM estimates the distribution of new infections acquired by group based on these factors within a Bayesian framework accounting for regional prior information on demographic and epidemiological characteristics from trials or observational studies. We validated and trained the model against direct observations of HIV incidence by group in seven rounds of cohort data from four studies (“sites”) conducted in Manicaland, Zimbabwe; Rakai, Uganda; Karonga, Malawi; and Kisesa, Tanzania. The IPM performed well, with the projections’ credible intervals for the proportion of new infections per group overlapping the data’s confidence intervals for all groups in all rounds of data. In terms of geographical distribution, the projections’ credible intervals overlapped the confidence intervals for four out of seven rounds, which were used as proxies for administrative divisions in a country. We assessed model performance after internal training (within one site) and external training (between sites) by comparing mean posterior log-likelihoods and used the best model to estimate the distribution of HIV incidence in six countries (Gabon, Kenya, Malawi, Rwanda, Swaziland, and Zambia) in the region. We subsequently

The Incidence Patterns Model to Estimate the Distribution of New HIV Infections in Sub-Saharan Africa: Development and Validation of a Mathematical Model.

PubMed

Bórquez, Annick; Cori, Anne; Pufall, Erica L; Kasule, Jingo; Slaymaker, Emma; Price, Alison; Elmes, Jocelyn; Zaba, Basia; Crampin, Amelia C; Kagaayi, Joseph; Lutalo, Tom; Urassa, Mark; Gregson, Simon; Hallett, Timothy B

2016-09-01

Programmatic planning in HIV requires estimates of the distribution of new HIV infections according to identifiable characteristics of individuals. In sub-Saharan Africa, robust routine data sources and historical epidemiological observations are available to inform and validate such estimates. We developed a predictive model, the Incidence Patterns Model (IPM), representing populations according to factors that have been demonstrated to be strongly associated with HIV acquisition risk: gender, marital/sexual activity status, geographic location, "key populations" based on risk behaviours (sex work, injecting drug use, and male-to-male sex), HIV and ART status within married or cohabiting unions, and circumcision status. The IPM estimates the distribution of new infections acquired by group based on these factors within a Bayesian framework accounting for regional prior information on demographic and epidemiological characteristics from trials or observational studies. We validated and trained the model against direct observations of HIV incidence by group in seven rounds of cohort data from four studies ("sites") conducted in Manicaland, Zimbabwe; Rakai, Uganda; Karonga, Malawi; and Kisesa, Tanzania. The IPM performed well, with the projections' credible intervals for the proportion of new infections per group overlapping the data's confidence intervals for all groups in all rounds of data. In terms of geographical distribution, the projections' credible intervals overlapped the confidence intervals for four out of seven rounds, which were used as proxies for administrative divisions in a country. We assessed model performance after internal training (within one site) and external training (between sites) by comparing mean posterior log-likelihoods and used the best model to estimate the distribution of HIV incidence in six countries (Gabon, Kenya, Malawi, Rwanda, Swaziland, and Zambia) in the region. We subsequently inferred the potential contribution of each

Mathematization in introductory physics

NASA Astrophysics Data System (ADS)

Brahmia, Suzanne M.

Mathematization is central to STEM disciplines as a cornerstone of the quantitative reasoning that characterizes these fields. Introductory physics is required for most STEM majors in part so that students develop expert-like mathematization. This dissertation describes coordinated research and curriculum development for strengthening mathematization in introductory physics; it blends scholarship in physics and mathematics education in the form of three papers. The first paper explores mathematization in the context of physics, and makes an original contribution to the measurement of physics students' struggle to mathematize. Instructors naturally assume students have a conceptual mastery of algebra before embarking on a college physics course because these students are enrolled in math courses beyond algebra. This paper provides evidence that refutes the validity of this assumption and categorizes some of the barriers students commonly encounter with quantification and representing ideas symbolically. The second paper develops a model of instruction that can help students progress from their starting points to their instructor's desired endpoints. Instructors recognize that the introductory physics course introduces new ideas at an astonishing rate. More than most physicists realize, however, the way that mathematics is used in the course is foreign to a large portion of class. This paper puts forth an instructional model that can move all students toward better quantitative and physical reasoning, despite the substantial variability of those students' initial states. The third paper describes the design and testing of curricular materials that foster mathematical creativity to prepare students to better understand physics reasoning. Few students enter introductory physics with experience generating equations in response to specific challenges involving unfamiliar quantities and units, yet this generative use of mathematics is typical of the thinking involved in

Mathematical Modelling for Patient Selection in Proton Therapy.

PubMed

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

2018-05-01

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

Mathematical Model Development and Simulation Support

NASA Technical Reports Server (NTRS)

Francis, Ronald C.; Tobbe, Patrick A.

2000-01-01

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

On a Mathematical Model with Noncompact Boundary Conditions Describing Bacterial Population

NASA Astrophysics Data System (ADS)

Boulanouar, Mohamed

2013-04-01

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

Mathematical Modeling: Are Prior Experiences Important?

ERIC Educational Resources Information Center

Czocher, Jennifer A.; Moss, Diana L.

2017-01-01

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

Mathematical model of marine diesel engine simulator for a new methodology of self propulsion tests

NASA Astrophysics Data System (ADS)

Izzuddin, Nur; Sunarsih, Priyanto, Agoes

2015-05-01

As a vessel operates in the open seas, a marine diesel engine simulator whose engine rotation is controlled to transmit through propeller shaft is a new methodology for the self propulsion tests to track the fuel saving in a real time. Considering the circumstance, this paper presents the real time of marine diesel engine simulator system to track the real performance of a ship through a computer-simulated model. A mathematical model of marine diesel engine and the propeller are used in the simulation to estimate fuel rate, engine rotating speed, thrust and torque of the propeller thus achieve the target vessel's speed. The input and output are a real time control system of fuel saving rate and propeller rotating speed representing the marine diesel engine characteristics. The self-propulsion tests in calm waters were conducted using a vessel model to validate the marine diesel engine simulator. The simulator then was used to evaluate the fuel saving by employing a new mathematical model of turbochargers for the marine diesel engine simulator. The control system developed will be beneficial for users as to analyze different condition of vessel's speed to obtain better characteristics and hence optimize the fuel saving rate.

Mathematical modeling of laser based potato cutting and peeling.

PubMed

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

2007-01-01

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

Mathematical modeling of enzyme production using Trichoderma harzianum P49P11 and sugarcane bagasse as carbon source.

PubMed

Gelain, Lucas; da Cruz Pradella, José Geraldo; da Costa, Aline Carvalho

2015-12-01

A mathematical model to describe the kinetics of enzyme production by the filamentous fungus Trichoderma harzianum P49P11 was developed using a low cost substrate as main carbon source (pretreated sugarcane bagasse). The model describes the cell growth, variation of substrate concentration and production of three kinds of enzymes (cellulases, beta-glucosidase and xylanase) in different sugarcane bagasse concentrations (5; 10; 20; 30; 40 gL(-1)). The 10 gL(-1) concentration was used to validate the model and the other to parameter estimation. The model for enzyme production has terms implicitly representing induction and repression. Substrate variation was represented by a simple degradation rate. The models seem to represent well the kinetics with a good fit for the majority of the assays. Validation results indicate that the models are adequate to represent the kinetics for a biotechnological process. Copyright © 2015 Elsevier Ltd. All rights reserved.

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.…

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.

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.

Automatic mathematical modeling for real time simulation system

NASA Technical Reports Server (NTRS)

Wang, Caroline; Purinton, Steve

1988-01-01

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

Review and verification of CARE 3 mathematical model and code

NASA Technical Reports Server (NTRS)

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

1983-01-01

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

Validation workflow for a clinical Bayesian network model in multidisciplinary decision making in head and neck oncology treatment.

PubMed

Cypko, Mario A; Stoehr, Matthaeus; Kozniewski, Marcin; Druzdzel, Marek J; Dietz, Andreas; Berliner, Leonard; Lemke, Heinz U

2017-11-01

Oncological treatment is being increasingly complex, and therefore, decision making in multidisciplinary teams is becoming the key activity in the clinical pathways. The increased complexity is related to the number and variability of possible treatment decisions that may be relevant to a patient. In this paper, we describe validation of a multidisciplinary cancer treatment decision in the clinical domain of head and neck oncology. Probabilistic graphical models and corresponding inference algorithms, in the form of Bayesian networks, can support complex decision-making processes by providing a mathematically reproducible and transparent advice. The quality of BN-based advice depends on the quality of the model. Therefore, it is vital to validate the model before it is applied in practice. For an example BN subnetwork of laryngeal cancer with 303 variables, we evaluated 66 patient records. To validate the model on this dataset, a validation workflow was applied in combination with quantitative and qualitative analyses. In the subsequent analyses, we observed four sources of imprecise predictions: incorrect data, incomplete patient data, outvoting relevant observations, and incorrect model. Finally, the four problems were solved by modifying the data and the model. The presented validation effort is related to the model complexity. For simpler models, the validation workflow is the same, although it may require fewer validation methods. The validation success is related to the model's well-founded knowledge base. The remaining laryngeal cancer model may disclose additional sources of imprecise predictions.

Mathematical models of continuous flow electrophoresis: Electrophoresis technology

NASA Technical Reports Server (NTRS)

Saville, Dudley A.

1986-01-01

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

An Investigation of the Validity and Reliability of the Adapted Mathematics Anxiety Rating Scale-Short Version (MARS-SV) among Turkish Students

ERIC Educational Resources Information Center

Baloglu, Mustafa

2010-01-01

This study adapted the Mathematics Anxiety Rating Scale-Short Version (MARS-SV) into Turkish and investigated the validity and reliability of the adapted instrument. Twenty-five bilingual experts agreed on the language validity, and 49 Turkish language experts agreed on the conformity and understandability of the scale's items. Thirty-two subject…

Assessment of Galileo modal test results for mathematical model verification

NASA Technical Reports Server (NTRS)

Trubert, M.

1984-01-01

The modal test program for the Galileo Spacecraft was completed at the Jet Propulsion Laboratory in the summer of 1983. The multiple sine dwell method was used for the baseline test. The Galileo Spacecraft is a rather complex 2433 kg structure made of a central core on which seven major appendages representing 30 percent of the total mass are attached, resulting in a high modal density structure. The test revealed a strong nonlinearity in several major modes. This nonlinearity discovered in the course of the test necessitated running additional tests at the unusually high response levels of up to about 21 g. The high levels of response were required to obtain a model verification valid at the level of loads for which the spacecraft was designed. Because of the high modal density and the nonlinearity, correlation between the dynamic mathematical model and the test results becomes a difficult task. Significant changes in the pre-test analytical model are necessary to establish confidence in the upgraded analytical model used for the final load verification. This verification, using a test verified model, is required by NASA to fly the Galileo Spacecraft on the Shuttle/Centaur launch vehicle in 1986.

Mathematical modeling of infectious disease dynamics

PubMed Central

Siettos, Constantinos I.; Russo, Lucia

2013-01-01

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

The Ability of Students’ Mathematical Proof in Determining the Validity of Argument Reviewed from Gender Differences

NASA Astrophysics Data System (ADS)

Feriyanto

2018-01-01

This research aims to describe the ability of students’ mathematical proof in determining the validity of argument reviewed from gender differences. The subjects of this research were one male and one female student of the fifth semester of Mathematic Education study program. The subjects were selected based on the highest mathematics ability which was assesed from their previous assignments and tests. In addition, the communication ability of the subjects was also considered in order to facilitate the researcher in conducting interviews. Based on the result of the test with direct and indirect proof, it could be concluded that the subjects were able to: 1) mention all facts/premises and write about what should be shown (conclusion) in direct proof and write additional premise in indirect proof; 2) connect facts/premises to concepts which must be mastered; 3) use equivalent concept to manipulate and organize the proof; 4) use the concept of syllogism and tollens mode to obtain the desired conclusion; 5) construct mathematical evidence systematically, and logically; 6) complement the reason for each step appropriately. The difference was that the male subject wrote the final conclusion, while the female subject did not write the final conclusion on the proof.

Study of ecological compensation in complex river networks based on a mathematical model.

PubMed

Wang, Xiao; Shen, Chunqi; Wei, Jun; Niu, Yong

2018-05-31

Transboundary water pollution has resulted in increasing conflicts between upstream and downstream administrative districts. Ecological compensation is an efficient means of restricting pollutant discharge and achieving sustainable utilization of water resources. The tri-provincial region of Taihu Basin is a typical river networks area. Pollutant flux across provincial boundaries in the Taihu Basin is hard to determine due to complex hydrologic and hydrodynamic conditions. In this study, ecological compensation estimation for the tri-provincial area based on a mathematical model is investigated for better environmental management. River discharge and water quality are predicted with the one-dimensional mathematical model and validated with field measurements. Different ecological compensation criteria are identified considering the notable regional discrepancy in sewage treatment costs. Finally, the total compensation payment is estimated. Our study indicates that Shanghai should be the receiver of payment from both Jiangsu and Zhenjiang in 2013, with 305 million and 300 million CNY, respectively. Zhejiang also contributes more pollutants to Jiangsu, and the compensation to Jiangsu is estimated as 9.3 million CNY. The proposed ecological compensation method provides an efficient way for solving the transboundary conflicts in a complex river networks area and is instructive for future policy-making.

Modeling eBook acceptance: A study on mathematics teachers

NASA Astrophysics Data System (ADS)

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

2014-12-01

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

Helicopter simulation validation using flight data

NASA Technical Reports Server (NTRS)

Key, D. L.; Hansen, R. S.; Cleveland, W. B.; Abbott, W. Y.

1982-01-01

A joint NASA/Army effort to perform a systematic ground-based piloted simulation validation assessment is described. The best available mathematical model for the subject helicopter (UH-60A Black Hawk) was programmed for real-time operation. Flight data were obtained to validate the math model, and to develop models for the pilot control strategy while performing mission-type tasks. The validated math model is to be combined with motion and visual systems to perform ground based simulation. Comparisons of the control strategy obtained in flight with that obtained on the simulator are to be used as the basis for assessing the fidelity of the results obtained in the simulator.

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

NASA Astrophysics Data System (ADS)

Easters, D. J.

2014-03-01

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

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.

Simulation validation of the XV-15 tilt-rotor research aircraft

NASA Technical Reports Server (NTRS)

Ferguson, S. W.; Hanson, G. D.; Churchill, G. B.

1984-01-01

The results of a simulation validation program of the XV-15 tilt-rotor research aircraft are detailed, covering such simulation aspects as the mathematical model, visual system, motion system, cab aural system, cab control loader system, pilot perceptual fidelity, and generic tilt rotor applications. Simulation validation was performed for the hover, low-speed, and sideward flight modes, with consideration of the in-ground rotor effect. Several deficiencies of the mathematical model and the simulation systems were identified in the course of the simulation validation project, and some were corrected. It is noted that NASA's Vertical Motion Simulator used in the program is an excellent tool for tilt-rotor and rotorcraft design, development, and pilot training.

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

PubMed

Polak, Justyna; Bartoszek, Mariola; Chorążewski, Mirosław

2015-07-22

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

The prediction of epidemics through mathematical modeling.

PubMed

Schaus, Catherine

2014-01-01

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

Identification of line-specific strategies for improving carotenoid production in synthetic maize through data-driven mathematical modeling.

PubMed

Comas, Jorge; Benfeitas, Rui; Vilaprinyo, Ester; Sorribas, Albert; Solsona, Francesc; Farré, Gemma; Berman, Judit; Zorrilla, Uxue; Capell, Teresa; Sandmann, Gerhard; Zhu, Changfu; Christou, Paul; Alves, Rui

2016-09-01

Plant synthetic biology is still in its infancy. However, synthetic biology approaches have been used to manipulate and improve the nutritional and health value of staple food crops such as rice, potato and maize. With current technologies, production yields of the synthetic nutrients are a result of trial and error, and systematic rational strategies to optimize those yields are still lacking. Here, we present a workflow that combines gene expression and quantitative metabolomics with mathematical modeling to identify strategies for increasing production yields of nutritionally important carotenoids in the seed endosperm synthesized through alternative biosynthetic pathways in synthetic lines of white maize, which is normally devoid of carotenoids. Quantitative metabolomics and gene expression data are used to create and fit parameters of mathematical models that are specific to four independent maize lines. Sensitivity analysis and simulation of each model is used to predict which gene activities should be further engineered in order to increase production yields for carotenoid accumulation in each line. Some of these predictions (e.g. increasing Zmlycb/Gllycb will increase accumulated β-carotenes) are valid across the four maize lines and consistent with experimental observations in other systems. Other predictions are line specific. The workflow is adaptable to any other biological system for which appropriate quantitative information is available. Furthermore, we validate some of the predictions using experimental data from additional synthetic maize lines for which no models were developed. © 2016 The Authors The Plant Journal © 2016 John Wiley & Sons Ltd.

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

NASA Astrophysics Data System (ADS)

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

2015-03-01

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

A heuristic mathematical model for the dynamics of sensory conflict and motion sickness

NASA Technical Reports Server (NTRS)

Oman, C. M.

1982-01-01

By consideration of the information processing task faced by the central nervous system in estimating body spatial orientation and in controlling active body movement using an internal model referenced control strategy, a mathematical model for sensory conflict generation is developed. The model postulates a major dynamic functional role for sensory conflict signals in movement control, as well as in sensory-motor adaptation. It accounts for the role of active movement in creating motion sickness symptoms in some experimental circumstance, and in alleviating them in others. The relationship between motion sickness produced by sensory rearrangement and that resulting from external motion disturbances is explicitly defined. A nonlinear conflict averaging model is proposed which describes dynamic aspects of experimentally observed subjective discomfort sensation, and suggests resulting behaviours. The model admits several possibilities for adaptive mechanisms which do not involve internal model updating. Further systematic efforts to experimentally refine and validate the model are indicated.

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.

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.

Design and Development Computer-Based E-Learning Teaching Material for Improving Mathematical Understanding Ability and Spatial Sense of Junior High School Students

NASA Astrophysics Data System (ADS)

Nurjanah; Dahlan, J. A.; Wibisono, Y.

2017-02-01

This paper aims to make a design and development computer-based e-learning teaching material for improving mathematical understanding ability and spatial sense of junior high school students. Furthermore, the particular aims are (1) getting teaching material design, evaluation model, and intrument to measure mathematical understanding ability and spatial sense of junior high school students; (2) conducting trials computer-based e-learning teaching material model, asessment, and instrument to develop mathematical understanding ability and spatial sense of junior high school students; (3) completing teaching material models of computer-based e-learning, assessment, and develop mathematical understanding ability and spatial sense of junior high school students; (4) resulting research product is teaching materials of computer-based e-learning. Furthermore, the product is an interactive learning disc. The research method is used of this study is developmental research which is conducted by thought experiment and instruction experiment. The result showed that teaching materials could be used very well. This is based on the validation of computer-based e-learning teaching materials, which is validated by 5 multimedia experts. The judgement result of face and content validity of 5 validator shows that the same judgement result to the face and content validity of each item test of mathematical understanding ability and spatial sense. The reliability test of mathematical understanding ability and spatial sense are 0,929 and 0,939. This reliability test is very high. While the validity of both tests have a high and very high criteria.

Two Mathematical Models of Nonlinear Vibrations

NASA Technical Reports Server (NTRS)

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

2007-01-01

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

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.

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

NASA Astrophysics Data System (ADS)

Bartley, Sarah R.; Ingram, Naomi

2017-12-01

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

Selection, calibration, and validation of models of tumor growth.

PubMed

Lima, E A B F; Oden, J T; Hormuth, D A; Yankeelov, T E; Almeida, R C

2016-11-01

This paper presents general approaches for addressing some of the most important issues in predictive computational oncology concerned with developing classes of predictive models of tumor growth. First, the process of developing mathematical models of vascular tumors evolving in the complex, heterogeneous, macroenvironment of living tissue; second, the selection of the most plausible models among these classes, given relevant observational data; third, the statistical calibration and validation of models in these classes, and finally, the prediction of key Quantities of Interest (QOIs) relevant to patient survival and the effect of various therapies. The most challenging aspects of this endeavor is that all of these issues often involve confounding uncertainties: in observational data, in model parameters, in model selection, and in the features targeted in the prediction. Our approach can be referred to as "model agnostic" in that no single model is advocated; rather, a general approach that explores powerful mixture-theory representations of tissue behavior while accounting for a range of relevant biological factors is presented, which leads to many potentially predictive models. Then representative classes are identified which provide a starting point for the implementation of OPAL, the Occam Plausibility Algorithm (OPAL) which enables the modeler to select the most plausible models (for given data) and to determine if the model is a valid tool for predicting tumor growth and morphology ( in vivo ). All of these approaches account for uncertainties in the model, the observational data, the model parameters, and the target QOI. We demonstrate these processes by comparing a list of models for tumor growth, including reaction-diffusion models, phase-fields models, and models with and without mechanical deformation effects, for glioma growth measured in murine experiments. Examples are provided that exhibit quite acceptable predictions of tumor growth in laboratory

The development of a model of culturally responsive science and mathematics teaching

NASA Astrophysics Data System (ADS)

Hernandez, Cecilia M.; Morales, Amanda R.; Shroyer, M. Gail

2013-12-01

This qualitative theoretical study was conducted in response to the current need for an inclusive and comprehensive model to guide the preparation and assessment of teacher candidates for culturally responsive teaching. The process of developing a model of culturally responsive teaching involved three steps: a comprehensive review of the literature; a synthesis of the literature into thematic categories to capture the dispositions and behaviors of culturally responsive teaching; and the piloting of these thematic categories with teacher candidates to validate the usefulness of the categories and to generate specific exemplars of behavior to represent each category. The model of culturally responsive teaching contains five thematic categories: (1) content integration, (2) facilitating knowledge construction, (3) prejudice reduction, (4) social justice, and (5) academic development. The current model is a promising tool for comprehensively defining culturally responsive teaching in the context of teacher education as well as to guide curriculum and assessment changes aimed to increase candidates' culturally responsive knowledge and skills in science and mathematics teaching.

Mathematical modeling of hydromechanical extrusion

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

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.

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…

Power Plant Model Validation Tool

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

The PPMV is used to validate generator model using disturbance recordings. The PPMV tool contains a collection of power plant models and model validation studies, as well as disturbance recordings from a number of historic grid events. The user can import data from a new disturbance into the database, which converts PMU and SCADA data into GE PSLF format, and then run the tool to validate (or invalidate) the model for a specific power plant against its actual performance. The PNNL PPMV tool enables the automation of the process of power plant model validation using disturbance recordings. The tool usesmore » PMU and SCADA measurements as input information. The tool automatically adjusts all required EPCL scripts and interacts with GE PSLF in the batch mode. The main tool features includes: The tool interacts with GE PSLF; The tool uses GE PSLF Play-In Function for generator model validation; Database of projects (model validation studies); Database of the historic events; Database of the power plant; The tool has advanced visualization capabilities; and The tool automatically generates reports« less

Unpacking the Logic of Mathematical Statements.

ERIC Educational Resources Information Center

Selden, John; Selden, Annie

1995-01-01

Investigated (n=61) undergraduates' ability to unpack informally written mathematical statements into the language of predicate calculus in an introduction to proofs and mathematical reasoning. Found that students were unable to construct proofs or validate them. Appendices are "A Sample Validation" and "Building a Statement Image." (MKR)

An Investigation of Pre-Service Middle School Mathematics Teachers' Ability to Conduct Valid Proofs, Methods Used, and Reasons for Invalid Arguments

ERIC Educational Resources Information Center

Demiray, Esra; Isiksal Bostan, Mine

2017-01-01

The purposes of this study are to investigate Turkish pre-service middle school mathematics teachers' ability in conducting valid proofs for statements regarding numbers and algebra in terms of their year of enrollment in a teacher education program, to determine the proof methods used in their valid proofs, and to examine the reasons for their…

Cooking Potatoes: Experimentation and Mathematical Modeling.

ERIC Educational Resources Information Center

Chen, Xiao Dong

2002-01-01

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

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.

Mathematical modeling of forest fire initiation in three dimensional setting

Treesearch

Valeriy Perminov

2007-01-01

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

Mathematical model for rhythmic protoplasmic movement in the true slime mold.

PubMed

Kobayashi, Ryo; Tero, Atsushi; Nakagaki, Toshiyuki

2006-08-01

The plasmodium of the true slime mold Physarum polycephalum is a large amoeboid organism that displays "smart" behavior such as chemotaxis and the ability to solve mazes and geometrical puzzles. These amoeboid behaviors are based on the dynamics of the viscoelastic protoplasm and its biochemical rhythms. By incorporating both these aspects, we constructed a mathematical model for the dynamics of the organism as a first step towards understanding the relation between protoplasmic movement and its unusual abilities. We tested the validity of the model by comparing it with physiological observation. Our model reproduces fundamental characteristics of the spatio-temporal pattern of the rhythmic movement: (1) the antiphase oscillation between frontal tip and rear when the front is freely extending; (2) the asynchronous oscillation pattern when the front is not freely extending; and (3) the formation of protoplasmic mounds over a longer time scale. Both our model and physiological observation suggest that cell stiffness plays a primary role in plasmodial behaviors, in contrast to the conventional theory of coupled oscillator systems.

About a mathematical model of market

NASA Astrophysics Data System (ADS)

Kulikov, D. A.

2017-01-01

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

Uncertainty and Complexity in Mathematical Modeling

ERIC Educational Resources Information Center

Cannon, Susan O.; Sanders, Mark

2017-01-01

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

[Mathematical models and epidemiological analysis].

PubMed

Gerasimov, A N

2010-01-01

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

Rigorous mathematical modelling for a Fast Corrector Power Supply in TPS

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

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

ERIC Educational Resources Information Center

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

2017-01-01

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

Examining of Model Eliciting Activities Developed by Mathematics Student Teachers

ERIC Educational Resources Information Center

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

2017-01-01

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

Visual Modeling as a Motivation for Studying Mathematics and Art

ERIC Educational Resources Information Center

Sendova, Evgenia; Grkovska, Slavica

2005-01-01

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

The stability of colorectal cancer mathematical models

NASA Astrophysics Data System (ADS)

Khairudin, Nur Izzati; Abdullah, Farah Aini

2013-04-01

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

Mathematical modeling of olive mill waste composting process.

PubMed

Vasiliadou, Ioanna A; Muktadirul Bari Chowdhury, Abu Khayer Md; Akratos, Christos S; Tekerlekopoulou, Athanasia G; Pavlou, Stavros; Vayenas, Dimitrios V

2015-09-01

The present study aimed at developing an integrated mathematical model for the composting process of olive mill waste. The multi-component model was developed to simulate the composting of three-phase olive mill solid waste with olive leaves and different materials as bulking agents. The modeling system included heat transfer, organic substrate degradation, oxygen consumption, carbon dioxide production, water content change, and biological processes. First-order kinetics were used to describe the hydrolysis of insoluble organic matter, followed by formation of biomass. Microbial biomass growth was modeled with a double-substrate limitation by hydrolyzed available organic substrate and oxygen using Monod kinetics. The inhibitory factors of temperature and moisture content were included in the system. The production and consumption of nitrogen and phosphorous were also included in the model. In order to evaluate the kinetic parameters, and to validate the model, six pilot-scale composting experiments in controlled laboratory conditions were used. Low values of hydrolysis rates were observed (0.002841/d) coinciding with the high cellulose and lignin content of the composting materials used. Model simulations were in good agreement with the experimental results. Sensitivity analysis was performed and the modeling efficiency was determined to further evaluate the model predictions. Results revealed that oxygen simulations were more sensitive on the input parameters of the model compared to those of water, temperature and insoluble organic matter. Finally, the Nash and Sutcliff index (E), showed that the experimental data of insoluble organic matter (E>0.909) and temperature (E>0.678) were better simulated than those of water. Copyright © 2015 Elsevier Ltd. All rights reserved.

Mathematical modeling of moving boundary problems in thermal energy storage

NASA Technical Reports Server (NTRS)

Solomon, A. D.

1980-01-01

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

A whole-body mathematical model for intracranial pressure dynamics.

PubMed

Lakin, William D; Stevens, Scott A; Tranmer, Bruce I; Penar, Paul L

2003-04-01

Most attempts to study intracranial pressure using lumped-parameter models have adopted the classical "Kellie-Monro Doctrine," which considers the intracranial space to be a closed system that is confined within the nearly-rigid skull, conserves mass, and has equal inflow and outflow. The present work revokes this Doctrine and develops a mathematical model for the dynamics of intracranial pressures, volumes, and flows that embeds the intracranial system in extensive whole-body physiology. The new model consistently introduces compartments representing the tissues and vasculature of the extradural portions of the body, including both the thoracic region and the lower extremities. In addition to vascular connections, a spinal-subarachnoid cerebrospinal fluid (CSF) compartment bridges intracranial and extracranial physiology allowing explict buffering of intracranial pressure fluctuations by the spinal theca. The model contains cerebrovascular autoregulation, regulation of systemic vascular pressures by the sympathetic nervous system, regulation of CSF production in the choroid plexus, a lymphatic system, colloid osmotic pressure effects, and realistic descriptions of cardiac output. To validate the model in situations involving normal physiology, the model's response to a realistic pulsatile cardiac output is examined. A well-known experimentally-derived intracranial pressure-volume relationship is recovered by using the model to simulate CSF infusion tests, and the effect on cerebral blood flow of a change in body position is also examined. Cardiac arrest and hemorrhagic shock are simulated to demonstrate the predictive capabilities of the model in pathological conditions.

Program Helps Generate Boundary-Element Mathematical Models

NASA Technical Reports Server (NTRS)

Goldberg, R. K.

1995-01-01

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

Mathematical modelling and numerical simulation of forces in milling process

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Mathematical properties and parameter estimation for transit compartment pharmacodynamic models.

PubMed

Yates, James W T

2008-07-03

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

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.

GetReal in mathematical modelling: a review of studies predicting drug effectiveness in the real world.

PubMed

Panayidou, Klea; Gsteiger, Sandro; Egger, Matthias; Kilcher, Gablu; Carreras, Máximo; Efthimiou, Orestis; Debray, Thomas P A; Trelle, Sven; Hummel, Noemi

2016-09-01

The performance of a drug in a clinical trial setting often does not reflect its effect in daily clinical practice. In this third of three reviews, we examine the applications that have been used in the literature to predict real-world effectiveness from randomized controlled trial efficacy data. We searched MEDLINE, EMBASE from inception to March 2014, the Cochrane Methodology Register, and websites of key journals and organisations and reference lists. We extracted data on the type of model and predictions, data sources, validation and sensitivity analyses, disease area and software. We identified 12 articles in which four approaches were used: multi-state models, discrete event simulation models, physiology-based models and survival and generalized linear models. Studies predicted outcomes over longer time periods in different patient populations, including patients with lower levels of adherence or persistence to treatment or examined doses not tested in trials. Eight studies included individual patient data. Seven examined cardiovascular and metabolic diseases and three neurological conditions. Most studies included sensitivity analyses, but external validation was performed in only three studies. We conclude that mathematical modelling to predict real-world effectiveness of drug interventions is not widely used at present and not well validated. © 2016 The Authors Research Synthesis Methods Published by John Wiley & Sons Ltd. © 2016 The Authors Research Synthesis Methods Published by John Wiley & Sons Ltd.

Mathematical Modeling of an Oscillating Droplet

NASA Technical Reports Server (NTRS)

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

2000-01-01

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

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

ERIC Educational Resources Information Center

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

2014-01-01

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

Partial Support of Meeting of the Board on Mathematical Sciences and Their Applications

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

Weidman, Scott

2014-08-31

During the performance period, BMSA released the following major reports: Transforming Combustion Research through Cyberinfrastructure (2011); Assessing the Reliability of Complex Models: Mathematical and Statistical Foundations of Verification, Validation, and Uncertainty Quantification (2012); Fueling Innovation and Discovery: The Mathematical Sciences in the 21st Century (2012); Aging and the Macroeconomy: Long-Term Implications of an Older Population (2012); The Mathematical Sciences in 2025 (2013); Frontiers in Massive Data Analysis (2013); and Developing a 21st Century Global Library for Mathematics Research (2014).

Understanding the Impact of Interventions to Prevent Antimicrobial Resistant Infections in the Long-Term Care Facility: A Review and Practical Guide to Mathematical Modeling.

PubMed

Rosello, Alicia; Horner, Carolyne; Hopkins, Susan; Hayward, Andrew C; Deeny, Sarah R

2017-02-01

OBJECTIVES (1) To systematically search for all dynamic mathematical models of infectious disease transmission in long-term care facilities (LTCFs); (2) to critically evaluate models of interventions against antimicrobial resistance (AMR) in this setting; and (3) to develop a checklist for hospital epidemiologists and policy makers by which to distinguish good quality models of AMR in LTCFs. METHODS The CINAHL, EMBASE, Global Health, MEDLINE, and Scopus databases were systematically searched for studies of dynamic mathematical models set in LTCFs. Models of interventions targeting methicillin-resistant Staphylococcus aureus in LTCFs were critically assessed. Using this analysis, we developed a checklist for good quality mathematical models of AMR in LTCFs. RESULTS AND DISCUSSION Overall, 18 papers described mathematical models that characterized the spread of infectious diseases in LTCFs, but no models of AMR in gram-negative bacteria in this setting were described. Future models of AMR in LTCFs require a more robust methodology (ie, formal model fitting to data and validation), greater transparency regarding model assumptions, setting-specific data, realistic and current setting-specific parameters, and inclusion of movement dynamics between LTCFs and hospitals. CONCLUSIONS Mathematical models of AMR in gram-negative bacteria in the LTCF setting, where these bacteria are increasingly becoming prevalent, are needed to help guide infection prevention and control. Improvements are required to develop outputs of sufficient quality to help guide interventions and policy in the future. We suggest a checklist of criteria to be used as a practical guide to determine whether a model is robust enough to test policy. Infect Control Hosp Epidemiol 2017;38:216-225.

Mathematical model of marine diesel engine simulator for a new methodology of self propulsion tests

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

Izzuddin, Nur; Sunarsih,; Priyanto, Agoes

As a vessel operates in the open seas, a marine diesel engine simulator whose engine rotation is controlled to transmit through propeller shaft is a new methodology for the self propulsion tests to track the fuel saving in a real time. Considering the circumstance, this paper presents the real time of marine diesel engine simulator system to track the real performance of a ship through a computer-simulated model. A mathematical model of marine diesel engine and the propeller are used in the simulation to estimate fuel rate, engine rotating speed, thrust and torque of the propeller thus achieve the targetmore » vessel’s speed. The input and output are a real time control system of fuel saving rate and propeller rotating speed representing the marine diesel engine characteristics. The self-propulsion tests in calm waters were conducted using a vessel model to validate the marine diesel engine simulator. The simulator then was used to evaluate the fuel saving by employing a new mathematical model of turbochargers for the marine diesel engine simulator. The control system developed will be beneficial for users as to analyze different condition of vessel’s speed to obtain better characteristics and hence optimize the fuel saving rate.« less

Development and validation of a piloted simulation of a helicopter and external sling load

NASA Technical Reports Server (NTRS)

Shaughnessy, J. D.; Deaux, T. N.; Yenni, K. R.

1979-01-01

A generalized, real time, piloted, visual simulation of a single rotor helicopter, suspension system, and external load is described and validated for the full flight envelope of the U.S. Army CH-54 helicopter and cargo container as an example. The mathematical model described uses modified nonlinear classical rotor theory for both the main rotor and tail rotor, nonlinear fuselage aerodynamics, an elastic suspension system, nonlinear load aerodynamics, and a loadground contact model. The implementation of the mathematical model on a large digital computing system is described, and validation of the simulation is discussed. The mathematical model is validated by comparing measured flight data with simulated data, by comparing linearized system matrices, eigenvalues, and eigenvectors with manufacturers' data, and by the subjective comparison of handling characteristics by experienced pilots. A visual landing display system for use in simulation which generates the pilot's forward looking real world display was examined and a special head up, down looking load/landing zone display is described.

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.

Mathematical model for predicting human vertebral fracture

NASA Technical Reports Server (NTRS)

Benedict, J. V.

1973-01-01

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

Establishment of the mathematical model for diagnosing the engine valve faults by genetic programming

NASA Astrophysics Data System (ADS)

Yang, Wen-Xian

2006-05-01

Available machine fault diagnostic methods show unsatisfactory performances on both on-line and intelligent analyses because their operations involve intensive calculations and are labour intensive. Aiming at improving this situation, this paper describes the development of an intelligent approach by using the Genetic Programming (abbreviated as GP) method. Attributed to the simple calculation of the mathematical model being constructed, different kinds of machine faults may be diagnosed correctly and quickly. Moreover, human input is significantly reduced in the process of fault diagnosis. The effectiveness of the proposed strategy is validated by an illustrative example, in which three kinds of valve states inherent in a six-cylinders/four-stroke cycle diesel engine, i.e. normal condition, valve-tappet clearance and gas leakage faults, are identified. In the example, 22 mathematical functions have been specially designed and 8 easily obtained signal features are used to construct the diagnostic model. Different from existing GPs, the diagnostic tree used in the algorithm is constructed in an intelligent way by applying a power-weight coefficient to each feature. The power-weight coefficients vary adaptively between 0 and 1 during the evolutionary process. Moreover, different evolutionary strategies are employed, respectively for selecting the diagnostic features and functions, so that the mathematical functions are sufficiently utilized and in the meantime, the repeated use of signal features may be fully avoided. The experimental results are illustrated diagrammatically in the following sections.

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.

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…

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Modelling Mathematics Problem Solving Item Responses Using a Multidimensional IRT Model

ERIC Educational Resources Information Center

Wu, Margaret; Adams, Raymond

2006-01-01

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

A Conceptual Model of Mathematical Reasoning for School Mathematics

ERIC Educational Resources Information Center

Jeannotte, Doris; Kieran, Carolyn

2017-01-01

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

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

ERIC Educational Resources Information Center

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

2016-01-01

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

Mathematical modeling of nitrous oxide production in an anaerobic/oxic/anoxic process.

PubMed

Ding, Xiaoqian; Zhao, Jianqiang; Hu, Bo; Chen, Ying; Ge, Guanghuan; Li, Xiaoling; Wang, Sha; Gao, Kun; Tian, Xiaolei

2016-12-01

This study incorporates three currently known nitrous oxide (N 2 O) production pathways: ammonium-oxidizing bacteria (AOB) denitrification, incomplete hydroxylamine (NH 2 OH) oxidation, and heterotrophic denitrification on intracellular polymers, into a mathematical model to describe N 2 O production in an anaerobic/oxic/anoxic (AOA) process for the first time. The developed model was calibrated and validated by four experimental cases, then evaluated by two independent anaerobic/aerobic (AO) studies from literature. The modeling results displayed good agreement with the measured data. N 2 O was primarily generated in the aerobic stage by AOB denitrification (67.84-81.64%) in the AOA system. Smaller amounts of N 2 O were produced via incomplete NH 2 OH oxidation (15.61-32.17%) and heterotrophic denitrification on intracellular polymers (0-12.47%). The high nitrite inhibition on N 2 O reductase led to the increased N 2 O accumulation in heterotrophic denitrification on intracellular polymers. The new model was capable of modeling nitrification-denitrification dynamics and heterotrophic denitrification on intracellular polymers in the AOA system. Copyright © 2016 Elsevier Ltd. All rights reserved.

Mathematical modelling of tissue formation in chondrocyte filter cultures.

PubMed

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

2011-12-17

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

Teaching Writing and Communication in a Mathematical Modeling Course

ERIC Educational Resources Information Center

Linhart, Jean Marie