Predicting disease progression from short biomarker series using expert advice algorithm.

PubMed

Morino, Kai; Hirata, Yoshito; Tomioka, Ryota; Kashima, Hisashi; Yamanishi, Kenji; Hayashi, Norihiro; Egawa, Shin; Aihara, Kazuyuki

2015-05-20

Well-trained clinicians may be able to provide diagnosis and prognosis from very short biomarker series using information and experience gained from previous patients. Although mathematical methods can potentially help clinicians to predict the progression of diseases, there is no method so far that estimates the patient state from very short time-series of a biomarker for making diagnosis and/or prognosis by employing the information of previous patients. Here, we propose a mathematical framework for integrating other patients' datasets to infer and predict the state of the disease in the current patient based on their short history. We extend a machine-learning framework of "prediction with expert advice" to deal with unstable dynamics. We construct this mathematical framework by combining expert advice with a mathematical model of prostate cancer. Our model predicted well the individual biomarker series of patients with prostate cancer that are used as clinical samples.

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

ERIC Educational Resources Information Center

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

2015-01-01

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

Mathematical Modeling Activities as a Useful Tool for Values Education

ERIC Educational Resources Information Center

Doruk, Bekir Kursat

2012-01-01

Values education is crucial since it is one of the factors to reach success in education in broader sense and in mathematics education in particular sense. It is also important for educating next generations of societies. However, previous research showed that expected importance for values education was not given in Mathematics courses. In a few…

Improving Mathematics: An Examination of the Effects of Specific Cognitive Abilities on College-Age Students' Mathematics Achievement

ERIC Educational Resources Information Center

Taub, Gordon E.; Benson, Nicholas; Szente, Judit

2014-01-01

This study investigated the effects of general intelligence and seven specific cognitive abilities on college-age students' mathematics achievement. The present investigation went beyond previous research by employing structural equation modeling. It also represents the first study to examine the direct and indirect effects of general and specific…

Optimal quality control of bakers' yeast fed-batch culture using population dynamics.

PubMed

Dairaku, K; Izumoto, E; Morikawa, H; Shioya, S; Takamatsu, T

1982-12-01

An optimal quality control policy for the overall specific growth rate of bakers' yeast, which maximizes the fermentative activity in the making of bread, was obtained by direct searching based on the mathematical model proposed previously. The mathematical model had described the age distribution of bakers' yeast which had an essential relationship to the ability of fermentation in the making of bread. The mathematical model is a simple aging model with two periods: Nonbudding and budding. Based on the result obtained by direct searching, the quality control of bakers' yeast fed-batch culture was performed and confirmed to be experimentally valid.

Using Incremental Rehearsal to Increase Fluency of Single-Digit Multiplication Facts with Children Identified as Learning Disabled in Mathematics Computation

ERIC Educational Resources Information Center

Burns, Matthew K.

2005-01-01

Previous research suggested that Incremental Rehearsal (IR; Tucker, 1989) led to better retention than other drill practices models. However, little research exists in the literature regarding drill models for mathematics and no studies were found that used IR to practice multiplication facts. Therefore, the current study used IR as an…

A mathematical model of transport and regional uptake of radioactive gases in the human respiratory system

NASA Astrophysics Data System (ADS)

Baek, Inseok

The purpose of this research is to describe the development of a mathematical model of diffusion, convection, and lateral transport into the airway wall and alveolar absorption for inhaled radioactive gases in the human conductive and respiratory airways based on a Single Path Trumpet-bell model (SPM). Mathematical simulation models have been used successfully to study transport, absorption into the blood through alveoli, and lung tissue uptake of soluble and nonreactive radioactive gases. Results from such simulations also show clearly that inhaled radioactive gases are absorbed into the lung tissues as well as into the blood through the alveoli. In contrast to previous reports in the literature, the present study found that blood uptake through alveoli is much greater than that calculated previously. Regional depositions in the lung from inhaled radioactive gases are presented as the result of this simulation. The committed effective dose to lung tissue due to submersion in radioactive clouds has been newly defined using the results of this simulation.

Development of the Mathematical Model for Ingot Quality Forecasting with Consideration of Thermal and Physical Characteristics of Mould Powder

NASA Astrophysics Data System (ADS)

Anisimov, K. N.; Loginov, A. M.; Gusev, M. P.; Zarubin, S. V.; Nikonov, S. V.; Krasnov, A. V.

2017-12-01

This paper presents the results of physical modelling of the mould powder skull in the gap between an ingot and the mould. Based on the results obtained from this and previous works, the mathematical model of mould powder behaviour in the gap and its influence on formation of surface defects was developed. The results of modelling satisfactorily conform to the industrial data on ingot surface defects.

Evaluation of a Mathematical Model of Rat Body Weight Regulation in Application to Caloric Restriction and Drug Treatment Studies.

PubMed

Selimkhanov, Jangir; Thompson, W Clayton; Patterson, Terrell A; Hadcock, John R; Scott, Dennis O; Maurer, Tristan S; Musante, Cynthia J

2016-01-01

The purpose of this work is to develop a mathematical model of energy balance and body weight regulation that can predict species-specific response to common pre-clinical interventions. To this end, we evaluate the ability of a previously published mathematical model of mouse metabolism to describe changes in body weight and body composition in rats in response to two short-term interventions. First, we adapt the model to describe body weight and composition changes in Sprague-Dawley rats by fitting to data previously collected from a 26-day caloric restriction study. The calibrated model is subsequently used to describe changes in rat body weight and composition in a 23-day cannabinoid receptor 1 antagonist (CB1Ra) study. While the model describes body weight data well, it fails to replicate body composition changes with CB1Ra treatment. Evaluation of a key model assumption about deposition of fat and fat-free masses shows a limitation of the model in short-term studies due to the constraint placed on the relative change in body composition components. We demonstrate that the model can be modified to overcome this limitation, and propose additional measurements to further test the proposed model predictions. These findings illustrate how mathematical models can be used to support drug discovery and development by identifying key knowledge gaps and aiding in the design of additional experiments to further our understanding of disease-relevant and species-specific physiology.

Evaluation of a Mathematical Model of Rat Body Weight Regulation in Application to Caloric Restriction and Drug Treatment Studies

PubMed Central

Selimkhanov, Jangir; Patterson, Terrell A.; Scott, Dennis O.; Maurer, Tristan S.; Musante, Cynthia J.

2016-01-01

The purpose of this work is to develop a mathematical model of energy balance and body weight regulation that can predict species-specific response to common pre-clinical interventions. To this end, we evaluate the ability of a previously published mathematical model of mouse metabolism to describe changes in body weight and body composition in rats in response to two short-term interventions. First, we adapt the model to describe body weight and composition changes in Sprague-Dawley rats by fitting to data previously collected from a 26-day caloric restriction study. The calibrated model is subsequently used to describe changes in rat body weight and composition in a 23-day cannabinoid receptor 1 antagonist (CB1Ra) study. While the model describes body weight data well, it fails to replicate body composition changes with CB1Ra treatment. Evaluation of a key model assumption about deposition of fat and fat-free masses shows a limitation of the model in short-term studies due to the constraint placed on the relative change in body composition components. We demonstrate that the model can be modified to overcome this limitation, and propose additional measurements to further test the proposed model predictions. These findings illustrate how mathematical models can be used to support drug discovery and development by identifying key knowledge gaps and aiding in the design of additional experiments to further our understanding of disease-relevant and species-specific physiology. PMID:27227543

Practical Effects of Classwide Mathematics Intervention

ERIC Educational Resources Information Center

VanDerHeyden, Amanda M.; Codding, Robin S.

2015-01-01

The current article presents additional analyses of a classwide mathematics intervention, from a previously reported randomized controlled trial, to offer new information about the treatment and to demonstrate the utility of different types of effect sizes. Multilevel modeling was used to examine treatment effects by race, sex, socioeconomic…

ILS Scattering Problem and Signal Detection Model

DOT National Transportation Integrated Search

1972-02-01

The construction of a mathematical model of The Instrument Landing System (ILS) multipath problem was undertaken. This report presents the theoretical basis for any such model, a critique of previous models and newly achieve developments in ILS model...

Authentic Integration: a model for integrating mathematics and science in the classroom

NASA Astrophysics Data System (ADS)

Treacy, Páraic; O'Donoghue, John

2014-07-01

Attempts at integrating mathematics and science have been made previously but no definitive, widely adopted teaching model has been developed to date. Research suggests that hands-on, practical, student-centred tasks should form a central element when designing an effective model for the integration of mathematics and science. Aided by this research, the author created a new model entitled 'Authentic Integration' which caters for the specific needs of integration of mathematics and science. This model requires that each lesson be based around a rich task which relates to the real world and ensures that hands-on group work, inquiry, and discussion are central to the lesson. It was found that Authentic Integration, when applied in four Irish post-primary schools, positively affected pupil understanding. The teachers who completed the intervention displayed a very positive attitude towards the approach, intimating that they would continue to implement the practice in their classrooms.

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

PubMed

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

2015-03-01

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

Students' Abstraction in Recognizing, Building with and Constructing a Quadrilateral

ERIC Educational Resources Information Center

Budiarto, Mega Teguh; Rahaju, Endah Budi; Hartono, Sugi

2017-01-01

This study aims to implement empirically students' abstraction with socio-cultural background of Indonesia. Abstraction is an activity that involves a vertical reorganization of previously constructed mathematics into a new mathematical structure. The principal components of the model are three dynamic nested epistemic actions: recognizing,…

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.

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.

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.

Atmospheric Dispersal and Dispostion of Tephra From a Potential Volcanic Eruption at Yucca Mountain, Nevada

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

G. Keating; W.Statham

2004-02-12

The purpose of this model report is to provide documentation of the conceptual and mathematical model (ASHPLUME) for atmospheric dispersal and subsequent deposition of ash on the land surface from a potential volcanic eruption at Yucca Mountain, Nevada. This report also documents the ash (tephra) redistribution conceptual model. The ASHPLUME conceptual model accounts for incorporation and entrainment of waste fuel particles associated with a hypothetical volcanic eruption through the Yucca Mountain repository and downwind transport of contaminated tephra. The ASHPLUME mathematical model describes the conceptual model in mathematical terms to allow for prediction of radioactive waste/ash deposition on the groundmore » surface given that the hypothetical eruptive event occurs. This model report also describes the conceptual model for tephra redistribution from a basaltic cinder cone. Sensitivity analyses and model validation activities for the ash dispersal and redistribution models are also presented. Analyses documented in this model report will improve and clarify the previous documentation of the ASHPLUME mathematical model and its application to the Total System Performance Assessment (TSPA) for the License Application (TSPA-LA) igneous scenarios. This model report also documents the redistribution model product outputs based on analyses to support the conceptual model.« less

Covariation between Variables in a Modelling Process: The ACODESA (Collaborative Learning, Scientific Debate and Self-Reflection) Method

ERIC Educational Resources Information Center

Hitt, Fernando; González-Martín, Alejandro S.

2015-01-01

Semiotic representations have been an important topic of study in mathematics education. Previous research implicitly placed more importance on the development of institutional representations of mathematical concepts in students rather than other types of representations. In the context of an extensive research project, in progress since 2005,…

Stories about Math: An Analysis of Students' Mathematical Autobiographies

ERIC Educational Resources Information Center

Latterell, Carmen M.; Wilson, Janelle L.

2016-01-01

This paper analyzes 16 preservice secondary mathematics education majors' mathematical autobiographies. Participants wrote about their previous experiences with mathematics. All participants discussed why they wanted to become mathematics teachers with the key factors being past experience with mathematics teachers, previous success in mathematics…

Formal verification of mathematical software

NASA Technical Reports Server (NTRS)

Sutherland, D.

1984-01-01

Methods are investigated for formally specifying and verifying the correctness of mathematical software (software which uses floating point numbers and arithmetic). Previous work in the field was reviewed. A new model of floating point arithmetic called the asymptotic paradigm was developed and formalized. Two different conceptual approaches to program verification, the classical Verification Condition approach and the more recently developed Programming Logic approach, were adapted to use the asymptotic paradigm. These approaches were then used to verify several programs; the programs chosen were simplified versions of actual mathematical software.

Conformal mapping in optical biosensor applications.

PubMed

Zumbrum, Matthew E; Edwards, David A

2015-09-01

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

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

Predicting electroporation of cells in an inhomogeneous electric field based on mathematical modeling and experimental CHO-cell permeabilization to propidium iodide determination.

PubMed

Dermol, Janja; Miklavčič, Damijan

2014-12-01

High voltage electric pulses cause electroporation of the cell membrane. Consequently, flow of the molecules across the membrane increases. In our study we investigated possibility to predict the percentage of the electroporated cells in an inhomogeneous electric field on the basis of the experimental results obtained when cells were exposed to a homogeneous electric field. We compared and evaluated different mathematical models previously suggested by other authors for interpolation of the results (symmetric sigmoid, asymmetric sigmoid, hyperbolic tangent and Gompertz curve). We investigated the density of the cells and observed that it has the most significant effect on the electroporation of the cells while all four of the mathematical models yielded similar results. We were able to predict electroporation of cells exposed to an inhomogeneous electric field based on mathematical modeling and using mathematical formulations of electroporation probability obtained experimentally using exposure to the homogeneous field of the same density of cells. Models describing cell electroporation probability can be useful for development and presentation of treatment planning for electrochemotherapy and non-thermal irreversible electroporation. Copyright © 2014 Elsevier B.V. All rights reserved.

On the Modeling of Vacuum Arc Remelting Process in Titanium Alloys

NASA Astrophysics Data System (ADS)

Patel, Ashish; Fiore, Daniel

2016-07-01

Mathematical modeling is routinely used in the process development and production of advanced aerospace alloys to gain greater insight into the effect of process parameters on final properties. This article describes the application of a 2-D mathematical VAR model presented at previous LMPC meetings. The impact of process parameters on melt pool geometry, solidification behavior, fluid-flow and chemistry in a Ti-6Al-4V ingot is discussed. Model predictions are validated against published data from a industrial size ingot, and results of a parametric study on particle dissolution are also discussed.

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.

The Latent Structure of Spatial Skills and Mathematics: A Replication of the Two-Factor Model

ERIC Educational Resources Information Center

Mix, Kelly S.; Levine, Susan C.; Cheng, Yi-Lang; Young, Christopher J.; Hambrick, David Z.; Konstantopoulos, Spyros

2017-01-01

In a previous study, Mix et al. (2016) reported that spatial skill and mathematics were composed of 2 highly correlated, domain-specific factors, with a few cross-domain loadings. The overall structure was consistent across grade (kindergarten, 3rd grade, 6th grade), but the cross-domain loadings varied with age. The present study sought to…

Mathematical Rigor vs. Conceptual Change: Some Early Results

NASA Astrophysics Data System (ADS)

Alexander, W. R.

2003-05-01

Results from two different pedagogical approaches to teaching introductory astronomy at the college level will be presented. The first of these approaches is a descriptive, conceptually based approach that emphasizes conceptual change. This descriptive class is typically an elective for non-science majors. The other approach is a mathematically rigorous treatment that emphasizes problem solving and is designed to prepare students for further study in astronomy. The mathematically rigorous class is typically taken by science majors. It also fulfills an elective science requirement for these science majors. The Astronomy Diagnostic Test version 2 (ADT 2.0) was used as an assessment instrument since the validity and reliability have been investigated by previous researchers. The ADT 2.0 was administered as both a pre-test and post-test to both groups. Initial results show no significant difference between the two groups in the post-test. However, there is a slightly greater improvement for the descriptive class between the pre and post testing compared to the mathematically rigorous course. There was great care to account for variables. These variables included: selection of text, class format as well as instructor differences. Results indicate that the mathematically rigorous model, doesn't improve conceptual understanding any better than the conceptual change model. Additional results indicate that there is a similar gender bias in favor of males that has been measured by previous investigators. This research has been funded by the College of Science and Mathematics at James Madison University.

A VARIABLE REACTIVITY MODEL FOR ION BINDING TO ENVIRONMENTAL SORBENTS

EPA Science Inventory

The conceptual and mathematical basis for a new general-composite modeling approach for ion binding to environmental sorbents is presented. The work extends the Simple Metal Sorption (SiMS) model previously presented for metal and proton binding to humic substances. A surface com...

Latent transition analysis of pre-service teachers' efficacy in mathematics and science

NASA Astrophysics Data System (ADS)

Ward, Elizabeth Kennedy

This study modeled changes in pre-service teacher efficacy in mathematics and science over the course of the final year of teacher preparation using latent transition analysis (LTA), a longitudinal form of analysis that builds on two modeling traditions (latent class analysis (LCA) and auto-regressive modeling). Data were collected using the STEBI-B, MTEBI-r, and the ABNTMS instruments. The findings suggest that LTA is a viable technique for use in teacher efficacy research. Teacher efficacy is modeled as a construct with two dimensions: personal teaching efficacy (PTE) and outcome expectancy (OE). Findings suggest that the mathematics and science teaching efficacy (PTE) of pre-service teachers is a multi-class phenomena. The analyses revealed a four-class model of PTE at the beginning and end of the final year of teacher training. Results indicate that when pre-service teachers transition between classes, they tend to move from a lower efficacy class into a higher efficacy class. In addition, the findings suggest that time-varying variables (attitudes and beliefs) and time-invariant variables (previous coursework, previous experiences, and teacher perceptions) are statistically significant predictors of efficacy class membership. Further, analyses suggest that the measures used to assess outcome expectancy are not suitable for LCA and LTA procedures.

The Mathematics of High School Physics

NASA Astrophysics Data System (ADS)

Kanderakis, Nikos

2016-10-01

In the seventeenth and eighteenth centuries, mathematicians and physical philosophers managed to study, via mathematics, various physical systems of the sublunar world through idealized and simplified models of these systems, constructed with the help of geometry. By analyzing these models, they were able to formulate new concepts, laws and theories of physics and then through models again, to apply these concepts and theories to new physical phenomena and check the results by means of experiment. Students' difficulties with the mathematics of high school physics are well known. Science education research attributes them to inadequately deep understanding of mathematics and mainly to inadequate understanding of the meaning of symbolic mathematical expressions. There seem to be, however, more causes of these difficulties. One of them, not independent from the previous ones, is the complex meaning of the algebraic concepts used in school physics (e.g. variables, parameters, functions), as well as the complexities added by physics itself (e.g. that equations' symbols represent magnitudes with empirical meaning and units instead of pure numbers). Another source of difficulties is that the theories and laws of physics are often applied, via mathematics, to simplified, and idealized physical models of the world and not to the world itself. This concerns not only the applications of basic theories but also all authentic end-of-the-chapter problems. Hence, students have to understand and participate in a complex interplay between physics concepts and theories, physical and mathematical models, and the real world, often without being aware that they are working with models and not directly with the real world.

Mathematical Analysis for Non-reciprocal-interaction-based Model of Collective Behavior

NASA Astrophysics Data System (ADS)

Kano, Takeshi; Osuka, Koichi; Kawakatsu, Toshihiro; Ishiguro, Akio

2017-12-01

In many natural and social systems, collective behaviors emerge as a consequence of non-reciprocal interaction between their constituents. As a first step towards understanding the core principle that underlies these phenomena, we previously proposed a minimal model of collective behavior based on non-reciprocal interactions by drawing inspiration from friendship formation in human society, and demonstrated via simulations that various non-trivial patterns emerge by changing parameters. In this study, a mathematical analysis of the proposed model wherein the system size is small is performed. Through the analysis, the mechanism of the transition between several patterns is elucidated.

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

ERIC Educational Resources Information Center

Soleimani, Ali

2013-01-01

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

Analysing the relationships between students and mathematics: a tale of two paradigms

NASA Astrophysics Data System (ADS)

Jorgensen, Robyn; Larkin, Kevin

2017-03-01

In this article, we argue the need to use inter-disciplinary paradigms to make sense of a range of findings from a research project. We developed a methodology using iPad diaries to uncover young students' thinking—mathematical, social and affective—so as to better understand their experiences of mathematics. These students, predominantly from year 3 to year 6, were drawn from economically and socially distinct schools in Queensland and New South Wales, Australia. This article builds on previous research, where we outlined the unique methodology that we developed over three iterations to collect student attitudinal comments regarding mathematics. The comments we collected gave significant insights into the experiences of, and possibilities for, the mathematics education of young learners. Here, we use these findings to explore the value of two paradigms to explain student experiences towards mathematics among primary school students from different social backgrounds. In so doing, we develop an explanatory model for the socially differentiated outcomes in students' responses and then use this explanatory model to analyse student responses from the two most socially disparate schools in our research.

Quantitative analysis of transverse bacterial migration induced by chemotaxis in a packed column with structured physical heterogeneity.

PubMed

Wang, Meng; Ford, Roseanne M

2010-01-15

A two-dimensional mathematical model was developed to simulate transport phenomena of chemotactic bacteria in a sand-packed column designed with structured physical heterogeneity in the presence of a localized chemical source. In contrast to mathematical models in previous research work, in which bacteria were typically treated as immobile colloids, this model incorporated a convective-like chemotaxis term to represent chemotactic migration. Consistency between experimental observation and model prediction supported the assertions that (1) dispersion-induced microbial transfer between adjacent conductive zones occurred at the interface and had little influence on bacterial transport in the bulk flow of the permeable layers and (2) the enhanced transverse bacterial migration in chemotactic experiments relative to nonchemotactic controls was mainly due to directed migration toward the chemical source zone. On the basis of parameter sensitivity analysis, chemotactic parameters determined in bulk aqueous fluid were adequate to predict the microbial transport in our intermediate-scale porous media system. Additionally, the analysis of adsorption coefficient values supported the observation of a previous study that microbial deposition to the surface of porous media might be decreased under the effect of chemoattractant gradients. By quantitatively describing bacterial transport and distribution in a heterogeneous system, this mathematical model serves to advance our understanding of chemotaxis and motility effects in granular media systems and provides insights for modeling microbial transport in in situ microbial processes.

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

PubMed

Wiratsudakul, Anuwat; Suparit, Parinya; Modchang, Charin

2018-01-01

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

Blooms' separation of the final exam of Engineering Mathematics II: Item reliability using Rasch measurement model

NASA Astrophysics Data System (ADS)

Fuaad, Norain Farhana Ahmad; Nopiah, Zulkifli Mohd; Tawil, Norgainy Mohd; Othman, Haliza; Asshaari, Izamarlina; Osman, Mohd Hanif; Ismail, Nur Arzilah

2014-06-01

In engineering studies and researches, Mathematics is one of the main elements which express physical, chemical and engineering laws. Therefore, it is essential for engineering students to have a strong knowledge in the fundamental of mathematics in order to apply the knowledge to real life issues. However, based on the previous results of Mathematics Pre-Test, it shows that the engineering students lack the fundamental knowledge in certain topics in mathematics. Due to this, apart from making improvements in the methods of teaching and learning, studies on the construction of questions (items) should also be emphasized. The purpose of this study is to assist lecturers in the process of item development and to monitor the separation of items based on Blooms' Taxonomy and to measure the reliability of the items itself usingRasch Measurement Model as a tool. By using Rasch Measurement Model, the final exam questions of Engineering Mathematics II (Linear Algebra) for semester 2 sessions 2012/2013 were analysed and the results will provide the details onthe extent to which the content of the item providesuseful information about students' ability. This study reveals that the items used in Engineering Mathematics II (Linear Algebra) final exam are well constructed but the separation of the items raises concern as it is argued that it needs further attention, as there is abig gap between items at several levels of Blooms' cognitive skill.

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

PubMed

Min, Kyung Duk; Cho, Sung Il

2018-03-19

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

The Modulus of Rupture from a Mathematical Point of View

NASA Astrophysics Data System (ADS)

Quintela, P.; Sánchez, M. T.

2007-04-01

The goal of this work is to present a complete mathematical study about the three-point bending experiments and the modulus of rupture of brittle materials. We will present the mathematical model associated to three-point bending experiments and we will use the asymptotic expansion method to obtain a new formula to calculate the modulus of rupture. We will compare the modulus of rupture of porcelain obtained with the previous formula with that obtained by using the classic theoretical formula. Finally, we will also present one and three-dimensional numerical simulations to compute the modulus of rupture.

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

PubMed

Braatz, Elise M; Coleman, Randolph A

2015-06-01

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

The experimentation of LC7E learning model on the linear program material in terms of interpersonal intelligence on Wonogiri vocational school students

NASA Astrophysics Data System (ADS)

Antinah; Kusmayadi, T. A.; Husodo, B.

2018-05-01

This study aims to determine the effect of learning model on student achievement in terms of interpersonal intelligence. The compared learning models are LC7E and Direct learning model. This type of research is a quasi-experimental with 2x3 factorial design. The population in this study is a Grade XI student of Wonogiri Vocational Schools. The sample selection had done by stratified cluster random sampling. Data collection technique used questionnaires, documentation and tests. The data analysis technique used two different unequal cell variance analysis which previously conducted prerequisite analysis for balance test, normality test and homogeneity test. he conclusions of this research are: 1) student learning achievement of mathematics given by LC7E learning model is better when compared with direct learning; 2) Mathematics learning achievement of students who have a high level of interpersonal intelligence is better than students with interpersonal intelligence in medium and low level. Students' mathematics learning achievement with interpersonal level of intelligence is better than those with low interpersonal intelligence on linear programming; 3) LC7E learning model resulted better on mathematics learning achievement compared with direct learning model for each category of students’ interpersonal intelligence level on linear program material.

The experimentation of LC7E learning model on the linear program material in terms of interpersonal intelligence on Wonogiri Vocational School students

NASA Astrophysics Data System (ADS)

Antinah; Kusmayadi, T. A.; Husodo, B.

2018-03-01

This study aimed to determine the effect of learning model on student achievement in terms of interpersonal intelligence. The compared learning models are LC7E and Direct learning model. This type of research is a quasi-experimental with 2x3 factorial design. The population in this study is a Grade XI student of Wonogiri Vocational Schools. The sample selection had done by stratified cluster random sampling. Data collection technique used questionnaires, documentation and tests. The data analysis technique used two different unequal cell variance analysis which previously conducted prerequisite analysis for balance test, normality test and homogeneity test. he conclusions of this research are: 1) student learning achievement of mathematics given by LC7E learning model is better when compared with direct learning; 2) Mathematics learning achievement of students who have a high level of interpersonal intelligence is better than students with interpersonal intelligence in medium and low level. Students’ mathematics learning achievement with interpersonal level of intelligence is better than those with low interpersonal intelligence on linear programming; 3) LC7E learning model resulted better on mathematics learning achievement compared with direct learning model for each category of students’ interpersonal intelligence level on linear program material.

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

PubMed

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

2018-01-05

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

Early Executive Function at Age Two Predicts Emergent Mathematics and Literacy at Age Five

PubMed Central

Mulder, Hanna; Verhagen, Josje; Van der Ven, Sanne H. G.; Slot, Pauline L.; Leseman, Paul P. M.

2017-01-01

Previous work has shown that individual differences in executive function (EF) are predictive of academic skills in preschoolers, kindergartners, and older children. Across studies, EF is a stronger predictor of emergent mathematics than literacy. However, research on EF in children below age three is scarce, and it is currently unknown whether EF, as assessed in toddlerhood, predicts emergent academic skills a few years later. This longitudinal study investigates whether early EF, assessed at two years, predicts (emergent) academic skills, at five years. It examines, furthermore, whether early EF is a significantly stronger predictor of emergent mathematics than of emergent literacy, as has been found in previous work on older children. A sample of 552 children was assessed on various EF and EF-precursor tasks at two years. At age five, these children performed several emergent mathematics and literacy tasks. Structural Equation Modeling was used to investigate the relationships between early EF and academic skills, modeled as latent factors. Results showed that early EF at age two was a significant and relatively strong predictor of both emergent mathematics and literacy at age five, after controlling for receptive vocabulary, parental education, and home language. Predictive relations were significantly stronger for mathematics than literacy, but only when a verbal short-term memory measure was left out as an indicator to the latent early EF construct. These findings show that individual differences in emergent academic skills just prior to entry into the formal education system can be traced back to individual differences in early EF in toddlerhood. In addition, these results highlight the importance of task selection when assessing early EF as a predictor of later outcomes, and call for further studies to elucidate the mechanisms through which individual differences in early EF and precursors to EF come about. PMID:29075209

Early Executive Function at Age Two Predicts Emergent Mathematics and Literacy at Age Five.

PubMed

Mulder, Hanna; Verhagen, Josje; Van der Ven, Sanne H G; Slot, Pauline L; Leseman, Paul P M

2017-01-01

Previous work has shown that individual differences in executive function (EF) are predictive of academic skills in preschoolers, kindergartners, and older children. Across studies, EF is a stronger predictor of emergent mathematics than literacy. However, research on EF in children below age three is scarce, and it is currently unknown whether EF, as assessed in toddlerhood, predicts emergent academic skills a few years later. This longitudinal study investigates whether early EF, assessed at two years, predicts (emergent) academic skills, at five years. It examines, furthermore, whether early EF is a significantly stronger predictor of emergent mathematics than of emergent literacy, as has been found in previous work on older children. A sample of 552 children was assessed on various EF and EF-precursor tasks at two years. At age five, these children performed several emergent mathematics and literacy tasks. Structural Equation Modeling was used to investigate the relationships between early EF and academic skills, modeled as latent factors. Results showed that early EF at age two was a significant and relatively strong predictor of both emergent mathematics and literacy at age five, after controlling for receptive vocabulary, parental education, and home language. Predictive relations were significantly stronger for mathematics than literacy, but only when a verbal short-term memory measure was left out as an indicator to the latent early EF construct. These findings show that individual differences in emergent academic skills just prior to entry into the formal education system can be traced back to individual differences in early EF in toddlerhood. In addition, these results highlight the importance of task selection when assessing early EF as a predictor of later outcomes, and call for further studies to elucidate the mechanisms through which individual differences in early EF and precursors to EF come about.

Benefits of detailed models of muscle activation and mechanics

NASA Technical Reports Server (NTRS)

Lehman, S. L.; Stark, L.

1981-01-01

Recent biophysical and physiological studies identified some of the detailed mechanisms involved in excitation-contraction coupling, muscle contraction, and deactivation. Mathematical models incorporating these mechanisms allow independent estimates of key parameters, direct interplay between basic muscle research and the study of motor control, and realistic model behaviors, some of which are not accessible to previous, simpler, models. The existence of previously unmodeled behaviors has important implications for strategies of motor control and identification of neural signals. New developments in the analysis of differential equations make the more detailed models feasible for simulation in realistic experimental situations.

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

PubMed

Yuki, Koichi; DiNardo, James A

2015-02-01

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

Using Bayesian Networks to Improve Knowledge Assessment

ERIC Educational Resources Information Center

Millan, Eva; Descalco, Luis; Castillo, Gladys; Oliveira, Paula; Diogo, Sandra

2013-01-01

In this paper, we describe the integration and evaluation of an existing generic Bayesian student model (GBSM) into an existing computerized testing system within the Mathematics Education Project (PmatE--Projecto Matematica Ensino) of the University of Aveiro. This generic Bayesian student model had been previously evaluated with simulated…

Integrating Partial Polarization into a Metal-Ferroelectric-Semiconductor Field Effect Transistor Model

NASA Technical Reports Server (NTRS)

MacLeod, Todd C.; Ho, Fat Duen

1999-01-01

The ferroelectric channel in a Metal-Ferroelectric-Semiconductor Field Effect Transistor (MFSFET) can partially change its polarization when the gate voltage near the polarization threshold voltage. This causes the MFSFET Drain current to change with repeated pulses of the same gate voltage near the polarization threshold voltage. A previously developed model [11, based on the Fermi-Dirac function, assumed that for a given gate voltage and channel polarization, a sin-le Drain current value would be generated. A study has been done to characterize the effects of partial polarization on the Drain current of a MFSFET. These effects have been described mathematically and these equations have been incorporated into a more comprehensive mathematical model of the MFSFET. The model takes into account the hysteresis nature of the MFSFET and the time dependent decay as well as the effects of partial polarization. This model defines the Drain current based on calculating the degree of polarization from previous gate pulses, the present Gate voltage, and the amount of time since the last Gate volta-e pulse.

A theory of drug tolerance and dependence I: a conceptual analysis.

PubMed

Peper, Abraham

2004-08-21

A mathematical model of drug tolerance and its underlying theory is presented. The model extends a first approach, published previously. The model is essentially more complex than the generally used model of homeostasis, which is demonstrated to fail in describing tolerance development to repeated drug administrations. The model assumes the development of tolerance to a repeatedly administered drug to be the result of a regulated adaptive process. The oral detection and analysis of exogenous substances is proposed to be the primary stimulus for the mechanism of drug tolerance. Anticipation and environmental cues are in the model considered secondary stimuli, becoming primary only in dependence and addiction or when the drug administration bypasses the natural-oral-route, as is the case when drugs are administered intravenously. The model considers adaptation to the effect of a drug and adaptation to the interval between drug taking autonomous tolerance processes. Simulations with the mathematical model demonstrate the model's behavior to be consistent with important characteristics of the development of tolerance to repeatedly administered drugs: the gradual decrease in drug effect when tolerance develops, the high sensitivity to small changes in drug dose, the rebound phenomenon and the large reactions following withdrawal in dependence. The mathematical model verifies the proposed theory and provides a basis for the implementation of mathematical models of specific physiological processes. In addition, it establishes a relation between the drug dose at any moment, and the resulting drug effect and relates the magnitude of the reactions following withdrawal to the rate of tolerance and other parameters involved in the tolerance process. The present paper analyses the concept behind the model. The next paper discusses the mathematical model.

Estimating tuberculosis incidence from primary survey data: a mathematical modeling approach.

PubMed

Pandey, S; Chadha, V K; Laxminarayan, R; Arinaminpathy, N

2017-04-01

There is an urgent need for improved estimations of the burden of tuberculosis (TB). To develop a new quantitative method based on mathematical modelling, and to demonstrate its application to TB in India. We developed a simple model of TB transmission dynamics to estimate the annual incidence of TB disease from the annual risk of tuberculous infection and prevalence of smear-positive TB. We first compared model estimates for annual infections per smear-positive TB case using previous empirical estimates from China, Korea and the Philippines. We then applied the model to estimate TB incidence in India, stratified by urban and rural settings. Study model estimates show agreement with previous empirical estimates. Applied to India, the model suggests an annual incidence of smear-positive TB of 89.8 per 100 000 population (95%CI 56.8-156.3). Results show differences in urban and rural TB: while an urban TB case infects more individuals per year, a rural TB case remains infectious for appreciably longer, suggesting the need for interventions tailored to these different settings. Simple models of TB transmission, in conjunction with necessary data, can offer approaches to burden estimation that complement those currently being used.

Application of a Model for Simulating the Vacuum Arc Remelting Process in Titanium Alloys

NASA Astrophysics Data System (ADS)

Patel, Ashish; Tripp, David W.; Fiore, Daniel

Mathematical modeling is routinely used in the process development and production of advanced aerospace alloys to gain greater insight into system dynamics and to predict the effect of process modifications or upsets on final properties. This article describes the application of a 2-D mathematical VAR model presented in previous LMPC meetings. The impact of process parameters on melt pool geometry, solidification behavior, fluid-flow and chemistry in Ti-6Al-4V ingots will be discussed. Model predictions were first validated against the measured characteristics of industrially produced ingots, and process inputs and model formulation were adjusted to match macro-etched pool shapes. The results are compared to published data in the literature. Finally, the model is used to examine ingot chemistry during successive VAR melts.

Validation of an instrument for mathematics enhancement teaching efficacy of Pacific Northwest agricultural educators

NASA Astrophysics Data System (ADS)

Jansen, Daniel J.

Teacher efficacy continues to be an important area of study in educational research. This study tested an instrument designed to assess the perceived efficacy of agricultural education teachers when engaged in lessons involving mathematics instruction. The study population of Oregon and Washington agricultural educators utilized in the validation of the instrument revealed important demographic findings and specific results related to teacher efficacy for the study population. An instrument was developed from the assimilation of three scales previously used and validated in efficacy research. Participants' mathematics teaching efficacy was assessed using a portion of the Mathematics Teaching Efficacy Beliefs Instrument (MTEBI), and personal mathematics efficacy was evaluated by the mathematics self-belief instrument which was derived from the Betz and Hackett's Mathematics Self-Efficacy Scale. The final scale, the Teachers' Sense of Efficacy Scale (TSES) created by Tschannen-Moran and Woolfolk Hoy, examined perceived personal teaching efficacy. Structural equation modeling was used as the statistical analyses tool to validate the instrument and examine correlations between efficacy constructs used to determine potential professional development needs of the survey population. As part of the data required for validation of the Mathematics Enhancement Teaching Efficacy instrument, demographic information defining the population of Oregon and Washington agricultural educators was obtained and reported. A hypothetical model derived from teacher efficacy literature was found to be an acceptable model to verify construct validity and determine strength of correlations between the scales that defined the instrument. The instrument produced an alpha coefficient of .905 for reliability. Both exploratory and confirmatory factor analyses were used to verify construct and discriminate validity. Specifics results related to the survey population of agricultural educators concluded that personal mathematics efficacy has a stronger correlation with mathematics teaching efficacy than personal teaching efficacy of teachers for this population. The implications of such findings suggest that professional development and pre-service preparation should be more focused on mathematics content knowledge rather than pedagogical knowledge when the objective is to enhance mathematics in interdisciplinary lessons.

Temperature coefficient for modeling denitrification in surface water sediments using the mass transfer coefficient

Treesearch

T.W. Appelboom; G.M. Chescheir; F. Birgand; R.W. Skaggs; J.W. Gilliam; D. Amatya

2010-01-01

Watershed modeling has become an important tool for researchers. Modeling nitrate transport within drainage networks requires quantifying the denitrification within the sediments in canals and streams. In a previous study, several of the authors developed an equation using a term called a mass transfer coefficient to mathematically describe sediment denitrification....

Temperature coefficient for modeling denitrification in surface water sediments using the mass transfer coefficient.

Treesearch

T.W. Appelboom; G.M. Chescheir; F. Birgand; R.W. Skaggs; J.W. Gilliam; D. Amatya

2010-01-01

Watershed modeling has become an important tool for researchers. Modeling nitrate transport within drainage networks requires quantifying the denitrification within the sediments in canals and streams. In a previous study, several of the authors developed an equation using a term called a mass transfer coefficient to mathematically describe sediment denitrification....

Uncharted waters: Bivalves of midway atoll and integrating mathematics into biology education

NASA Astrophysics Data System (ADS)

McCully, Kristin M.

To protect and conserve the Earth's biodiversity and ecosystem services, it is important not only to understand and conserve species and ecosystems, but also to instill an understanding and appreciation for biodiversity and ecosystem services in the next generations of both scientists and citizens. Thus, this dissertation combines research into the ecology and identity of large bivalves at Midway Atoll in the Northwestern Hawaiian Islands (NWHI) with research on pedagogical strategies for integrating mathematics into undergraduate biology education. The NWHI is one of the few remaining large, mainly intact, predator-dominated coral reef ecosystems and one of the world's largest marine protected areas. Previous bivalve studies focused on the black-lipped pearl oyster, Pinctada margaritifera, which was heavily harvested in the late 1920s, has not recovered, and is now a candidate species for restoration. First, I combined remote sensing, geographic information systems, SCUBA, and mathematical modeling to quantify the abundance, spatial distributions, and filtration capacity of large epifaunal bivalves at Midway Atoll. These bivalves are most abundant on the forereef outside the atoll, but densities are much lower than reported on other reefs, and Midway's bivalves are unlikely to affect plankton abundance and productivity inside the lagoon. Second, I used molecular techniques and phylogenetic reconstructions to identify pearl oysters (Pinctada) from Midway Atoll as P. maculata , a species not previously reported in Hawaii. As a small morphologically cryptic species, P. maculata may be a native species that has not been collected previously, a native species that has been identified incorrectly as the morphologically similar P. radiata, or it may be a recent introduction or natural range extension from the western Pacific. Finally, I review science education literature integrating mathematics into undergraduate biology curricula, and then present and evaluate a computer inquiry module using learner-centered teaching strategies to introduce structured population (matrix) models in an upper-division ecology course. Using pre- and post-test surveys and student interviews, I concluded that students accomplished the module's learning goals: to use matrix models to assess and protect populations and to better appreciate the importance and uses of mathematics in ecology and conservation.

Mathematical Description of Dendrimer Structure

NASA Technical Reports Server (NTRS)

Majoros, Istvan J.; Mehta, Chandan B.; Baker, James R., Jr.

2004-01-01

Characteristics of starburst dendrimers can be easily attributed to the multiplicity of the monomers used to synthesize them. The molecular weight, degree of polymerization, number of terminal groups and branch points for each generation of a dendrimer can be calculated using mathematical formulas incorporating these variables. Mathematical models for the calculation of degree of polymerization, molecular weight, and number of terminal groups and branching groups previously published were revised and elaborated on for poly(amidoamine) (PAMAM) dendrimers, and introduced for poly(propyleneimine) (POPAM) dendrimers and the novel POPAM-PAMAM hybrid, which we call the POMAM dendrimer. Experimental verification of the relationship between theoretical and actual structure for the PAMAM dendrimer was also established.

Available clinical markers of treatment outcome integrated in mathematical models to guide therapy in HIV infection.

PubMed

Vergu, Elisabeta; Mallet, Alain; Golmard, Jean-Louis

2004-02-01

Because treatment failure in many HIV-infected persons may be due to multiple causes, including resistance to antiretroviral agents, it is important to better tailor drug therapy to individual patients. This improvement requires the prediction of treatment outcome from baseline immunological or virological factors, and from results of resistance tests. Here, we review briefly the available clinical factors that have an impact on therapy outcome, and discuss the role of a predictive modelling approach integrating these factors proposed in a previous work. Mathematical and statistical models could become essential tools to address questions that are difficult to study clinically and experimentally, thereby guiding decisions in the choice of individualized drug regimens.

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

PubMed Central

Wiratsudakul, Anuwat; Suparit, Parinya

2018-01-01

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

Cell Surface Mechanochemistry and the Determinants of Bleb Formation, Healing, and Travel Velocity

PubMed Central

Manakova, Kathryn; Yan, Huaming; Lowengrub, John; Allard, Jun

2016-01-01

Blebs are pressure-driven cell protrusions implicated in cellular functions such as cell division, apoptosis, and cell motility, including motility of protease-inhibited cancer cells. Because of their mechanical nature, blebs inform us about general cell-surface mechanics, including membrane dynamics, pressure propagation throughout the cytoplasm, and the architecture and dynamics of the actin cortex. Mathematical models including detailed fluid dynamics have previously been used to understand bleb expansion. Here, we develop mathematical models in two and three dimensions on longer timescales that recapitulate the full bleb life cycle, including both expansion and healing by cortex reformation, in terms of experimentally accessible biophysical parameters such as myosin contractility, osmotic pressure, and turnover of actin and ezrin. The model provides conditions under which blebbing occurs, and naturally gives rise to traveling blebs. The model predicts conditions under which blebs travel or remain stationary, as well as the bleb traveling velocity, a quantity that has remained elusive in previous models. As previous studies have used blebs as reporters of membrane tension and pressure dynamics within the cell, we have used our system to investigate various pressure equilibration models and dynamic, nonuniform membrane tension to account for the shape of a traveling bleb. We also find that traveling blebs tend to expand in all directions unless otherwise constrained. One possible constraint could be provided by spatial heterogeneity in, for example, adhesion density. PMID:27074688

Mathematical modeling of a continuous alcoholic fermentation process in a two-stage tower reactor cascade with flocculating yeast recycle.

PubMed

de Oliveira, Samuel Conceição; de Castro, Heizir Ferreira; Visconti, Alexandre Eliseu Stourdze; Giudici, Reinaldo

2015-03-01

Experiments of continuous alcoholic fermentation of sugarcane juice with flocculating yeast recycle were conducted in a system of two 0.22-L tower bioreactors in series, operated at a range of dilution rates (D 1 = D 2 = 0.27-0.95 h(-1)), constant recycle ratio (α = F R /F = 4.0) and a sugar concentration in the feed stream (S 0) around 150 g/L. The data obtained in these experimental conditions were used to adjust the parameters of a mathematical model previously developed for the single-stage process. This model considers each of the tower bioreactors as a perfectly mixed continuous reactor and the kinetics of cell growth and product formation takes into account the limitation by substrate and the inhibition by ethanol and biomass, as well as the substrate consumption for cellular maintenance. The model predictions agreed satisfactorily with the measurements taken in both stages of the cascade. The major differences with respect to the kinetic parameters previously estimated for a single-stage system were observed for the maximum specific growth rate, for the inhibition constants of cell growth and for the specific rate of substrate consumption for cell maintenance. Mathematical models were validated and used to simulate alternative operating conditions as well as to analyze the performance of the two-stage process against that of the single-stage process.

A Computational Model of the Rainbow Trout Hypothalamus-Pituitary-Ovary-Liver Axis

PubMed Central

Gillies, Kendall; Krone, Stephen M.; Nagler, James J.; Schultz, Irvin R.

2016-01-01

Reproduction in fishes and other vertebrates represents the timely coordination of many endocrine factors that culminate in the production of mature, viable gametes. In recent years there has been rapid growth in understanding fish reproductive biology, which has been motivated in part by recognition of the potential effects that climate change, habitat destruction and contaminant exposure can have on natural and cultured fish populations. New approaches to understanding the impacts of these stressors are being developed that require a systems biology approach with more biologically accurate and detailed mathematical models. We have developed a multi-scale mathematical model of the female rainbow trout hypothalamus-pituitary-ovary-liver axis to use as a tool to help understand the functioning of the system and for extrapolation of laboratory findings of stressor impacts on specific components of the axis. The model describes the essential endocrine components of the female rainbow trout reproductive axis. The model also describes the stage specific growth of maturing oocytes within the ovary and permits the presence of sub-populations of oocytes at different stages of development. Model formulation and parametrization was largely based on previously published in vivo and in vitro data in rainbow trout and new data on the synthesis of gonadotropins in the pituitary. Model predictions were validated against several previously published data sets for annual changes in gonadotropins and estradiol in rainbow trout. Estimates of select model parameters can be obtained from in vitro assays using either quantitative (direct estimation of rate constants) or qualitative (relative change from control values) approaches. This is an important aspect of mathematical models as in vitro, cell-based assays are expected to provide the bulk of experimental data for future risk assessments and will require quantitative physiological models to extrapolate across biological scales. PMID:27096735

A Computational Model of the Rainbow Trout Hypothalamus-Pituitary-Ovary-Liver Axis.

PubMed

Gillies, Kendall; Krone, Stephen M; Nagler, James J; Schultz, Irvin R

2016-04-01

Reproduction in fishes and other vertebrates represents the timely coordination of many endocrine factors that culminate in the production of mature, viable gametes. In recent years there has been rapid growth in understanding fish reproductive biology, which has been motivated in part by recognition of the potential effects that climate change, habitat destruction and contaminant exposure can have on natural and cultured fish populations. New approaches to understanding the impacts of these stressors are being developed that require a systems biology approach with more biologically accurate and detailed mathematical models. We have developed a multi-scale mathematical model of the female rainbow trout hypothalamus-pituitary-ovary-liver axis to use as a tool to help understand the functioning of the system and for extrapolation of laboratory findings of stressor impacts on specific components of the axis. The model describes the essential endocrine components of the female rainbow trout reproductive axis. The model also describes the stage specific growth of maturing oocytes within the ovary and permits the presence of sub-populations of oocytes at different stages of development. Model formulation and parametrization was largely based on previously published in vivo and in vitro data in rainbow trout and new data on the synthesis of gonadotropins in the pituitary. Model predictions were validated against several previously published data sets for annual changes in gonadotropins and estradiol in rainbow trout. Estimates of select model parameters can be obtained from in vitro assays using either quantitative (direct estimation of rate constants) or qualitative (relative change from control values) approaches. This is an important aspect of mathematical models as in vitro, cell-based assays are expected to provide the bulk of experimental data for future risk assessments and will require quantitative physiological models to extrapolate across biological scales.

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

PubMed

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

2012-02-28

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

CORRECTING FOR MEASUREMENT ERROR IN LATENT VARIABLES USED AS PREDICTORS*

PubMed Central

Schofield, Lynne Steuerle

2015-01-01

This paper represents a methodological-substantive synergy. A new model, the Mixed Effects Structural Equations (MESE) model which combines structural equations modeling and item response theory is introduced to attend to measurement error bias when using several latent variables as predictors in generalized linear models. The paper investigates racial and gender disparities in STEM retention in higher education. Using the MESE model with 1997 National Longitudinal Survey of Youth data, I find prior mathematics proficiency and personality have been previously underestimated in the STEM retention literature. Pre-college mathematics proficiency and personality explain large portions of the racial and gender gaps. The findings have implications for those who design interventions aimed at increasing the rates of STEM persistence among women and under-represented minorities. PMID:26977218

Dice and Disease in the Classroom.

ERIC Educational Resources Information Center

Stor, Marilyn; Briggs, William L.

1998-01-01

Presents a mathematics activity to model the exponential growth of the common cold, AIDS, or any other communicable disease. Underscores the effect that a friend's or partner's previous behavior may have on a current relationship and on society at large. (ASK)

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

PubMed

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

2018-01-01

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

Correlated receptor transport processes buffer single-cell heterogeneity

PubMed Central

Kallenberger, Stefan M.; Unger, Anne L.; Legewie, Stefan; Lymperopoulos, Konstantinos; Eils, Roland

2017-01-01

Cells typically vary in their response to extracellular ligands. Receptor transport processes modulate ligand-receptor induced signal transduction and impact the variability in cellular responses. Here, we quantitatively characterized cellular variability in erythropoietin receptor (EpoR) trafficking at the single-cell level based on live-cell imaging and mathematical modeling. Using ensembles of single-cell mathematical models reduced parameter uncertainties and showed that rapid EpoR turnover, transport of internalized EpoR back to the plasma membrane, and degradation of Epo-EpoR complexes were essential for receptor trafficking. EpoR trafficking dynamics in adherent H838 lung cancer cells closely resembled the dynamics previously characterized by mathematical modeling in suspension cells, indicating that dynamic properties of the EpoR system are widely conserved. Receptor transport processes differed by one order of magnitude between individual cells. However, the concentration of activated Epo-EpoR complexes was less variable due to the correlated kinetics of opposing transport processes acting as a buffering system. PMID:28945754

Cognitive tutor: applied research in mathematics education.

PubMed

Ritter, Steven; Anderson, John R; Koedinger, Kenneth R; Corbett, Albert

2007-04-01

For 25 years, we have been working to build cognitive models of mathematics, which have become a basis for middle- and high-school curricula. We discuss the theoretical background of this approach and evidence that the resulting curricula are more effective than other approaches to instruction. We also discuss how embedding a well specified theory in our instructional software allows us to dynamically evaluate the effectiveness of our instruction at a more detailed level than was previously possible. The current widespread use of the software is allowing us to test hypotheses across large numbers of students. We believe that this will lead to new approaches both to understanding mathematical cognition and to improving instruction.

Modification of the Mathematical Model of the Thermoelectric Module of a Thermostating Coating

NASA Astrophysics Data System (ADS)

Zarubin, V. S.; Kuvyrkin, G. N.; Savel'eva, I. Yu.

2017-03-01

A modification has been made of the previously constructed mathematical model of a fragment of a flat thermostating coating including a thermoelectric module based on the variation formulation of the stationary problem of heat conduction in an inhomogeneous solid body. With the use of the Fourier finite integral transform the dependences have been obtained for calculating the temperature distribution in the heat insulating layer in the vicinity of the thermoelectric element and commutating conductors. This enabled us to refine one of the diagnostic variables of the model — the total heat resistance of the heat insulator between commutating plates and conductors of the thermoelectric module influencing the energy characteristics of the thermostating coating under investigation.

Numerical simulation of the structure of the high-latitude ionospheric F region during meridional HF propagation

NASA Astrophysics Data System (ADS)

Andreev, M. Yu.; Mingaleva, G. I.; Mingalev, V. S.

2007-08-01

A previously developed model of the high-latitude ionosphere is used to calculate the distribution of the ionospheric parameters in the polar region. A specific method for specifying input parameters of the mathematical model, using the experimental data obtained by the method of satellite radio tomography, is used in this case. The spatial distributions of the ionospheric parameters characterized by a complex inhomogeneous structure in the high-latitude region, calculated with the help of the mathematical model, are used to simulate the HF propagation along the meridionally oriented radio paths extending from middle to high latitudes. The method for improving the HF communication between a midlatitude transmitter and a polar-cap receiver is proposed.

Estimating tuberculosis incidence from primary survey data: a mathematical modeling approach

PubMed Central

Chadha, V. K.; Laxminarayan, R.; Arinaminpathy, N.

2017-01-01

SUMMARY BACKGROUND: There is an urgent need for improved estimations of the burden of tuberculosis (TB). OBJECTIVE: To develop a new quantitative method based on mathematical modelling, and to demonstrate its application to TB in India. DESIGN: We developed a simple model of TB transmission dynamics to estimate the annual incidence of TB disease from the annual risk of tuberculous infection and prevalence of smear-positive TB. We first compared model estimates for annual infections per smear-positive TB case using previous empirical estimates from China, Korea and the Philippines. We then applied the model to estimate TB incidence in India, stratified by urban and rural settings. RESULTS: Study model estimates show agreement with previous empirical estimates. Applied to India, the model suggests an annual incidence of smear-positive TB of 89.8 per 100 000 population (95%CI 56.8–156.3). Results show differences in urban and rural TB: while an urban TB case infects more individuals per year, a rural TB case remains infectious for appreciably longer, suggesting the need for interventions tailored to these different settings. CONCLUSIONS: Simple models of TB transmission, in conjunction with necessary data, can offer approaches to burden estimation that complement those currently being used. PMID:28284250

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

M. A. Wasiolek

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

A model of yeast glycolysis based on a consistent kinetic characterisation of all its enzymes

PubMed Central

Smallbone, Kieran; Messiha, Hanan L.; Carroll, Kathleen M.; Winder, Catherine L.; Malys, Naglis; Dunn, Warwick B.; Murabito, Ettore; Swainston, Neil; Dada, Joseph O.; Khan, Farid; Pir, Pınar; Simeonidis, Evangelos; Spasić, Irena; Wishart, Jill; Weichart, Dieter; Hayes, Neil W.; Jameson, Daniel; Broomhead, David S.; Oliver, Stephen G.; Gaskell, Simon J.; McCarthy, John E.G.; Paton, Norman W.; Westerhoff, Hans V.; Kell, Douglas B.; Mendes, Pedro

2013-01-01

We present an experimental and computational pipeline for the generation of kinetic models of metabolism, and demonstrate its application to glycolysis in Saccharomyces cerevisiae. Starting from an approximate mathematical model, we employ a “cycle of knowledge” strategy, identifying the steps with most control over flux. Kinetic parameters of the individual isoenzymes within these steps are measured experimentally under a standardised set of conditions. Experimental strategies are applied to establish a set of in vivo concentrations for isoenzymes and metabolites. The data are integrated into a mathematical model that is used to predict a new set of metabolite concentrations and reevaluate the control properties of the system. This bottom-up modelling study reveals that control over the metabolic network most directly involved in yeast glycolysis is more widely distributed than previously thought. PMID:23831062

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

NASA Astrophysics Data System (ADS)

Hyhlík, Tomáš

2016-03-01

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

BioModels: expanding horizons to include more modelling approaches and formats

PubMed Central

Nguyen, Tung V N; Graesslin, Martin; Hälke, Robert; Ali, Raza; Schramm, Jochen; Wimalaratne, Sarala M; Kothamachu, Varun B; Rodriguez, Nicolas; Swat, Maciej J; Eils, Jurgen; Eils, Roland; Laibe, Camille; Chelliah, Vijayalakshmi

2018-01-01

Abstract BioModels serves as a central repository of mathematical models representing biological processes. It offers a platform to make mathematical models easily shareable across the systems modelling community, thereby supporting model reuse. To facilitate hosting a broader range of model formats derived from diverse modelling approaches and tools, a new infrastructure for BioModels has been developed that is available at http://www.ebi.ac.uk/biomodels. This new system allows submitting and sharing of a wide range of models with improved support for formats other than SBML. It also offers a version-control backed environment in which authors and curators can work collaboratively to curate models. This article summarises the features available in the current system and discusses the potential benefit they offer to the users over the previous system. In summary, the new portal broadens the scope of models accepted in BioModels and supports collaborative model curation which is crucial for model reproducibility and sharing. PMID:29106614

Mathematical modeling of white adipocyte exocytosis predicts adiponectin secretion and quantifies the rates of vesicle exo- and endocytosis.

PubMed

Brännmark, Cecilia; Lövfors, William; Komai, Ali M; Axelsson, Tom; El Hachmane, Mickaël F; Musovic, Saliha; Paul, Alexandra; Nyman, Elin; Olofsson, Charlotta S

2017-12-08

Adiponectin is a hormone secreted from white adipocytes and takes part in the regulation of several metabolic processes. Although the pathophysiological importance of adiponectin has been thoroughly investigated, the mechanisms controlling its release are only partly understood. We have recently shown that adiponectin is secreted via regulated exocytosis of adiponectin-containing vesicles, that adiponectin exocytosis is stimulated by cAMP-dependent mechanisms, and that Ca 2+ and ATP augment the cAMP-triggered secretion. However, much remains to be discovered regarding the molecular and cellular regulation of adiponectin release. Here, we have used mathematical modeling to extract detailed information contained within our previously obtained high-resolution patch-clamp time-resolved capacitance recordings to produce the first model of adiponectin exocytosis/secretion that combines all mechanistic knowledge deduced from electrophysiological experimental series. This model demonstrates that our previous understanding of the role of intracellular ATP in the control of adiponectin exocytosis needs to be revised to include an additional ATP-dependent step. Validation of the model by introduction of data of secreted adiponectin yielded a very close resemblance between the simulations and experimental results. Moreover, we could show that Ca 2+ -dependent adiponectin endocytosis contributes to the measured capacitance signal, and we were able to predict the contribution of endocytosis to the measured exocytotic rate under different experimental conditions. In conclusion, using mathematical modeling of published and newly generated data, we have obtained estimates of adiponectin exo- and endocytosis rates, and we have predicted adiponectin secretion. We believe that our model should have multiple applications in the study of metabolic processes and hormonal control thereof. © 2017 by The American Society for Biochemistry and Molecular Biology, Inc.

Neurally and mathematically motivated architecture for language and thought.

PubMed

Perlovsky, L I; Ilin, R

2010-01-01

Neural structures of interaction between thinking and language are unknown. This paper suggests a possible architecture motivated by neural and mathematical considerations. A mathematical requirement of computability imposes significant constraints on possible architectures consistent with brain neural structure and with a wealth of psychological knowledge. How language interacts with cognition. Do we think with words, or is thinking independent from language with words being just labels for decisions? Why is language learned by the age of 5 or 7, but acquisition of knowledge represented by learning to use this language knowledge takes a lifetime? This paper discusses hierarchical aspects of language and thought and argues that high level abstract thinking is impossible without language. We discuss a mathematical technique that can model the joint language-thought architecture, while overcoming previously encountered difficulties of computability. This architecture explains a contradiction between human ability for rational thoughtful decisions and irrationality of human thinking revealed by Tversky and Kahneman; a crucial role in this contradiction might be played by language. The proposed model resolves long-standing issues: how the brain learns correct words-object associations; why animals do not talk and think like people. We propose the role played by language emotionality in its interaction with thought. We relate the mathematical model to Humboldt's "firmness" of languages; and discuss possible influence of language grammar on its emotionality. Psychological and brain imaging experiments related to the proposed model are discussed. Future theoretical and experimental research is outlined.

Neurally and Mathematically Motivated Architecture for Language and Thought

PubMed Central

Perlovsky, L.I; Ilin, R

2010-01-01

Neural structures of interaction between thinking and language are unknown. This paper suggests a possible architecture motivated by neural and mathematical considerations. A mathematical requirement of computability imposes significant constraints on possible architectures consistent with brain neural structure and with a wealth of psychological knowledge. How language interacts with cognition. Do we think with words, or is thinking independent from language with words being just labels for decisions? Why is language learned by the age of 5 or 7, but acquisition of knowledge represented by learning to use this language knowledge takes a lifetime? This paper discusses hierarchical aspects of language and thought and argues that high level abstract thinking is impossible without language. We discuss a mathematical technique that can model the joint language-thought architecture, while overcoming previously encountered difficulties of computability. This architecture explains a contradiction between human ability for rational thoughtful decisions and irrationality of human thinking revealed by Tversky and Kahneman; a crucial role in this contradiction might be played by language. The proposed model resolves long-standing issues: how the brain learns correct words-object associations; why animals do not talk and think like people. We propose the role played by language emotionality in its interaction with thought. We relate the mathematical model to Humboldt’s “firmness” of languages; and discuss possible influence of language grammar on its emotionality. Psychological and brain imaging experiments related to the proposed model are discussed. Future theoretical and experimental research is outlined. PMID:21673788

Mathematical modeling of human brain physiological data

NASA Astrophysics Data System (ADS)

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

2013-12-01

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

Mathematical literacy in Plant Physiology undergraduates: results of interventions aimed at improving students' performance

NASA Astrophysics Data System (ADS)

Vila, Francisca; Sanz, Amparo

2013-09-01

The importance of mathematical literacy in any scientific career is widely recognized. However, various studies report lack of numeracy and mathematical literacy in students from various countries. In the present work, we present a detailed study of the mathematical literacy of Spanish undergraduate students of Biology enrolled in a Plant Physiology course. We have performed individual analyses of results obtained during the period 2000-2011, for questions in the examinations requiring and not requiring mathematical skills. Additionally, we present the outcome of two interventions introduced with the aim of helping students improve their prospects for success in the course. Our results confirm previous research showing students' deficiencies in mathematical skills. However, the scores obtained for mathematical questions in the examinations are good predictors of the final grades attained in Plant Physiology, as there are strong correlations at the individual level between results for questions requiring and not requiring mathematical skills. The introduction of a laboratory session devoted to strengthening the application of students' previously acquired mathematical knowledge did not change significantly the results obtained for mathematical questions. Since mathematical abilities of students entering university have declined in recent years, this intervention may have helped to maintain students' performance to a level comparable to that of previous years. The outcome of self-assessment online tests indicates that although Mathematics anxiety is lower than during examinations, the poor results obtained for questions requiring mathematical skills are, at least in part, due to a lack of self-efficacy.

The contribution of parent-child numeracy activities to young Chinese children's mathematical ability.

PubMed

Huang, Qi; Zhang, Xiao; Liu, Yingyi; Yang, Wen; Song, Zhanmei

2017-09-01

A growing body of recent research has shown that parent-child mathematical activities have a strong effect on children's mathematical learning. However, this research was conducted predominantly in Western societies and focused mainly on mothers' involvement in such activities. This study aimed to examine both mother-child and father-child numeracy activities in Hong Kong Chinese families and both parents' unique roles in predicting young Chinese children's mathematics ability. A sample of 104 Hong Kong Chinese children aged approximately 5 years and their mothers and fathers participated in this study. Mothers and fathers independently reported the frequency of their own numeracy activities with their children. Children were assessed individually using two measures of mathematical ability. Hierarchical regression models were used to investigate the contribution of parent-child numeracy activities to children's mathematical ability. Mothers' participation in number skill activities and fathers' participation in number game and application activities significantly predicted their children's mathematical performance even after controlling for background variables and children's language ability. This study extends previous research with a sample of Chinese kindergarten children and shows that parent-child numeracy activities are related to young children's mathematical ability. The findings highlight the important roles that mothers and fathers play in their young children's mathematical learning. © 2017 The British Psychological Society.

Application of simple mathematical expressions to relate the half-lives of xenobiotics in rats to values in humans.

PubMed

Ward, Keith W; Erhardt, Paul; Bachmann, Kenneth

2005-01-01

Previous publications from GlaxoSmithKline and University of Toledo laboratories convey our independent attempts to predict the half-lives of xenobiotics in humans using data obtained from rats. The present investigation was conducted to compare the performance of our published models against a common dataset obtained by merging the two sets of rat versus human half-life (hHL) data previously used by each laboratory. After combining data, mathematical analyses were undertaken by deploying both of our previous models, namely the use of an empirical algorithm based on a best-fit model and the use of rat-to-human liver blood flow ratios as a half-life correction factor. Both qualitative and quantitative analyses were performed, as well as evaluation of the impact of molecular properties on predictability. The merged dataset was remarkably diverse with respect to physiochemical and pharmacokinetic (PK) properties. Application of both models revealed similar predictability, depending upon the measure of stipulated accuracy. Certain molecular features, particularly rotatable bond count and pK(a), appeared to influence the accuracy of prediction. This collaborative effort has resulted in an improved understanding and appreciation of the value of rats to serve as a surrogate for the prediction of xenobiotic half-lives in humans when clinical pharmacokinetic studies are not possible or practicable.

Thermomechanical Stresses Analysis of a Single Event Burnout Process

NASA Astrophysics Data System (ADS)

Tais, Carlos E.; Romero, Eduardo; Demarco, Gustavo L.

2009-06-01

This work analyzes the thermal and mechanical effects arising in a power Diffusion Metal Oxide Semiconductor (DMOS) during a Single Event Burnout (SEB) process. For studying these effects we propose a more detailed simulation structure than the previously used by other authors, solving the mathematical models by means of the Finite Element Method. We use a cylindrical heat generation region, with 5 W, 10 W, 50 W and 100 W for emulating the thermal phenomena occurring during SEB processes, avoiding the complexity of the mathematical treatment of the ion-semiconductor interaction.

Mathematical analysis of deception.

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

Rogers, Deanna Tamae Koike; Durgin, Nancy Ann

This report describes the results of a three year research project about the use of deception in information protection. The work involved a collaboration between Sandia employees and students in the Center for Cyber Defenders (CCD) and at the University of California at Davis. This report includes a review of the history of deception, a discussion of some cognitive issues, an overview of previous work in deception, the results of experiments on the effects of deception on an attacker, and a mathematical model of error types associated with deception in computer systems.

From Preface to Practice: A Narrative Study of Women Learning to Teach Mathematics

ERIC Educational Resources Information Center

Stoehr, Kathleen Jablon

2014-01-01

My dissertation research explored the experiences of mathematics anxieties in women elementary preservice teachers while learning mathematics as K-12 students and while learning to teach mathematics. Previous studies conducted in mathematics teacher education have emphasized the importance of preservice teachers' mathematical knowledge for…

Causal Connections between Mathematical Language and Mathematical Knowledge: A Dialogic Reading Intervention

ERIC Educational Resources Information Center

Purpura, David J.; Napoli, Amy R.; Wehrspann, Elizabeth A.; Gold, Zachary S.

2017-01-01

The acquisition of early mathematical knowledge is critical for successful long-term academic development. Mathematical language is one of the strongest predictors of children's early mathematical success. Findings from previous studies have provided correlational evidence supporting the importance of mathematical language to the development of…

A Spatio-Temporal Model of Notch Signalling in the Zebrafish Segmentation Clock: Conditions for Synchronised Oscillatory Dynamics

PubMed Central

Terry, Alan J.; Sturrock, Marc; Dale, J. Kim; Maroto, Miguel; Chaplain, Mark A. J.

2011-01-01

In the vertebrate embryo, tissue blocks called somites are laid down in head-to-tail succession, a process known as somitogenesis. Research into somitogenesis has been both experimental and mathematical. For zebrafish, there is experimental evidence for oscillatory gene expression in cells in the presomitic mesoderm (PSM) as well as evidence that Notch signalling synchronises the oscillations in neighbouring PSM cells. A biological mechanism has previously been proposed to explain these phenomena. Here we have converted this mechanism into a mathematical model of partial differential equations in which the nuclear and cytoplasmic diffusion of protein and mRNA molecules is explictly considered. By performing simulations, we have found ranges of values for the model parameters (such as diffusion and degradation rates) that yield oscillatory dynamics within PSM cells and that enable Notch signalling to synchronise the oscillations in two touching cells. Our model contains a Hill coefficient that measures the co-operativity between two proteins (Her1, Her7) and three genes (her1, her7, deltaC) which they inhibit. This coefficient appears to be bounded below by the requirement for oscillations in individual cells and bounded above by the requirement for synchronisation. Consistent with experimental data and a previous spatially non-explicit mathematical model, we have found that signalling can increase the average level of Her1 protein. Biological pattern formation would be impossible without a certain robustness to variety in cell shape and size; our results possess such robustness. Our spatially-explicit modelling approach, together with new imaging technologies that can measure intracellular protein diffusion rates, is likely to yield significant new insight into somitogenesis and other biological processes. PMID:21386903

A spatio-temporal model of Notch signalling in the zebrafish segmentation clock: conditions for synchronised oscillatory dynamics.

PubMed

Terry, Alan J; Sturrock, Marc; Dale, J Kim; Maroto, Miguel; Chaplain, Mark A J

2011-02-28

In the vertebrate embryo, tissue blocks called somites are laid down in head-to-tail succession, a process known as somitogenesis. Research into somitogenesis has been both experimental and mathematical. For zebrafish, there is experimental evidence for oscillatory gene expression in cells in the presomitic mesoderm (PSM) as well as evidence that Notch signalling synchronises the oscillations in neighbouring PSM cells. A biological mechanism has previously been proposed to explain these phenomena. Here we have converted this mechanism into a mathematical model of partial differential equations in which the nuclear and cytoplasmic diffusion of protein and mRNA molecules is explicitly considered. By performing simulations, we have found ranges of values for the model parameters (such as diffusion and degradation rates) that yield oscillatory dynamics within PSM cells and that enable Notch signalling to synchronise the oscillations in two touching cells. Our model contains a Hill coefficient that measures the co-operativity between two proteins (Her1, Her7) and three genes (her1, her7, deltaC) which they inhibit. This coefficient appears to be bounded below by the requirement for oscillations in individual cells and bounded above by the requirement for synchronisation. Consistent with experimental data and a previous spatially non-explicit mathematical model, we have found that signalling can increase the average level of Her1 protein. Biological pattern formation would be impossible without a certain robustness to variety in cell shape and size; our results possess such robustness. Our spatially-explicit modelling approach, together with new imaging technologies that can measure intracellular protein diffusion rates, is likely to yield significant new insight into somitogenesis and other biological processes.

Reduced modeling of signal transduction – a modular approach

PubMed Central

Koschorreck, Markus; Conzelmann, Holger; Ebert, Sybille; Ederer, Michael; Gilles, Ernst Dieter

2007-01-01

Background Combinatorial complexity is a challenging problem in detailed and mechanistic mathematical modeling of signal transduction. This subject has been discussed intensively and a lot of progress has been made within the last few years. A software tool (BioNetGen) was developed which allows an automatic rule-based set-up of mechanistic model equations. In many cases these models can be reduced by an exact domain-oriented lumping technique. However, the resulting models can still consist of a very large number of differential equations. Results We introduce a new reduction technique, which allows building modularized and highly reduced models. Compared to existing approaches further reduction of signal transduction networks is possible. The method also provides a new modularization criterion, which allows to dissect the model into smaller modules that are called layers and can be modeled independently. Hallmarks of the approach are conservation relations within each layer and connection of layers by signal flows instead of mass flows. The reduced model can be formulated directly without previous generation of detailed model equations. It can be understood and interpreted intuitively, as model variables are macroscopic quantities that are converted by rates following simple kinetics. The proposed technique is applicable without using complex mathematical tools and even without detailed knowledge of the mathematical background. However, we provide a detailed mathematical analysis to show performance and limitations of the method. For physiologically relevant parameter domains the transient as well as the stationary errors caused by the reduction are negligible. Conclusion The new layer based reduced modeling method allows building modularized and strongly reduced models of signal transduction networks. Reduced model equations can be directly formulated and are intuitively interpretable. Additionally, the method provides very good approximations especially for macroscopic variables. It can be combined with existing reduction methods without any difficulties. PMID:17854494

Basic mathematical rules are encoded by primate prefrontal cortex neurons

PubMed Central

Bongard, Sylvia; Nieder, Andreas

2010-01-01

Mathematics is based on highly abstract principles, or rules, of how to structure, process, and evaluate numerical information. If and how mathematical rules can be represented by single neurons, however, has remained elusive. We therefore recorded the activity of individual prefrontal cortex (PFC) neurons in rhesus monkeys required to switch flexibly between “greater than” and “less than” rules. The monkeys performed this task with different numerical quantities and generalized to set sizes that had not been presented previously, indicating that they had learned an abstract mathematical principle. The most prevalent activity recorded from randomly selected PFC neurons reflected the mathematical rules; purely sensory- and memory-related activity was almost absent. These data show that single PFC neurons have the capacity to represent flexible operations on most abstract numerical quantities. Our findings support PFC network models implementing specific “rule-coding” units that control the flow of information between segregated input, memory, and output layers. We speculate that these neuronal circuits in the monkey lateral PFC could readily have been adopted in the course of primate evolution for syntactic processing of numbers in formalized mathematical systems. PMID:20133872

Eighth Grade Algebra Course Placement and Student Motivation for Mathematics

PubMed Central

Simzar, Rahila M.; Domina, Thurston; Tran, Cathy

2016-01-01

This study uses student panel data to examine the association between Algebra placement and student motivation for mathematics. Changes in achievement goals, expectancy, and task value for students in eighth grade Algebra are compared with those of peers placed in lower-level mathematics courses (N = 3,306). In our sample, students placed in Algebra reported an increase in performance-avoidance goals as well as decreases in academic self-efficacy and task value. These relations were attenuated for students who had high mathematics achievement prior to Algebra placement. Whereas all students reported an overall decline in performance-approach goals over the course of eighth grade, previously high-achieving students reported an increase in these goals. Lastly, previously high-achieving students reported an increase in mastery goals. These findings suggest that while previously high-achieving students may benefit motivationally from eighth grade Algebra placement, placing previously average- and low-performing students in Algebra can potentially undermine their motivation for mathematics. PMID:26942210

Eighth Grade Algebra Course Placement and Student Motivation for Mathematics.

PubMed

Simzar, Rahila M; Domina, Thurston; Tran, Cathy

2016-01-01

This study uses student panel data to examine the association between Algebra placement and student motivation for mathematics. Changes in achievement goals, expectancy, and task value for students in eighth grade Algebra are compared with those of peers placed in lower-level mathematics courses (N = 3,306). In our sample, students placed in Algebra reported an increase in performance-avoidance goals as well as decreases in academic self-efficacy and task value. These relations were attenuated for students who had high mathematics achievement prior to Algebra placement. Whereas all students reported an overall decline in performance-approach goals over the course of eighth grade, previously high-achieving students reported an increase in these goals. Lastly, previously high-achieving students reported an increase in mastery goals. These findings suggest that while previously high-achieving students may benefit motivationally from eighth grade Algebra placement, placing previously average- and low-performing students in Algebra can potentially undermine their motivation for mathematics.

Mathematical background and attitudes toward statistics in a sample of Spanish college students.

PubMed

Carmona, José; Martínez, Rafael J; Sánchez, Manuel

2005-08-01

To examine the relation of mathematical background and initial attitudes toward statistics of Spanish college students in social sciences the Survey of Attitudes Toward Statistics was given to 827 students. Multivariate analyses tested the effects of two indicators of mathematical background (amount of exposure and achievement in previous courses) on the four subscales. Analysis suggested grades in previous courses are more related to initial attitudes toward statistics than the number of mathematics courses taken. Mathematical background was related with students' affective responses to statistics but not with their valuing of statistics. Implications of possible research are discussed.

Mathematical modelling of sewage sludge incineration in a bubbling fluidised bed with special consideration for thermally-thick fuel particles.

PubMed

Yang, Yao Bin; Sharifi, Vida; Swithenbank, Jim

2008-11-01

Fluidised bed combustor (FBC) is one of the key technologies for sewage sludge incineration. In this paper, a mathematical model is developed for the simulation of a large-scale sewage sludge incineration plant. The model assumes the bed consisting of a fast-gas phase, an emulsion phase and a fuel particle phase with specific consideration for thermally-thick fuel particles. The model further improves over previous works by taking into account throughflow inside the bubbles as well as the floating and random movement of the fuel particles inside the bed. Validation against both previous lab-scale experiments and operational data of a large-scale industrial plant was made. Calculation results indicate that combustion split between the bed and the freeboard can range from 60/40 to 90/10 depending on the fuel particle distribution across the bed height under the specific conditions. The bed performance is heavily affected by the variation in sludge moisture level. The response time to variation in feeding rate is different for different parameters, from 6 min for outlet H2O, 10 min for O2, to 34 min for bed temperature.

Mathematics Anxiety: One Size Does Not Fit All

ERIC Educational Resources Information Center

Stoehr, Kathleen Jablon

2017-01-01

Mathematics educators agree elementary teachers should possess confidence and competence in teaching mathematics. Many prospective elementary teachers (particularly women) pursue careers in elementary teaching despite personal repeated experiences of mathematics anxiety. Previous studies of mathematics anxiety have tended to focus on physical…

Variational Integrators for Interconnected Lagrange-Dirac Systems

NASA Astrophysics Data System (ADS)

Parks, Helen; Leok, Melvin

2017-10-01

Interconnected systems are an important class of mathematical models, as they allow for the construction of complex, hierarchical, multiphysics, and multiscale models by the interconnection of simpler subsystems. Lagrange-Dirac mechanical systems provide a broad category of mathematical models that are closed under interconnection, and in this paper, we develop a framework for the interconnection of discrete Lagrange-Dirac mechanical systems, with a view toward constructing geometric structure-preserving discretizations of interconnected systems. This work builds on previous work on the interconnection of continuous Lagrange-Dirac systems (Jacobs and Yoshimura in J Geom Mech 6(1):67-98, 2014) and discrete Dirac variational integrators (Leok and Ohsawa in Found Comput Math 11(5), 529-562, 2011). We test our results by simulating some of the continuous examples given in Jacobs and Yoshimura (2014).

Mathematical modeling of energy metabolism and hemodynamics of WHO grade II gliomas using in vivo MR data.

PubMed

Guillevin, Rémy; Menuel, Carole; Vallée, Jean-Noël; Françoise, Jean-Pierre; Capelle, Laurent; Habas, Christophe; De Marco, Giovanni; Chiras, Jacques; Costalat, Robert

2011-01-01

Therapeutic management of low-grade gliomas (LGG) is a challenge because they have undergone anaplastic transformation with variable delay. Today, only progressive volume growth on successive MRI allows an in vivo monitoring of this evolution. On the other hand, multinuclear spectroscopy and perfusion available during MRI may also provide assessment of metabolic changes underlying morphological modifications. To overcome this drawback, we developed a mathematical model of the metabolism and the hemodynamic of gliomas, based on a physiological model previously published, and including the MR parameters. This allows us to suggest that some specific profiles of metabolic and hemodynamic changes would be good indicators of potential anaplastic transformation. Copyright © 2010 Académie des sciences. Published by Elsevier SAS. All rights reserved.

Simulating Bone Loss in Microgravity Using Mathematical Formulations of Bone Remodeling

NASA Technical Reports Server (NTRS)

Pennline, James A.

2009-01-01

Most mathematical models of bone remodeling are used to simulate a specific bone disease, by disrupting the steady state or balance in the normal remodeling process, and to simulate a therapeutic strategy. In this work, the ability of a mathematical model of bone remodeling to simulate bone loss as a function of time under the conditions of microgravity is investigated. The model is formed by combining a previously developed set of biochemical, cellular dynamics, and mechanical stimulus equations in the literature with two newly proposed equations; one governing the rate of change of the area of cortical bone tissue in a cross section of a cylindrical section of bone and one governing the rate of change of calcium in the bone fluid. The mechanical stimulus comes from a simple model of stress due to a compressive force on a cylindrical section of bone which can be reduced to zero to mimic the effects of skeletal unloading in microgravity. The complete set of equations formed is a system of first order ordinary differential equations. The results of selected simulations are displayed and discussed. Limitations and deficiencies of the model are also discussed as well as suggestions for further research.

A mechanistic model for bromodeoxyuridine dilution naturally explains labelling data of self-renewing T cell populations

PubMed Central

Ganusov, Vitaly V.; De Boer, Rob J.

2013-01-01

Bromodeoxyuridine (BrdU) is widely used in immunology to detect cell division, and several mathematical models have been proposed to estimate proliferation and death rates of lymphocytes from BrdU labelling and de-labelling curves. One problem in interpreting BrdU data is explaining the de-labelling curves. Because shortly after label withdrawal, BrdU+ cells are expected to divide into BrdU+ daughter cells, one would expect a flat down-slope. As for many cell types, the fraction of BrdU+ cells decreases during de-labelling, previous mathematical models had to make debatable assumptions to be able to account for the data. We develop a mechanistic model tracking the number of divisions that each cell has undergone in the presence and absence of BrdU, and allow cells to accumulate and dilute their BrdU content. From the same mechanistic model, one can naturally derive expressions for the mean BrdU content (MBC) of all cells, or the MBC of the BrdU+ subset, which is related to the mean fluorescence intensity of BrdU that can be measured in experiments. The model is extended to include subpopulations with different rates of division and death (i.e. kinetic heterogeneity). We fit the extended model to previously published BrdU data from memory T lymphocytes in simian immunodeficiency virus-infected and uninfected macaques, and find that the model describes the data with at least the same quality as previous models. Because the same model predicts a modest decline in the MBC of BrdU+ cells, which is consistent with experimental observations, BrdU dilution seems a natural explanation for the observed down-slopes in self-renewing populations. PMID:23034350

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

PubMed

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

2015-09-01

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

The structural identifiability and parameter estimation of a multispecies model for the transmission of mastitis in dairy cows with postmilking teat disinfection.

PubMed

White, L J; Evans, N D; Lam, T J G M; Schukken, Y H; Medley, G F; Godfrey, K R; Chappell, M J

2002-01-01

A mathematical model for the transmission of two interacting classes of mastitis causing bacterial pathogens in a herd of dairy cows is presented and applied to a specific data set. The data were derived from a field trial of a specific measure used in the control of these pathogens, where half the individuals were subjected to the control and in the others the treatment was discontinued. The resultant mathematical model (eight non-linear simultaneous ordinary differential equations) therefore incorporates heterogeneity in the host as well as the infectious agent and consequently the effects of control are intrinsic in the model structure. A structural identifiability analysis of the model is presented demonstrating that the scope of the novel method used allows application to high order non-linear systems. The results of a simultaneous estimation of six unknown system parameters are presented. Previous work has only estimated a subset of these either simultaneously or individually. Therefore not only are new estimates provided for the parameters relating to the transmission and control of the classes of pathogens under study, but also information about the relationships between them. We exploit the close link between mathematical modelling, structural identifiability analysis, and parameter estimation to obtain biological insights into the system modelled.

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

PubMed

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

2017-03-07

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

Discrete-Time Mapping for an Impulsive Goodwin Oscillator with Three Delays

NASA Astrophysics Data System (ADS)

Churilov, Alexander N.; Medvedev, Alexander; Zhusubaliyev, Zhanybai T.

A popular biomathematics model of the Goodwin oscillator has been previously generalized to a more biologically plausible construct by introducing three time delays to portray the transport phenomena arising due to the spatial distribution of the model states. The present paper addresses a similar conversion of an impulsive version of the Goodwin oscillator that has found application in mathematical modeling, e.g. in endocrine systems with pulsatile hormone secretion. While the cascade structure of the linear continuous part pertinent to the Goodwin oscillator is preserved in the impulsive Goodwin oscillator, the static nonlinear feedback of the former is substituted with a pulse modulation mechanism thus resulting in hybrid dynamics of the closed-loop system. To facilitate the analysis of the mathematical model under investigation, a discrete mapping propagating the continuous state variables through the firing times of the impulsive feedback is derived. Due to the presence of multiple time delays in the considered model, previously developed mapping derivation approaches are not applicable here and a novel technique is proposed and applied. The mapping captures the dynamics of the original hybrid system and is instrumental in studying complex nonlinear phenomena arising in the impulsive Goodwin oscillator. A simulation example is presented to demonstrate the utility of the proposed approach in bifurcation analysis.

Building Knowledge Structures by Testing Helps Children with Mathematical Learning Difficulty

ERIC Educational Resources Information Center

Zhang, Yiyun; Zhou, Xinlin

2016-01-01

Mathematical learning difficulty (MLD) is prevalent in the development of mathematical abilities. Previous interventions for children with MLD have focused on number sense or basic mathematical skills. This study investigated whether mathematical performance of fifth grade children with MLD could be improved by developing knowledge structures by…

A Predictive Mathematical Model of Muscle Forces for Children with Cerebral Palsy

ERIC Educational Resources Information Center

Lee, Samuel C. K.; Ding, Jun; Prosser, Laura A.; Wexler, Anthony S.; Binder-Macleod, Stuart A.

2009-01-01

Aim: The purpose of this study was to determine if our previously developed muscle model could be used to predict forces of the quadriceps femoris and triceps surae muscles of children with spastic diplegic cerebral palsy (CP). Method: Twenty-two children with CP (12 males, 10 females; mean age 10y, SD 2y, range 7-13y; Gross Motor Function…

Representational Flexibility and Problem-Solving Ability in Fraction and Decimal Number Addition: A Structural Model

ERIC Educational Resources Information Center

Deliyianni, Eleni; Gagatsis, Athanasios; Elia, Iliada; Panaoura, Areti

2016-01-01

The aim of this study was to propose and validate a structural model in fraction and decimal number addition, which is founded primarily on a synthesis of major theoretical approaches in the field of representations in Mathematics and also on previous research on the learning of fractions and decimals. The study was conducted among 1,701 primary…

An Emergentist Model for Writing in Mathematics.

ERIC Educational Resources Information Center

Hoh, Pau-San; Kirtland, Joe

In spite of the widespread implementation of Writing Across the Curriculum (WAC), there remains little concrete evidence of the writing-thinking connection. This paper proposes a new research method that tracks students' performance and production at a deeper level of specificity than that in previous investigations of this relationship, e.g., in…

Building a better Faraday cage

NASA Astrophysics Data System (ADS)

MartinAlfven; Wright, David; skocpol; Rounce, Graham; Richfield, Jon; W, Nick; wheelsonfire

2015-11-01

In reply to the physicsworld.com news article “Are Faraday cages less effective than previously thought?” (15 September, http://ow.ly/SfklO), about a study that indicated, based on mathematical modelling, that conducting wire-mesh cages may not be as good at excluding electromagnetic radiation as is commonly assumed.

Chaos for cardiac arrhythmias through a one-dimensional modulation equation for alternans

PubMed Central

Dai, Shu; Schaeffer, David G.

2010-01-01

Instabilities in cardiac dynamics have been widely investigated in recent years. One facet of this work has studied chaotic behavior, especially possible correlations with fatal arrhythmias. Previously chaotic behavior was observed in various models, specifically in the breakup of spiral and scroll waves. In this paper we study cardiac dynamics and find spatiotemporal chaotic behavior through the Echebarria–Karma modulation equation for alternans in one dimension. Although extreme parameter values are required to produce chaos in this model, it seems significant mathematically that chaos may occur by a different mechanism from previous observations. PMID:20590327

Mathematical modelling of prostate cancer growth and its application to hormone therapy.

PubMed

Tanaka, Gouhei; Hirata, Yoshito; Goldenberg, S Larry; Bruchovsky, Nicholas; Aihara, Kazuyuki

2010-11-13

Hormone therapy in the form of androgen deprivation is a major treatment for advanced prostate cancer. However, if such therapy is overly prolonged, tumour cells may become resistant to this treatment and result in recurrent fatal disease. Long-term hormone deprivation also is associated with side effects poorly tolerated by patients. In contrast, intermittent hormone therapy with alternating on- and off-treatment periods is a possible clinical strategy to delay progression to hormone-refractory disease with the advantage of reduced side effects during the off-treatment periods. In this paper, we first overview previous studies on mathematical modelling of prostate tumour growth under intermittent hormone therapy. The model is categorized into a hybrid dynamical system because switching between on-treatment and off-treatment intervals is treated in addition to continuous dynamics of tumour growth. Next, we present an extended model of stochastic differential equations and examine how well the model is able to capture the characteristics of authentic serum prostate-specific antigen (PSA) data. We also highlight recent advances in time-series analysis and prediction of changes in serum PSA concentrations. Finally, we discuss practical issues to be considered towards establishment of mathematical model-based tailor-made medicine, which defines how to realize personalized hormone therapy for individual patients based on monitored serum PSA levels.

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-step strategies with 'new' ultrasound-based models predict high-risk endometrial cancers with good accuracy and do this better than do previously developed models. Copyright © 2013 ISUOG. Published by John Wiley & Sons Ltd.

The cryptoendolithic microbial environment in the Ross Desert of Antarctica: mathematical models of the thermal regime

NASA Technical Reports Server (NTRS)

Nienow, J. A.; McKay, C. P.; Friedmann, E. I.

1988-01-01

Microbial activity in the Antarctic cryptoendolithic habitat is regulated primarily by temperature. Previous field studies have provided some information on the thermal regime in this habitat, but this type of information is limited by the remoteness of the site and the harsh climatic conditions. Therefore, a mathematical model of the endolithic thermal regime was constructed to augment the field data. This model enabled the parameters affecting the horizontal and altitudinal distribution of the community to be examined. The model predicts that colonization should be possible on surfaces with zenith angle less than 15 degrees. At greater zenith angles, colonization should be restricted to surfaces with azimuth angles less than 135 degrees or greater than 225 degrees. The upper elevational limit of the community should be less than 2,500 m. The thermal regime probably does not influence the zonation of the community within a rock.

Empirical validation of the triple-code model of numerical processing for complex math operations using functional MRI and group Independent Component Analysis of the mental addition and subtraction of fractions.

PubMed

Schmithorst, Vincent J; Brown, Rhonda Douglas

2004-07-01

The suitability of a previously hypothesized triple-code model of numerical processing, involving analog magnitude, auditory verbal, and visual Arabic codes of representation, was investigated for the complex mathematical task of the mental addition and subtraction of fractions. Functional magnetic resonance imaging (fMRI) data from 15 normal adult subjects were processed using exploratory group Independent Component Analysis (ICA). Separate task-related components were found with activation in bilateral inferior parietal, left perisylvian, and ventral occipitotemporal areas. These results support the hypothesized triple-code model corresponding to the activated regions found in the individual components and indicate that the triple-code model may be a suitable framework for analyzing the neuropsychological bases of the performance of complex mathematical tasks. Copyright 2004 Elsevier Inc.

A dynamic, climate-driven model of Rift Valley fever.

PubMed

Leedale, Joseph; Jones, Anne E; Caminade, Cyril; Morse, Andrew P

2016-03-31

Outbreaks of Rift Valley fever (RVF) in eastern Africa have previously occurred following specific rainfall dynamics and flooding events that appear to support the emergence of large numbers of mosquito vectors. As such, transmission of the virus is considered to be sensitive to environmental conditions and therefore changes in climate can impact the spatiotemporal dynamics of epizootic vulnerability. Epidemiological information describing the methods and parameters of RVF transmission and its dependence on climatic factors are used to develop a new spatio-temporal mathematical model that simulates these dynamics and can predict the impact of changes in climate. The Liverpool RVF (LRVF) model is a new dynamic, process-based model driven by climate data that provides a predictive output of geographical changes in RVF outbreak susceptibility as a result of the climate and local livestock immunity. This description of the multi-disciplinary process of model development is accessible to mathematicians, epidemiological modellers and climate scientists, uniting dynamic mathematical modelling, empirical parameterisation and state-of-the-art climate information.

Modelling the behaviour of uranium-series radionuclides in soils and plants taking into account seasonal variations in soil hydrology.

PubMed

Pérez-Sánchez, D; Thorne, M C

2014-05-01

In a previous paper, a mathematical model for the behaviour of (79)Se in soils and plants was described. Subsequently, a review has been published relating to the behaviour of (238)U-series radionuclides in soils and plants. Here, we bring together those two strands of work to describe a new mathematical model of the behaviour of (238)U-series radionuclides entering soils in solution and their uptake by plants. Initial studies with the model that are reported here demonstrate that it is a powerful tool for exploring the behaviour of this decay chain or subcomponents of it in soil-plant systems under different hydrological regimes. In particular, it permits studies of the degree to which secular equilibrium assumptions are appropriate when modelling this decay chain. Further studies will be undertaken and reported separately examining sensitivities of model results to input parameter values and also applying the model to sites contaminated with (238)U-series radionuclides. Copyright © 2013 Elsevier Ltd. All rights reserved.

Comparing the cognitive differences resulting from modeling instruction: Using computer microworld and physical object instruction to model real world problems

NASA Astrophysics Data System (ADS)

Oursland, Mark David

This study compared the modeling achievement of students receiving mathematical modeling instruction using the computer microworld, Interactive Physics, and students receiving instruction using physical objects. Modeling instruction included activities where students applied the (a) linear model to a variety of situations, (b) linear model to two-rate situations with a constant rate, (c) quadratic model to familiar geometric figures. Both quantitative and qualitative methods were used to analyze achievement differences between students (a) receiving different methods of modeling instruction, (b) with different levels of beginning modeling ability, or (c) with different levels of computer literacy. Student achievement was analyzed quantitatively through a three-factor analysis of variance where modeling instruction, beginning modeling ability, and computer literacy were used as the three independent factors. The SOLO (Structure of the Observed Learning Outcome) assessment framework was used to design written modeling assessment instruments to measure the students' modeling achievement. The same three independent factors were used to collect and analyze the interviews and observations of student behaviors. Both methods of modeling instruction used the data analysis approach to mathematical modeling. The instructional lessons presented problem situations where students were asked to collect data, analyze the data, write a symbolic mathematical equation, and use equation to solve the problem. The researcher recommends the following practice for modeling instruction based on the conclusions of this study. A variety of activities with a common structure are needed to make explicit the modeling process of applying a standard mathematical model. The modeling process is influenced strongly by prior knowledge of the problem context and previous modeling experiences. The conclusions of this study imply that knowledge of the properties about squares improved the students' ability to model a geometric problem more than instruction in data analysis modeling. The uses of computer microworlds such as Interactive Physics in conjunction with cooperative groups are a viable method of modeling instruction.

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

PubMed

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

2018-06-19

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

Finding exact constants in a Markov model of Zipfs law generation

NASA Astrophysics Data System (ADS)

Bochkarev, V. V.; Lerner, E. Yu.; Nikiforov, A. A.; Pismenskiy, A. A.

2017-12-01

According to the classical Zipfs law, the word frequency is a power function of the word rank with an exponent -1. The objective of this work is to find multiplicative constant in a Markov model of word generation. Previously, the case of independent letters was mathematically strictly investigated in [Bochkarev V V and Lerner E Yu 2017 International Journal of Mathematics and Mathematical Sciences Article ID 914374]. Unfortunately, the methods used in this paper cannot be generalized in case of Markov chains. The search of the correct formulation of the Markov generalization of this results was performed using experiments with different ergodic matrices of transition probability P. Combinatory technique allowed taking into account all the words with probability of more than e -300 in case of 2 by 2 matrices. It was experimentally proved that the required constant in the limit is equal to the value reciprocal to conditional entropy of matrix row P with weights presenting the elements of the vector π of the stationary distribution of the Markov chain.

Correlates of Mathematics Anxiety.

ERIC Educational Resources Information Center

McCoy, Leah, P.

1992-01-01

Presents a survey of 78 pre- and in-service elementary teachers in a midwestern region to examine the relationship between mathematics anxiety, perceptual preference, and previous mathematics instructional experiences with workbooks and manipulatives. Results indicate that the variables significant in predicting mathematics anxiety were…

Mathematical Modeling of Intravascular Blood Coagulation under Wall Shear Stress

PubMed Central

Rukhlenko, Oleksii S.; Dudchenko, Olga A.; Zlobina, Ksenia E.; Guria, Georgy Th.

2015-01-01

Increased shear stress such as observed at local stenosis may cause drastic changes in the permeability of the vessel wall to procoagulants and thus initiate intravascular blood coagulation. In this paper we suggest a mathematical model to investigate how shear stress-induced permeability influences the thrombogenic potential of atherosclerotic plaques. Numerical analysis of the model reveals the existence of two hydrodynamic thresholds for activation of blood coagulation in the system and unveils typical scenarios of thrombus formation. The dependence of blood coagulation development on the intensity of blood flow, as well as on geometrical parameters of atherosclerotic plaque is described. Relevant parametric diagrams are drawn. The results suggest a previously unrecognized role of relatively small plaques (resulting in less than 50% of the lumen area reduction) in atherothrombosis and have important implications for the existing stenting guidelines. PMID:26222505

Runge-Kutta method for wall shear stress of blood flow in stenosed artery

NASA Astrophysics Data System (ADS)

Awaludin, Izyan Syazana; Ahmad, Rokiah@Rozita

2014-06-01

A mathematical model of blood flow through stenotic artery is considered. A stenosis is defined as the partial occlusion of the blood vessels due to the accumulation of cholesterols, fats and the abnormal growth of tissue on the artery walls. The development of stenosis in the artery is one of the factors that cause problem in blood circulation system. This study was conducted to determine the wall shear stress of blood flow in stenosed artery. Modified mathematical model is used to analyze the relationship of the wall shear stress versus the length and height of stenosis. The existing models that have been created by previous researchers are solved using fourth order Runge-Kutta method. Numerical results show that the wall shear stress is proportionate to the length and height of stenosis.

Mathematics Anxiety and Statistics Anxiety. Shared but Also Unshared Components and Antagonistic Contributions to Performance in Statistics

PubMed Central

Paechter, Manuela; Macher, Daniel; Martskvishvili, Khatuna; Wimmer, Sigrid; Papousek, Ilona

2017-01-01

In many social science majors, e.g., psychology, students report high levels of statistics anxiety. However, these majors are often chosen by students who are less prone to mathematics and who might have experienced difficulties and unpleasant feelings in their mathematics courses at school. The present study investigates whether statistics anxiety is a genuine form of anxiety that impairs students' achievements or whether learners mainly transfer previous experiences in mathematics and their anxiety in mathematics to statistics. The relationship between mathematics anxiety and statistics anxiety, their relationship to learning behaviors and to performance in a statistics examination were investigated in a sample of 225 undergraduate psychology students (164 women, 61 men). Data were recorded at three points in time: At the beginning of term students' mathematics anxiety, general proneness to anxiety, school grades, and demographic data were assessed; 2 weeks before the end of term, they completed questionnaires on statistics anxiety and their learning behaviors. At the end of term, examination scores were recorded. Mathematics anxiety and statistics anxiety correlated highly but the comparison of different structural equation models showed that they had genuine and even antagonistic contributions to learning behaviors and performance in the examination. Surprisingly, mathematics anxiety was positively related to performance. It might be that students realized over the course of their first term that knowledge and skills in higher secondary education mathematics are not sufficient to be successful in statistics. Part of mathematics anxiety may then have strengthened positive extrinsic effort motivation by the intention to avoid failure and may have led to higher effort for the exam preparation. However, via statistics anxiety mathematics anxiety also had a negative contribution to performance. Statistics anxiety led to higher procrastination in the structural equation model and, therefore, contributed indirectly and negatively to performance. Furthermore, it had a direct negative impact on performance (probably via increased tension and worry in the exam). The results of the study speak for shared but also unique components of statistics anxiety and mathematics anxiety. They are also important for instruction and give recommendations to learners as well as to instructors. PMID:28790938

Mathematics Anxiety and Statistics Anxiety. Shared but Also Unshared Components and Antagonistic Contributions to Performance in Statistics.

PubMed

Paechter, Manuela; Macher, Daniel; Martskvishvili, Khatuna; Wimmer, Sigrid; Papousek, Ilona

2017-01-01

In many social science majors, e.g., psychology, students report high levels of statistics anxiety. However, these majors are often chosen by students who are less prone to mathematics and who might have experienced difficulties and unpleasant feelings in their mathematics courses at school. The present study investigates whether statistics anxiety is a genuine form of anxiety that impairs students' achievements or whether learners mainly transfer previous experiences in mathematics and their anxiety in mathematics to statistics. The relationship between mathematics anxiety and statistics anxiety, their relationship to learning behaviors and to performance in a statistics examination were investigated in a sample of 225 undergraduate psychology students (164 women, 61 men). Data were recorded at three points in time: At the beginning of term students' mathematics anxiety, general proneness to anxiety, school grades, and demographic data were assessed; 2 weeks before the end of term, they completed questionnaires on statistics anxiety and their learning behaviors. At the end of term, examination scores were recorded. Mathematics anxiety and statistics anxiety correlated highly but the comparison of different structural equation models showed that they had genuine and even antagonistic contributions to learning behaviors and performance in the examination. Surprisingly, mathematics anxiety was positively related to performance. It might be that students realized over the course of their first term that knowledge and skills in higher secondary education mathematics are not sufficient to be successful in statistics. Part of mathematics anxiety may then have strengthened positive extrinsic effort motivation by the intention to avoid failure and may have led to higher effort for the exam preparation. However, via statistics anxiety mathematics anxiety also had a negative contribution to performance. Statistics anxiety led to higher procrastination in the structural equation model and, therefore, contributed indirectly and negatively to performance. Furthermore, it had a direct negative impact on performance (probably via increased tension and worry in the exam). The results of the study speak for shared but also unique components of statistics anxiety and mathematics anxiety. They are also important for instruction and give recommendations to learners as well as to instructors.

Early Mathematical Competencies and Later Outcomes: Insights from the Longitudinal Study of Australian Children

ERIC Educational Resources Information Center

MacDonald, Amy; Carmichael, Colin

2016-01-01

International research suggests that early mathematical competences predicts later mathematical outcomes. In this paper, we build on our previous study of young children's mathematical competencies (MacDonald & Carmichael, 2015) to explore the relationship between mathematical competencies at 4-5 years, as measured by teacher ratings, and…

Math Is Like a Lion Hunting a Sleeping Gazelle: Preservice Elementary Teachers' Metaphors of Mathematics

ERIC Educational Resources Information Center

Latterell, Carmen M.; Wilson, Janelle L.

2016-01-01

Preservice elementary teachers hold a variety of beliefs about mathematics and mathematics learning, which influence their teaching. Previous research has shown that preservice elementary teachers believe that mathematics is doing arithmetic. However, it is unclear if preservice elementary teachers truly believe that mathematics is only…

Analysis of Hepatic Blood Flow Using Chaotic Models

PubMed Central

Cohen, M. E.; Moazamipour, H.; Hudson, D. L.; Anderson, M. F.

1990-01-01

The study of chaos in physical systems is an important new theoretical development in modeling which has emerged in the last fifteen years. It is particularly useful in explaining phenomena which arise in nonlinear dynamic systems, for which previous mathematical models produced results with intractable solutions. Analysis of blood flow is such an application. In the work described here, chaotic models are used to analyze hepatic artery and portal vein blood flow obtained from a pulsed Doppler ultrasonic flowmeter implanted in dogs. ImagesFigure 3

Validation of a mathematical model of the bovine estrous cycle for cows with different estrous cycle characteristics.

PubMed

Boer, H M T; Butler, S T; Stötzel, C; Te Pas, M F W; Veerkamp, R F; Woelders, H

2017-11-01

A recently developed mechanistic mathematical model of the bovine estrous cycle was parameterized to fit empirical data sets collected during one estrous cycle of 31 individual cows, with the main objective to further validate the model. The a priori criteria for validation were (1) the resulting model can simulate the measured data correctly (i.e. goodness of fit), and (2) this is achieved without needing extreme, probably non-physiological parameter values. We used a least squares optimization procedure to identify parameter configurations for the mathematical model to fit the empirical in vivo measurements of follicle and corpus luteum sizes, and the plasma concentrations of progesterone, estradiol, FSH and LH for each cow. The model was capable of accommodating normal variation in estrous cycle characteristics of individual cows. With the parameter sets estimated for the individual cows, the model behavior changed for 21 cows, with improved fit of the simulated output curves for 18 of these 21 cows. Moreover, the number of follicular waves was predicted correctly for 18 of the 25 two-wave and three-wave cows, without extreme parameter value changes. Estimation of specific parameters confirmed results of previous model simulations indicating that parameters involved in luteolytic signaling are very important for regulation of general estrous cycle characteristics, and are likely responsible for differences in estrous cycle characteristics between cows.

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

PubMed

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

2007-09-01

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

A Generalized Quantum-Inspired Decision Making Model for Intelligent Agent

PubMed Central

Loo, Chu Kiong

2014-01-01

A novel decision making for intelligent agent using quantum-inspired approach is proposed. A formal, generalized solution to the problem is given. Mathematically, the proposed model is capable of modeling higher dimensional decision problems than previous researches. Four experiments are conducted, and both empirical experiments results and proposed model's experiment results are given for each experiment. Experiments showed that the results of proposed model agree with empirical results perfectly. The proposed model provides a new direction for researcher to resolve cognitive basis in designing intelligent agent. PMID:24778580

Sensitivity analysis as an aid in modelling and control of (poorly-defined) ecological systems. [closed ecological systems

NASA Technical Reports Server (NTRS)

Hornberger, G. M.; Rastetter, E. B.

1982-01-01

A literature review of the use of sensitivity analyses in modelling nonlinear, ill-defined systems, such as ecological interactions is presented. Discussions of previous work, and a proposed scheme for generalized sensitivity analysis applicable to ill-defined systems are included. This scheme considers classes of mathematical models, problem-defining behavior, analysis procedures (especially the use of Monte-Carlo methods), sensitivity ranking of parameters, and extension to control system design.

A Mathematical Model of Neonatal Rat Atrial Monolayers with Constitutively Active Acetylcholine-Mediated K+ Current

PubMed Central

Majumder, Rupamanjari; Jangsangthong, Wanchana; Feola, Iolanda; Ypey, Dirk L.; Pijnappels, Daniël A.; Panfilov, Alexander V.

2016-01-01

Atrial fibrillation (AF) is the most frequent form of arrhythmia occurring in the industrialized world. Because of its complex nature, each identified form of AF requires specialized treatment. Thus, an in-depth understanding of the bases of these arrhythmias is essential for therapeutic development. A variety of experimental studies aimed at understanding the mechanisms of AF are performed using primary cultures of neonatal rat atrial cardiomyocytes (NRAMs). Previously, we have shown that the distinct advantage of NRAM cultures is that they allow standardized, systematic, robust re-entry induction in the presence of a constitutively-active acetylcholine-mediated K+ current (IKACh-c). Experimental studies dedicated to mechanistic explorations of AF, using these cultures, often use computer models for detailed electrophysiological investigations. However, currently, no mathematical model for NRAMs is available. Therefore, in the present study we propose the first model for the action potential (AP) of a NRAM with constitutively-active acetylcholine-mediated K+ current (IKACh-c). The descriptions of the ionic currents were based on patch-clamp data obtained from neonatal rats. Our monolayer model closely mimics the action potential duration (APD) restitution and conduction velocity (CV) restitution curves presented in our previous in vitro studies. In addition, the model reproduces the experimentally observed dynamics of spiral wave rotation, in the absence and in the presence of drug interventions, and in the presence of localized myofibroblast heterogeneities. PMID:27332890

Early Years Students' Relationships with Mathematics

ERIC Educational Resources Information Center

Takeuchi, Miwa Aoki; Towers, Jo; Plosz, Jennifer

2016-01-01

Early years mathematics experiences have been shown to be a significant predictor for students' school readiness and future mathematics achievement. Previous research also indicates an important connection between emotion and mathematics learning. How do students in early years education in Alberta describe their emotional relationship with…

Exploring the mechanism of βamyloid toxicity attenuation by multivalent sialic acid polymers through the use of mathematical models

PubMed Central

Cowan, Christopher B.; Patel, Dhara A.; Good, Theresa A.

2009-01-01

β-Amyloid peptide (Aβ), the primary protein component in senile plaques associated with Alzheimer’s disease (AD), has been implicated in neurotoxicity associated with AD. Previous studies have shown that the Aβ-neuronal membrane interaction plays a role in the mechanism of Aβ toxicity. More specifically, it is thought that Aβ interacts with ganglioside rich and sialic acid rich regions of cell surfaces. In light of such evidence, we have used a number of different sialic acid compounds of different valency or number of sialic acid moieties per molecule to attenuate Aβ toxicity in a cell culture model. In this work, we proposed various mathematical models of Aβ interaction with both the cell membrane and with the multivalent sialic acid compounds, designed to act as membrane mimics. These models allow us to explore the mechanism of action of this class of sialic acid membrane mimics in attenuating the toxicity of Aβ. The mathematical models, when compared with experimental data, facilitate the discrimination between different modes of action of these materials. Understanding the mechanism of action of Aβ toxicity inhibitors should provide insight into the design of the next generation of molecules that could be used to prevent Aβ toxicity associated with Alzheimer’s disease. PMID:19217912

Integrated Formulation of Beacon-Based Exception Analysis for Multimissions

NASA Technical Reports Server (NTRS)

Mackey, Ryan; James, Mark; Park, Han; Zak, Mickail

2003-01-01

Further work on beacon-based exception analysis for multimissions (BEAM), a method of real-time, automated diagnosis of a complex electromechanical systems, has greatly expanded its capability and suitability of application. This expanded formulation, which fully integrates physical models and symbolic analysis, is described. The new formulation of BEAM expands upon previous advanced techniques for analysis of signal data, utilizing mathematical modeling of the system physics, and expert-system reasoning,

Reaching the Mountaintop: Addressing the Common Core Standards in Mathematics for Students with Mathematics Difficulties

ERIC Educational Resources Information Center

Powell, Sarah R.; Fuchs, Lynn S.; Fuchs, Doug

2013-01-01

The Common Core State Standards provide teachers with a framework of necessary mathematics skills across grades K-12, which vary considerably from previous mathematics standards. In this article, we discuss concerns about the implications of the Common Core for students with mathematics difficulties (MD), given that students with MD, by…

Mathematical modeling of chemical composition modification and etching of polymers under the atomic oxygen influence

NASA Astrophysics Data System (ADS)

Chirskaia, Natalia; Novikov, Lev; Voronina, Ekaterina

2016-07-01

Atomic oxygen (AO) of the upper atmosphere is one of the most important space factors that can cause degradation of spacecraft surface. In our previous mathematical model the Monte Carlo method and the "large particles" approximation were used for simulating processes of polymer etching under the influence of AO [1]. The interaction of enlarged AO particles with the polymer was described in terms of probabilities of reactions such as etching of polymer and specular and diffuse scattering of the AO particles on polymer. The effects of atomic oxygen on protected polymers and microfiller containing composites were simulated. The simulation results were in quite good agreement with the results of laboratory experiments on magnetoplasmadynamic accelerator of the oxygen plasma of SINP MSU [2]. In this paper we present a new model that describes the reactions of AO interactions with polymeric materials in more detail. Reactions of formation and further emission of chemical compounds such as CO, CO _{2}, H _{2}O, etc. cause the modification of the chemical composition of the polymer and change the probabilities of its consequent interaction with the AO. The simulation results are compared with the results of previous simulation and with the results of laboratory experiments. The reasons for the differences between the results of natural experiments on spacecraft, laboratory experiments and simulations are discussed. N. Chirskaya, M. Samokhina, Computer modeling of polymer structures degradation under the atomic oxygen exposure, WDS'12 Proceedings of Contributed Papers: Part III - Physics, Matfyzpress Prague, 2012, pp. 30-35. E. Voronina, L. Novikov, V. Chernik, N. Chirskaya, K. Vernigorov, G. Bondarenko, and A. Gaidar, Mathematical and experimental simulation of impact of atomic oxygen of the earth's upper atmosphere on nanostructures and polymer composites, Inorganic Materials: Applied Research, 2012, vol. 3, no. 2, pp. 95-101.

Exploring Differential Bundle Functioning in Mathematics by Gender: The Effect of Hierarchical Modelling

ERIC Educational Resources Information Center

Ong, Yoke Mooi; Williams, Julian; Lamprianou, Iasonas

2013-01-01

Researchers interested in exploring substantive group differences are increasingly attending to bundles of items (or testlets): the aim is to understand how gender differences, for instance, are explained by differential performances on different types or bundles of items, hence differential bundle functioning (DBF). Some previous work has…

Using the Fennema-Sherman Mathematics Attitude Scales with lower-primary teachers

NASA Astrophysics Data System (ADS)

Ren, Lixin; Green, Jennifer L.; Smith, Wendy M.

2016-06-01

The Fennema-Sherman Mathematics Attitude Scales (FSMAS) are among the most popular instruments used in studies of attitudes toward mathematics. However, the FSMAS has been mainly used among student populations and rarely used with teachers. In the present study, three scales from the FSMAS— Confidence, Effectance Motivation, and Anxiety—were revised and used with lower-primary (kindergarten to third grade) teachers. This study includes three parts: (1) a pilot study to ensure the modifications made to the FSMAS were appropriate to use with teachers, (2) confirmatory factor analyses to assess the factor structure of the revised FSMAS with 225 lower-primary teachers, and (3) measurement invariance analyses using data from a similar sample of 171 lower-primary teachers to examine whether the revised FSMAS measures each construct in the same way as in the previous sample. The final three-factor model, after removing three problematic items, achieves acceptable model fit, with each construct meeting all conditions for strict measurement invariance. Additionally, repeated measures analyses were performed on data collected from 39 in-service lower-primary teachers who participated in an elementary mathematics specialist program to examine the use of the revised FSMAS in program evaluation. Overall results suggest that researchers and program evaluators may use the revised FSMAS to reliably measure lower-primary teachers' mathematical attitudes, and it can be a valuable tool for evaluating the effectiveness of professional development programs.

Applying multibeam sonar and mathematical modeling for mapping seabed substrate and biota of offshore shallows

NASA Astrophysics Data System (ADS)

Herkül, Kristjan; Peterson, Anneliis; Paekivi, Sander

2017-06-01

Both basic science and marine spatial planning are in a need of high resolution spatially continuous data on seabed habitats and biota. As conventional point-wise sampling is unable to cover large spatial extents in high detail, it must be supplemented with remote sensing and modeling in order to fulfill the scientific and management needs. The combined use of in situ sampling, sonar scanning, and mathematical modeling is becoming the main method for mapping both abiotic and biotic seabed features. Further development and testing of the methods in varying locations and environmental settings is essential for moving towards unified and generally accepted methodology. To fill the relevant research gap in the Baltic Sea, we used multibeam sonar and mathematical modeling methods - generalized additive models (GAM) and random forest (RF) - together with underwater video to map seabed substrate and epibenthos of offshore shallows. In addition to testing the general applicability of the proposed complex of techniques, the predictive power of different sonar-based variables and modeling algorithms were tested. Mean depth, followed by mean backscatter, were the most influential variables in most of the models. Generally, mean values of sonar-based variables had higher predictive power than their standard deviations. The predictive accuracy of RF was higher than that of GAM. To conclude, we found the method to be feasible and with predictive accuracy similar to previous studies of sonar-based mapping.

Anaerobic Threshold by Mathematical Model in Healthy and Post-Myocardial Infarction Men.

PubMed

Novais, L D; Silva, E; Simões, R P; Sakabe, D I; Martins, L E B; Oliveira, L; Diniz, C A R; Gallo, L; Catai, A M

2016-02-01

The aim of this study was to determine the anaerobic threshold (AT) in a population of healthy and post-myocardial infarction men by applying Hinkley's mathematical method and comparing its performance to the ventilatory visual method. This mathematical model, in lieu of observer-dependent visual determination, can produce more reliable results due to the uniformity of the procedure. 17 middle-aged men (55±3 years) were studied in 2 groups: 9 healthy men (54±2 years); and 8 men with previous myocardial infarction (57±3 years). All subjects underwent an incremental ramp exercise test until physical exhaustion. Breath-by-breath ventilatory variables, heart rate (HR), and vastus lateralis surface electromyography (sEMG) signal were collected throughout the test. Carbon dioxide output (V˙CO2), HR, and sEMG were studied, and the AT determination methods were compared using correlation coefficients and Bland-Altman plots. Parametric statistical tests were applied with significance level set at 5%. No significant differences were found in the HR, sEMG, and ventilatory variables at AT between the different methods, such as the intensity of effort relative to AT. Moreover, important concordance and significant correlations were observed between the methods. We concluded that the mathematical model was suitable for detecting the AT in both healthy and myocardial infarction subjects. © Georg Thieme Verlag KG Stuttgart · New York.

Tragic mathematics: romantic narratives and the refounding of mathematics in the early nineteenth century.

PubMed

Alexander, Amir R

2006-12-01

A new, Romantic type of mathematical story appeared in the early nineteenth century that was radically different from the sober narrative characteristic of the previous generation of mathematicians. At the same time, a new mathematical practice emerged that differed sharply from the understanding and practice of mathematics during the Enlightenment. These parallel developments are inseparable: the new type of mathematical practice went hand in hand with the new mathematical story.

Mathematical model of phase transformations and elastoplastic stress in the water spray quenching of steel bars

NASA Astrophysics Data System (ADS)

Nagasaka, Y.; Brimacombe, J. K.; Hawbolt, E. B.; Samarasekera, I. V.; Hernandez-Morales, B.; Chidiac, S. E.

1993-04-01

A mathematical model, based on the finite-element technique and incorporating thermo-elasto-plastic behavior during the water spray quenching of steel, has been developed. In the model, the kinetics of diffusion-dependent phase transformation and martensitic transformation have been coupled with the transient heat flow to predict the microstructural evolution of the steel. Furthermore, an elasto-plastic constitutive relation has been applied to calculate internal stresses resulting from phase changes as well as temperature variation. The computer code has been verified for internal consistency with previously published results for pure iron bars. The model has been applied to the water spray quenching of two grades of steel bars, 1035 carbon and nickel-chromium alloyed steel; the calculated temperature, hardness, distortion, and residual stresses in the bars agreed well with experimental measurements. The results show that the phase changes occurring during this process affect the internal stresses significantly and must be included in the thermomechanical model.

How to mathematically optimize drug regimens using optimal control.

PubMed

Moore, Helen

2018-02-01

This article gives an overview of a technique called optimal control, which is used to optimize real-world quantities represented by mathematical models. I include background information about the historical development of the technique and applications in a variety of fields. The main focus here is the application to diseases and therapies, particularly the optimization of combination therapies, and I highlight several such examples. I also describe the basic theory of optimal control, and illustrate each of the steps with an example that optimizes the doses in a combination regimen for leukemia. References are provided for more complex cases. The article is aimed at modelers working in drug development, who have not used optimal control previously. My goal is to make this technique more accessible in the biopharma community.

Prospective Elementary Teachers' Aesthetic Experience and Relationships to Mathematics

ERIC Educational Resources Information Center

Chen, Rong-Ji

2017-01-01

Previous research has adopted various approaches to examining teachers' and students' relationships to mathematics. The current study extended this line of research and investigated six prospective elementary school teachers' experiences in mathematics and how they saw themselves as learners of mathematics. One-on-one interviews with the…

Mathematical simulation of forced expiration.

PubMed

Elad, D; Kamm, R D; Shapiro, A H

1988-07-01

Flow limitation during forced expiration is simulated by a mathematical model. This model draws on the pressure-area law obtained in the accompanying paper, and the methods of analysis for one-dimensional flow in collapsible tubes developed by Shapiro (Trans. ASME J. Biomech. Eng. 99: 126-147, 1977). These methods represent an improvement over previous models in that 1) the effects of changing lung volume and of parenchymal-bronchial interdependence are simulated; 2) a more realistic representation of collapsed airways is employed; 3) a solution is obtained mouthward of the flow-limiting site by allowing for a smooth transition from sub- to supercritical flow speeds, then matching mouth pressure by imposing an elastic jump (an abrupt transition from super- to subcritical flow speeds) at the appropriate location; and 4) the effects of levels of effort (or vacuum pressure) in excess of those required to produce incipient flow limitation are examined, including the effects of potential physiological limitation.

A study of stiffness, residual strength and fatigue life relationships for composite laminates

NASA Technical Reports Server (NTRS)

Ryder, J. T.; Crossman, F. W.

1983-01-01

Qualitative and quantitative exploration of the relationship between stiffness, strength, fatigue life, residual strength, and damage of unnotched, graphite/epoxy laminates subjected to tension loading. Clarification of the mechanics of the tension loading is intended to explain previous contradictory observations and hypotheses; to develop a simple procedure to anticipate strength, fatigue life, and stiffness changes; and to provide reasons for the study of more complex cases of compression, notches, and spectrum fatigue loading. Mathematical models are developed based upon analysis of the damage states. Mathematical models were based on laminate analysis, free body type modeling or a strain energy release rate. Enough understanding of the tension loaded case is developed to allow development of a proposed, simple procedure for calculating strain to failure, stiffness, strength, data scatter, and shape of the stress-life curve for unnotched laminates subjected to tension load.

Mathematical model of temephos resistance in Aedes aegypti mosquito population

NASA Astrophysics Data System (ADS)

Aldila, D.; Nuraini, N.; Soewono, E.; Supriatna, A. K.

2014-03-01

Aedes aegypti is the main vector of dengue disease in many tropical and sub-tropical countries. Dengue became major public concern in these countries due to the unavailability of vaccine or drugs for dengue disease in the market. Hence, the only way to control the spread of DF and DHF is by controlling the vectors carrying the disease, for instance with fumigation, temephos or genetic manipulation. Many previous studies conclude that Aedes aegypti may develop resistance to many kind of insecticide, including temephos. Mathematical model for transmission of temephos resistance in Aedes aegypti population is discussed in this paper. Nontrivial equilibrium point of the system and the corresponding existence are shown analytically. The model analysis have shown epidemiological trends condition that permits the coexistence of nontrivial equilibrium is given analytically. Numerical results are given to show parameter sensitivity and some cases of worsening effect values for illustrating possible conditions in the field.

Full non-linear treatment of the global thermospheric wind system. I - Mathematical method and analysis of forces. II - Results and comparison with observations

NASA Technical Reports Server (NTRS)

Blum, P. W.; Harris, I.

1975-01-01

The equations of horizontal motion of the neutral atmosphere between 120 and 500 km are integrated with the inclusion of all nonlinear terms of the convective derivative and the viscous forces due to vertical and horizontal velocity gradients. Empirical models of the distribution of neutral and charged particles are assumed to be known. The model of velocities developed is a steady state model. In Part I the mathematical method used in the integration of the Navier-Stokes equations is described and the various forces are analyzed. Results of the method given in Part I are presented with comparison with previous calculations and observations of upper atmospheric winds. Conclusions are that nonlinear effects are only significant in the equatorial region, especially at solstice conditions and that nonlinear effects do not produce any superrotation.

Math anxiety: Brain cortical network changes in anticipation of doing mathematics.

PubMed

Klados, Manousos A; Pandria, Niki; Micheloyannis, Sifis; Margulies, Daniel; Bamidis, Panagiotis D

2017-12-01

Following our previous work regarding the involvement of math anxiety (MA) in math-oriented tasks, this study tries to explore the differences in the cerebral networks' topology between self-reported low math-anxious (LMA) and high math-anxious (HMA) individuals, during the anticipation phase prior to a mathematical related experiment. For this reason, multichannel EEG recordings were adopted, while the solution of the inverse problem was applied in a generic head model, in order to obtain the cortical signals. The cortical networks have been computed for each band separately, using the magnitude square coherence metric. The main graph theoretical parameters, showed differences in segregation and integration in almost all EEG bands of the HMAs in comparison to LMAs, indicative of a great influence of the anticipatory anxiety prior to mathematical performance. Copyright © 2017 Elsevier B.V. All rights reserved.

Preface for the special issue of Mathematical Biosciences and Engineering, BIOCOMP 2012.

PubMed

Buonocore, Aniello; Di Crescenzo, Antonio; Hastings, Alan

2014-04-01

The International Conference "BIOCOMP2012 - Mathematical Modeling and Computational Topics in Biosciences'', was held in Vietri sul Mare (Italy), June 4-8, 2012. It was dedicated to the Memory of Professor Luigi M. Ricciardi (1942-2011), who was a visionary and tireless promoter of the 3 previous editions of the BIOCOMP conference series. We thought that the best way to honor his memory was to continue the BIOCOMP program. Over the years, this conference promoted scientific activities related to his wide interests and scientific expertise, which ranged in various areas of applications of mathematics, probability and statistics to biosciences and cybernetics, also with emphasis on computational problems. We are pleased that many of his friends and colleagues, as well as many other scientists, were attracted by the goals of this recent event and offered to contribute to its success.

Skolem and pessimism about proof in mathematics.

PubMed

Cohen, Paul J

2005-10-15

Attitudes towards formalization and proof have gone through large swings during the last 150 years. We sketch the development from Frege's first formalization, to the debates over intuitionism and other schools, through Hilbert's program and the decisive blow of the Gödel Incompleteness Theorem. A critical role is played by the Skolem-Lowenheim Theorem, which showed that no first-order axiom system can characterize a unique infinite model. Skolem himself regarded this as a body blow to the belief that mathematics can be reliably founded only on formal axiomatic systems. In a remarkably prescient paper, he even sketches the possibility of interesting new models for set theory itself, something later realized by the method of forcing. This is in contrast to Hilbert's belief that mathematics could resolve all its questions. We discuss the role of new axioms for set theory, questions in set theory itself, and their relevance for number theory. We then look in detail at what the methods of the predicate calculus, i.e. mathematical reasoning, really entail. The conclusion is that there is no reasonable basis for Hilbert's assumption. The vast majority of questions even in elementary number theory, of reasonable complexity, are beyond the reach of any such reasoning. Of course this cannot be proved and we present only plausibility arguments. The great success of mathematics comes from considering 'natural problems', those which are related to previous work and offer a good chance of being solved. The great glories of human reasoning, beginning with the Greek discovery of geometry, are in no way diminished by this pessimistic view. We end by wishing good health to present-day mathematics and the mathematics of many centuries to come.

Physical disintegration of toilet papers in wastewater systems: experimental analysis and mathematical modeling.

PubMed

Eren, Beytullah; Karadagli, Fatih

2012-03-06

Physical disintegration of representative toilet papers was investigated in this study to assess their disintegration potential in sewer systems. Characterization of toilet papers from different parts of the world indicated two main categories as premium and average quality. Physical disintegration experiments were conducted with representative products from each category according to standard protocols with improvements. The experimental results were simulated by mathematical model to estimate best-fit values of disintegration rate coefficients and fractional distribution ratios. Our results from mathematical modeling and experimental work show that premium products release more amounts of small fibers and disintegrate more slowly than average ones. Comparison of the toilet papers with the tampon applicators studied previously indicates that premium quality toilet papers present significant potential to persist in sewer pipes. Comparison of turbulence level in our experimental setup with those of partial flow conditions in sewer pipes indicates that drains and small sewer pipes are critical sections where disintegration of toilet papers will be limited. For improvement, requirements for minimum pipe slopes may be increased to sustain transport and disintegration of flushable products in small pipes. In parallel, toilet papers can be improved to disintegrate rapidly in sewer systems, while they meet consumer expectations.

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

PubMed

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

2005-05-01

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

The Relationship between Handedness and Mathematics Is Non-linear and Is Moderated by Gender, Age, and Type of Task.

PubMed

Sala, Giovanni; Signorelli, Michela; Barsuola, Giulia; Bolognese, Martina; Gobet, Fernand

2017-01-01

The relationship between handedness and mathematical ability is still highly controversial. While some researchers have claimed that left-handers are gifted in mathematics and strong right-handers perform the worst in mathematical tasks, others have more recently proposed that mixed-handers are the most disadvantaged group. However, the studies in the field differ with regard to the ages and the gender of the participants, and the type of mathematical ability assessed. To disentangle these discrepancies, we conducted five studies in several Italian schools (total participants: N = 2,314), involving students of different ages (six to seventeen) and a range of mathematical tasks (e.g., arithmetic and reasoning). The results show that (a) linear and quadratic functions are insufficient for capturing the link between handedness and mathematical ability; (b) the percentage of variance in mathematics scores explained by handedness was larger than in previous studies (between 3 and 10% vs. 1%), and (c) the effect of handedness on mathematical ability depended on age, type of mathematical tasks, and gender. In accordance with previous research, handedness does represent a correlate of achievement in mathematics, but the shape of this relationship is more complicated than has been argued so far.

The Relationship between Handedness and Mathematics Is Non-linear and Is Moderated by Gender, Age, and Type of Task

PubMed Central

Sala, Giovanni; Signorelli, Michela; Barsuola, Giulia; Bolognese, Martina; Gobet, Fernand

2017-01-01

The relationship between handedness and mathematical ability is still highly controversial. While some researchers have claimed that left-handers are gifted in mathematics and strong right-handers perform the worst in mathematical tasks, others have more recently proposed that mixed-handers are the most disadvantaged group. However, the studies in the field differ with regard to the ages and the gender of the participants, and the type of mathematical ability assessed. To disentangle these discrepancies, we conducted five studies in several Italian schools (total participants: N = 2,314), involving students of different ages (six to seventeen) and a range of mathematical tasks (e.g., arithmetic and reasoning). The results show that (a) linear and quadratic functions are insufficient for capturing the link between handedness and mathematical ability; (b) the percentage of variance in mathematics scores explained by handedness was larger than in previous studies (between 3 and 10% vs. 1%), and (c) the effect of handedness on mathematical ability depended on age, type of mathematical tasks, and gender. In accordance with previous research, handedness does represent a correlate of achievement in mathematics, but the shape of this relationship is more complicated than has been argued so far. PMID:28649210

Mathematical and physical model of gravity-fed infusion outflow: application to soft-bag-packed solutions.

PubMed

Simon, N; Décaudin, B; Lannoy, D; Barthélémy, C; Lemdani, M; Odou, P

2011-12-01

Gravity-fed infusion (GFI) systems are acknowledged as being unable to keep their flow-rate constant. This may affect drug plasma levels such as aminoglycosides. Numerous factors have previously been cited, but their relative importance has never been quantified so far. The objective of this work is to identify the main factors that influence GFI in vitro outflow and to propose a mathematical model of flow-rate evolution as a function of time. In this model, pressure loss and infusion device creep have been considered as the main variation factors. Concomitantly, two experiments were undertaken. Firstly, the flow-rate evolution of an in vitro infusion of 250 mL of dextrose 5% was assessed. Secondly, the creep occurring on an infusion device was measured through a stress relaxation experiment. The experimental infusion flow-rate decreased by as much as 28.5% over 1 h. Simulated and experimental data are well correlated (r = 0.987; P < 0.0001). The maximum creep effect happens during the first 15 min of infusion. In this work, height of the liquid in the bag and tube creep were found to be the main variation factors in GFI flow-rate. This new mathematical model should help to explain the differences observed in drug plasma levels with gravity-fed devices.

The Implementation of an Interdisciplinary Co-planning Team Model Among Mathematics and Science Teachers

NASA Astrophysics Data System (ADS)

Brown, Michelle Cetner

In recent years, Science, Technology, Engineering, and Mathematics (STEM) education has become a significant focus of numerous theoretical and commentary articles as researchers have advocated for active and conceptually integrated learning in classrooms. Drawing connections between previously isolated subjects, especially mathematics and science, has been shown to increase student engagement, performance, and critical thinking skills. However, obstacles exist to the widespread implementation of integrated curricula in schools, such as teacher knowledge and school structure and culture. The Interdisciplinary Co-planning Team (ICT) model, in which teachers of different subjects come together regularly to discuss connections between content and to plan larger interdisciplinary activities and smaller examples and discussion points, offers a method for teachers to create sustainable interdisciplinary experiences for students within the bounds of the current school structure. The ICT model is designed to be an iterative, flexible model, providing teachers with both a regular time to come together as "experts" and "teach" each other important concepts from their separate disciplines, and then to bring their shared knowledge and language back to their own classrooms to implement with their students in ways that fit their individual classes. In this multiple-case study, which aims to describe the nature of the co-planning process, the nature of plans, and changes in teacher beliefs as a result of co-planning, three pairs of secondary mathematics and science teachers participated in a 10-week intervention with the ICT model. Each pair constituted one case. Data included observations, interviews, and artifact collection. All interviews, whole-group sessions, and co-planning sessions were transcribed and coded using both theory-based and data-based codes. Finally, a cross-case comparison was used to present similarities and differences across cases. Findings suggest that the ICT model can be implemented with pairs of mathematics and science teachers to create a sustainable way to share experience and expertise, and to create powerful interdisciplinary experiences for their students. In addition, there is evidence that participation with the ICT model positively influences teacher beliefs about the nature of mathematics and science, about teaching and learning, and about interdisciplinary connections. These findings seem to hold across grades, school type, and personal experience. Future implementation of the ICT model on a larger scale is recommended to continue to observe the effects on teachers and students.

An Introduction to Equilibrium Thermodynamics: A Rational Approach to Its Teaching. Part 1: Notation and Mathematics.

ERIC Educational Resources Information Center

Williams, Donald F.; Glasser, David

1991-01-01

Introduces and develops mathematical notation to assist undergraduate students in overcoming conceptual difficulties involving the underlying mathematics of state functions, which tend to be different from functions encountered by students in previous mathematical courses, because of the need to manipulate special types of partial derivatives and…

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…

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 distributions of alleles, in the case of haploid non-recombining loci such as mitochondrial and Y-chromosome loci in humans. Copyright © 2016 Elsevier Inc. All rights reserved.

Optimal healthcare decision making under multiple mathematical models: application in prostate cancer screening.

PubMed

Bertsimas, Dimitris; Silberholz, John; Trikalinos, Thomas

2018-03-01

Important decisions related to human health, such as screening strategies for cancer, need to be made without a satisfactory understanding of the underlying biological and other processes. Rather, they are often informed by mathematical models that approximate reality. Often multiple models have been made to study the same phenomenon, which may lead to conflicting decisions. It is natural to seek a decision making process that identifies decisions that all models find to be effective, and we propose such a framework in this work. We apply the framework in prostate cancer screening to identify prostate-specific antigen (PSA)-based strategies that perform well under all considered models. We use heuristic search to identify strategies that trade off between optimizing the average across all models' assessments and being "conservative" by optimizing the most pessimistic model assessment. We identified three recently published mathematical models that can estimate quality-adjusted life expectancy (QALE) of PSA-based screening strategies and identified 64 strategies that trade off between maximizing the average and the most pessimistic model assessments. All prescribe PSA thresholds that increase with age, and 57 involve biennial screening. Strategies with higher assessments with the pessimistic model start screening later, stop screening earlier, and use higher PSA thresholds at earlier ages. The 64 strategies outperform 22 previously published expert-generated strategies. The 41 most "conservative" ones remained better than no screening with all models in extensive sensitivity analyses. We augment current comparative modeling approaches by identifying strategies that perform well under all models, for various degrees of decision makers' conservativeness.

Projection multiplex recording of computer-synthesised one-dimensional Fourier holograms for holographic memory systems: mathematical and experimental modelling

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

Betin, A Yu; Bobrinev, V I; Verenikina, N M

A multiplex method of recording computer-synthesised one-dimensional Fourier holograms intended for holographic memory devices is proposed. The method potentially allows increasing the recording density in the previously proposed holographic memory system based on the computer synthesis and projection recording of data page holograms. (holographic memory)

ATMOSPHERIC DISPERSAL AND DEPOSITION OF TEPHRA FROM A POTENTIAL VOLCANIC ERUPTION AT YUCCA MOUNTAIN, NEVADA

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

C. Harrington

2004-10-25

The purpose of this model report is to provide documentation of the conceptual and mathematical model (Ashplume) for atmospheric dispersal and subsequent deposition of ash on the land surface from a potential volcanic eruption at Yucca Mountain, Nevada. This report also documents the ash (tephra) redistribution conceptual model. These aspects of volcanism-related dose calculation are described in the context of the entire igneous disruptive events conceptual model in ''Characterize Framework for Igneous Activity'' (BSC 2004 [DIRS 169989], Section 6.1.1). The Ashplume conceptual model accounts for incorporation and entrainment of waste fuel particles associated with a hypothetical volcanic eruption through themore » Yucca Mountain repository and downwind transport of contaminated tephra. The Ashplume mathematical model describes the conceptual model in mathematical terms to allow for prediction of radioactive waste/ash deposition on the ground surface given that the hypothetical eruptive event occurs. This model report also describes the conceptual model for tephra redistribution from a basaltic cinder cone. Sensitivity analyses and model validation activities for the ash dispersal and redistribution models are also presented. Analyses documented in this model report update the previous documentation of the Ashplume mathematical model and its application to the Total System Performance Assessment (TSPA) for the License Application (TSPA-LA) igneous scenarios. This model report also documents the redistribution model product outputs based on analyses to support the conceptual model. In this report, ''Ashplume'' is used when referring to the atmospheric dispersal model and ''ASHPLUME'' is used when referencing the code of that model. Two analysis and model reports provide direct inputs to this model report, namely ''Characterize Eruptive Processes at Yucca Mountain, Nevada and Number of Waste Packages Hit by Igneous Intrusion''. This model report provides direct inputs to the TSPA, which uses the ASHPLUME software described and used in this model report. Thus, ASHPLUME software inputs are inputs to this model report for ASHPLUME runs in this model report. However, ASHPLUME software inputs are outputs of this model report for ASHPLUME runs by TSPA.« less

Controlling Release Kinetics of PLG Microspheres Using a Manufacturing Technique

NASA Astrophysics Data System (ADS)

Berchane, Nader

2005-11-01

Controlled drug delivery offers numerous advantages compared with conventional free dosage forms, in particular: improved efficacy and patient compliance. Emulsification is a widely used technique to entrap drugs in biodegradable microspheres for controlled drug delivery. The size of the formed microspheres has a significant influence on drug release kinetics. Despite the advantages of controlled drug delivery, previous attempts to achieve predetermined release rates have seen limited success. This study develops a tool to tailor desired release kinetics by combining microsphere batches of specified mean diameter and size distribution. A fluid mechanics based correlation that predicts the average size of Poly(Lactide-co-Glycolide) [PLG] microspheres from the manufacturing technique, is constructed and validated by comparison with experimental results. The microspheres produced are accurately represented by the Rosin-Rammler mathematical distribution function. A mathematical model is formulated that incorporates the microsphere distribution function to predict the release kinetics from mono-dispersed and poly-dispersed populations. Through this mathematical model, different release kinetics can be achieved by combining different sized populations in different ratios. The resulting design tool should prove useful for the pharmaceutical industry to achieve designer release kinetics.

An improvement in the calculation of the efficiency of oxidative phosphorylation and rate of energy dissipation in mitochondria

NASA Astrophysics Data System (ADS)

Ghafuri, Mohazabeh; Golfar, Bahareh; Nosrati, Mohsen; Hoseinkhani, Saman

2014-12-01

The process of ATP production is one of the most vital processes in living cells which happens with a high efficiency. Thermodynamic evaluation of this process and the factors involved in oxidative phosphorylation can provide a valuable guide for increasing the energy production efficiency in research and industry. Although energy transduction has been studied qualitatively in several researches, there are only few brief reviews based on mathematical models on this subject. In our previous work, we suggested a mathematical model for ATP production based on non-equilibrium thermodynamic principles. In the present study, based on the new discoveries on the respiratory chain of animal mitochondria, Golfar's model has been used to generate improved results for the efficiency of oxidative phosphorylation and the rate of energy loss. The results calculated from the modified coefficients for the proton pumps of the respiratory chain enzymes are closer to the experimental results and validate the model.

Mathematical Modeling in Mathematics Education: Basic Concepts and Approaches

ERIC Educational Resources Information Center

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

2014-01-01

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

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

ERIC Educational Resources Information Center

Schwerdtfeger, Sara

2017-01-01

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

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…

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

PubMed

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

2017-11-22

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

A Mathematical Model to Predict and Maintain the Neutral Buoyancy of Suited Astronauts

NASA Technical Reports Server (NTRS)

Clowers, Kurt; Jaramillo, Marcos; Nguyen, Daniel; Sweet, Robert; Rajulu, Sudhakar

2006-01-01

A previous study reported that inadequate weigh outs of suited subjects contribute to fatigue and the risk of injury during training in the Neutral Buoyancy Laboratory (NBL). Another study suggested that shoulder injuries observed in suited subjects who train in the NBL may be attributed to excessive righting moments caused by a non-optimal weigh out. The purpose of this study was to develop a mathematical model to predict and maintain the neutral buoyancy of suited subjects during training operations at the NBL. Due to time constraints, one certified NBL support diver served as a subject (height: 66.54 in; weight: 182 lbs) for this study and only one complete test was conducted. The study was divided into two runs for which the first run required the NBL divers to perform a weigh out similar to a suited astronaut on a scuba diver wearing a mock Portable Life Support System and a Displays and Control Module. For the second run, the same subject and equipment were weighed out according to the mathematical model. The objective of each run was to achieve a neutrally buoyant subject floating 450 to the pool floor. Motion data was collected using two underwater cameras and analyzed using Dartfish video analysis software while force and moment data were recorded using an AMTI force plate. The results from the NBL divers visual run indicate that the subject was floating at an angle of 29.50 while the resultant force and moment data were 1.139 lb and 1.125 ft-lb respectively. The mathematical model s weigh out resulted in the subject floating at an angle of 37.40 and a resultant force of 0.765 lb and resultant moment of 1.248 ft-lb. The mathematical model was better able to orient the subject and reduce resultant moment and force as compared to the NBL divers.

Toward a complex system understanding of bipolar disorder: A chaotic model of abnormal circadian activity rhythms in euthymic bipolar disorder.

PubMed

Hadaeghi, Fatemeh; Hashemi Golpayegani, Mohammad Reza; Jafari, Sajad; Murray, Greg

2016-08-01

In the absence of a comprehensive neural model to explain the underlying mechanisms of disturbed circadian function in bipolar disorder, mathematical modeling is a helpful tool. Here, circadian activity as a response to exogenous daily cycles is proposed to be the product of interactions between neuronal networks in cortical (cognitive processing) and subcortical (pacemaker) areas of the brain. To investigate the dynamical aspects of the link between disturbed circadian activity rhythms and abnormalities of neurotransmitter functioning in frontal areas of the brain, we developed a novel mathematical model of a chaotic system which represents fluctuations in circadian activity in bipolar disorder as changes in the model's parameters. A novel map-based chaotic system was developed to capture disturbances in circadian activity across the two extreme mood states of bipolar disorder. The model uses chaos theory to characterize interplay between neurotransmitter functions and rhythm generation; it aims to illuminate key activity phenomenology in bipolar disorder, including prolonged sleep intervals, decreased total activity and attenuated amplitude of the diurnal activity rhythm. To test our new cortical-circadian mathematical model of bipolar disorder, we utilized previously collected locomotor activity data recorded from normal subjects and bipolar patients by wrist-worn actigraphs. All control parameters in the proposed model have an important role in replicating the different aspects of circadian activity rhythm generation in the brain. The model can successfully replicate deviations in sleep/wake time intervals corresponding to manic and depressive episodes of bipolar disorder, in which one of the excitatory or inhibitory pathways is abnormally dominant. Although neuroimaging research has strongly implicated a reciprocal interaction between cortical and subcortical regions as pathogenic in bipolar disorder, this is the first model to mathematically represent this multilevel explanation of the phenomena of bipolar disorder. © The Royal Australian and New Zealand College of Psychiatrists 2016.

The new version of the Institute of Numerical Mathematics Sigma Ocean Model (INMSOM) for simulation of Global Ocean circulation and its variability

NASA Astrophysics Data System (ADS)

Gusev, Anatoly; Fomin, Vladimir; Diansky, Nikolay; Korshenko, Evgeniya

2017-04-01

In this paper, we present the improved version of the ocean general circulation sigma-model developed in the Institute of Numerical Mathematics of the Russian Academy of Sciences (INM RAS). The previous version referred to as INMOM (Institute of Numerical Mathematics Ocean Model) is used as the oceanic component of the IPCC climate system model INMCM (Institute of Numerical Mathematics Climate Model (Volodin et al 2010,2013). Besides, INMOM as the only sigma-model was used for simulations according to CORE-II scenario (Danabasoglu et al. 2014,2016; Downes et al. 2015; Farneti et al. 2015). In general, INMOM results are comparable to ones of other OGCMs and were used for investigation of climatic variations in the North Atlantic (Gusev and Diansky 2014). However, detailed analysis of some CORE-II INMOM results revealed some disadvantages of the INMOM leading to considerable errors in reproducing some ocean characteristics. So, the mass transport in the Antarctic Circumpolar Current (ACC) was overestimated. As well, there were noticeable errors in reproducing thermohaline structure of the ocean. After analysing the previous results, the new version of the OGCM was developed. It was decided to entitle is INMSOM (Institute of Numerical Mathematics Sigma Ocean Model). The new title allows one to distingwish the new model, first, from its older version, and second, from another z-model developed in the INM RAS and referred to as INMIO (Institute of Numerical Mathematics and Institute of Oceanology ocean model) (Ushakov et al. 2016). There were numerous modifications in the model, some of them are as follows. 1) Formulation of the ocean circulation problem in terms of full free surface with taking into account water amount variation. 2) Using tensor form of lateral viscosity operator invariant to rotation. 3) Using isopycnal diffusion including Gent-McWilliams mixing. 4) Using atmospheric forcing computation according to NCAR methodology (Large and Yeager 2009). 5) Improvement river runoff algorithm accounting the total amount of discharged water. 6) Using explicit leapfrog time scheme for all lateral operators and implicit Euler scheme for vertical diffusion and viscosity. The INMSOM is tested by reproducing World Ocean circulation and thermohaline characteristics using the well-proved CORE dataset. The presentation is devoted to the analysis of new INMSOM simulation results, estimation of their quality and comparison to the ones previously obtained with the INMOM. The main aim of the INMSOM development is using it as the oceanic component of the next version of INMCM. The work was supported by the Russian Foundation for Basic Research (grants № 16-05-00534 and № 15-05-07539) References 1. Danabasoglu, G., Yeager S.G., Bailey D., et al., 2014: North Atlantic simulations in Coordinated Ocean-ice Reference Experiments phase II (CORE-II). Part I: Mean states. Ocean Modelling, 73, 76-107. 2. Danabasoglu, G., Yeager S.G., Kim W.M. et al., 2016: North Atlantic simulations in Coordinated Ocean-ice Reference Experiments phase II (CORE-II). Part II: Inter-annual to decadal variability. Ocean Modelling, 97, 65-90. 3. Downes S.M., Farneti R., Uotila P. et al. An assessment of Southern Ocean water masses and sea ice during 1988-2007 in a suite of interannual CORE-II simulations. Ocean Modelling (2015), 94, 67-94. 4. Farneti R., Downes S.M., Griffies S.M. et al. An assessment of Antarctic Circumpolar Current and Southern Ocean Meridional Overturning Circulation during 1958-2007 in a suite of interannual CORE-II simulations, Ocean Modelling (2015), 93, 84-120. 5. Gusev A.V. and Diansky N.A. Numerical simulation of the World ocean circulation and its climatic variability for 1948-2007 using the INMOM. Izvestiya, Atmospheric and Oceanic Physics, 2014, V. 50, N. 1, P. 1-12 6. Large, W., Yeager, S., 2009. The global climatology of an interannually varying air-sea flux data set. Clim Dyn, V. 33, P. 341-364. 7. Ushakov K.V., Grankina T.B., Ibraev R.A. Modeling the water circulation in the North Atlantic in the scope of the CORE-II experiment. Izvestiya, Atmospheric and Oceanic Physics. 2016. V. 52, № 4, P. 365-375

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…

Number of infection events per cell during HIV-1 cell-free infection.

PubMed

Ito, Yusuke; Remion, Azaria; Tauzin, Alexandra; Ejima, Keisuke; Nakaoka, Shinji; Iwasa, Yoh; Iwami, Shingo; Mammano, Fabrizio

2017-07-26

HIV-1 accumulates changes in its genome through both recombination and mutation during the course of infection. For recombination to occur, a single cell must be infected by two HIV strains. These coinfection events were experimentally demonstrated to occur more frequently than would be expected for independent infection events and do not follow a random distribution. Previous mathematical modeling approaches demonstrated that differences in target cell susceptibility can explain the non-randomness, both in the context of direct cell-to-cell transmission, and in the context of free virus transmission (Q. Dang et al., Proc. Natl. Acad. Sci. USA 101:632-7, 2004: K. M. Law et al., Cell reports 15:2711-83, 2016). Here, we build on these notions and provide a more detailed and extensive quantitative framework. We developed a novel mathematical model explicitly considering the heterogeneity of target cells and analysed datasets of cell-free HIV-1 single and double infection experiments in cell culture. Particularly, in contrast to the previous studies, we took into account the different susceptibility of the target cells as a continuous distribution. Interestingly, we showed that the number of infection events per cell during cell-free HIV-1 infection follows a negative-binomial distribution, and our model reproduces these datasets.

Optimal back-extrapolation method for estimating plasma volume in humans using the indocyanine green dilution method.

PubMed

Polidori, David; Rowley, Clarence

2014-07-22

The indocyanine green dilution method is one of the methods available to estimate plasma volume, although some researchers have questioned the accuracy of this method. We developed a new, physiologically based mathematical model of indocyanine green kinetics that more accurately represents indocyanine green kinetics during the first few minutes postinjection than what is assumed when using the traditional mono-exponential back-extrapolation method. The mathematical model is used to develop an optimal back-extrapolation method for estimating plasma volume based on simulated indocyanine green kinetics obtained from the physiological model. Results from a clinical study using the indocyanine green dilution method in 36 subjects with type 2 diabetes indicate that the estimated plasma volumes are considerably lower when using the traditional back-extrapolation method than when using the proposed back-extrapolation method (mean (standard deviation) plasma volume = 26.8 (5.4) mL/kg for the traditional method vs 35.1 (7.0) mL/kg for the proposed method). The results obtained using the proposed method are more consistent with previously reported plasma volume values. Based on the more physiological representation of indocyanine green kinetics and greater consistency with previously reported plasma volume values, the new back-extrapolation method is proposed for use when estimating plasma volume using the indocyanine green dilution method.

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…

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.

The Applied Mathematics for Power Systems (AMPS)

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

Chertkov, Michael

2012-07-24

Increased deployment of new technologies, e.g., renewable generation and electric vehicles, is rapidly transforming electrical power networks by crossing previously distinct spatiotemporal scales and invalidating many traditional approaches for designing, analyzing, and operating power grids. This trend is expected to accelerate over the coming years, bringing the disruptive challenge of complexity, but also opportunities to deliver unprecedented efficiency and reliability. Our Applied Mathematics for Power Systems (AMPS) Center will discover, enable, and solve emerging mathematics challenges arising in power systems and, more generally, in complex engineered networks. We will develop foundational applied mathematics resulting in rigorous algorithms and simulation toolboxesmore » for modern and future engineered networks. The AMPS Center deconstruction/reconstruction approach 'deconstructs' complex networks into sub-problems within non-separable spatiotemporal scales, a missing step in 20th century modeling of engineered networks. These sub-problems are addressed within the appropriate AMPS foundational pillar - complex systems, control theory, and optimization theory - and merged or 'reconstructed' at their boundaries into more general mathematical descriptions of complex engineered networks where important new questions are formulated and attacked. These two steps, iterated multiple times, will bridge the growing chasm between the legacy power grid and its future as a complex engineered network.« less

Enjoying mathematics or feeling competent in mathematics? Reciprocal effects on mathematics achievement and perceived math effort expenditure.

PubMed

Pinxten, Maarten; Marsh, Herbert W; De Fraine, Bieke; Van Den Noortgate, Wim; Van Damme, Jan

2014-03-01

The multidimensionality of the academic self-concept in terms of domain specificity has been well established in previous studies, whereas its multidimensionality in terms of motivational functions (the so-called affect-competence separation) needs further examination. This study aims at exploring differential effects of enjoyment and competence beliefs on two external validity criteria in the field of mathematics. Data analysed in this study were part of a large-scale longitudinal research project. Following a five-wave design, math enjoyment, math competence beliefs, math achievement, and perceived math effort expenditure measures were repeatedly collected from a cohort of 4,724 pupils in Grades 3-7. Confirmatory factor analysis (CFA) was used to test the internal factor structure of the math self-concept. Additionally, a series of nested models was tested using structural equation modelling to examine longitudinal reciprocal interrelations between math competence beliefs and math enjoyment on the one hand and math achievement and perceived math effort expenditure on the other. Our results showed that CFA models with separate factors for math enjoyment and math competence beliefs fit the data substantially better than models without it. Furthermore, differential relationships between both constructs and the two educational outcomes were observed. Math competence beliefs had positive effects on math achievement and negative effects on perceived math effort expenditure. Math enjoyment had (mild) positive effects on subsequent perceived effort expenditure and math competence beliefs. This study provides further support for the affect-competence separation. Theoretical issues regarding adequate conceptualization and practical consequences for practitioners are discussed. © 2013 The British Psychological Society.

Scattering and Diffraction of Elastodynamic Waves in a Concentric Cylindrical Phantom for MR Elastography

PubMed Central

Schwartz, Benjamin L.; Yin, Ziying; Yaşar, Temel K.; Liu, Yifei; Khan, Altaf A.; Ye, Allen Q.; Royston, Thomas J.; Magin, Richard L.

2016-01-01

Aim The focus of this paper is to report on the design and construction of a multiply connected phantom for use in magnetic resonance elasography (MRE)–an imaging technique that allows for the non-invasive visualization of the displacement field throughout an object from externally driven harmonic motion–as well as its inverse modeling with a closed-form analytic solution which is derived herein from first principles. Methods Mathematically, the phantom is described as two infinite concentric circular cylinders with unequal complex shear moduli, harmonically vibrated at the exterior surface in a direction along their common axis. Each concentric cylinder is made of a hydrocolloid with its own specific solute concentration. They are assembled in a multi-step process for which custom scaffolding was designed and built. A customized spin-echo based MR elastography sequence with a sinusoidal motion-sensitizing gradient was used for data acquisition on a 9.4 T Agilent small-animal MR scanner. Complex moduli obtained from the inverse model are used to solve the forward problem with a finite element method. Results Both complex shear moduli show a significant frequency dependence (p < 0.001) in keeping with previous work. Conclusion The novel multiply connected phantom and mathematical model are validated as a viable tool for MRE studies. Significance On a small enough scale much of physiology can be mathematically modeled with basic geometric shapes, e.g. a cylinder representing a blood vessel. This work demonstrates the possibility of elegant mathematical analysis of phantoms specifically designed and carefully constructed for biomedical MRE studies. PMID:26886963

Prediction of inspiratory flow shapes during sleep with a mathematic model of upper airway forces.

PubMed

Aittokallio, Tero; Gyllenberg, Mats; Saaresranta, Tarja; Polo, Olli

2003-11-01

To predict the airflow dynamics during sleep using a mathematic model that incorporates a number of static and dynamic upper airway forces, and to compare the numerical results to clinical flow data recorded from patients with sleep-disordered breathing on and off various treatment options. Upper airway performance was modeled in virtual subjects characterized by parameter settings that describe common combinations of risk factors predisposing to upper airway collapse during sleep. The treatments effect were induced by relevant changes of the initial parameter values. Computer simulations at our website (http://www.utu.fi/ml/sovmat/bio/). Risk factors considered in the simulation settings were sex, obesity, pharyngeal collapsibility, and decreased phasic activity of pharyngeal muscles. The effects of weight loss, pharyngeal surgery, nasal continuous positive airway pressure, and respiratory stimulation on the inspiratory flow characteristics were tested with the model. Numerical predictions were investigated by means of 3 measurable inspiratory airflow characteristics: initial slope, total volume, and flow shape. The model was able to reproduce the inspiratory flow shape characteristics that have previously been described in the literature. Simulation results also supported the observations that a multitude of factors underlie the pharyngeal collapse and, therefore, certain medical therapies that are effective in some conditions may prove ineffective in others. A mathematic model integrating the current knowledge of upper airway physiology is able to predict individual treatment responses. The model provides a framework for designing novel and potentially feasible treatment alternatives for sleep-disordered breathing.

Generation of action potentials in a mathematical model of corticotrophs.

PubMed Central

LeBeau, A P; Robson, A B; McKinnon, A E; Donald, R A; Sneyd, J

1997-01-01

Corticotropin-releasing hormone (CRH) is an important regulator of adrenocorticotropin (ACTH) secretion from pituitary corticotroph cells. The intracellular signaling system that underlies this process involves modulation of voltage-sensitive Ca2+ channel activity, which leads to the generation of Ca2+ action potentials and influx of Ca2+. However, the mechanisms by which Ca2+ channel activity is modulated in corticotrophs are not currently known. We investigated this process in a Hodgkin-Huxley-type mathematical model of corticotroph plasma membrane electrical responses. We found that an increase in the L-type Ca2+ current was sufficient to generate action potentials from a previously resting state of the model. The increase in the L-type current could be elicited by either a shift in the voltage dependence of the current toward more negative potentials, or by an increase in the conductance of the current. Although either of these mechanisms is potentially responsible for the generation of action potentials, previous experimental evidence favors the former mechanism, with the magnitude of the shift required being consistent with the experimental findings. The model also shows that the T-type Ca2+ current plays a role in setting the excitability of the plasma membrane, but does not appear to contribute in a dynamic manner to action potential generation. Inhibition of a K+ conductance that is active at rest also affects the excitability of the plasma membrane. PMID:9284294

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 model to compare the relative tensile strength of the cornea after PRK, LASIK, and small incision lenticule extraction.

PubMed

Reinstein, Dan Z; Archer, Timothy J; Randleman, J Bradley

2013-07-01

To develop a mathematical model to estimate the relative differences in postoperative stromal tensile strength following photorefractive keratectomy (PRK), LASIK, and small incision lenticule extraction (SMILE). Using previously published data where in vitro corneal stromal tensile strength was determined as a function of depth, a mathematical model was built to calculate the relative remaining tensile strength by fitting the data with a fourth order polynomial function yielding a high correlation coefficient (R(2) = 0.930). Calculating the area under this function provided a measure of total stromal tensile strength (TTS), based only on the residual stromal layer for PRK or LASIK and the residual stromal layers above and below the lenticule interface for SMILE. Postoperative TTS was greatest after SMILE, followed by PRK, then LASIK; for example, in a 550-μm cornea after 100-μm tissue removal, postoperative TTS was 75% for SMILE (130-μm cap), 68% for PRK, and 54% for LASIK (110-μm flap). The postoperative TTS decreased for thinner corneal pachymetry for all treatment types. In LASIK, the postoperative TTS decreased with increasing flap thickness by 0.22%/μm, but increased by 0.08%/μm for greater cap thickness in SMILE. The model predicted that SMILE lenticule thickness could be approximately 100 μm greater than the LASIK ablation depth and still have equivalent corneal strength (equivalent to approximately 7.75 diopters). This mathematical model predicts that the postoperative TTS is considerably higher after SMILE than both PRK and LASIK, as expected given that the strongest anterior lamellae remain intact. Consequently, SMILE should be able to correct higher levels of myopia. Copyright 2013, SLACK Incorporated.

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

PubMed Central

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

2015-01-01

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

Vacuum effects over the closing of enterocutaneous fistulae: a mathematical modeling approach.

PubMed

Cattoni, D I; Chara, O

2008-01-01

Enterocutaneous fistulae are pathological communications between the intestinal lumen and the abdominal skin. Under surgery the mortality of this pathology is very high, therefore a vacuum applying system has been carried previously on attempting to close these fistulae. The objective of this article is the understanding of how these treatments might work through deterministic mathematical modelling. Four models are here proposed based on several assumptions involving: the conservation of the flow in the fistula, a low enough Reynolds number justifying a laminar flow, the use of Poiseuille law to model the movement of the fistulous liquid, as well as phenomenological equations including the fistula tissue and intermediate chamber compressibility. Interestingly, the four models show fistulae closing behaviour during experimental time (t<60 sec). To compare the models, both, simulations and pressure measurements, carried out on the vacuum connected to the patients, are performed. Time course of pressure are then simulated (from each model) and fitted to the experimental data. The model which best describes actual measurements shows exponential pumping flux kinetics. Applying this model, numerical relationship between the fistula compressibility and closure time is presented. The models here developed would contribute to clarify the treatment mechanism and, eventually, improve the fistulae treatment.

Multiscale modelling and analysis of collective decision making in swarm robotics.

PubMed

Vigelius, Matthias; Meyer, Bernd; Pascoe, Geoffrey

2014-01-01

We present a unified approach to describing certain types of collective decision making in swarm robotics that bridges from a microscopic individual-based description to aggregate properties. Our approach encompasses robot swarm experiments, microscopic and probabilistic macroscopic-discrete simulations as well as an analytic mathematical model. Following up on previous work, we identify the symmetry parameter, a measure of the progress of the swarm towards a decision, as a fundamental integrated swarm property and formulate its time evolution as a continuous-time Markov process. Contrary to previous work, which justified this approach only empirically and a posteriori, we justify it from first principles and derive hard limits on the parameter regime in which it is applicable.

Dynamical insurance models with investment: Constrained singular problems for integrodifferential equations

NASA Astrophysics Data System (ADS)

Belkina, T. A.; Konyukhova, N. B.; Kurochkin, S. V.

2016-01-01

Previous and new results are used to compare two mathematical insurance models with identical insurance company strategies in a financial market, namely, when the entire current surplus or its constant fraction is invested in risky assets (stocks), while the rest of the surplus is invested in a risk-free asset (bank account). Model I is the classical Cramér-Lundberg risk model with an exponential claim size distribution. Model II is a modification of the classical risk model (risk process with stochastic premiums) with exponential distributions of claim and premium sizes. For the survival probability of an insurance company over infinite time (as a function of its initial surplus), there arise singular problems for second-order linear integrodifferential equations (IDEs) defined on a semiinfinite interval and having nonintegrable singularities at zero: model I leads to a singular constrained initial value problem for an IDE with a Volterra integral operator, while II model leads to a more complicated nonlocal constrained problem for an IDE with a non-Volterra integral operator. A brief overview of previous results for these two problems depending on several positive parameters is given, and new results are presented. Additional results are concerned with the formulation, analysis, and numerical study of "degenerate" problems for both models, i.e., problems in which some of the IDE parameters vanish; moreover, passages to the limit with respect to the parameters through which we proceed from the original problems to the degenerate ones are singular for small and/or large argument values. Such problems are of mathematical and practical interest in themselves. Along with insurance models without investment, they describe the case of surplus completely invested in risk-free assets, as well as some noninsurance models of surplus dynamics, for example, charity-type models.

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

ERIC Educational Resources Information Center

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

2016-01-01

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

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

ERIC Educational Resources Information Center

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

2016-01-01

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

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…

CFD Analysis of the SBXC Glider Airframe

DTIC Science & Technology

2016-06-01

mathematically on finite element methods. To validate and verify the methodology developed, a mathematical comparison was made with the previous research data...greater than 15 m/s. 14. SUBJECT TERMS finite element method, computational fluid dynamics, Y Plus, mesh element quality, aerodynamic data, fluid...based mathematically on finite element methods. To validate and verify the methodology developed, a mathematical comparison was made with the

An Exploration of the Common Content Knowledge of High School Mathematics Teachers

ERIC Educational Resources Information Center

Bansilal, Sarah; Brijlall, Deonarain; Mkhwanazi, Thokozani

2014-01-01

Many studies point to the problem of poor mathematics content knowledge of mathematics teachers in South Africa. The purpose of this study was to investigate teachers' knowledge of the mathematics they are themselves teaching. Data was generated from the teachers' (n = 253) written responses to test that was a shortened form of a previous Grade 12…

Graphing Calculators as Tools

ERIC Educational Resources Information Center

Browning, Christine A.; Garza-Kling, Gina

2010-01-01

Middle school mathematics classrooms are changing. The curriculum has changed as well. Instead of an annual return to previously encountered topics, many middle school students encounter mathematics of a varying nature, characterized in "Principles and Standards for School Mathematics" (NCTM 2000) as the five Content Standards of Number and…

Using the Unified Modelling Language (UML) to guide the systemic description of biological processes and systems.

PubMed

Roux-Rouquié, Magali; Caritey, Nicolas; Gaubert, Laurent; Rosenthal-Sabroux, Camille

2004-07-01

One of the main issues in Systems Biology is to deal with semantic data integration. Previously, we examined the requirements for a reference conceptual model to guide semantic integration based on the systemic principles. In the present paper, we examine the usefulness of the Unified Modelling Language (UML) to describe and specify biological systems and processes. This makes unambiguous representations of biological systems, which would be suitable for translation into mathematical and computational formalisms, enabling analysis, simulation and prediction of these systems behaviours.

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.

A stochastic optimization model under modeling uncertainty and parameter certainty for groundwater remediation design--part I. Model development.

PubMed

He, L; Huang, G H; Lu, H W

2010-04-15

Solving groundwater remediation optimization problems based on proxy simulators can usually yield optimal solutions differing from the "true" ones of the problem. This study presents a new stochastic optimization model under modeling uncertainty and parameter certainty (SOMUM) and the associated solution method for simultaneously addressing modeling uncertainty associated with simulator residuals and optimizing groundwater remediation processes. This is a new attempt different from the previous modeling efforts. The previous ones focused on addressing uncertainty in physical parameters (i.e. soil porosity) while this one aims to deal with uncertainty in mathematical simulator (arising from model residuals). Compared to the existing modeling approaches (i.e. only parameter uncertainty is considered), the model has the advantages of providing mean-variance analysis for contaminant concentrations, mitigating the effects of modeling uncertainties on optimal remediation strategies, offering confidence level of optimal remediation strategies to system designers, and reducing computational cost in optimization processes. 2009 Elsevier B.V. All rights reserved.

Study of grid independence of finite element method on MHD free convective casson fluid flow with slip effect

NASA Astrophysics Data System (ADS)

Raju, R. Srinivasa; Ramesh, K.

2018-05-01

The purpose of this work is to study the grid independence of finite element method on MHD Casson fluid flow past a vertically inclined plate filled in a porous medium in presence of chemical reaction, heat absorption, an external magnetic field and slip effect has been investigated. For this study of grid independence, a mathematical model is developed and analyzed by using appropriate mathematical technique, called finite element method. Grid study discussed with the help of numerical values of velocity, temperature and concentration profiles in tabular form. avourable comparisons with previously published work on various special cases of the problem are obtained.

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

ERIC Educational Resources Information Center

Zbiek, Rose Mary; Conner, Annamarie

2006-01-01

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

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

ERIC Educational Resources Information Center

Thrasher, Emily Plunkett

2016-01-01

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

Statistical mechanics of simple models of protein folding and design.

PubMed Central

Pande, V S; Grosberg, A Y; Tanaka, T

1997-01-01

It is now believed that the primary equilibrium aspects of simple models of protein folding are understood theoretically. However, current theories often resort to rather heavy mathematics to overcome some technical difficulties inherent in the problem or start from a phenomenological model. To this end, we take a new approach in this pedagogical review of the statistical mechanics of protein folding. The benefit of our approach is a drastic mathematical simplification of the theory, without resort to any new approximations or phenomenological prescriptions. Indeed, the results we obtain agree precisely with previous calculations. Because of this simplification, we are able to present here a thorough and self contained treatment of the problem. Topics discussed include the statistical mechanics of the random energy model (REM), tests of the validity of REM as a model for heteropolymer freezing, freezing transition of random sequences, phase diagram of designed ("minimally frustrated") sequences, and the degree to which errors in the interactions employed in simulations of either folding and design can still lead to correct folding behavior. Images FIGURE 2 FIGURE 3 FIGURE 4 FIGURE 6 PMID:9414231

Feasibility study for automatic reduction of phase change imagery

NASA Technical Reports Server (NTRS)

Nossaman, G. O.

1971-01-01

The feasibility of automatically reducing a form of pictorial aerodynamic heating data is discussed. The imagery, depicting the melting history of a thin coat of fusible temperature indicator painted on an aerodynamically heated model, was previously reduced by manual methods. Careful examination of various lighting theories and approaches led to an experimentally verified illumination concept capable of yielding high-quality imagery. Both digital and video image processing techniques were applied to reduction of the data, and it was demonstrated that either method can be used to develop superimposed contours. Mathematical techniques were developed to find the model-to-image and the inverse image-to-model transformation using six conjugate points, and methods were developed using these transformations to determine heating rates on the model surface. A video system was designed which is able to reduce the imagery rapidly, economically and accurately. Costs for this system were estimated. A study plan was outlined whereby the mathematical transformation techniques developed to produce model coordinate heating data could be applied to operational software, and methods were discussed and costs estimated for obtaining the digital information necessary for this software.

Effects of low-level chronic irradiation on the radiosensitivity of mammals: Modeling studies

NASA Astrophysics Data System (ADS)

Smirnova, O. A.

Mathematical models of the major hematopoietic lines are used to study the modifying effects of low-level chronic preirradiation on radiosensitivity of mammals which resulted in their reduced radiosensitivity (acquired radioresistance) and elevated radiosensitivity (hypersensitivity) to the subsequent radiation exposure. These effects of preirradiation manifest themselves, respectively, in decreased and increased mortality of preirradiated experimental animals (mice) after challenge acute exposure in comparison with that for previously nonirradiated ones. Analysis of the modeling results reveals the biological mechanisms of these radioprotection and radiosensitization effects, and enables one to estimate the ranges of dose rate and duration of chronic preirradiation where these effects are realized. Juxtapositions of the modeling predictions with the relevant experimental data show their qualitative agreement. All this testifies to the importance of accounting the nonlinear effect of low-level chronic irradiation on radiosensitivity of the hematopoiesis system and organism as a whole, when the radiation risk for astronauts on long-term space missions is estimated. The developed models of hematopoiesis can be used, after appropriate identification, as a component of the mathematical tools for radiation risk assessment.

A mathematical model of intracellular behavior of microalgae for predicting growth and intracellular components syntheses under nutrient replete and deplete conditions.

PubMed

Ryu, Kyung Hwan; Sung, Min-Gyu; Kim, Boeun; Heo, Seongmin; Chang, Yong Keun; Lee, Jay H

2018-06-13

Microalgae is a promising biomass source for renewable fuels and chemicals production. To describe microalgal behavior and improve their cultivation, various kinetic models have been proposed. However, previous works have focused on biomass formation and lipids production only, even though carbohydrates and proteins are also important products, not only for understanding the metabolic behavior of microalgae but also for enhancing the economic viability through value-added side products. In this research, a new mathematical model is proposed to explain core biological mechanisms of growth and macromolecules syntheses based on the central metabolism of carbon and nitrogen. In the model, microalgal growth is separated as hyperplasia and hypertrophy, to describe the cell growth more precisely under nutrient-replete and -deplete conditions. Sensitivity analysis performed using the model indicates that cell state (e.g., cell death rate) has a strong effect on the lipid production explaining the difficulty of reproducing a microalgae culture experiment. This article is protected by copyright. All rights reserved. This article is protected by copyright. All rights reserved.

Reflective Modeling in Teacher Education.

ERIC Educational Resources Information Center

Shealy, Barry E.

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

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

ERIC Educational Resources Information Center

Karali, Diren; Durmus, Soner

2015-01-01

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

[Optimization of the parameters of microcirculatory structural adaptation model based on improved quantum-behaved particle swarm optimization algorithm].

PubMed

Pan, Qing; Yao, Jialiang; Wang, Ruofan; Cao, Ping; Ning, Gangmin; Fang, Luping

2017-08-01

The vessels in the microcirculation keep adjusting their structure to meet the functional requirements of the different tissues. A previously developed theoretical model can reproduce the process of vascular structural adaptation to help the study of the microcirculatory physiology. However, until now, such model lacks the appropriate methods for its parameter settings with subsequent limitation of further applications. This study proposed an improved quantum-behaved particle swarm optimization (QPSO) algorithm for setting the parameter values in this model. The optimization was performed on a real mesenteric microvascular network of rat. The results showed that the improved QPSO was superior to the standard particle swarm optimization, the standard QPSO and the previously reported Downhill algorithm. We conclude that the improved QPSO leads to a better agreement between mathematical simulation and animal experiment, rendering the model more reliable in future physiological studies.

Linear Mapping of Numbers onto Space Requires Attention

ERIC Educational Resources Information Center

Anobile, Giovanni; Cicchini, Guido Marco; Burr, David C.

2012-01-01

Mapping of number onto space is fundamental to mathematics and measurement. Previous research suggests that while typical adults with mathematical schooling map numbers veridically onto a linear scale, pre-school children and adults without formal mathematics training, as well as individuals with dyscalculia, show strong compressive,…

Patterns of Individual Differences in Conceptual Understanding and Arithmetical Skill: A Meta-Analysis

ERIC Educational Resources Information Center

Gilmore, Camilla K.; Papadatou-Pastou, Marietta

2009-01-01

Some theories from cognitive psychology and mathematics education suggest that children's understanding of mathematical concepts develops together with their knowledge of mathematical procedures. However, previous research into children's understanding of the inverse relationship between addition and subtraction suggests that there are individual…

Business Mathematics Curriculum Guide.

ERIC Educational Resources Information Center

Ebersole, Benjamin P., Comp.; And Others

This revised course in business mathematics emphasizes computations needed for problem solving, but greater attention is focused on mathematical principles that were developed in previous grades. In addition, the course aims to develop further an understanding of business principles and practices which can be used in gainful employment and in the…

"My math and me": Nursing students' previous experiences in learning mathematics.

PubMed

Røykenes, Kari

2016-01-01

In this paper, 11 narratives about former experiences in learning of mathematics written by nursing students are thematically analyzed. Most students had a positive relationship with the subject in primary school, when they found mathematics fun and were able to master the subject. For some, a change occurred in the transition to lower secondary school. The reasons for this change was found in the subject (increased difficulty), the teachers (movement of teachers, numerous substitute teachers), the class environment and size (many pupils, noise), and the student him- or herself (silent and anonymous pupil). This change was also found in the transition from lower to higher secondary school. By contrast, some students had experienced changes that were positive, and their mathematics teacher was a significant factor in this positive change. The paper emphasizes the importance of previous experiences in learning mathematics to nursing students when learning about drug calculation. Copyright © 2015. Published by Elsevier Ltd.

Extension of Liouville Formalism to Postinstability Dynamics

NASA Technical Reports Server (NTRS)

Zak, Michail

2003-01-01

A mathematical formalism has been developed for predicting the postinstability motions of a dynamic system governed by a system of nonlinear equations and subject to initial conditions. Previously, there was no general method for prediction and mathematical modeling of postinstability behaviors (e.g., chaos and turbulence) in such a system. The formalism of nonlinear dynamics does not afford means to discriminate between stable and unstable motions: an additional stability analysis is necessary for such discrimination. However, an additional stability analysis does not suggest any modifications of a mathematical model that would enable the model to describe postinstability motions efficiently. The most important type of instability that necessitates a postinstability description is associated with positive Lyapunov exponents. Such an instability leads to exponential growth of small errors in initial conditions or, equivalently, exponential divergence of neighboring trajectories. The development of the present formalism was undertaken in an effort to remove positive Lyapunov exponents. The means chosen to accomplish this is coupling of the governing dynamical equations with the corresponding Liouville equation that describes the evolution of the flow of error probability. The underlying idea is to suppress the divergences of different trajectories that correspond to different initial conditions, without affecting a target trajectory, which is one that starts with prescribed initial conditions.

Shrinkage and porosity evolution during air-drying of non-cellular food systems: Experimental data versus mathematical modelling.

PubMed

Nguyen, Thanh Khuong; Khalloufi, Seddik; Mondor, Martin; Ratti, Cristina

2018-01-01

In the present work, the impact of glass transition on shrinkage of non-cellular food systems (NCFS) during air-drying will be assessed from experimental data and the interpretation of a 'shrinkage' function involved in a mathematical model. Two NCFS made from a mixture of water/maltodextrin/agar (w/w/w: 1/0.15/0.015) were created out of maltodextrins with dextrose equivalent 19 (MD19) or 36 (MD36). The NCFS made with MD19 had 30°C higher Tg than those with MD36. This information indicated that, during drying, the NCFS with MD19 would pass from rubbery to glassy state sooner than NCFS MD36, for which glass transition only happens close to the end of drying. For the two NCFS, porosity and volume reduction as a function of moisture content were captured with high accuracy when represented by the mathematical models previously developed. No significant differences in porosity and in maximum shrinkage between both samples during drying were observed. As well, no change in the slope of the shrinkage curve as a function of moisture content was perceived. These results indicate that glass transition alone is not a determinant factor in changes of porosity or volume during air-drying. Copyright © 2017 Elsevier Ltd. All rights reserved.

Blood circulation in the lower limbs

NASA Astrophysics Data System (ADS)

Pen'kovskiy, V. I.; Korsakova, N. K.

2018-03-01

Blood circulation process in inferior limbs is considered in the terms of the previously proposed mathematical model of sanguimotion in living organism tissues. The model includes the equations of homogeneous fluid flower in heterogeneous medium that consists of two or more interpenetrating continua. The continua (distributing net of arteries and collecting net of veins) interact through ramified capillary net. A volume of blood flowering from arterial net to venous one is proportional to pressure (head) difference in the nets. Some analytical solutions and numerical results are given.

Description of bioremediation of soils using the model of a multistep system of microorganisms

NASA Astrophysics Data System (ADS)

Lubysheva, A. I.; Potashev, K. A.; Sofinskaya, O. A.

2018-01-01

The paper deals with the development of a mathematical model describing the interaction of a multi-step system of microorganisms in soil polluted with oil products. Each step in this system uses products of vital activity of the previous step to feed. Six different models of the multi-step system are considered. The equipping of the models with coefficients was carried out from the condition of minimizing the residual of the calculated and experimental data using an original algorithm based on the Levenberg-Marquardt method in combination with the Monte Carlo method for the initial approximation finding.

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

NASA Astrophysics Data System (ADS)

Fasni, Nurli; Fatimah, Siti; Yulanda, Syerli

2017-05-01

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

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…

A STUDY OF THE EFFECTS OF EXPERIMENTAL PROGRAMS ON PUPIL ACHIEVEMENT OBSERVED DURING FIRST THREE YEARS OF THE PROJECT, SECONDARY MATHEMATICS EVALUATION PROJECT. INTERIM REPORT.

ERIC Educational Resources Information Center

ERICKSEN, GERALD L.; RYAN, JAMES J.

A REPORT IS GIVEN OF THE FIRST 3 YEARS OF A FIELD STUDY CONDUCTED TO DETERMINE THE EFFECTIVENESS OF SEVERAL PROTOTYPE, SECONDARY MATHEMATICS PROGRAMS THAT WERE PRODUCED BY DIFFERENT CURRICULUM DEVELOPMENT GROUPS. MATHEMATICS TEACHERS WHO HAD NO PREVIOUS EXPERIENCE WITH "MODERN" OR EXPERIMENTAL APPROACHES TO MATHEMATICS TAUGHT A SELECTED…

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

ERIC Educational Resources Information Center

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

2016-01-01

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

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

ERIC Educational Resources Information Center

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

2017-01-01

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

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

ERIC Educational Resources Information Center

Horton, Robert M.; Leonard, William H.

2005-01-01

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

A mathematical model for malaria transmission with asymptomatic carriers and two age groups in the human population.

PubMed

Beretta, Edoardo; Capasso, Vincenzo; Garao, Dario G

2018-06-01

In this paper a conceptual mathematical model of malaria transmission proposed in a previous paper has been analyzed in a deeper detail. Among its key epidemiological features of this model, two-age-classes (child and adult) and asymptomatic carriers have been included. The extra mortality of mosquitoes due to the use of long-lasting treated mosquito nets (LLINs) and Indoor Residual Spraying (IRS) has been included too. By taking advantage of the natural double time scale of the parasite and the human populations, it has been possible to provide interesting threshold results. In particular it has been shown that key parameters can be identified such that below a threshold level, built on these parameters, the epidemic tends to extinction, while above another threshold level it tends to a nontrivial endemic state, for which an interval estimate has been provided. Numerical simulations confirm the analytical results. Copyright © 2018 Elsevier Inc. All rights reserved.

The Effect of Explanations on Mathematical Reasoning Tasks

ERIC Educational Resources Information Center

Norqvist, Mathias

2018-01-01

Studies in mathematics education often point to the necessity for students to engage in more cognitively demanding activities than just solving tasks by applying given solution methods. Previous studies have shown that students that engage in creative mathematically founded reasoning to construct a solution method, perform significantly better in…

Progress Monitoring in Middle School Mathematics: Options and Issues

ERIC Educational Resources Information Center

Foegen, Anne

2008-01-01

This study investigated the technical features of six potential progress-monitoring measures in mathematics appropriate for use at the middle school level, including two commercially available measures for sixth-grade mathematics, two measures used in previous middle school studies, and two new measures of numeracy concepts. Five hundred…

CCSSM: Teaching in Grades 3 and 4

ERIC Educational Resources Information Center

Barlow, Angela T.; Harmon, Shannon

2012-01-01

Common Core State Standards for Mathematics (CCSSM) is different from the objectives that many teachers have previously experienced in their state frameworks. Although the mathematical topics of the two may be the same, the mathematical expectations within the Standards require a deeper understanding by teachers and students. In this article, the…

Making Connections

ERIC Educational Resources Information Center

Turner, Paul

2015-01-01

This article aims to illustrate a process of making connections, not between mathematics and other activities, but within mathematics itself--between diverse parts of the subject. Novel connections are still possible in previously explored mathematics when the material happens to be unfamiliar, as may be the case for a learner at any career stage.…

TIMSS 2011 International Results in Mathematics

ERIC Educational Resources Information Center

Mullis, Ina V. S.; Martin, Michael O.; Foy, Pierre; Arora, Alka

2012-01-01

The "TIMSS 2011 International Results in Mathematics" summarizes fourth and eighth grade student achievement in each of the 63 countries and 14 benchmarking entities which participated in TIMSS 2011. The report includes trends in mathematics achievement over time for participants in the previous TIMSS 1995, 1999, 2003, and 2007…

Learning to Teach Mathematics with Technology: A Survey of Professional Development Needs, Experiences and Impacts

ERIC Educational Resources Information Center

Bennison, Anne; Goos, Merrilyn

2010-01-01

The potential for digital technologies to enhance students' mathematics learning is widely recognised, and use of computers and graphics calculators is now encouraged or required by secondary school mathematics curriculum documents throughout Australia. However, previous research indicates that effective integration of technology into classroom…

Writing to Learn Mathematics: An Update

ERIC Educational Resources Information Center

Teuscher, Dawn; Kulinna, Pamala Hodges; Crooker, Carol

2015-01-01

This study investigated 309 secondary mathematics teachers', from 50 school districts, perceptions of Writing to Learn Mathematics (WTLM) strategies. A modified version of a previously validated instrument was used for an online survey (Silver, 1999). Only 45% of teachers who participated in the survey were familiar with WTLM. The majority of…

Student Perceptions of Writing Projects in a University Differential-Equations Course

ERIC Educational Resources Information Center

Latulippe, Christine; Latulippe, Joe

2014-01-01

This qualitative study surveyed 102 differential-equations students in order to investigate how students participating in writing projects in university-level mathematics courses perceive the benefits of writing in the mathematics classroom. Based on previous literature on writing in mathematics, students were asked specifically about the benefits…

Mathematical Modeling and Pure Mathematics

ERIC Educational Resources Information Center

Usiskin, Zalman

2015-01-01

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

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

ERIC Educational Resources Information Center

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

2017-01-01

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

Controlling acrylamide in French fry and potato chip models and a mathematical model of acrylamide formation: acrylamide: acidulants, phytate and calcium.

PubMed

Park, Yeonhwa; Yang, Heewon; Storkson, Jayne M; Albright, Karen J; Liu, Wei; Lindsay, Robert C; Pariza, Michael W

2005-01-01

We previously reported that in potato chip and French fry models, the formation of acrylamide can be reduced by controlling pH during processing steps, either by organic (acidulants) or inorganic acids. Use of phytate, a naturally occurring chelator, with or without Ca++ (or divalent ions), can reduce acrylamide formation in both models. However, since phytate itself is acidic, the question remains as to whether the effect of phytate is due to pH alone or to additional effects. In the French fry model, the effects on acrylamide formation of pH, phytate, and/or Ca++ in various combinations were tested in either blanching or soaking (after blanching) steps. All treatments significantly reduced acrylamide levels compared to control. Among variables tested, pH may be the single most important factor for reducing acrylamide levels, while there were independent effects of phytate and/or Ca++ in this French fry model. We also developed a mathematical formula to estimate the final concentration of acrylamide in a potato chip model, using variables that can affect acrylamide formation: glucose and asparagine concentrations, cut potato surface area and shape, cooking temperature and time, and other processing conditions.

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

ERIC Educational Resources Information Center

Czocher, Jennifer A.

2016-01-01

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

An Experimental Approach to Mathematical Modeling in Biology

ERIC Educational Resources Information Center

Ledder, Glenn

2008-01-01

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

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

ERIC Educational Resources Information Center

Stohlmann, Micah S.

2017-01-01

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

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)…

Estimating the production, consumption and export of cannabis: The Dutch case.

PubMed

van der Giessen, Mark; van Ooyen-Houben, Marianne M J; Moolenaar, Debora E G

2016-05-01

Quantifying an illegal phenomenon like a drug market is inherently complex due to its hidden nature and the limited availability of reliable information. This article presents findings from a recent estimate of the production, consumption and export of Dutch cannabis and discusses the opportunities provided by, and limitations of, mathematical models for estimating the illegal cannabis market. The data collection consisted of a comprehensive literature study, secondary analyses on data from available registrations (2012-2014) and previous studies, and expert opinion. The cannabis market was quantified with several mathematical models. The data analysis included a Monte Carlo simulation to come to a 95% interval estimate (IE) and a sensitivity analysis to identify the most influential indicators. The annual production of Dutch cannabis was estimated to be between 171 and 965tons (95% IE of 271-613tons). The consumption was estimated to be between 28 and 119tons, depending on the inclusion or exclusion of non-residents (95% IE of 51-78tons or 32-49tons respectively). The export was estimated to be between 53 and 937tons (95% IE of 206-549tons or 231-573tons, respectively). Mathematical models are valuable tools for the systematic assessment of the size of illegal markets and determining the uncertainty inherent in the estimates. The estimates required the use of many assumptions and the availability of reliable indicators was limited. This uncertainty is reflected in the wide ranges of the estimates. The estimates are sensitive to 10 of the 45 indicators. These 10 account for 86-93% of the variation found. Further research should focus on improving the variables and the independence of the mathematical models. Copyright © 2016 Elsevier B.V. All rights reserved.

Mechanistic, Mathematical Model to Predict the Dynamics of Tissue Genesis in Bone Defects via Mechanical Feedback and Mediation of Biochemical Factors

PubMed Central

Moore, Shannon R.; Saidel, Gerald M.; Knothe, Ulf; Knothe Tate, Melissa L.

2014-01-01

The link between mechanics and biology in the generation and the adaptation of bone has been well studied in context of skeletal development and fracture healing. Yet, the prediction of tissue genesis within - and the spatiotemporal healing of - postnatal defects, necessitates a quantitative evaluation of mechano-biological interactions using experimental and clinical parameters. To address this current gap in knowledge, this study aims to develop a mechanistic mathematical model of tissue genesis using bone morphogenetic protein (BMP) to represent of a class of factors that may coordinate bone healing. Specifically, we developed a mechanistic, mathematical model to predict the dynamics of tissue genesis by periosteal progenitor cells within a long bone defect surrounded by periosteum and stabilized via an intramedullary nail. The emergent material properties and mechanical environment associated with nascent tissue genesis influence the strain stimulus sensed by progenitor cells within the periosteum. Using a mechanical finite element model, periosteal surface strains are predicted as a function of emergent, nascent tissue properties. Strains are then input to a mechanistic mathematical model, where mechanical regulation of BMP-2 production mediates rates of cellular proliferation, differentiation and tissue production, to predict healing outcomes. A parametric approach enables the spatial and temporal prediction of endochondral tissue regeneration, assessed as areas of cartilage and mineralized bone, as functions of radial distance from the periosteum and time. Comparing model results to histological outcomes from two previous studies of periosteum-mediated bone regeneration in a common ovine model, it was shown that mechanistic models incorporating mechanical feedback successfully predict patterns (spatial) and trends (temporal) of bone tissue regeneration. The novel model framework presented here integrates a mechanistic feedback system based on the mechanosensitivity of periosteal progenitor cells, which allows for modeling and prediction of tissue regeneration on multiple length and time scales. Through combination of computational, physical and engineering science approaches, the model platform provides a means to test new hypotheses in silico and to elucidate conditions conducive to endogenous tissue genesis. Next generation models will serve to unravel intrinsic differences in bone genesis by endochondral and intramembranous mechanisms. PMID:24967742

Genomic signal processing: from matrix algebra to genetic networks.

PubMed

Alter, Orly

2007-01-01

DNA microarrays make it possible, for the first time, to record the complete genomic signals that guide the progression of cellular processes. Future discovery in biology and medicine will come from the mathematical modeling of these data, which hold the key to fundamental understanding of life on the molecular level, as well as answers to questions regarding diagnosis, treatment, and drug development. This chapter reviews the first data-driven models that were created from these genome-scale data, through adaptations and generalizations of mathematical frameworks from matrix algebra that have proven successful in describing the physical world, in such diverse areas as mechanics and perception: the singular value decomposition model, the generalized singular value decomposition model comparative model, and the pseudoinverse projection integrative model. These models provide mathematical descriptions of the genetic networks that generate and sense the measured data, where the mathematical variables and operations represent biological reality. The variables, patterns uncovered in the data, correlate with activities of cellular elements such as regulators or transcription factors that drive the measured signals and cellular states where these elements are active. The operations, such as data reconstruction, rotation, and classification in subspaces of selected patterns, simulate experimental observation of only the cellular programs that these patterns represent. These models are illustrated in the analyses of RNA expression data from yeast and human during their cell cycle programs and DNA-binding data from yeast cell cycle transcription factors and replication initiation proteins. Two alternative pictures of RNA expression oscillations during the cell cycle that emerge from these analyses, which parallel well-known designs of physical oscillators, convey the capacity of the models to elucidate the design principles of cellular systems, as well as guide the design of synthetic ones. In these analyses, the power of the models to predict previously unknown biological principles is demonstrated with a prediction of a novel mechanism of regulation that correlates DNA replication initiation with cell cycle-regulated RNA transcription in yeast. These models may become the foundation of a future in which biological systems are modeled as physical systems are today.

Mathematical Modeling: A Structured Process

ERIC Educational Resources Information Center

Anhalt, Cynthia Oropesa; Cortez, Ricardo

2015-01-01

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

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

ERIC Educational Resources Information Center

Suppes, Patrick

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

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

ERIC Educational Resources Information Center

Lingefjard, Thomas; Holmquist, Mikael

2005-01-01

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

Mathematical Modeling in the Undergraduate Curriculum

ERIC Educational Resources Information Center

Toews, Carl

2012-01-01

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

Teachers' Conceptions of Mathematical Modeling

ERIC Educational Resources Information Center

Gould, Heather

2013-01-01

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

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

NASA Astrophysics Data System (ADS)

Irawan, Adi; Mardiyana; Retno Sari Saputro, Dewi

2017-06-01

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

Steady state phosphorus mass balance model during hemodialysis based on a pseudo one-compartment kinetic model.

PubMed

Leypoldt, John K; Agar, Baris U; Akonur, Alp; Gellens, Mary E; Culleton, Bruce F

2012-11-01

Mathematical models of phosphorus kinetics and mass balance during hemodialysis are in early development. We describe a theoretical phosphorus steady state mass balance model during hemodialysis based on a novel pseudo one-compartment kinetic model. The steady state mass balance model accounted for net intestinal absorption of phosphorus and phosphorus removal by both dialysis and residual kidney function. Analytical mathematical solutions were derived to describe time-dependent intradialytic and interdialytic serum phosphorus concentrations assuming hemodialysis treatments were performed symmetrically throughout a week. Results from the steady state phosphorus mass balance model are described for thrice weekly hemodialysis treatment prescriptions only. The analysis predicts 1) a minimal impact of dialyzer phosphorus clearance on predialysis serum phosphorus concentration using modern, conventional hemodialysis technology, 2) variability in the postdialysis-to-predialysis phosphorus concentration ratio due to differences in patient-specific phosphorus mobilization, and 3) the importance of treatment time in determining the predialysis serum phosphorus concentration. We conclude that a steady state phosphorus mass balance model can be developed based on a pseudo one-compartment kinetic model and that predictions from this model are consistent with previous clinical observations. The predictions from this mass balance model are theoretical and hypothesis-generating only; additional prospective clinical studies will be required for model confirmation.

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

ERIC Educational Resources Information Center

Daher, Wajeeh M.; Shahbari, Juhaina Awawdeh

2015-01-01

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

Characteristics of good mathematics lecturers based on students and lecturers perspectives

NASA Astrophysics Data System (ADS)

Hapsari, Trusti; Putri, Dian Permana; Raharjo, Jajo Firman

2017-05-01

This study aims to determine the characteristics of good mathematics lecturers based on students' and lecturers' perspectivesand compare the characteristics of good lecturers/ teachers which are in accordance with the findings of some previous studies and the theories. This study is survey study. The Data were collected through questionnaires and interview. The population consists of some mathematics students from the first level through the third level and some mathematics education lecturers of a private university in West Java. Qualitative analysis was undertaken to examine the results of questionnaires and interviews. The finding shows that the characteristic of good mathematics lecturers is inspiring. They can inspire other mathematics lecturers and educators in general. Based on the students and lecturers' perspective, some characteristics of good mathematics lecturers are mastering the materials well, being on time, being objective, understanding the students, presenting the materials with clearly, and being disciplined. Some other characteristic mentioned are: teaching eagerly, being unhurried, being friendly, giving exemplary and preparing the lesson well. These characteristics are not much different from the characteristics described by some previous researchers and some theories of experts, i.e. mastering the subject matters well, pedagogic, and work wholeheartedly.

Multiscale Modelling and Analysis of Collective Decision Making in Swarm Robotics

PubMed Central

Vigelius, Matthias; Meyer, Bernd; Pascoe, Geoffrey

2014-01-01

We present a unified approach to describing certain types of collective decision making in swarm robotics that bridges from a microscopic individual-based description to aggregate properties. Our approach encompasses robot swarm experiments, microscopic and probabilistic macroscopic-discrete simulations as well as an analytic mathematical model. Following up on previous work, we identify the symmetry parameter, a measure of the progress of the swarm towards a decision, as a fundamental integrated swarm property and formulate its time evolution as a continuous-time Markov process. Contrary to previous work, which justified this approach only empirically and a posteriori, we justify it from first principles and derive hard limits on the parameter regime in which it is applicable. PMID:25369026

Optimal back-extrapolation method for estimating plasma volume in humans using the indocyanine green dilution method

PubMed Central

2014-01-01

Background The indocyanine green dilution method is one of the methods available to estimate plasma volume, although some researchers have questioned the accuracy of this method. Methods We developed a new, physiologically based mathematical model of indocyanine green kinetics that more accurately represents indocyanine green kinetics during the first few minutes postinjection than what is assumed when using the traditional mono-exponential back-extrapolation method. The mathematical model is used to develop an optimal back-extrapolation method for estimating plasma volume based on simulated indocyanine green kinetics obtained from the physiological model. Results Results from a clinical study using the indocyanine green dilution method in 36 subjects with type 2 diabetes indicate that the estimated plasma volumes are considerably lower when using the traditional back-extrapolation method than when using the proposed back-extrapolation method (mean (standard deviation) plasma volume = 26.8 (5.4) mL/kg for the traditional method vs 35.1 (7.0) mL/kg for the proposed method). The results obtained using the proposed method are more consistent with previously reported plasma volume values. Conclusions Based on the more physiological representation of indocyanine green kinetics and greater consistency with previously reported plasma volume values, the new back-extrapolation method is proposed for use when estimating plasma volume using the indocyanine green dilution method. PMID:25052018

Mathematical modeling in realistic mathematics education

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Mathematical 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.

Mathematical Models for the Apparent Mass of the Seated Human Body Exposed to Vertical Vibration

NASA Astrophysics Data System (ADS)

Wei, L.; Griffin, M. J.

1998-05-01

Alternative mathematical models of the vertical apparent mass of the seated human body are developed. The optimum parameters of four models (two single-degree-of-freedom models and two two-degree-of-freedom models) are derived from the mean measured apparent masses of 60 subjects (24 men, 24 women, 12 children) previously reported. The best fits were obtained by fitting the phase data with single-degree-of-freedom and two-degree-of-freedom models having rigid support structures. For these two models, curve fitting was performed on each of the 60 subjects (so as to obtain optimum model parameters for each subject), for the averages of each of the three groups of subjects, and for the entire group of subjects. The values obtained are tabulated. Use of a two-degree-of-freedom model provided a better fit to the phase of the apparent mass at frequencies greater than about 8 Hz and an improved fit to the modulus of the apparent mass at frequencies around 5 Hz. It is concluded that the two-degree-of-freedom model provides an apparent mass similar to that of the human body, but this does not imply that the body moves in the same manner as the masses in this optimized two-degree-of-freedom model.

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

ERIC Educational Resources Information Center

Mischo, Christoph; Maaß, Katja

2013-01-01

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

Leaning on Mathematical Habits of Mind

ERIC Educational Resources Information Center

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

2018-01-01

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

Mathematical model of a gene regulatory network reconciles effects of genetic perturbations on hematopoietic stem cell emergence.

PubMed

Narula, Jatin; Williams, C J; Tiwari, Abhinav; Marks-Bluth, Jonathon; Pimanda, John E; Igoshin, Oleg A

2013-07-15

Interlinked gene regulatory networks (GRNs) are vital for the spatial and temporal control of gene expression during development. The hematopoietic transcription factors (TFs) Scl, Gata2 and Fli1 form one such densely connected GRN which acts as a master regulator of embryonic hematopoiesis. This triad has been shown to direct the specification of the hemogenic endothelium and emergence of hematopoietic stem cells (HSCs) in response to Notch1 and Bmp4-Smad signaling. Here we employ previously published data to construct a mathematical model of this GRN network and use this model to systematically investigate the network dynamical properties. Our model uses a statistical-thermodynamic framework to describe the combinatorial regulation of gene expression and reconciles, mechanistically, several previously published but unexplained results from different genetic perturbation experiments. In particular, our results demonstrate how the interactions of Runx1, an essential hematopoietic TF, with components of the Bmp4 signaling pathway allow it to affect triad activation and acts as a key regulator of HSC emergence. We also explain why heterozygous deletion of this essential TF, Runx1, speeds up the network dynamics leading to accelerated HSC emergence. Taken together our results demonstrate that the triad, a master-level controller of definitive hematopoiesis, is an irreversible bistable switch whose dynamical properties are modulated by Runx1 and components of the Bmp4 signaling pathway. Copyright © 2013 Elsevier Inc. All rights reserved.

Coexistence trend contingent to Mediterranean oaks with different leaf habits.

PubMed

Di Paola, Arianna; Paquette, Alain; Trabucco, Antonio; Mereu, Simone; Valentini, Riccardo; Paparella, Francesco

2017-05-01

In a previous work we developed a mathematical model to explain the co-occurrence of evergreen and deciduous oak groups in the Mediterranean region, regarded as one of the distinctive features of Mediterranean biodiversity. The mathematical analysis showed that a stabilizing mechanism resulting from niche difference (i.e. different water use and water stress tolerance) between groups allows their coexistence at intermediate values of suitable soil water content. A simple formal derivation of the model expresses this hypothesis in a testable form linked uniquely to the actual evapotranspiration of forests community. In the present work we ascertain whether this simplified conclusion possesses some degree of explanatory power by comparing available data on oaks distributions and remotely sensed evapotranspiration (MODIS product) in a large-scale survey embracing the western Mediterranean area. Our findings confirmed the basic assumptions of model addressed on large scale, but also revealed asymmetric responses to water use and water stress tolerance between evergreen and deciduous oaks that should be taken into account to increase the understating of species interactions and, ultimately, improve the modeling capacity to explain co-occurrence.

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

NASA Technical Reports Server (NTRS)

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

1973-01-01

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

Designing Tasks to Promote and Assess Mathematical Transfer in Primary School Children

ERIC Educational Resources Information Center

Clark, Julie; Page, Shaileigh; Thornton, Steve

2013-01-01

This study aims to design learning situations and tasks that promote and assess the capacity of primary school children to transfer mathematical knowledge to new contexts. We discuss previous studies investigating mathematical transfer, and particularly the strengths and limitations of tasks used to assess transfer in these studies. We describe…

That Figures. A Mathematics Resource Package for Intermediate Grades. Revised.

ERIC Educational Resources Information Center

Hintz, Marilyn; Ziegler, Jerry

This resource package deals with elementary level mathematics in daily living, substituting newspapers as a refreshing change from mathematics texts. A total of 40 exercises are intended to provide review and reinforcement for skills previously taught in formal lessons. Skill or concept areas included are: reading large numbers; basic operations;…

A Reconceptualized Framework for "Opportunity to Learn" in School Mathematics

ERIC Educational Resources Information Center

Walkowiak, Temple A.; Pinter, Holly H.; Berry, Robert Q.

2017-01-01

We present a reconceptualized framework for opportunity to learn (OTL) in school mathematics that builds on previous conceptualizations of OTL and includes features related to both quantity (i.e., time) and quality. Our framework draws on existing literature and on our own observational research of mathematics teaching practices. Through the…

Investigating the Effects of a Math-Enhanced Agricultural Teaching Methods Course

ERIC Educational Resources Information Center

Stripling, Christopher T.; Roberts, T. Grady

2013-01-01

Numerous calls have been made for agricultural education to support core academic subject matter including mathematics. Previous research has shown that the incorporation of mathematics content into a teaching methods course had a positive effect on preservice teachers' mathematics content knowledge. The purpose of this study was to investigate…

STUDY OF VARIABLES ASSOCIATED WITH FINAL GRADES IN MATHEMATICS COURSES.

ERIC Educational Resources Information Center

DAVIS, ELTON C.; RISSER, JOHN J.

THIS STUDY WAS CONDUCTED IN ORDER TO DETERMINE THE RELATIVE VALUE OF PREVIOUS GRADES IN MATHEMATICS COURSES, THE OVERALL HIGH SCHOOL GRADE POINT AVERAGE, AND THE PLACEMENT TEST IN MATHEMATICS DEVELOPED AT THE COLLEGE AS PREDICTORS OF ACHIEVEMENT IN INTRODUCTORY AND INTERMEDIATE ALGEBRA, IN COLLEGE ALGEBRA, IN TRIGONOMETRY, AND IN ANALYTIC GEOMETRY…

Mapping Variation in Children's Mathematical Reasoning: The Case of "What Else Belongs?"

ERIC Educational Resources Information Center

Vale, Colleen; Widjaja, Wanty; Herbert, Sandra; Bragg, Leicha A.; Loong, Esther Yoon-Kin

2017-01-01

Explaining appears to dominate primary teachers' understanding of mathematical reasoning when it is not confused with problem solving. Drawing on previous literature of mathematical reasoning, we generate a view of the critical aspects of reasoning that may assist primary teachers when designing and enacting tasks to elicit and develop…

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

ERIC Educational Resources Information Center

Kjeldsen, Tinne Hoff; Blomhøj, Morten

2013-01-01

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

How Ordinary Meaning Underpins the Meaning of Mathematics.

ERIC Educational Resources Information Center

Ormell, Christopher

1991-01-01

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

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

PubMed

Ganusov, Vitaly V

2016-01-01

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

Novel mathematical model to estimate ball impact force in soccer.

PubMed

Iga, Takahito; Nunome, Hiroyuki; Sano, Shinya; Sato, Nahoko; Ikegami, Yasuo

2017-11-22

To assess ball impact force during soccer kicking is important to quantify from both performance and chronic injury prevention perspectives. We aimed to verify the appropriateness of previous models used to estimate ball impact force and to propose an improved model to better capture the time history of ball impact force. A soccer ball was fired directly onto a force platform (10 kHz) at five realistic kicking ball velocities and ball behaviour was captured by a high-speed camera (5,000 Hz). The time history of ball impact force was estimated using three existing models and two new models. A new mathematical model that took into account a rapid change in ball surface area and heterogeneous ball deformation showed a distinctive advantage to estimate the peak forces and its occurrence times and to reproduce time history of ball impact forces more precisely, thereby reinforcing the possible mechanics of 'footballer's ankle'. Ball impact time was also systematically shortened when ball velocity increases in contrast to practical understanding for producing faster ball velocity, however, the aspect of ball contact time must be considered carefully from practical point of view.

The contribution of spatial ability to mathematics achievement in middle childhood.

PubMed

Gilligan, Katie A; Flouri, Eirini; Farran, Emily K

2017-11-01

Strong spatial skills are associated with success in science, technology, engineering, and mathematics (STEM) domains. Although there is convincing evidence that spatial skills are a reliable predictor of mathematical achievement in preschool children and in university students, there is a lack of research exploring associations between spatial and mathematics achievement during the primary school years. To address this question, this study explored associations between mathematics and spatial skills in children aged 5 and 7years. The study sample included 12,099 children who participated in both Wave 3 (mean age=5; 02 [years; months]) and Wave 4 (mean age=7; 03) of the Millennium Cohort Study. Measures included a standardised assessment of mathematics and the Pattern Construction subscale of the British Ability Scales II to assess intrinsic-dynamic spatial skills. Spatial skills at 5 and 7years of age explained a significant 8.8% of the variation in mathematics achievement at 7years, above that explained by other predictors of mathematics, including gender, socioeconomic status, ethnicity, and language skills. This percentage increased to 22.6% without adjustment for language skills. This study expands previous findings by using a large-scale longitudinal sample of primary school children, a population that has been largely omitted from previous research exploring associations between spatial ability and mathematics achievement. The finding that early and concurrent spatial skills contribute to mathematics achievement at 7years of age highlights the potential of spatial skills as a novel target in the design of mathematics interventions for children in this age range. Crown Copyright © 2017. Published by Elsevier Inc. All rights reserved.

Challenges for Complex Microbial Ecosystems: Combination of Experimental Approaches with Mathematical Modeling

PubMed Central

Haruta, Shin; Yoshida, Takehito; Aoi, Yoshiteru; Kaneko, Kunihiko; Futamata, Hiroyuki

2013-01-01

In the past couple of decades, molecular ecological techniques have been developed to elucidate microbial diversity and distribution in microbial ecosystems. Currently, modern techniques, represented by meta-omics and single cell observations, are revealing the incredible complexity of microbial ecosystems and the large degree of phenotypic variation. These studies propound that microbiological techniques are insufficient to untangle the complex microbial network. This minireview introduces the application of advanced mathematical approaches in combination with microbiological experiments to microbial ecological studies. These combinational approaches have successfully elucidated novel microbial behaviors that had not been recognized previously. Furthermore, the theoretical perspective also provides an understanding of the plasticity, robustness and stability of complex microbial ecosystems in nature. PMID:23995424

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…

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

PubMed Central

Ganusov, Vitaly V.

2016-01-01

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

Using Covariation Reasoning to Support Mathematical Modeling

ERIC Educational Resources Information Center

Jacobson, Erik

2014-01-01

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

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…

Shaping the Future of Mathematics Education. Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia (33rd, Freemantle, Western Australia, Australia, July 3-7, 2010)

ERIC Educational Resources Information Center

Sparrow, Len, Ed.; Kissane, Barry, Ed.; Hurst, Chris, Ed.

2010-01-01

These collected papers are a record of the proceedings of the 33rd Annual Conference of the Mathematics Education Research Group of Australasia entitled, "Shaping the Future of Mathematics Education." The conference is held in Fremantle, as was the previous conference a decade earlier. Keynote speakers are discussing issues that are emerging more…

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.

OMV: A simplified mathematical model of the orbital maneuvering vehicle

NASA Technical Reports Server (NTRS)

Teoh, W.

1984-01-01

A model of the orbital maneuvering vehicle (OMV) is presented which contains several simplications. A set of hand controller signals may be used to control the motion of the OMV. Model verification is carried out using a sequence of tests. The dynamic variables generated by the model are compared, whenever possible, with the corresponding analytical variables. The results of the tests show conclusively that the present model is behaving correctly. Further, this model interfaces properly with the state vector transformation module (SVX) developed previously. Correct command sentence sequences are generated by the OMV and and SVX system, and these command sequences can be used to drive the flat floor simulation system at MSFC.

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…

Three-dimensional FLASH Laser Radar Range Estimation via Blind Deconvolution

DTIC Science & Technology

2009-10-01

scene can result in errors due to several factors including the optical spatial impulse response, detector blurring, photon noise , timing jitter, and...estimation error include spatial blur, detector blurring, noise , timing jitter, and inter-sample targets. Unlike previous research, this paper ac- counts...for pixel coupling by defining the range image mathematical model as a 2D convolution between the system spatial impulse response and the object (target

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

ERIC Educational Resources Information Center

Wright, Vince

2014-01-01

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

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

ERIC Educational Resources Information Center

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

2016-01-01

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

Teaching Mathematical Modeling in Mathematics Education

ERIC Educational Resources Information Center

Saxena, Ritu; Shrivastava, Keerty; Bhardwaj, Ramakant

2016-01-01

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

Enjoying Mathematics or Feeling Competent in Mathematics? Reciprocal Effects on Mathematics Achievement and Perceived Math Effort Expenditure

ERIC Educational Resources Information Center

Pinxten, Maarten; Marsh, Herbert W.; De Fraine, Bieke; Van Den Noortgate, Wim; Van Damme, Jan

2014-01-01

Background: The multidimensionality of the academic self-concept in terms of domain specificity has been well established in previous studies, whereas its multidimensionality in terms of motivational functions (the so-called affect-competence separation) needs further examination. Aim: This study aims at exploring differential effects of enjoyment…

Utilizing the M-Scan to Measure Standards-Based Mathematics Teaching Practices: Affordances and Limitations

ERIC Educational Resources Information Center

Walkowiak, Temple A.; Berry, Robert Q.; Pinter, Holly H.; Jacobson, Erik D.

2018-01-01

The Mathematics Scan (M-Scan), a content-specific observational measure, was utilized to examine the extent to which "standards-based mathematics teaching practices" were present in three focal lessons. While previous studies have provided evidence of validity of the inferences drawn from M-Scan data, no prior work has investigated the…

Finding "Mathematics": Parents Questioning School-Centered Approaches to Involvement in Children's Mathematics Learning

ERIC Educational Resources Information Center

Jay, Tim; Rose, Jo; Simmons, Ben

2017-01-01

This paper reports on a study of parental involvement in children's mathematics learning in the context of a series of workshops carried out in four primary schools in the United Kingdom. Previous research suggests that, while there are high correlations between parental involvement and positive student outcomes, it can be difficult to raise…

Slope across the Curriculum: Principles and Standards for School Mathematics and Common Core State Standards

ERIC Educational Resources Information Center

Nagle, Courtney; Moore-Russo, Deborah

2014-01-01

This article provides an initial comparison of the Principles and Standards for School Mathematics and the Common Core State Standards for Mathematics by examining the fundamental notion of slope. Each set of standards is analyzed using eleven previously identified conceptualizations of slope. Both sets of standards emphasize Functional Property,…

Cognitive Benefits and Costs of Bilingualism in Elementary School Students: The Case of Mathematical Word Problems

ERIC Educational Resources Information Center

Kempert, Sebastian; Saalbach, Henrik; Hardy, Ilonca

2011-01-01

Previous research has emphasized the importance of language for learning mathematics. This is especially true when mathematical problems have to be extracted from a meaningful context, as in arithmetic word problems. Bilingual learners with a low command of the instructional language thus may face challenges when dealing with mathematical…

What's Happening in the Mathematical Sciences, 1993-1994.

ERIC Educational Resources Information Center

Cipra, Barry

1993-01-01

This document consists of the first two volumes of a new annual serial devoted to surveying some of the important developments in the mathematical sciences in the previous year or so. Mathematics is constantly growing and changing, reaching out to other areas of science and helping to solve some of the major problems facing society. Volumes 1 and…

Mathematics Instruction for Students with Emotional and Behavioral Disorders: A Best-Evidence Synthesis

ERIC Educational Resources Information Center

Ralston, Nicole C.; Benner, Gregory J.; Tsai, Shu-Fei; Riccomini, Paul J.; Nelson, J. Ron

2014-01-01

The authors report findings of a best-evidence synthesis of the effects of mathematics instruction on the mathematics skills of students with emotional and behavioral disorders. The goal of the synthesis was to extend previous research by (a) detailing independent variables, instructional components, and outcome measures for each study; (b)…

Mathematical Experiences and Parental Involvement of Parents Who Are and Who Are Not Mathematicians

ERIC Educational Resources Information Center

Antolin Drešar, Darja; Lipovec, Alenka

2017-01-01

Previous studies suggest that parental involvement in children's mathematics education is more established for parents who feel competent in mathematics. This qualitative study aimed to gain an in-depth insight into the experiences of parental involvement of two different groups of parents: those who are mathematicians and those who are not. Data…

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).

HIV Model Parameter Estimates from Interruption Trial Data including Drug Efficacy and Reservoir Dynamics

PubMed Central

Luo, Rutao; Piovoso, Michael J.; Martinez-Picado, Javier; Zurakowski, Ryan

2012-01-01

Mathematical models based on ordinary differential equations (ODE) have had significant impact on understanding HIV disease dynamics and optimizing patient treatment. A model that characterizes the essential disease dynamics can be used for prediction only if the model parameters are identifiable from clinical data. Most previous parameter identification studies for HIV have used sparsely sampled data from the decay phase following the introduction of therapy. In this paper, model parameters are identified from frequently sampled viral-load data taken from ten patients enrolled in the previously published AutoVac HAART interruption study, providing between 69 and 114 viral load measurements from 3–5 phases of viral decay and rebound for each patient. This dataset is considerably larger than those used in previously published parameter estimation studies. Furthermore, the measurements come from two separate experimental conditions, which allows for the direct estimation of drug efficacy and reservoir contribution rates, two parameters that cannot be identified from decay-phase data alone. A Markov-Chain Monte-Carlo method is used to estimate the model parameter values, with initial estimates obtained using nonlinear least-squares methods. The posterior distributions of the parameter estimates are reported and compared for all patients. PMID:22815727

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

NASA Astrophysics Data System (ADS)

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

2016-02-01

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

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 obtain a good approximation of the biological trials data. It is worth mentioning that by manipulating the different parameters of the model the effectiveness of the immunotherapy may increase. This last suggests that different protocols could be implemented by the Immunotherapy Laboratory of UNAM in order to improve their results.

The use of concrete learning objects taken from the history of mathematics in mathematics education

NASA Astrophysics Data System (ADS)

Bütüner, Suphi Önder

2016-11-01

This study aimed to reveal the effects of teaching with concrete learning objects taken from the history of mathematics on student achievement. Being a quasi-experimental study, it was conducted with two grade 8 classes in a secondary school located in Trabzon. The experimental group consisted of 27 students and the control group consisted of 25. Data were collected by using worksheets, an achievement exam and written opinion forms. The data from the achievement exam were analysed by using the Mann-Whitney U-test while the data from written opinion forms were analysed through content analysis. The Mann-Whitney U-test results showed a significant difference between the mean ranks of the experimental and control groups in favour of the former. Findings from the written opinion forms suggested that the students found the activities to be instructive and fun, enjoyed using concrete models in their classes, and learned from discovering the rules. It was also found that students had previously not engaged in similar activities and had only experienced the history of mathematics through the life stories and works of mathematicians and the representation of ancient numbers at the beginning of each unit.

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

Design, processing and testing of LSI arrays, hybrid microelectronics task

NASA Technical Reports Server (NTRS)

Himmel, R. P.; Stuhlbarg, S. M.; Ravetti, R. G.; Zulueta, P. J.; Rothrock, C. W.

1979-01-01

Mathematical cost models previously developed for hybrid microelectronic subsystems were refined and expanded. Rework terms related to substrate fabrication, nonrecurring developmental and manufacturing operations, and prototype production are included. Sample computer programs were written to demonstrate hybrid microelectric applications of these cost models. Computer programs were generated to calculate and analyze values for the total microelectronics costs. Large scale integrated (LST) chips utilizing tape chip carrier technology were studied. The feasibility of interconnecting arrays of LSU chips utilizing tape chip carrier and semiautomatic wire bonding technology was demonstrated.

Discussion and revision of the mathematical modeling tool described in the previously published article "Modeling HIV Transmission risk among Mozambicans prior to their initiating highly active antiretroviral therapy".

PubMed

Cassels, Susan; Pearson, Cynthia R; Kurth, Ann E; Martin, Diane P; Simoni, Jane M; Matediana, Eduardo; Gloyd, Stephen

2009-07-01

Mathematical models are increasingly used in social and behavioral studies of HIV transmission; however, model structures must be chosen carefully to best answer the question at hand and conclusions must be interpreted cautiously. In Pearson et al. (2007), we presented a simple analytically tractable deterministic model to estimate the number of secondary HIV infections stemming from a population of HIV-positive Mozambicans and to evaluate how the estimate would change under different treatment and behavioral scenarios. In a subsequent application of the model with a different data set, we observed that the model produced an unduly conservative estimate of the number of new HIV-1 infections. In this brief report, our first aim is to describe a revision of the model to correct for this underestimation. Specifically, we recommend adjusting the population-level sexually transmitted infection (STI) parameters to be applicable to the individual-level model specification by accounting for the proportion of individuals uninfected with an STI. In applying the revised model to the original data, we noted an estimated 40 infections/1000 HIV-positive persons per year (versus the original 23 infections/1000 HIV-positive persons per year). In addition, the revised model estimated that highly active antiretroviral therapy (HAART) along with syphilis and herpes simplex virus type 2 (HSV-2) treatments combined could reduce HIV-1 transmission by 72% (versus 86% according to the original model). The second aim of this report is to discuss the advantages and disadvantages of mathematical models in the field and the implications of model interpretation. We caution that simple models should be used for heuristic purposes only. Since these models do not account for heterogeneity in the population and significantly simplify HIV transmission dynamics, they should be used to describe general characteristics of the epidemic and demonstrate the importance or sensitivity of parameters in the model.

Experimental advances and preliminary mathematical modeling of the Swiss-roll mixed-reactant direct borohydride fuel cell

NASA Astrophysics Data System (ADS)

Aziznia, Amin; Oloman, Colin W.; Gyenge, Előd L.

2014-11-01

The Swiss-roll single-cell mixed reactant (SR-MRFC) borohydride - oxygen fuel cell equipped with Pt/carbon cloth 3D anode and either MnO2 or Ag gas-diffusion cathodes is investigated by a combination of experimental studies and preliminary mathematical modeling of the polarization curve. We investigate the effects of four variables: cathode side metallic mesh fluid distributor, separator type (Nafion 112® vs. Viledon®), cathode catalyst (MnO2 vs. Ag), and the hydrophilic pore volume fraction of the gas-diffusion cathode. Using a two-phase feed of alkaline borohydride solution (1 M NaBH4 - 2 M NaOH) and O2 gas in an SR-MRFC equipped with Pt/C 3D anode, MnO2 gas diffusion cathode, Viledon® porous diaphragm, expanded mesh cathode-side fluid distributor, the maximum superficial power density is 2230 W m-2 at 323 K and 105 kPa(abs). The latter superficial power density is almost 3.5 times higher than our previously reported superficial power density for the same catalyst combinations. Furthermore, with a Pt anode and Ag cathode catalyst combination, a superficial power density of 2500 W m-2 is achieved with superior performance durability compared to the MnO2 cathode. The fuel cell results are substantiated by impedance spectroscopy analysis and preliminary mathematical model predictions based on mixed potential theory.

Preservice Secondary Teachers' Conceptions from a Mathematical Modeling Activity and Connections to the Common Core State Standards

ERIC Educational Resources Information Center

Stohlmann, Micah; Maiorca, Cathrine; Olson, Travis A.

2015-01-01

Mathematical modeling is an essential integrated piece of the Common Core State Standards. However, researchers have shown that mathematical modeling activities can be difficult for teachers to implement. Teachers are more likely to implement mathematical modeling activities if they have their own successful experiences with such activities. This…

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

ERIC Educational Resources Information Center

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

2015-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2013-07-01

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

Towards a Rational Model for the Triple Velocity Correlations of Turbulence

NASA Technical Reports Server (NTRS)

Younis, B. A.; Gatski, T. B.; Speziale, C. G.

1999-01-01

This paper presents a rational approach to modelling the triple velocity correlations that appear in the transport equations for the Reynolds stresses. All existing models of these correlations have largely been formulated on phenomenological grounds and are defective in one important aspect: they all neglect to allow for the dependence of these correlations on the local gradients of mean velocity. The mathematical necessity for this dependence will be demonstrated in the paper. The present contribution lies in the novel use of Group Representation Theory to determine the most general tensorial form of these correlations in terms of all the second- and third-order tensor quantities that appear in the exact equations that govern their evolution. The requisite representation did not exist in the literature and therefore had to be developed specifically for this purpose by Professor G. F. Smith. The outcome of this work is a mathematical framework for the construction of algebraic, explicit, and rational models for the triple velocity correlations that are theoretically consistent and include all the correct dependencies. Previous models are reviewed, and all are shown to be an incomplete subset of this new representation, even to lowest order.

Effects of Humidity Swings on Adsorption Columns for Air Revitalization: Modeling and Experiments

NASA Technical Reports Server (NTRS)

LeVan, M. Douglas; Finn, John E.

1997-01-01

The goal of this research was to develop a dynamic model which can predict the effect of humidity swings on activated carbon adsorption beds used to remove trace contaminants from the atmosphere in spacecraft. Specifically, the model was to be incorporated into a computer simulation to predict contaminant concentrations exiting the bed as a function of time after a humidity swing occurs. Predicted breakthrough curves were to be compared to experimentally measured results. In all respects the research was successful. The two major aspects of this research were the mathematical model and the experiments. Experiments were conducted by Mr. Appel using a fixed-bed apparatus at NASA-Ames Research Center during the summers of 1994 and 1995 and during the first 8 months of 1996. Mr. Appel conducted most of his mathematical modeling work at the University of Virginia. The simulation code was used to predict breakthrough curves using adsorption equilibrium correlations developed previously by M. D. LeVan's research group at the University of Virginia. These predictions were compared with the experimental measurements, and this led to improvements in both the simulation code and the apparatus.

The dispersion releaser technology is an effective method for testing drug release from nanosized drug carriers.

PubMed

Janas, Christine; Mast, Marc-Phillip; Kirsamer, Li; Angioni, Carlo; Gao, Fiona; Mäntele, Werner; Dressman, Jennifer; Wacker, Matthias G

2017-06-01

The dispersion releaser (DR) is a dialysis-based setup for the analysis of the drug release from nanosized drug carriers. It is mounted into dissolution apparatus2 of the United States Pharmacopoeia. The present study evaluated the DR technique investigating the drug release of the model compound flurbiprofen from drug solution and from nanoformulations composed of the drug and the polymer materials poly (lactic acid), poly (lactic-co-glycolic acid) or Eudragit®RSPO. The drug loaded nanocarriers ranged in size between 185.9 and 273.6nm and were characterized by a monomodal size distribution (PDI<0.1). The membrane permeability constants of flurbiprofen were calculated and mathematical modeling was applied to obtain the normalized drug release profiles. For comparing the sensitivities of the DR and the dialysis bag technique, the differences in the membrane permeation rates were calculated. Finally, different formulation designs of flurbiprofen were sensitively discriminated using the DR technology. The mechanism of drug release from the nanosized carriers was analyzed by applying two mathematical models described previously, the reciprocal powered time model and the three parameter model. Copyright © 2017 Elsevier B.V. All rights reserved.

The Effects of a Tier 3 Intervention on the Mathematics Performance of Second Grade Students With Severe Mathematics Difficulties.

PubMed

Bryant, Brian R; Bryant, Diane Pedrotty; Porterfield, Jennifer; Dennis, Minyi Shih; Falcomata, Terry; Valentine, Courtney; Brewer, Chelsea; Bell, Kathy

2016-01-01

The purpose of this study was to determine the effectiveness of a systematic, explicit, intensive Tier 3 (tertiary) intervention on the mathematics performance of students in second grade with severe mathematics difficulties. A multiple-baseline design across groups of participants showed improved mathematics performance on number and operations concepts and procedures, which are the foundation for later mathematics success. In the previous year, 12 participants had experienced two doses (first and second semesters) of a Tier 2 intervention. In second grade, the participants continued to demonstrate low performance, falling below the 10th percentile on a researcher-designed universal screener and below the 16th percentile on a distal measure, thus qualifying for the intensive intervention. A project interventionist, who met with the students 5 days a week for 10 weeks (9 weeks for one group), conducted the intensive intervention. The intervention employed more intensive instructional design features than the previous Tier 2 secondary instruction, and also included weekly games to reinforce concepts and skills from the lessons. Spring results showed significantly improved mathematics performance (scoring at or above the 25th percentile) for most of the students, thus making them eligible to exit the Tier 3 intervention. © Hammill Institute on Disabilities 2014.

Transmission Dinamics Model Of Dengue Fever

NASA Astrophysics Data System (ADS)

Debora; Rendy; Rahmi

2018-01-01

Dengue fever is an endemic disease that is transmitted through the Aedes aegypti mosquito vector. The disease is present in more than 100 countries in America, Africa, and Asia, especially tropical countries. Differential equations can be used to represent the spread of dengue virus occurring in time intervals and model in the form of mathematical models. The mathematical model in this study tries to represent the spread of dengue fever based on the data obtained and the assumptions used. The mathematical model used is a mathematical model consisting of Susceptible (S), Infected (I), Viruses (V) subpopulations. The SIV mathematical model is then analyzed to see the solution behaviour of the system.

Topographical optimization of structures for use in musical instruments and other applications

NASA Astrophysics Data System (ADS)

Kirkland, William Brandon

Mallet percussion instruments such as the xylophone, marimba, and vibraphone have been produced and tuned since their inception by arduously grinding the keys to achieve harmonic ratios between their 1st, 2 nd, and 3rd transverse modes. In consideration of this, it would be preferable to have defined mathematical models such that the keys of these instruments can be produced quickly and reliably. Additionally, physical modeling of these keys or beams provides a useful application of non-uniform beam vibrations as studied by Euler-Bernoulli and Timoshenko beam theories. This thesis work presents a literature review of previous studies regarding mallet percussion instrument design and optimization of non-uniform keys. The progression of previous research from strictly mathematical approaches to finite element methods is shown, ultimately arriving at the most current optimization techniques used by other authors. However, previous research varies slightly in the relative degree of accuracy to which a non-uniform beam can be modeled. Typically, accuracies are shown in literature as 1% to 2% error. While this seems attractive, musical tolerances require 0.25% error and beams are otherwise unsuitable. This research seeks to build on and add to the previous field research by optimizing beam topology and machining keys within tolerances that no further tuning is required. The optimization methods relied on finite element analysis and used harmonic modal frequencies as constraints rather than arguments of an error function to be optimized. Instead, the beam mass was minimized while the modal frequency constraints were required to be satisfied within 0.25% tolerance. The final optimized and machined keys of an A4 vibraphone were shown to be accurate within the required musical tolerances, with strong resonance at the designed frequencies. The findings solidify a systematic method for designing musical structures for accuracy and repeatability upon manufacture.

Mathematical Modeling: Convoying Merchant Ships

ERIC Educational Resources Information Center

Mathews, Susann M.

2004-01-01

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

Making the Most of Modeling Tasks

ERIC Educational Resources Information Center

Wernet, Jamie L.; Lawrence, Kevin A.; Gilbertson, Nicholas J.

2015-01-01

While there is disagreement among mathematics educators about some aspects of its meaning, mathematical modeling generally involves taking a real-world scenario and translating it into the mathematical world (Niss, Blum, and Galbraith 2007). The complete modeling process involves describing situations posed in problems with mathematical concepts,…

Programming biological models in Python using PySB.

PubMed

Lopez, Carlos F; Muhlich, Jeremy L; Bachman, John A; Sorger, Peter K

2013-01-01

Mathematical equations are fundamental to modeling biological networks, but as networks get large and revisions frequent, it becomes difficult to manage equations directly or to combine previously developed models. Multiple simultaneous efforts to create graphical standards, rule-based languages, and integrated software workbenches aim to simplify biological modeling but none fully meets the need for transparent, extensible, and reusable models. In this paper we describe PySB, an approach in which models are not only created using programs, they are programs. PySB draws on programmatic modeling concepts from little b and ProMot, the rule-based languages BioNetGen and Kappa and the growing library of Python numerical tools. Central to PySB is a library of macros encoding familiar biochemical actions such as binding, catalysis, and polymerization, making it possible to use a high-level, action-oriented vocabulary to construct detailed models. As Python programs, PySB models leverage tools and practices from the open-source software community, substantially advancing our ability to distribute and manage the work of testing biochemical hypotheses. We illustrate these ideas using new and previously published models of apoptosis.

Programming biological models in Python using PySB

PubMed Central

Lopez, Carlos F; Muhlich, Jeremy L; Bachman, John A; Sorger, Peter K

2013-01-01

Mathematical equations are fundamental to modeling biological networks, but as networks get large and revisions frequent, it becomes difficult to manage equations directly or to combine previously developed models. Multiple simultaneous efforts to create graphical standards, rule-based languages, and integrated software workbenches aim to simplify biological modeling but none fully meets the need for transparent, extensible, and reusable models. In this paper we describe PySB, an approach in which models are not only created using programs, they are programs. PySB draws on programmatic modeling concepts from little b and ProMot, the rule-based languages BioNetGen and Kappa and the growing library of Python numerical tools. Central to PySB is a library of macros encoding familiar biochemical actions such as binding, catalysis, and polymerization, making it possible to use a high-level, action-oriented vocabulary to construct detailed models. As Python programs, PySB models leverage tools and practices from the open-source software community, substantially advancing our ability to distribute and manage the work of testing biochemical hypotheses. We illustrate these ideas using new and previously published models of apoptosis. PMID:23423320

Improving mathematical problem solving ability through problem-based learning and authentic assessment for the students of Bali State Polytechnic

NASA Astrophysics Data System (ADS)

Darma, I. K.

2018-01-01

This research is aimed at determining: 1) the differences of mathematical problem solving ability between the students facilitated with problem-based learning model and conventional learning model, 2) the differences of mathematical problem solving ability between the students facilitated with authentic and conventional assessment model, and 3) interaction effect between learning and assessment model on mathematical problem solving. The research was conducted in Bali State Polytechnic, using the 2x2 experiment factorial design. The samples of this research were 110 students. The data were collected using a theoretically and empirically-validated test. Instruments were validated by using Aiken’s approach of technique content validity and item analysis, and then analyzed using anova stylistic. The result of the analysis shows that the students facilitated with problem-based learning and authentic assessment models get the highest score average compared to the other students, both in the concept understanding and mathematical problem solving. The result of hypothesis test shows that, significantly: 1) there is difference of mathematical problem solving ability between the students facilitated with problem-based learning model and conventional learning model, 2) there is difference of mathematical problem solving ability between the students facilitated with authentic assessment model and conventional assessment model, and 3) there is interaction effect between learning model and assessment model on mathematical problem solving. In order to improve the effectiveness of mathematics learning, collaboration between problem-based learning model and authentic assessment model can be considered as one of learning models in class.

Influence of Problem-Based Learning Model of Learning to the Mathematical Communication Ability of Students of Grade XI IPA SMAN 14 Padang

NASA Astrophysics Data System (ADS)

Nisa, I. M.

2018-04-01

The ability of mathematical communication is one of the goals of learning mathematics expected to be mastered by students. However, reality in the field found that the ability of mathematical communication the students of grade XI IPA SMA Negeri 14 Padang have not developed optimally. This is evident from the low test results of communication skills mathematically done. One of the factors that causes this happens is learning that has not been fully able to facilitate students to develop mathematical communication skills well. By therefore, to improve students' mathematical communication skills required a model in the learning activities. One of the models learning that can be used is Problem Based learning model Learning (PBL). The purpose of this study is to see whether the ability the students' mathematical communication using the PBL model better than the students' mathematical communication skills of the learning using conventional learning in Class XI IPA SMAN 14 Padang. This research type is quasi experiment with design Randomized Group Only Design. Population in this research that is student of class XI IPA SMAN 14 Padang with sample class XI IPA 3 and class XI IPA 4. Data retrieval is done by using communication skill test mathematically shaped essay. To test the hypothesis used U-Mann test Whitney. Based on the results of data analysis, it can be concluded that the ability mathematical communication of students whose learning apply more PBL model better than the students' mathematical communication skills of their learning apply conventional learning in class XI IPA SMA 14 Padang at α = 0.05. This indicates that the PBL learning model effect on students' mathematical communication ability.

Predicting the safety and efficacy of buffer therapy to raise tumour pHe: an integrative modelling study.

PubMed

Martin, N K; Robey, I F; Gaffney, E A; Gillies, R J; Gatenby, R A; Maini, P K

2012-03-27

Clinical positron emission tomography imaging has demonstrated the vast majority of human cancers exhibit significantly increased glucose metabolism when compared with adjacent normal tissue, resulting in an acidic tumour microenvironment. Recent studies demonstrated reducing this acidity through systemic buffers significantly inhibits development and growth of metastases in mouse xenografts. We apply and extend a previously developed mathematical model of blood and tumour buffering to examine the impact of oral administration of bicarbonate buffer in mice, and the potential impact in humans. We recapitulate the experimentally observed tumour pHe effect of buffer therapy, testing a model prediction in vivo in mice. We parameterise the model to humans to determine the translational safety and efficacy, and predict patient subgroups who could have enhanced treatment response, and the most promising combination or alternative buffer therapies. The model predicts a previously unseen potentially dangerous elevation in blood pHe resulting from bicarbonate therapy in mice, which is confirmed by our in vivo experiments. Simulations predict limited efficacy of bicarbonate, especially in humans with more aggressive cancers. We predict buffer therapy would be most effectual: in elderly patients or individuals with renal impairments; in combination with proton production inhibitors (such as dichloroacetate), renal glomular filtration rate inhibitors (such as non-steroidal anti-inflammatory drugs and angiotensin-converting enzyme inhibitors), or with an alternative buffer reagent possessing an optimal pK of 7.1-7.2. Our mathematical model confirms bicarbonate acts as an effective agent to raise tumour pHe, but potentially induces metabolic alkalosis at the high doses necessary for tumour pHe normalisation. We predict use in elderly patients or in combination with proton production inhibitors or buffers with a pK of 7.1-7.2 is most promising.

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

NASA Astrophysics Data System (ADS)

Plotnitsky, Arkady

2017-06-01

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

A Primer for Mathematical Modeling

ERIC Educational Resources Information Center

Sole, Marla

2013-01-01

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

Strategies to Support Students' Mathematical Modeling

ERIC Educational Resources Information Center

Jung, Hyunyi

2015-01-01

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

Mathematical Modeling in the High School Curriculum

ERIC Educational Resources Information Center

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

2016-01-01

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

Modeling dynamic processes at stage of formation of parts previously subjected to high-energy laser effects

NASA Astrophysics Data System (ADS)

Efimov, A. E.; Maksarov, V. V.; Timofeev, D. Y.

2018-03-01

The present paper states the impact of a technological system on piece’s roughness and shape accuracy via simulation modeling. For this purpose, a theory was formulated and a mathematical model was generated to justify self-oscillations in a system. The method of oscillations eliminations based on workpiece’s high-energy laser irradiation with the purpose of further processing were suggested in compliance with the adopted theory and model. Modeling the behaviour of a system with the transient phenomenon indicated the tendency of reducing self-oscillations in unstable processing modes, which has a positive effect under the conditions of practical implementation over piece’s roughness and accuracy.

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…

The Nation's Report Card [TM]: Mathematics 2003 and 2005: Performance in Puerto Rico. Highlights. NCES 2007--459

ERIC Educational Resources Information Center

Baxter, G.P.; Bleeker, M.M.; Waits, T.L.; Salvucci, S.

2007-01-01

This report presents highlights of the results for fourth-and eighth-grade students in Puerto Rico for the 2003 and 2005 National Assessment of Educational Progress (NAEP) in mathematics. The NAEP mathematics assessment was administered to public school students in Puerto Rico for the first time in 2003. Although NAEP had previously administered…

How Do Higher-Education Students Use Their Initial Understanding to Deal with Contextual Logic-Based Problems in Discrete Mathematics?

ERIC Educational Resources Information Center

Lubis, Asrin; Nasution, Andrea Arifsyah

2017-01-01

Mathematical reasoning in logical context has now received much attention in the mathematics curriculum documents of many countries, including Indonesia. In Indonesia, students start formally learning about logic when they pursue to senior-high school. Before, they previously have many experiences to deal with logic, but the earlier assignments do…

Four Seventh Grade Students Who Qualify for Academic Intervention Services in Mathematics Learning Multi-Digit Multiplication with the Montessori Checkerboard

ERIC Educational Resources Information Center

Donabella, Mark A.; Rule, Audrey C.

2008-01-01

This article describes the positive impact of Montessori manipulative materials on four seventh grade students who qualified for academic intervention services because of previous low state test scores in mathematics. This mathematics technique for teaching multi-digit multiplication uses a placemat-sized quilt with different color-coded squares…

"Boys Press All the Buttons and Hope It Will Help": Upper Secondary School Teachers' Gendered Conceptions about Students' Mathematical Reasoning

ERIC Educational Resources Information Center

Sumpter, Lovisa

2016-01-01

Previous results show that Swedish upper secondary school teachers attribute gender to cases describing different types of mathematical reasoning. The purpose of this study was to investigate how these teachers gender stereotype aspects of students' mathematical reasoning by studying the symbols that were attributed to boys and girls,…

Propagation of a Gaussian-beam wave in general anisotropic turbulence

NASA Astrophysics Data System (ADS)

Andrews, L. C.; Phillips, R. L.; Crabbs, R.

2014-10-01

Mathematical models for a Gaussian-beam wave propagating through anisotropic non-Kolmogorov turbulence have been developed in the past by several researchers. In previous publications, the anisotropic spatial power spectrum model was based on the assumption that propagation was in the z direction with circular symmetry maintained in the orthogonal xy-plane throughout the path. In the present analysis, however, the anisotropic spectrum model is no longer based on a single anisotropy parameter—instead, two such parameters are introduced in the orthogonal xyplane so that circular symmetry in this plane is no longer required. In addition, deviations from the 11/3 power-law behavior in the spectrum model are allowed by assuming power-law index variations 3 < α < 4 . In the current study we develop theoretical models for beam spot size, spatial coherence, and scintillation index that are valid in weak irradiance fluctuation regimes as well as in deep turbulence, or strong irradiance fluctuation regimes. These new results are compared with those derived from the more specialized anisotropic spectrum used in previous analyses.

The S factor--a new derived hemodynamic oxygenation parameter--a useful tool for simplified mathematical modeling of global problems of oxygen transport.

PubMed

Farrell, K; Wasser, T

1997-01-01

We describe a new derived hemodynamic oxygenation parameter, the S factor (S). The factor is based on oxygen delivery and oxygen consumption and can range from -3 to 1. It allows simplified mathematical modeling of clinical problems of oxygen transport and can be applied to many clinical situations. A new hemodynamic oxygenation parameter, the S factor (S), is introduced as an aid to mathematical modeling. It is defined as follows: [formula: see text] (DO2 = oxygen delivery, VO2 = oxygen consumption) S can theoretically vary from -3 (DO2 = VO2) to +1 (VO2 = 0). When DO2/VO2 = 4 (ie. OER = 0.25), S = 0. An S < 0 implies utilization of reserve oxygen transport capacity. An S > 0 implies increased oxygen delivery in relation to oxygen consumption (ie. "shunted oxygen delivery"). By algebraic manipulation and substitution of the components of DO2 into Equation 1: DO2 = Q x Ca x 10 DO2 = Q [(Hb)(Sat)(1.36) + PaO2(.0031)] 10 (2) the following equations can be derived: [formula: see text] [formula: see text] Ca - Cv (Ca = arterial content, Cv = venous content) can be determined by substituting components of oxygen consumption: VO2 = Q (Ca - Cv) x 10 (5) into equation 1 and solving for Ca - Cv. [formula: see text] Equation 6 can be simplified to: [formula: see text] A previously defined relationship between mixed venous PO2 (PvO2) and DO2/VO2 (where calculated P50 is 26.6 +/- 1.0) can be used to modify S in a clinically relevant manner. PvO2 = 5.44D O2/VO2 + 18.16 (8) The relationship between S and PvO2 can be defined by substituting Equation 4 into Equation 1 and solving for PvO2 PvO2 = [21.76/(1-S)] + 18.16 (9) As an example, at a PvO2 of 28 torr (anaerobic threshold), S = -1.2. The relationship between PvO2 and S is shown in Figure 1. S, which can also be defined as 1-4(VO2/DO2) or 1-4(OER), is a useful tool for mathematical modeling of global problems of oxygen transport because the previously derived equations with the S value allow the components of oxygen transport to be interrelated in a clinically relevant manner. Additional advantages of using S in mathematical modeling are: 1. Conceptually it 'fits' in that in regards to the sign (+ or -), as a -S implies utilization of reserve oxygen transport capacity and a +S implies wasted or excess oxygen delivery (shunted). 2. These concepts are easily quantified using the S factor. 3. It 'spreads out' the difference between values for parameters (OER or S) integrating components of oxygen transport, ie. in the 'normal state' regarding oxygen transport, OER = 0.25 and S = 0. At the anaerobic threshold (PvO2 = 28 torr), OER = 0.55 and S = -1.2. Thus, the change in OER from 'normal state' to anaerobic threshold is 0.3 (0.55-0.25) and the change in S is 1.2. This represents a four-fold increase. Four examples of mathematical modeling of global problems of oxygen transport using the S factor are described below.

Mathematical Modeling: Challenging the Figured Worlds of Elementary Mathematics

ERIC Educational Resources Information Center

Wickstrom, Megan H.

2017-01-01

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

Mathematics Teachers' Ideas about Mathematical Models: A Diverse Landscape

ERIC Educational Resources Information Center

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

2014-01-01

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

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

ERIC Educational Resources Information Center

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

2013-01-01

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

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

NASA Technical Reports Server (NTRS)

Shitzer, A.

1972-01-01

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

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.

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.

Modeling the Growth of Filamentous Fungi at the Particle Scale in Solid-State Fermentation Systems.

PubMed

Sugai-Guérios, Maura Harumi; Balmant, Wellington; Furigo, Agenor; Krieger, Nadia; Mitchell, David Alexander

2015-01-01

Solid-state fermentation (SSF) with filamentous fungi is a promising technique for the production of a range of biotechnological products and has the potential to play an important role in future biorefineries. The performance of such processes is intimately linked with the mycelial mode of growth of these fungi: Not only is the production of extracellular enzymes related to morphological characteristics, but also the mycelium can affect bed properties and, consequently, the efficiency of heat and mass transfer within the bed. A mathematical model that describes the development of the fungal mycelium in SSF systems at the particle scale would be a useful tool for investigating these phenomena, but, as yet, a sufficiently complete model has not been proposed. This review presents the biological and mass transfer phenomena that should be included in such a model and then evaluates how these phenomena have been modeled previously in the SSF and related literature. We conclude that a discrete lattice-based model that uses differential equations to describe the mass balances of the components within the system would be most appropriate and that mathematical expressions for describing the individual phenomena are available in the literature. It remains for these phenomena to be integrated into a complete model describing the development of fungal mycelia in SSF systems.

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

NASA Astrophysics Data System (ADS)

Afrizal, Irfan Mufti; Dachlan, Jarnawi Afghani

2017-05-01

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

Mathematical modelling in developmental biology.

PubMed

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

2013-06-01

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

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.

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.

3D Thermal and Mechanical Analysis of a Single Event Burnout

NASA Astrophysics Data System (ADS)

Peretti, Gabriela; Demarco, Gustavo; Romero, Eduardo; Tais, Carlos

2015-08-01

This paper presents a study related to thermal and mechanical behavior of power DMOS transistors during a Single Event Burnout (SEB) process. We use a cylindrical heat generation region for emulating the thermal and mechanical phenomena related to the SEB. In this way, it is avoided the complexity of the mathematical treatment of the ion-device interaction. This work considers locating the heat generation region in positions that are more realistic than the ones used in previous work. For performing the study, we formulate and validate a new 3D model for the transistor that maintains the computational cost at reasonable level. The resulting mathematical models are solved by means of the Finite Element Method. The simulations results show that the failure dynamics is dominated by the mechanical stress in the metal layer. Additionally, the time to failure depends on the heat source position, for a given power and dimension of the generation region. The results suggest that 3D modeling should be considered for a detailed study of thermal and mechanical effects induced by SEBs.

Thermal Imaging Applied to Cryocrystallography: Cryocooling and Beam Heating (Part I)

NASA Technical Reports Server (NTRS)

Snell, Edward; Bellamy, Henry; Rosenbaum, Gerd; vanderWoerd, Mark; Kazmierczak, Michael

2006-01-01

Thermal imaging provides a non-invasive method to study both the cryocooling process and the heating due to the X-ray beam interaction with a sample. The method has been used successfully to image cryocooling in a number of experimental situations, i.e. cooling as a function of sample volume and as a function of cryostream orientation. Although there are experimental limitations to the method, it has proved a powerful technique to aid cryocrystallography development. Due to the rapid spatial temperature information provided about the sample it is also a powerful tool in the testing of mathematical models. Recently thermal imaging has been used to measure the temperature distribution on both a model and typical crystal samples illuminated with an X-ray beam produced by an undulator. A brief overview of thermal imaging and previous results will be presented. In addition, a detailed description of the calibration and experimental aspects of the beam heating measurements will be described. This will complement the following talk on the mathematical modeling and analysis of the results.

Mathematical Model of a Telomerase Transcriptional Regulatory Network Developed by Cell-Based Screening: Analysis of Inhibitor Effects and Telomerase Expression Mechanisms

PubMed Central

Bilsland, Alan E.; Stevenson, Katrina; Liu, Yu; Hoare, Stacey; Cairney, Claire J.; Roffey, Jon; Keith, W. Nicol

2014-01-01

Cancer cells depend on transcription of telomerase reverse transcriptase (TERT). Many transcription factors affect TERT, though regulation occurs in context of a broader network. Network effects on telomerase regulation have not been investigated, though deeper understanding of TERT transcription requires a systems view. However, control over individual interactions in complex networks is not easily achievable. Mathematical modelling provides an attractive approach for analysis of complex systems and some models may prove useful in systems pharmacology approaches to drug discovery. In this report, we used transfection screening to test interactions among 14 TERT regulatory transcription factors and their respective promoters in ovarian cancer cells. The results were used to generate a network model of TERT transcription and to implement a dynamic Boolean model whose steady states were analysed. Modelled effects of signal transduction inhibitors successfully predicted TERT repression by Src-family inhibitor SU6656 and lack of repression by ERK inhibitor FR180204, results confirmed by RT-QPCR analysis of endogenous TERT expression in treated cells. Modelled effects of GSK3 inhibitor 6-bromoindirubin-3′-oxime (BIO) predicted unstable TERT repression dependent on noise and expression of JUN, corresponding with observations from a previous study. MYC expression is critical in TERT activation in the model, consistent with its well known function in endogenous TERT regulation. Loss of MYC caused complete TERT suppression in our model, substantially rescued only by co-suppression of AR. Interestingly expression was easily rescued under modelled Ets-factor gain of function, as occurs in TERT promoter mutation. RNAi targeting AR, JUN, MXD1, SP3, or TP53, showed that AR suppression does rescue endogenous TERT expression following MYC knockdown in these cells and SP3 or TP53 siRNA also cause partial recovery. The model therefore successfully predicted several aspects of TERT regulation including previously unknown mechanisms. An extrapolation suggests that a dominant stimulatory system may programme TERT for transcriptional stability. PMID:24550717

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

ERIC Educational Resources Information Center

Gould, Heather; Wasserman, Nicholas H.

2014-01-01

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

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

ERIC Educational Resources Information Center

Jacobs, Gerrie J.; Durandt, Rina

2017-01-01

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

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

PubMed

Gilbert, Scott F

2018-01-31

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

A system-level mathematical model of Basal Ganglia motor-circuit for kinematic planning of arm movements.

PubMed

Salimi-Badr, Armin; Ebadzadeh, Mohammad Mehdi; Darlot, Christian

2018-01-01

In this paper, a novel system-level mathematical model of the Basal Ganglia (BG) for kinematic planning, is proposed. An arm composed of several segments presents a geometric redundancy. Thus, selecting one trajectory among an infinite number of possible ones requires overcoming redundancy, according to some kinds of optimization. Solving this optimization is assumed to be the function of BG in planning. In the proposed model, first, a mathematical solution of kinematic planning is proposed for movements of a redundant arm in a plane, based on minimizing energy consumption. Next, the function of each part in the model is interpreted as a possible role of a nucleus of BG. Since the kinematic variables are considered as vectors, the proposed model is presented based on the vector calculus. This vector model predicts different neuronal populations in BG which is in accordance with some recent experimental studies. According to the proposed model, the function of the direct pathway is to calculate the necessary rotation of each joint, and the function of the indirect pathway is to control each joint rotation considering the movement of the other joints. In the proposed model, the local feedback loop between Subthalamic Nucleus and Globus Pallidus externus is interpreted as a local memory to store the previous amounts of movements of the other joints, which are utilized by the indirect pathway. In this model, activities of dopaminergic neurons would encode, at short-term, the error between the desired and actual positions of the end-effector. The short-term modulating effect of dopamine on Striatum is also modeled as cross product. The model is simulated to generate the commands of a redundant manipulator. The performance of the model is studied for different reaching movements between 8 points in a plane. Finally, some symptoms of Parkinson's disease such as bradykinesia and akinesia are simulated by modifying the model parameters, inspired by the dopamine depletion. Copyright © 2017 Elsevier Ltd. All rights reserved.

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

NASA Technical Reports Server (NTRS)

Wang, Caroline; Purinton, Steve

1989-01-01

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

Design Criteria for Low Profile Flange Calculations

NASA Technical Reports Server (NTRS)

Leimbach, K. R.

1973-01-01

An analytical method and a design procedure to develop flanged separable pipe connectors are discussed. A previously established algorithm is the basis for calculating low profile flanges. The characteristics and advantages of the low profile flange are analyzed. The use of aluminum, titanium, and plastics for flange materials is described. Mathematical models are developed to show the mechanical properties of various flange configurations. A computer program for determining the structural stability of the flanges is described.

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

PubMed

Hoskinson, Anne-Marie

2010-01-01

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

Engineering physics and mathematics division

NASA Astrophysics Data System (ADS)

Sincovec, R. F.

1995-07-01

This report provides a record of the research activities of the Engineering Physics and Mathematics Division for the period 1 Jan. 1993 - 31 Dec. 1994. This report is the final archival record of the EPM Division. On 1 Oct. 1994, ORELA was transferred to Physics Division and on 1 Jan. 1995, the Engineering Physics and Mathematics Division and the Computer Applications Division reorganized to form the Computer Science and Mathematics Division and the Computational Physics and Engineering Division. Earlier reports in this series are identified on the previous pages, along with the progress reports describing ORNL's research in the mathematical sciences prior to 1984 when those activities moved into the Engineering Physics and Mathematics Division.

Large Variations in HIV-1 Viral Load Explained by Shifting-Mosaic Metapopulation Dynamics

PubMed Central

Lythgoe, Katrina A.; Blanquart, François

2016-01-01

The viral population of HIV-1, like many pathogens that cause systemic infection, is structured and differentiated within the body. The dynamics of cellular immune trafficking through the blood and within compartments of the body has also received wide attention. Despite these advances, mathematical models, which are widely used to interpret and predict viral and immune dynamics in infection, typically treat the infected host as a well-mixed homogeneous environment. Here, we present mathematical, analytical, and computational results that demonstrate that consideration of the spatial structure of the viral population within the host radically alters predictions of previous models. We study the dynamics of virus replication and cytotoxic T lymphocytes (CTLs) within a metapopulation of spatially segregated patches, representing T cell areas connected by circulating blood and lymph. The dynamics of the system depend critically on the interaction between CTLs and infected cells at the within-patch level. We show that for a wide range of parameters, the system admits an unexpected outcome called the shifting-mosaic steady state. In this state, the whole body’s viral population is stable over time, but the equilibrium results from an underlying, highly dynamic process of local infection and clearance within T-cell centers. Notably, and in contrast to previous models, this new model can explain the large differences in set-point viral load (SPVL) observed between patients and their distribution, as well as the relatively low proportion of cells infected at any one time, and alters the predicted determinants of viral load variation. PMID:27706164

Think Pair Share Using Realistic Mathematics Education Approach in Geometry Learning

NASA Astrophysics Data System (ADS)

Afthina, H.; Mardiyana; Pramudya, I.

2017-09-01

This research aims to determine the impact of mathematics learning applying Think Pair Share (TPS) using Realistic Mathematics Education (RME) viewed from mathematical-logical intelligence in geometry learning. Method that used in this research is quasi experimental research The result of this research shows that (1) mathematics achievement applying TPS using RME approach gives a better result than those applying direct learning model; (2) students with high mathematical-logical intelligence can reach a better mathematics achievement than those with average and low one, whereas students with average mathematical-logical intelligence can reach a better achievement than those with low one; (3) there is no interaction between learning model and the level of students’ mathematical-logical intelligence in giving a mathematics achievement. The impact of this research is that TPS model using RME approach can be applied in mathematics learning so that students can learn more actively and understand the material more, and mathematics learning become more meaningful. On the other hand, internal factors of students must become a consideration toward the success of students’ mathematical achievement particularly in geometry material.

Preserving Pelicans with Models That Make Sense

ERIC Educational Resources Information Center

Moore, Tamara J.; Doerr, Helen M.; Glancy, Aran W.; Ntow, Forster D.

2015-01-01

Getting students to think deeply about mathematical concepts is not an easy job, which is why we often use problem-solving tasks to engage students in higher-level mathematical thinking. Mathematical modeling, one of the mathematical practices found in the Common Core State Standards for Mathematics (CCSSM), is a type of problem solving that can…

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

ERIC Educational Resources Information Center

Ludwig, Patrice; Tongen, Anthony; Walton, Brian

2018-01-01

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

A high-frequency lung injury mechanism in blunt thoracic impact.

PubMed

Grimal, Quentin; Naïli, Salah; Watzky, Alexandre

2005-06-01

When a mechanical load is applied very rapidly to the thoracic wall, part of the internal damage is suspected to be due to a "high-frequency" injury mechanism, that is, a phenomenon in which waves are involved. This paper addresses a specific high-frequency mechanism for lung injury in which a stress wave is generated through rapid acceleration of the body wall. Displacement-related injuries, which are rather "low-frequency" phenomena, are not considered. The present work was done in the context of assessing behind armor blunt trauma (injury to thoracic organs occurring when a bullet is stopped by a body armor) through mathematical modeling. One aspect of the thorax response to high-speed blunt impact and an associated injury mechanism are investigated based on an idealized model of thorax and a set of computations presented in previous papers. The injury mechanism considered elucidates a possible mathematical relationship between the acceleration at the surface of the thoracic wall and the occurrence of lung injury.

Tracing Growth of Teachers' Classroom Interactions with Representations of Functions in the Connected Classroom

NASA Astrophysics Data System (ADS)

Morton, Brian Lee

The purpose of this study is to create an empirically based theoretic model of change of the use and treatment of representations of functions with the use of Connected Classroom Technology (CCT) using data previously collected for the Classroom Connectivity in Promoting Mathematics and Science Achievement (CCMS) project. Qualitative analysis of videotapes of three algebra teachers' instruction focused on different categories thought to influence teaching representations with technology: representations, discourse, technology, and decisions. Models for rating teachers low, medium, or high for each of these categories were created using a priori codes and grounded methodology. A cross case analysis was conducted after the completion of the case studies by comparing and contrasting the three cases. Data revealed that teachers' decisions shifted to incorporate the difference in student ideas/representations made visible by the CCT into their instruction and ultimately altered their orientation to mathematics teaching. The shift in orientation seemed to lead to the teachers' growth with regards to representations, discourse, and technology.

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.

Artificial intelligence: a new approach for prescription and monitoring of hemodialysis therapy.

PubMed

Akl, A I; Sobh, M A; Enab, Y M; Tattersall, J

2001-12-01

The effect of dialysis on patients is conventionally predicted using a formal mathematical model. This approach requires many assumptions of the processes involved, and validation of these may be difficult. The validity of dialysis urea modeling using a formal mathematical model has been challenged. Artificial intelligence using neural networks (NNs) has been used to solve complex problems without needing a mathematical model or an understanding of the mechanisms involved. In this study, we applied an NN model to study and predict concentrations of urea during a hemodialysis session. We measured blood concentrations of urea, patient weight, and total urea removal by direct dialysate quantification (DDQ) at 30-minute intervals during the session (in 15 chronic hemodialysis patients). The NN model was trained to recognize the evolution of measured urea concentrations and was subsequently able to predict hemodialysis session time needed to reach a target solute removal index (SRI) in patients not previously studied by the NN model (in another 15 chronic hemodialysis patients). Comparing results of the NN model with the DDQ model, the prediction error was 10.9%, with a not significant difference between predicted total urea nitrogen (UN) removal and measured UN removal by DDQ. NN model predictions of time showed a not significant difference with actual intervals needed to reach the same SRI level at the same patient conditions, except for the prediction of SRI at the first 30-minute interval, which showed a significant difference (P = 0.001). This indicates the sensitivity of the NN model to what is called patient clearance time; the prediction error was 8.3%. From our results, we conclude that artificial intelligence applications in urea kinetics can give an idea of intradialysis profiling according to individual clinical needs. In theory, this approach can be extended easily to other solutes, making the NN model a step forward to achieving artificial-intelligent dialysis control.

Preface.

PubMed

Ditlevsen, Susanne; Lansky, Petr

2016-06-01

This Special Issue of Mathematical Biosciences and Engineering contains 11 selected papers presented at the Neural Coding 2014 workshop. The workshop was held in the royal city of Versailles in France, October 6-10, 2014. This was the 11th of a series of international workshops on this subject, the first held in Prague (1995), then Versailles (1997), Osaka (1999), Plymouth (2001), Aulla (2003), Marburg (2005), Montevideo (2007), Tainan (2009), Limassol (2010), and again in Prague (2012). Also selected papers from Prague were published as a special issue of Mathematical Biosciences and Engineering and in this way a tradition was started. Similarly to the previous workshops, this was a single track multidisciplinary event bringing together experimental and computational neuroscientists. The Neural Coding Workshops are traditionally biennial symposia. They are relatively small in size, interdisciplinary with major emphasis on the search for common principles in neural coding. The workshop was conceived to bring together scientists from different disciplines for an in-depth discussion of mathematical model-building and computational strategies. Further information on the meeting can be found at the NC2014 website at https://colloque6.inra.fr/neural_coding_2014. The meeting was supported by French National Institute for Agricultural Research, the world's leading institution in this field. This Special Issue of Mathematical Biosciences and Engineering contains 11 selected papers presented at the Neural Coding 2014 workshop. The workshop was held in the royal city of Versailles in France, October 6-10, 2014. This was the 11th of a series of international workshops on this subject, the first held in Prague (1995), then Versailles (1997), Osaka (1999), Plymouth (2001), Aulla (2003), Marburg (2005), Montevideo (2007), Tainan (2009), Limassol (2010), and again in Prague (2012). Also selected papers from Prague were published as a special issue of Mathematical Biosciences and Engineering and in this way a tradition was started. Similarly to the previous workshops, this was a single track multidisciplinary event bringing together experimental and computational neuroscientists. The Neural Coding Workshops are traditionally biennial symposia. They are relatively small in size, interdisciplinary with major emphasis on the search for common principles in neural coding. The workshop was conceived to bring together scientists from different disciplines for an in-depth discussion of mathematical model-building and computational strategies. Further information on the meeting can be found at the NC2014 website at https://colloque6.inra.fr/neural_coding_2014. The meeting was supported by French National Institute for Agricultural Research, the world's leading institution in this field. Understanding how the brain processes information is one of the most challenging subjects in neuroscience. The papers presented in this special issue show a small corner of the huge diversity of this field, and illustrate how scientists with different backgrounds approach this vast subject. The diversity of disciplines engaged in these investigations is remarkable: biologists, mathematicians, physicists, psychologists, computer scientists, and statisticians, all have original tools and ideas by which to try to elucidate the underlying mechanisms. In this issue, emphasis is put on mathematical modeling of single neurons. A variety of problems in computational neuroscience accompanied with a rich diversity of mathematical tools and approaches are presented. We hope it will inspire and challenge the readers in their own research. We would like to thank the authors for their valuable contributions and the referees for their priceless effort of reviewing the manuscripts. Finally, we would like to thank Yang Kuang for supporting us and making this publication possible.

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.

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)

Effect of viscosity on tear drainage and ocular residence time.

PubMed

Zhu, Heng; Chauhan, Anuj

2008-08-01

An increase in residence time of dry eye medications including artificial tears will likely enhance therapeutic benefits. The drainage rates and the residence time of eye drops depend on the viscosity of the instilled fluids. However, a quantitative understanding of the dependence of drainage rates and the residence time on viscosity is lacking. The current study aims to develop a mathematical model for the drainage of Newtonian fluids and also for power-law non-Newtonian fluids of different viscosities. This study is an extension of our previous study on the mathematical model of tear drainage. The tear drainage model is modified to describe the drainage of Newtonian fluids with viscosities higher than the tear viscosity and power-law non-Newtonian fluids with rheological parameters obtained from fitting experimental data in literature. The drainage rate through canaliculi was derived from the modified drainage model and was incorporated into a tear mass balance to calculate the transients of total solute quantity in ocular fluids and the bioavailability of instilled drugs. For Newtonian fluids, increasing the viscosity does not affect the drainage rate unless the viscosity exceeds a critical value of about 4.4 cp. The viscosity has a maximum impact on drainage rate around a value of about 100 cp. The trends are similar for shear thinning power law fluids. The transients of total solute quantity, and the residence time agrees at least qualitatively with experimental studies. A mathematical model has been developed for the drainage of Newtonian fluids and power-law fluids through canaliculi. The model can quantitatively explain different experimental observations on the effect of viscosity on the residence of instilled fluids on the ocular surface. The current study is helpful for understanding the mechanism of fluid drainage from the ocular surface and for improving the design of dry eye treatments.

Modelling and simulation of a pervaporation process using tubular module for production of anhydrous ethanol

NASA Astrophysics Data System (ADS)

Hieu, Nguyen Huu

2017-09-01

Pervaporation is a potential process for the final step of ethanol biofuel production. In this study, a mathematical model was developed based on the resistance-in-series model and a simulation was carried out using the specialized simulation software COMSOL Multiphysics to describe a tubular type pervaporation module with membranes for the dehydration of ethanol solution. The permeance of membranes, operating conditions, and feed conditions in the simulation were referred from experimental data reported previously in literature. Accordingly, the simulated temperature and density profiles of pure water and ethanol-water mixture were validated based on existing published data.

Mixed model of dietary fat effect on postprandial glucose-insulin metabolism from carbohydrates in type 1 diabetes.

PubMed

Yamamoto Noguchi, Claudia Cecilia; Kunikane, Noriaki; Hashimoto, Shogo; Furutani, Eiko

2015-08-01

In this study we introduce an extension of a previously developed model of glucose-insulin metabolism in type 1 diabetes (T1D) from carbohydrates that includes the effect of dietary fat on postprandial glycemia. We include two compartments that represent plasma triglyceride and nonesterified fatty acid (NEFA) concentration, in addition to a mathematical representation of delayed gastric emptying and insulin resistance, which are the most well-known effects of dietary fat metabolism. Simulation results show that postprandial glucose as well as lipid levels in our model approximates clinical data from T1D patients.

[Building mathematics in imagination].

PubMed

Patras, Frédéric

2015-01-01

The extraordinary quantitative achievements of contemporary science often hide their qualitative dimension. In mathematics, the understanding of fundamental theoretical phenomena we have got today goes much beyond that achieved in previous periods. This also holds when it comes to the theorisation of mathematical practice.Philosophically, these changes remain largely to be properly analyzed. The present article will address this issue from the point of view of Bachelard's epistemology.

A Descriptive, Survey Research Study of the Student Characteristics Influencing the Four Theoretical Sources of Mathematical Self-Efficacy of College Freshmen

ERIC Educational Resources Information Center

Locklear, Tonja Motley

2012-01-01

The Sources of Middle School Mathematics Self-Efficacy Scale (Usher & Pajares, 2009) was adapted for use in this study investigating the impact that gender, race, sexual orientation, hometown location (rural, suburban, or urban), high school GPA, college GPA and letter grade of a mathematics course in the previous semester had on the four…

Software Quality Metrics Enhancements. Volume 1

DTIC Science & Technology

1980-04-01

the mathematical relationships which relate metrics to ratings of the various quality factors) for factors which were not validated previously were...function, provides a mathematical relationship between the metrics and the quality factors. (3) Validation of these normalization functions was performed by...samples, further research is needed before a high degree of confidence can be placed on the mathematical relationships established to date l (3.3.3) 6

Mathematics Through Science, Part II: Graphing, Equations and Linear Functions. Student Text. Revised Edition.

ERIC Educational Resources Information Center

Bolduc, Elroy J., Jr.; And Others

The purpose of this text is to teach learning and understanding of mathematics at grades seven through nine through the use of science experiments. Previous knowledge of science on the part of students or teachers is not necessary. The text is designed to be usable with any mathematics textbook in common use. The material can be covered in four…

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

USGS Publications Warehouse

Kuniansky, Eve L.

2014-01-01

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

A revised model of fluid transport optimization in Physarum polycephalum.

PubMed

Bonifaci, Vincenzo

2017-02-01

Optimization of fluid transport in the slime mold Physarum polycephalum has been the subject of several modeling efforts in recent literature. Existing models assume that the tube adaptation mechanism in P. polycephalum's tubular network is controlled by the sheer amount of fluid flow through the tubes. We put forward the hypothesis that the controlling variable may instead be the flow's pressure gradient along the tube. We carry out the stability analysis of such a revised mathematical model for a parallel-edge network, proving that the revised model supports the global flow-optimizing behavior of the slime mold for a substantially wider class of response functions compared to previous models. Simulations also suggest that the same conclusion may be valid for arbitrary network topologies.

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

ERIC Educational Resources Information Center

Al Duwairi, Ahmed

2013-01-01

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

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

ERIC Educational Resources Information Center

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

2015-01-01

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

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…

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.

Sampling and sensitivity analyses tools (SaSAT) for computational modelling

PubMed Central

Hoare, Alexander; Regan, David G; Wilson, David P

2008-01-01

SaSAT (Sampling and Sensitivity Analysis Tools) is a user-friendly software package for applying uncertainty and sensitivity analyses to mathematical and computational models of arbitrary complexity and context. The toolbox is built in Matlab®, a numerical mathematical software package, and utilises algorithms contained in the Matlab® Statistics Toolbox. However, Matlab® is not required to use SaSAT as the software package is provided as an executable file with all the necessary supplementary files. The SaSAT package is also designed to work seamlessly with Microsoft Excel but no functionality is forfeited if that software is not available. A comprehensive suite of tools is provided to enable the following tasks to be easily performed: efficient and equitable sampling of parameter space by various methodologies; calculation of correlation coefficients; regression analysis; factor prioritisation; and graphical output of results, including response surfaces, tornado plots, and scatterplots. Use of SaSAT is exemplified by application to a simple epidemic model. To our knowledge, a number of the methods available in SaSAT for performing sensitivity analyses have not previously been used in epidemiological modelling and their usefulness in this context is demonstrated. PMID:18304361

A mathematical description of the inclusive fitness theory.

PubMed

Wakano, Joe Yuichiro; Ohtsuki, Hisashi; Kobayashi, Yutaka

2013-03-01

Recent developments in the inclusive fitness theory have revealed that the direction of evolution can be analytically predicted in a wider class of models than previously thought, such as those models dealing with network structure. This paper aims to provide a mathematical description of the inclusive fitness theory. Specifically, we provide a general framework based on a Markov chain that can implement basic models of inclusive fitness. Our framework is based on the probability distribution of "offspring-to-parent map", from which the key concepts of the theory, such as fitness function, relatedness and inclusive fitness, are derived in a straightforward manner. We prove theorems showing that inclusive fitness always provides a correct prediction on which of two competing genes more frequently appears in the long run in the Markov chain. As an application of the theorems, we prove a general formula of the optimal dispersal rate in the Wright's island model with recurrent mutations. We also show the existence of the critical mutation rate, which does not depend on the number of islands and below which a positive dispersal rate evolves. Our framework can also be applied to lattice or network structured populations. Copyright © 2012 Elsevier Inc. All rights reserved.

A mathematical model of the volume, pH, and ion content regulation in reticulocytes. Application to the pathophysiology of sickle cell dehydration.

PubMed Central

Lew, V L; Freeman, C J; Ortiz, O E; Bookchin, R M

1991-01-01

We developed a mathematical model of the reticulocyte, seeking to explain how a cell with similar volume but much higher ionic traffic than the mature red cell (RBC) regulates its volume, pH, and ion content in physiological and abnormal conditions. Analysis of the fluxbalance required by reticulocytes to conserve volume and composition predicted the existence of previously unsuspected Na(+)-dependent Cl- entry mechanisms. Unlike mature RBCs, reticulocytes did not tend to return to their original state after brief perturbations. The model predicted hysteresis and drift in cell pH, volume, and ion contents after transient alterations in membrane permeability or medium composition; irreversible cell dehydration could thus occur by brief K+ permeabilization, transient medium acidification, or the replacement of external Na+ with an impermeant cation. Both the hysteresis and drift after perturbations were shown to depend on the pHi dependence of the K:Cl cotransport, a major reticulocyte transporter. This behavior suggested a novel mechanism for the generation of irreversibly sickled cells directly from reticulocytes, rather than in a stepwise, progressive manner from discocytes. Experimental tests of the model's predictions and the hypothesis are described in the following paper. PMID:1985088

Energy supply and demand modeling. February 1985-March 1988 (A Bibliography from the NTIS data base). Report for February 1985-March 1988

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

Not Available

1990-06-01

This bibliography contains citations concerning the use of mathematical models in trend analysis and forecasting of energy supply and demand factors. Models are presented for the industrial, transportation, and residential sectors. Aspects of long term energy strategies and markets are discussed at the global, national, state, and regional levels. Energy demand and pricing, and econometrics of energy, are explored for electric utilities and natural resources, such as coal, oil, and natural gas. Energy resources are modeled both for fuel usage and for reserves. (This updated bibliography contains 201 citations, none of which are new entries to the previous edition.)

Energy supply and demand modeling. February 1985-March 1988 (Citations from the NTIS data base). Report for February 1985-March 1988

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

Not Available

1988-04-01

This bibliography contains citations concerning the utilization of mathematical models in trend analysis and forecasting of energy supply and demand factors. Models are presented for the industrial, transportation, and residential sectors. Aspects of long-term energy strategies and markets are discussed at the global, national, state, and regional levels. Energy demand and pricing, and econometrics of energy, are explored for electric utilities and natural resources, such as coal, oil, and natural gas. Energy resources are modeled both for fuel usage and for reserves. (This updated bibliography contains 201 citations, 129 of which are new entries to the previous edition.)

Energy supply and demand modeling. April 1988-June 1990 (A Bibliography from the NTIS data base). Report for April 1988-June 1990

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

Not Available

1990-06-01

This bibliography contains citations concerning the use of mathematical models in trend analysis and forecasting of energy supply and demand factors. Models are presented for the industrial, transportation, and residential sectors. Aspects of long term energy strategies and markets are discussed at the global, national, state, and regional levels. Energy demand and pricing, and econometrics of energy, are explored for electric utilities and natural resources, such as coal, oil, and natural gas. Energy resources are modeled both for fuel usage and for reserves. (This updated bibliography contains 200 citations, all of which are new entries to the previous edition.)

Ephaptic conduction in a cardiac strand model with 3D electrodiffusion

PubMed Central

Mori, Yoichiro; Fishman, Glenn I.; Peskin, Charles S.

2008-01-01

We study cardiac action potential propagation under severe reduction in gap junction conductance. We use a mathematical model of cellular electrical activity that takes into account both three-dimensional geometry and ionic concentration effects. Certain anatomical and biophysical parameters are varied to see their impact on cardiac action potential conduction velocity. This study uncovers quantitative features of ephaptic propagation that differ from previous studies based on one-dimensional models. We also identify a mode of cardiac action potential propagation in which the ephaptic and gap-junction-mediated mechanisms alternate. Our study demonstrates the usefulness of this modeling approach for electrophysiological systems especially when detailed membrane geometry plays an important role. PMID:18434544

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

ERIC Educational Resources Information Center

Campbell, William James

2017-01-01

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

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…

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…

"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…

An Analysis of Pre-Service Mathematics Teachers' Performance in Modelling Tasks in Terms of Spatial Visualisation Ability

ERIC Educational Resources Information Center

Tasova, Halil Ibrahim; Delice, Ali

2012-01-01

Mathematical modelling involves mathematical constructions chosen to represent some real world situations and the relationships among them; it is the process of expressing a real world situation mathematically. Visualisation can play a significant role in the development of thinking or understanding mathematical concepts, and also makes abstract…

Non—Linear Flood Assessment with Neural Network

NASA Astrophysics Data System (ADS)

Murariu, Gabriel; Puscasu, Gheorghe; Gogoncea, Vlad

2010-01-01

In our days, theoretical investigations are used in obtaining the mathematical model for the studied systems or processes. In general, the dynamics of the system are deeply nonlinear, complex or unknown. Generally speaking, such complex structure is a set of interconnected components. The common approach is therefore to start from measurements of the behavior of the system and the external influences (inputs) and try to determine a mathematical relation between them without going into the details of what is actually happening inside the system. Such strategy had known a great success during the time and it was applied for a large class of multifaceted processes. Accepting this approach, there could be investigated the climatic phenomena. In this paper is presented, in a comparative way, a non-linear water flood assessment made in a very sensitive area of the Lower Danube zone where, in the past years, a series of climatic problems have been happening. In these conditions, climatic risk factor management is a necessity. In a regular way, there could be considered and designed nonlinear models for the climatic factors' analysis by using a huge historical evidence data archive. In a previous paper we reached a notable intermediary result basing on a mathematical model constructed on internal recurrent neural network structure. Such approach had been presented considering the internal state estimation when no measurements coming from the sensors are available for system states. A modified backpropagation algorithm had been introduced in order to train the internal recurrent neural networks for nonlinear system identification. In this paper is exposed a comparative study between a numerical advances based on fluid dynamics' equations and our previous approach, based on internal recurrent neural networks (IRNN). The numerical approaching was made in order to succeed in building a physics model of a water flow evaluation and further, to achieve including the rainfall contributions. This condition is necessary for prediction and it is the first step toward a DSS—Decision Support System in the area. The relationship between the simulated results and the registered data allows considering our particular method to be useful for considered water flood assessment.

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

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.

Control of Crazyflie nano quadcopter using Simulink

NASA Astrophysics Data System (ADS)

Gopabhat Madhusudhan, Meghana

This thesis focuses on developing a mathematical model in Simulink to Crazyflie, an open source platform. Attitude, altitude and position controllers of a Crazyflie are designed in the mathematical model. The mathematical model is developed based on the quadcopter system dynamics using a non-linear approach. The parameters of translational and rotational dynamics of the quadcopter system are linearized and tuned individually. The tuned attitude and altitude controllers from the mathematical model are implemented on real time Crazyflie Simulink model to achieve autonomous and controlled flight.

Computational modeling of the cell-autonomous mammalian circadian oscillator.

PubMed

Podkolodnaya, Olga A; Tverdokhleb, Natalya N; Podkolodnyy, Nikolay L

2017-02-24

This review summarizes various mathematical models of cell-autonomous mammalian circadian clock. We present the basics necessary for understanding of the cell-autonomous mammalian circadian oscillator, modern experimental data essential for its reconstruction and some special problems related to the validation of mathematical circadian oscillator models. This work compares existing mathematical models of circadian oscillator and the results of the computational studies of the oscillating systems. Finally, we discuss applications of the mathematical models of mammalian circadian oscillator for solving specific problems in circadian rhythm biology.

Students’ errors in solving combinatorics problems observed from the characteristics of RME modeling

NASA Astrophysics Data System (ADS)

Meika, I.; Suryadi, D.; Darhim

2018-01-01

This article was written based on the learning evaluation results of students’ errors in solving combinatorics problems observed from the characteristics of Realistic Mathematics Education (RME); that is modeling. Descriptive method was employed by involving 55 students from two international-based pilot state senior high schools in Banten. The findings of the study suggested that the students still committed errors in simplifying the problem as much 46%; errors in making mathematical model (horizontal mathematization) as much 60%; errors in finishing mathematical model (vertical mathematization) as much 65%; and errors in interpretation as well as validation as much 66%.

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…

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.

What’s about Peer Tutoring Learning Model?

NASA Astrophysics Data System (ADS)

Muthma'innah, M.

2017-09-01

Mathematics learning outcomes in Indonesia in general is still far from satisfactory. One effort that could be expected to solve the problem is to apply the model of peer tutoring learning in mathematics. This study aims to determine whether the results of students’ mathematics learning can be enhanced through peer tutoring learning models. This type of research is the study of literature, so that the method used is to summarize and analyze the results of relevant research that has been done. Peer tutoring learning model is a model of learning in which students learn in small groups that are grouped with different ability levels, all group members to work together and help each other to understand the material. By paying attention to the syntax of the learning, then learning will be invaluable peer tutoring for students who served as teachers and students are taught. In mathematics, the implementation of this learning model can make students understand each other mathematical concepts and help students in solving mathematical problems that are poorly understood, due to the interaction between students in learning. Then it will be able to improve learning outcomes in mathematics. The impact, it can be applied in mathematics learning.

Structural analysis of eyespots: dynamics of morphogenic signals that govern elemental positions in butterfly wings

PubMed Central

2012-01-01

Background To explain eyespot colour-pattern determination in butterfly wings, the induction model has been discussed based on colour-pattern analyses of various butterfly eyespots. However, a detailed structural analysis of eyespots that can serve as a foundation for future studies is still lacking. In this study, fundamental structural rules related to butterfly eyespots are proposed, and the induction model is elaborated in terms of the possible dynamics of morphogenic signals involved in the development of eyespots and parafocal elements (PFEs) based on colour-pattern analysis of the nymphalid butterfly Junonia almana. Results In a well-developed eyespot, the inner black core ring is much wider than the outer black ring; this is termed the inside-wide rule. It appears that signals are wider near the focus of the eyespot and become narrower as they expand. Although fundamental signal dynamics are likely to be based on a reaction-diffusion mechanism, they were described well mathematically as a type of simple uniformly decelerated motion in which signals associated with the outer and inner black rings of eyespots and PFEs are released at different time points, durations, intervals, and initial velocities into a two-dimensional field of fundamentally uniform or graded resistance; this produces eyespots and PFEs that are diverse in size and structure. The inside-wide rule, eyespot distortion, structural differences between small and large eyespots, and structural changes in eyespots and PFEs in response to physiological treatments were explained well using mathematical simulations. Natural colour patterns and previous experimental findings that are not easily explained by the conventional gradient model were also explained reasonably well by the formal mathematical simulations performed in this study. Conclusions In a mode free from speculative molecular interactions, the present study clarifies fundamental structural rules related to butterfly eyespots, delineates a theoretical basis for the induction model, and proposes a mathematically simple mode of long-range signalling that may reflect developmental mechanisms associated with butterfly eyespots. PMID:22409965

Structural analysis of eyespots: dynamics of morphogenic signals that govern elemental positions in butterfly wings.

PubMed

Otaki, Joji M

2012-03-13

To explain eyespot colour-pattern determination in butterfly wings, the induction model has been discussed based on colour-pattern analyses of various butterfly eyespots. However, a detailed structural analysis of eyespots that can serve as a foundation for future studies is still lacking. In this study, fundamental structural rules related to butterfly eyespots are proposed, and the induction model is elaborated in terms of the possible dynamics of morphogenic signals involved in the development of eyespots and parafocal elements (PFEs) based on colour-pattern analysis of the nymphalid butterfly Junonia almana. In a well-developed eyespot, the inner black core ring is much wider than the outer black ring; this is termed the inside-wide rule. It appears that signals are wider near the focus of the eyespot and become narrower as they expand. Although fundamental signal dynamics are likely to be based on a reaction-diffusion mechanism, they were described well mathematically as a type of simple uniformly decelerated motion in which signals associated with the outer and inner black rings of eyespots and PFEs are released at different time points, durations, intervals, and initial velocities into a two-dimensional field of fundamentally uniform or graded resistance; this produces eyespots and PFEs that are diverse in size and structure. The inside-wide rule, eyespot distortion, structural differences between small and large eyespots, and structural changes in eyespots and PFEs in response to physiological treatments were explained well using mathematical simulations. Natural colour patterns and previous experimental findings that are not easily explained by the conventional gradient model were also explained reasonably well by the formal mathematical simulations performed in this study. In a mode free from speculative molecular interactions, the present study clarifies fundamental structural rules related to butterfly eyespots, delineates a theoretical basis for the induction model, and proposes a mathematically simple mode of long-range signalling that may reflect developmental mechanisms associated with butterfly eyespots.

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.

Pulsatile flow in ventricular catheters for hydrocephalus

NASA Astrophysics Data System (ADS)

Giménez, Á.; Galarza, M.; Thomale, U.; Schuhmann, M. U.; Valero, J.; Amigó, J. M.

2017-05-01

The obstruction of ventricular catheters (VCs) is a major problem in the standard treatment of hydrocephalus, the flow pattern of the cerebrospinal fluid (CSF) being one important factor thereof. As a first approach to this problem, some of the authors studied previously the CSF flow through VCs under time-independent boundary conditions by means of computational fluid dynamics in three-dimensional models. This allowed us to derive a few basic principles which led to designs with improved flow patterns regarding the obstruction problem. However, the flow of the CSF has actually a pulsatile nature because of the heart beating and blood flow. To address this fact, here we extend our previous computational study to models with oscillatory boundary conditions. The new results will be compared with the results for constant flows and discussed. It turns out that the corrections due to the pulsatility of the CSF are quantitatively small, which reinforces our previous findings and conclusions. This article is part of the themed issue `Mathematical methods in medicine: neuroscience, cardiology and pathology'.

Student perceptions of writing projects in a university differential-equations course

NASA Astrophysics Data System (ADS)

Latulippe, Christine; Latulippe, Joe

2014-01-01

This qualitative study surveyed 102 differential-equations students in order to investigate how students participating in writing projects in university-level mathematics courses perceive the benefits of writing in the mathematics classroom. Based on previous literature on writing in mathematics, students were asked specifically about the benefits of writing projects as a means to explore practical uses of mathematics, deepen content knowledge, and strengthen communication. Student responses indicated an awareness of these benefits, supporting justifications commonly cited by instructors assigning writing projects. Open-ended survey responses highlighted additional themes which students associated with writing in mathematics, including using software programs and technology, working in groups, and stimulating interest in mathematics. This study provides student feedback to support the use of writing projects in mathematics, as well as student input, which can be utilized to strengthen the impact of writing projects in mathematics.

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.

A Cognitive Analysis of Students’ Mathematical Problem Solving Ability on Geometry

NASA Astrophysics Data System (ADS)

Rusyda, N. A.; Kusnandi, K.; Suhendra, S.

2017-09-01

The purpose of this research is to analyze of mathematical problem solving ability of students in one of secondary school on geometry. This research was conducted by using quantitative approach with descriptive method. Population in this research was all students of that school and the sample was twenty five students that was chosen by purposive sampling technique. Data of mathematical problem solving were collected through essay test. The results showed the percentage of achievement of mathematical problem solving indicators of students were: 1) solve closed mathematical problems with context in math was 50%; 2) solve the closed mathematical problems with the context beyond mathematics was 24%; 3) solving open mathematical problems with contexts in mathematics was 35%; And 4) solving open mathematical problems with contexts outside mathematics was 44%. Based on the percentage, it can be concluded that the level of achievement of mathematical problem solving ability in geometry still low. This is because students are not used to solving problems that measure mathematical problem solving ability, weaknesses remember previous knowledge, and lack of problem solving framework. So the students’ ability of mathematical problems solving need to be improved with implement appropriate learning strategy.

The Effects of Mathematical Modeling on Creative Production Ability and Self-Directed Learning Attitude

ERIC Educational Resources Information Center

Kim, Sun Hee; Kim, Soojin

2010-01-01

What should we do to educate the mathematically gifted and how should we do it? In this research, to satisfy diverse mathematical and cognitive demands of the gifted who have excellent learning ability and task tenacity in mathematics, we sought to apply mathematical modeling. One of the objectives of the gifted education in Korea is cultivating…

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…

The Beneficial Role of Random Strategies in Social and Financial Systems

NASA Astrophysics Data System (ADS)

Biondo, Alessio Emanuele; Pluchino, Alessandro; Rapisarda, Andrea

2013-05-01

In this paper we focus on the beneficial role of random strategies in social sciences by means of simple mathematical and computational models. We briefly review recent results obtained by two of us in previous contributions for the case of the Peter principle and the efficiency of a Parliament. Then, we develop a new application of random strategies to the case of financial trading and discuss in detail our findings about forecasts of markets dynamics.

Representations of the Extended Poincare Superalgebras in Four Dimensions

NASA Astrophysics Data System (ADS)

Griffis, John D.

Eugene Wigner used the Poincare group to induce representations from the fundamental internal space-time symmetries of (special) relativistic quantum particles. Wigner's students spent considerable amount of time translating passages of this paper into more detailed and accessible papers and books. In 1975, R. Haag et al. investigated the possible extensions of the symmetries of relativistic quantum particles. They showed that the only consistent (super)symmetric extensions to the standard model of physics are obtained by using super charges to generate the odd part of a Lie superalgebra whose even part is generated by the Poincare group; this theory has become known as supersymmetry. In this paper, R. Haag et al. used a notation called supermultiplets to give the dimension of a representation and its multiplicity; this notation is described mathematically in chapter 5 of this thesis. By 1980 S. Ferrara et al. began classifying the representations of these algebras for dimensions greater than four, and in 1986 Strathdee published considerable work listing some representations for the Poincare superalgebra in any finite dimension. This work has been continued to date. We found the work of S. Ferrara et al. to be essential to our understanding extended supersymmetries. However, this paper was written using imprecise language meant for physicists, so it was far from trivial to understand the mathematical interpretation of this work. In this thesis, we provide a "translation" of the previous results (along with some other literature on the Extended Poincare Superalgebras) into a rigorous mathematical setting, which makes the subject more accessible to a larger audience. Having a mathematical model allows us to give explicit results and detailed proofs. Further, this model allows us to see beyond just the physical interpretation and it allows investigation by a purely mathematically adept audience. Our work was motivated by a paper written in 2012 by M. Chaichian et al, which classified all of the unitary, irreducible representations of the extended Poincare superalgebra in three dimensions. We consider only the four dimensional case, which is of interest to physicists working on quantum supergravity models without cosmological constant, and we provide explicit branching rules for the invariant subgroups corresponding to the most physically relevant symmetries of the irreducible representations of the Extended Poincare Superalgebra in four dimensions. However, it is possible to further generalize this work into any finite dimension. Such work would classify all possible finitely extended supersymmetric models.

Nonlinear mathematical modeling and sensitivity analysis of hydraulic drive unit

NASA Astrophysics Data System (ADS)

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

2015-09-01

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

Reconstruction of extended Petri nets from time series data and its application to signal transduction and to gene regulatory networks

PubMed Central

2011-01-01

Background Network inference methods reconstruct mathematical models of molecular or genetic networks directly from experimental data sets. We have previously reported a mathematical method which is exclusively data-driven, does not involve any heuristic decisions within the reconstruction process, and deliveres all possible alternative minimal networks in terms of simple place/transition Petri nets that are consistent with a given discrete time series data set. Results We fundamentally extended the previously published algorithm to consider catalysis and inhibition of the reactions that occur in the underlying network. The results of the reconstruction algorithm are encoded in the form of an extended Petri net involving control arcs. This allows the consideration of processes involving mass flow and/or regulatory interactions. As a non-trivial test case, the phosphate regulatory network of enterobacteria was reconstructed using in silico-generated time-series data sets on wild-type and in silico mutants. Conclusions The new exact algorithm reconstructs extended Petri nets from time series data sets by finding all alternative minimal networks that are consistent with the data. It suggested alternative molecular mechanisms for certain reactions in the network. The algorithm is useful to combine data from wild-type and mutant cells and may potentially integrate physiological, biochemical, pharmacological, and genetic data in the form of a single model. PMID:21762503

Maximizing the nurses' preferences in nurse scheduling problem: mathematical modeling and a meta-heuristic algorithm

NASA Astrophysics Data System (ADS)

Jafari, Hamed; Salmasi, Nasser

2015-09-01

The nurse scheduling problem (NSP) has received a great amount of attention in recent years. In the NSP, the goal is to assign shifts to the nurses in order to satisfy the hospital's demand during the planning horizon by considering different objective functions. In this research, we focus on maximizing the nurses' preferences for working shifts and weekends off by considering several important factors such as hospital's policies, labor laws, governmental regulations, and the status of nurses at the end of the previous planning horizon in one of the largest hospitals in Iran i.e., Milad Hospital. Due to the shortage of available nurses, at first, the minimum total number of required nurses is determined. Then, a mathematical programming model is proposed to solve the problem optimally. Since the proposed research problem is NP-hard, a meta-heuristic algorithm based on simulated annealing (SA) is applied to heuristically solve the problem in a reasonable time. An initial feasible solution generator and several novel neighborhood structures are applied to enhance performance of the SA algorithm. Inspired from our observations in Milad hospital, random test problems are generated to evaluate the performance of the SA algorithm. The results of computational experiments indicate that the applied SA algorithm provides solutions with average percentage gap of 5.49 % compared to the upper bounds obtained from the mathematical model. Moreover, the applied SA algorithm provides significantly better solutions in a reasonable time than the schedules provided by the head nurses.

Chronic Stereotype Threat Is Associated With Mathematical Achievement on Representative Sample of Secondary Schoolgirls: The Role of Gender Identification, Working Memory, and Intellectual Helplessness

PubMed Central

Bedyńska, Sylwia; Krejtz, Izabela; Sedek, Grzegorz

2018-01-01

Stereotype threat affects performance in many different groups across many different domains. Despite a large body of experimental research on situational stereotype threat, little attention has been paid to the consequences of repeated experience of stereotype threat. Using structural equation modeling on data from a representative sample of girls from secondary schools, the current research examined the relations of chronic stereotype threat with mathematical achievement, and effectiveness of working memory functions. Moving beyond past theory, this study examined a new mechanism by which chronic stereotype threat decreases school achievement – namely intellectual helplessness. We assumed that repeated experience of stereotype threat works as intellectual helplessness training. After the phase of cognitive mobilization, cognitive exhaustion appears, because the individual has no gain from intense cognitive effort. Corroborating previous research on acute stereotype threat, we demonstrated that chronic stereotype threat is negatively associated with mathematical achievement. Additionally, it was also associated with lower effectiveness of working memory functions, which seems to show depletion of working memory as an effect of chronic stereotype threat. The results also demonstrated that both mediational paths from chronic stereotype threat to mathematical achievement: through working memory depletion and through intellectual helplessness were significant but only for girls that were highly identified with their gender group. In sum, we extended a well-established model of acute stereotype threat to its chronic version and suggested a new mechanism of chronic stereotype threat, which involves intellectual helplessness. Implications for stereotype threat theory and educational practice are discussed. PMID:29666599

Chronic Stereotype Threat Is Associated With Mathematical Achievement on Representative Sample of Secondary Schoolgirls: The Role of Gender Identification, Working Memory, and Intellectual Helplessness.

PubMed

Bedyńska, Sylwia; Krejtz, Izabela; Sedek, Grzegorz

2018-01-01

Stereotype threat affects performance in many different groups across many different domains. Despite a large body of experimental research on situational stereotype threat, little attention has been paid to the consequences of repeated experience of stereotype threat. Using structural equation modeling on data from a representative sample of girls from secondary schools, the current research examined the relations of chronic stereotype threat with mathematical achievement, and effectiveness of working memory functions. Moving beyond past theory, this study examined a new mechanism by which chronic stereotype threat decreases school achievement - namely intellectual helplessness. We assumed that repeated experience of stereotype threat works as intellectual helplessness training. After the phase of cognitive mobilization, cognitive exhaustion appears, because the individual has no gain from intense cognitive effort. Corroborating previous research on acute stereotype threat, we demonstrated that chronic stereotype threat is negatively associated with mathematical achievement. Additionally, it was also associated with lower effectiveness of working memory functions, which seems to show depletion of working memory as an effect of chronic stereotype threat. The results also demonstrated that both mediational paths from chronic stereotype threat to mathematical achievement: through working memory depletion and through intellectual helplessness were significant but only for girls that were highly identified with their gender group. In sum, we extended a well-established model of acute stereotype threat to its chronic version and suggested a new mechanism of chronic stereotype threat, which involves intellectual helplessness. Implications for stereotype threat theory and educational practice are discussed.

Don't aim too high for your kids: Parental overaspiration undermines students' learning in mathematics.

PubMed

Murayama, Kou; Pekrun, Reinhard; Suzuki, Masayuki; Marsh, Herbert W; Lichtenfeld, Stephanie

2016-11-01

Previous research has suggested that parents' aspirations for their children's academic attainment can have a positive influence on children's actual academic performance. Possible negative effects of parental overaspiration, however, have found little attention in the psychological literature. Employing a dual-change score model with longitudinal data from a representative sample of German school children and their parents (N = 3,530; Grades 5 to 10), we showed that parental aspiration and children's mathematical achievement were linked by positive reciprocal relations over time. Importantly, we also found that parental aspiration that exceeded their expectation (i.e., overaspiration) had negative reciprocal relations with children's mathematical achievement. These results were fairly robust after controlling for a variety of demographic and cognitive variables such as children's gender, age, intelligence, school type, and family socioeconomic status. The results were also replicated with an independent sample of U.S. parents and their children. These findings suggest that unrealistically high parental aspiration can be detrimental for children's achievement. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

Near Identifiability of Dynamical Systems

NASA Technical Reports Server (NTRS)

Hadaegh, F. Y.; Bekey, G. A.

1987-01-01

Concepts regarding approximate mathematical models treated rigorously. Paper presents new results in analysis of structural identifiability, equivalence, and near equivalence between mathematical models and physical processes they represent. Helps establish rigorous mathematical basis for concepts related to structural identifiability and equivalence revealing fundamental requirements, tacit assumptions, and sources of error. "Structural identifiability," as used by workers in this field, loosely translates as meaning ability to specify unique mathematical model and set of model parameters that accurately predict behavior of corresponding physical system.

How to Develop Teachers' Mathematical Molding Teaching Skills

ERIC Educational Resources Information Center

Mrayyan, Salwa

2016-01-01

This study aimed at developing some of the mathematical modelling skills necessary for the student teachers in mathematics education College. Modeling involves making genuine choices, modeling problems have many possible justifiable answers, modeling problems matter to the end-user who needs to understand something or make a decision. Modeling…

Model Eliciting Activities: Fostering 21st Century Learners

ERIC Educational Resources Information Center

Stohlmann, Micah

2013-01-01

Real world mathematical modeling activities can develop needed and valuable 21st century skills. The knowledge and skills to become adept at mathematical modeling need to develop over time and students in the elementary grades should have experiences with mathematical modeling. For this to occur elementary teachers need to have positive…

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…

Modeling and validation of autoinducer-mediated bacterial gene expression in microfluidic environments

PubMed Central

Austin, Caitlin M.; Stoy, William; Su, Peter; Harber, Marie C.; Bardill, J. Patrick; Hammer, Brian K.; Forest, Craig R.

2014-01-01

Biosensors exploiting communication within genetically engineered bacteria are becoming increasingly important for monitoring environmental changes. Currently, there are a variety of mathematical models for understanding and predicting how genetically engineered bacteria respond to molecular stimuli in these environments, but as sensors have miniaturized towards microfluidics and are subjected to complex time-varying inputs, the shortcomings of these models have become apparent. The effects of microfluidic environments such as low oxygen concentration, increased biofilm encapsulation, diffusion limited molecular distribution, and higher population densities strongly affect rate constants for gene expression not accounted for in previous models. We report a mathematical model that accurately predicts the biological response of the autoinducer N-acyl homoserine lactone-mediated green fluorescent protein expression in reporter bacteria in microfluidic environments by accommodating these rate constants. This generalized mass action model considers a chain of biomolecular events from input autoinducer chemical to fluorescent protein expression through a series of six chemical species. We have validated this model against experimental data from our own apparatus as well as prior published experimental results. Results indicate accurate prediction of dynamics (e.g., 14% peak time error from a pulse input) and with reduced mean-squared error with pulse or step inputs for a range of concentrations (10 μM–30 μM). This model can help advance the design of genetically engineered bacteria sensors and molecular communication devices. PMID:25379076

Group investigation with scientific approach in mathematics learning

NASA Astrophysics Data System (ADS)

Indarti, D.; Mardiyana; Pramudya, I.

2018-03-01

The aim of this research is to find out the effect of learning model toward mathematics achievement. This research is quasi-experimental research. The population of research is all VII grade students of Karanganyar regency in the academic year of 2016/2017. The sample of this research was taken using stratified cluster random sampling technique. Data collection was done based on mathematics achievement test. The data analysis technique used one-way ANOVA following the normality test with liliefors method and homogeneity test with Bartlett method. The results of this research is the mathematics learning using Group Investigation learning model with scientific approach produces the better mathematics learning achievement than learning with conventional model on material of quadrilateral. Group Investigation learning model with scientific approach can be used by the teachers in mathematics learning, especially in the material of quadrilateral, which is can improve the mathematics achievement.

Formally verifying Ada programs which use real number types

NASA Technical Reports Server (NTRS)

Sutherland, David

1986-01-01

Formal verification is applied to programs which use real number arithmetic operations (mathematical programs). Formal verification of a program P consists of creating a mathematical model of F, stating the desired properties of P in a formal logical language, and proving that the mathematical model has the desired properties using a formal proof calculus. The development and verification of the mathematical model are discussed.

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…

Sustained virological response with intravenous silibinin: individualized IFN-free therapy via real-time modelling of HCV kinetics.

PubMed

Dahari, Harel; Shteingart, Shimon; Gafanovich, Inna; Cotler, Scott J; D'Amato, Massimo; Pohl, Ralf T; Weiss, Gali; Ashkenazi, Yaakov J; Tichler, Thomas; Goldin, Eran; Lurie, Yoav

2015-02-01

Intravenous silibinin (SIL) is a potent antiviral agent against hepatitis C virus (HCV) genotype-1. In this proof of concept case-study we tested: (i) whether interferon-alfa (IFN)-free treatment with SIL plus ribavirin (RBV) can achieve sustained virological response (SVR); (ii) whether SIL is safe and feasible for prolonged duration of treatment and (iii) whether mathematical modelling of early on-treatment HCV kinetics can guide duration of therapy to achieve SVR. A 44 year-old female HCV-(genotype-1)-infected patient who developed severe psychiatric adverse events to a previous course of pegIFN+RBV, initiated combination treatment with 1200 mg/day of SIL, 1200 mg/day of RBV and 6000 u/day vitamin D. Blood samples were collected frequently till week 4, thereafter every 1-12 weeks until the end of therapy. The standard biphasic mathematical model with time-varying SIL effectiveness was used to predict the duration of therapy to achieve SVR. Based on modelling the observed viral kinetics during the first 3 weeks of treatment, SVR was predicted to be achieved within 34 weeks of therapy. Provided with this information, the patient agreed to complete 34 weeks of treatment. IFN-free treatment with SIL+RBV was feasible, safe and achieved SVR (week-33). We report, for the first time, the use of real-time mathematical modelling of HCV kinetics to individualize duration of IFN-free therapy and to empower a patient to participate in shared decision making regarding length of treatment. SIL-based individualized therapy provides a treatment option for patients who do not respond to or cannot receive other HCV agents and should be further validated. © 2014 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

Sustained virological response with intravenous silibinin: individualized IFN-free therapy via real-time modeling of HCV kinetics

PubMed Central

Dahari, Harel; Shteingart, Shimon; Gafanovich, Inna; Cotler, Scott J.; D'Amato, Massimo; Pohl, Ralf T.; Weiss, Gali; Ashkenazi, Yaakov Jack; Tichler, Thomas; Goldin, Eran; Lurie, Yoav

2014-01-01

Background & Aims Intravenous silibinin (SIL) is a potent antiviral agent against hepatitis C virus (HCV) genotype-1. In this proof of concept case-study we tested: (i) whether interferon-alfa (IFN)-free treatment with SIL plus ribavirin (RBV) can achieve sustained virological response (SVR), (ii) whether SIL is safe and feasible for prolonged duration of treatment, and (iii) whether mathematical modeling of early on-treatment HCV kinetics can guide duration of therapy to achieve SVR. Methods A 44 year-old female HCV-(genotype-1)-infected patient who developed severe psychiatric adverse events to a previous course of pegIFN+RBV, initiated combination treatment with 1200 mg/day of SIL, 1200 mg/day of RBV and 6000 u/day vitamin D. Blood samples were collected frequently till week 4, thereafter every 1 to 12 weeks until the end of therapy. The standard-biphasic-mathematical model was used to predict the duration of therapy to achieve SVR. Results Based on modeling the observed viral kinetics during the first 3 weeks of treatment, SVR was predicted to be achieved within 34 weeks of therapy. Provided with this information, the patient agreed to complete 34 weeks of treatment. IFN-free treatment with SIL+RBV was feasible, safe, and achieved SVR (week-33). Conclusions We report, for the first time, the use of real-time mathematical modeling of HCV kinetics to individualize duration of IFN-free therapy and to empower a patient to participate in shared decision making regarding length of treatment. SIL-based individualized therapy provides a treatment option for patients who do not respond to or cannot receive other HCV agents and should be further validated. PMID:25251042

Demand modelling of passenger air travel: An analysis and extension, volume 2

NASA Technical Reports Server (NTRS)

Jacobson, I. D.

1978-01-01

Previous intercity travel demand models in terms of their ability to predict air travel in a useful way and the need for disaggregation in the approach to demand modelling are evaluated. The viability of incorporating non-conventional factors (i.e. non-econometric, such as time and cost) in travel demand forecasting models are determined. The investigation of existing models is carried out in order to provide insight into their strong points and shortcomings. The model is characterized as a market segmentation model. This is a consequence of the strengths of disaggregation and its natural evolution to a usable aggregate formulation. The need for this approach both pedagogically and mathematically is discussed. In addition this volume contains two appendices which should prove useful to the non-specialist in the area.

What can formal methods offer to digital flight control systems design

NASA Technical Reports Server (NTRS)

Good, Donald I.

1990-01-01

Formal methods research begins to produce methods which will enable mathematic modeling of the physical behavior of digital hardware and software systems. The development of these methods directly supports the NASA mission of increasing the scope and effectiveness of flight system modeling capabilities. The conventional, continuous mathematics that is used extensively in modeling flight systems is not adequate for accurate modeling of digital systems. Therefore, the current practice of digital flight control system design has not had the benefits of extensive mathematical modeling which are common in other parts of flight system engineering. Formal methods research shows that by using discrete mathematics, very accurate modeling of digital systems is possible. These discrete modeling methods will bring the traditional benefits of modeling to digital hardware and hardware design. Sound reasoning about accurate mathematical models of flight control systems can be an important part of reducing risk of unsafe flight control.

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

ERIC Educational Resources Information Center

Tian, Xiaoxi

2014-01-01

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

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…

The analytical representation of viscoelastic material properties using optimization techniques

NASA Technical Reports Server (NTRS)

Hill, S. A.

1993-01-01

This report presents a technique to model viscoelastic material properties with a function of the form of the Prony series. Generally, the method employed to determine the function constants requires assuming values for the exponential constants of the function and then resolving the remaining constants through linear least-squares techniques. The technique presented here allows all the constants to be analytically determined through optimization techniques. This technique is employed in a computer program named PRONY and makes use of commercially available optimization tool developed by VMA Engineering, Inc. The PRONY program was utilized to compare the technique against previously determined models for solid rocket motor TP-H1148 propellant and V747-75 Viton fluoroelastomer. In both cases, the optimization technique generated functions that modeled the test data with at least an order of magnitude better correlation. This technique has demonstrated the capability to use small or large data sets and to use data sets that have uniformly or nonuniformly spaced data pairs. The reduction of experimental data to accurate mathematical models is a vital part of most scientific and engineering research. This technique of regression through optimization can be applied to other mathematical models that are difficult to fit to experimental data through traditional regression techniques.

Six challenges in modelling for public health policy.

PubMed

Metcalf, C J E; Edmunds, W J; Lessler, J

2015-03-01

The World Health Organisation's definition of public health refers to all organized measures to prevent disease, promote health, and prolong life among the population as a whole (World Health Organization, 2014). Mathematical modelling plays an increasingly important role in helping to guide the most high impact and cost-effective means of achieving these goals. Public health programmes are usually implemented over a long period of time with broad benefits to many in the community. Clinical trials are seldom large enough to capture these effects. Observational data may be used to evaluate a programme after it is underway, but have limited value in helping to predict the future impact of a proposed policy. Furthermore, public health practitioners are often required to respond to new threats, for which there is little or no previous data on which to assess the threat. Computational and mathematical models can help to assess potential threats and impacts early in the process, and later aid in interpreting data from complex and multifactorial systems. As such, these models can be critical tools in guiding public health action. However, there are a number of challenges in achieving a successful interface between modelling and public health. Here, we discuss some of these challenges. Copyright © 2014 The Authors. Published by Elsevier B.V. All rights reserved.

Simulation of action potential propagation in plants.

PubMed

Sukhov, Vladimir; Nerush, Vladimir; Orlova, Lyubov; Vodeneev, Vladimir

2011-12-21

Action potential is considered to be one of the primary responses of a plant to action of various environmental factors. Understanding plant action potential propagation mechanisms requires experimental investigation and simulation; however, a detailed mathematical model of plant electrical signal transmission is absent. Here, the mathematical model of action potential propagation in plants has been worked out. The model is a two-dimensional system of excitable cells; each of them is electrically coupled with four neighboring ones. Ion diffusion between excitable cell apoplast areas is also taken into account. The action potential generation in a single cell has been described on the basis of our previous model. The model simulates active and passive signal transmission well enough. It has been used to analyze theoretically the influence of cell to cell electrical conductivity and H(+)-ATPase activity on the signal transmission in plants. An increase in cell to cell electrical conductivity has been shown to stimulate an increase in the length constant, the action potential propagation velocity and the temperature threshold, while the membrane potential threshold being weakly changed. The growth of H(+)-ATPase activity has been found to induce the increase of temperature and membrane potential thresholds and the reduction of the length constant and the action potential propagation velocity. Copyright © 2011 Elsevier Ltd. All rights reserved.

Including Thermal Fluctuations in Actomyosin Stable States Increases the Predicted Force per Motor and Macroscopic Efficiency in Muscle Modelling

PubMed Central

2016-01-01

Muscle contractions are generated by cyclical interactions of myosin heads with actin filaments to form the actomyosin complex. To simulate actomyosin complex stable states, mathematical models usually define an energy landscape with a corresponding number of wells. The jumps between these wells are defined through rate constants. Almost all previous models assign these wells an infinite sharpness by imposing a relatively simple expression for the detailed balance, i.e., the ratio of the rate constants depends exponentially on the sole myosin elastic energy. Physically, this assumption corresponds to neglecting thermal fluctuations in the actomyosin complex stable states. By comparing three mathematical models, we examine the extent to which this hypothesis affects muscle model predictions at the single cross-bridge, single fiber, and organ levels in a ceteris paribus analysis. We show that including fluctuations in stable states allows the lever arm of the myosin to easily and dynamically explore all possible minima in the energy landscape, generating several backward and forward jumps between states during the lifetime of the actomyosin complex, whereas the infinitely sharp minima case is characterized by fewer jumps between states. Moreover, the analysis predicts that thermal fluctuations enable a more efficient contraction mechanism, in which a higher force is sustained by fewer attached cross-bridges. PMID:27626630

The Trade-Off Mechanism in Mammalian Circadian Clock Model with Two Time Delays

NASA Astrophysics Data System (ADS)

Yan, Jie; Kang, Xiaxia; Yang, Ling

Circadian clock is an autonomous oscillator which orchestrates the daily rhythms of physiology and behaviors. This study is devoted to explore how a positive feedback loop affects the dynamics of mammalian circadian clock. We simplify an experimentally validated mathematical model in our previous work, to a nonlinear differential equation with two time delays. This simplified mathematical model incorporates the pacemaker of mammalian circadian clock, a negative primary feedback loop, and a critical positive auxiliary feedback loop, Rev-erbα/Cry1 loop. We perform analytical studies of the system. Delay-dependent conditions for the asymptotic stability of the nontrivial positive steady state of the model are investigated. We also prove the existence of Hopf bifurcation, which leads to self-sustained oscillation of mammalian circadian clock. Our theoretical analyses show that the oscillatory regime is reduced upon the participation of the delayed positive auxiliary loop. However, further simulations reveal that the auxiliary loop can enable the circadian clock gain widely adjustable amplitudes and robust period. Thus, the positive auxiliary feedback loop may provide a trade-off mechanism, to use the small loss in the robustness of oscillation in exchange for adaptable flexibility in mammalian circadian clock. The results obtained from the model may gain new insights into the dynamics of biological oscillators with interlocked feedback loops.

The evolutionary dynamics of receptor binding avidity in influenza A: a mathematical model for a new antigenic drift hypothesis

PubMed Central

Yuan, Hsiang-Yu; Koelle, Katia

2013-01-01

The most salient feature of influenza evolution in humans is its antigenic drift. This process is characterized by structural changes in the virus's B-cell epitopes and ultimately results in the ability of the virus to evade immune recognition and thereby reinfect previously infected hosts. Until recently, amino acid substitutions in epitope regions of the viral haemagglutinin were thought to be positively selected for their ability to reduce antibody binding and therefore were thought to be responsible for driving antigenic drift. However, a recent hypothesis put forward by Hensley and co-workers posits that cellular receptor binding avidity is the dominant phenotype under selection, with antigenic drift being a side effect of these binding avidity changes. Here, we present a mathematical formulation of this new antigenic drift model and use it to show how rates of antigenic drift depend on epidemiological parameters. We further use the model to evaluate how two different vaccination strategies can impact antigenic drift rates and ultimately disease incidence levels. Finally, we discuss the assumptions present in the model formulation, predictions of the model, and future work that needs to be done to determine the consistency of this hypothesis with known patterns of influenza's genetic and antigenic evolution. PMID:23382426

Fuzzy differential inclusions in atmospheric and medical cybernetics.

PubMed

Majumdar, Kausik Kumar; Majumder, Dwijesh Dutta

2004-04-01

Uncertainty management in dynamical systems is receiving attention in artificial intelligence, particularly in the fields of qualitative and model based reasoning. Fuzzy dynamical systems occupy a very important position in the class of uncertain systems. It is well established that the fuzzy dynamical systems represented by a set of fuzzy differential inclusions (FDI) are very convenient tools for modeling and simulation of various uncertain systems. In this paper, we discuss about the mathematical modeling of two very complex natural phenomena by means of FDIs. One of them belongs to the atmospheric cybernetics (the term has been used in a broad sense) of the genesis of a cyclonic storm (cyclogenesis), and the other belongs to the bio-medical cybernetics of the evolution of tumor in a human body. Since a discussion of the former already appears in a previous paper by the first author, here, we present very briefly a theoretical formalism of cyclone formation. On the other hand, we treat the latter system more elaborately. We solve the FDIs with the help of an algorithm developed in this paper to numerically simulate the mathematical models. From the simulation results thus obtained, we have drawn a number of interesting conclusions, which have been verified, and this vindicates the validity of our models.

Mathematical Model of Solid Food Pasteurization by Ohmic Heating: Influence of Process Parameters

PubMed Central

2014-01-01

Pasteurization of a solid food undergoing ohmic heating has been analysed by means of a mathematical model, involving the simultaneous solution of Laplace's equation, which describes the distribution of electrical potential within a food, the heat transfer equation, using a source term involving the displacement of electrical potential, the kinetics of inactivation of microorganisms likely to be contaminating the product. In the model, thermophysical and electrical properties as function of temperature are used. Previous works have shown the occurrence of heat loss from food products to the external environment during ohmic heating. The current model predicts that, when temperature gradients are established in the proximity of the outer ohmic cell surface, more cold areas are present at junctions of electrodes with lateral sample surface. For these reasons, colder external shells are the critical areas to be monitored, instead of internal points (typically geometrical center) as in classical pure conductive heat transfer. Analysis is carried out in order to understand the influence of pasteurisation process parameters on this temperature distribution. A successful model helps to improve understanding of these processing phenomenon, which in turn will help to reduce the magnitude of the temperature differential within the product and ultimately provide a more uniformly pasteurized product. PMID:24574874

Mathematical model of solid food pasteurization by ohmic heating: influence of process parameters.

PubMed

Marra, Francesco

2014-01-01

Pasteurization of a solid food undergoing ohmic heating has been analysed by means of a mathematical model, involving the simultaneous solution of Laplace's equation, which describes the distribution of electrical potential within a food, the heat transfer equation, using a source term involving the displacement of electrical potential, the kinetics of inactivation of microorganisms likely to be contaminating the product. In the model, thermophysical and electrical properties as function of temperature are used. Previous works have shown the occurrence of heat loss from food products to the external environment during ohmic heating. The current model predicts that, when temperature gradients are established in the proximity of the outer ohmic cell surface, more cold areas are present at junctions of electrodes with lateral sample surface. For these reasons, colder external shells are the critical areas to be monitored, instead of internal points (typically geometrical center) as in classical pure conductive heat transfer. Analysis is carried out in order to understand the influence of pasteurisation process parameters on this temperature distribution. A successful model helps to improve understanding of these processing phenomenon, which in turn will help to reduce the magnitude of the temperature differential within the product and ultimately provide a more uniformly pasteurized product.

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

PubMed

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

2007-03-01

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

[Representation and mathematical analysis of human crystalline lens].

PubMed

Tălu, Stefan; Giovanzana, Stefano; Tălu, Mihai

2011-01-01

The surface of human crystalline lens can be described and analyzed using mathematical models based on parametric representations, used in biomechanical studies and 3D solid modeling of the lens. The mathematical models used in lens biomechanics allow the study and the behavior of crystalline lens on variables and complex dynamic loads. Also, the lens biomechanics has the potential to improve the results in the development of intraocular lenses and cataract surgery. The paper presents the most representative mathematical models currently used for the modeling of human crystalline lens, both optically and biomechanically.

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 of computer-based science simulations. Although there are several exceptional computer-based science simulations designed for mathematics classes (see, e.g. Kinetic Book (http://www.kineticbooks.com/) or Gizmos (http://www.explorelearning.com/)), we concentrate mainly on the PhET Interactive Simulations developed at the University of Colorado at Boulder (http://phet.colorado.edu/) in generating our argument that computer simulations more accurately represent the contextual characteristics of scientific phenomena than their textual descriptions.

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 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.

Kinetic modelling of a diesel-polluted clayey soil bioremediation process.

PubMed

Fernández, Engracia Lacasa; Merlo, Elena Moliterni; Mayor, Lourdes Rodríguez; Camacho, José Villaseñor

2016-07-01

A mathematical model is proposed to describe a diesel-polluted clayey soil bioremediation process. The reaction system under study was considered a completely mixed closed batch reactor, which initially contacted a soil matrix polluted with diesel hydrocarbons, an aqueous liquid-specific culture medium and a microbial inoculation. The model coupled the mass transfer phenomena and the distribution of hydrocarbons among four phases (solid, S; water, A; non-aqueous liquid, NAPL; and air, V) with Monod kinetics. In the first step, the model simulating abiotic conditions was used to estimate only the mass transfer coefficients. In the second step, the model including both mass transfer and biodegradation phenomena was used to estimate the biological kinetic and stoichiometric parameters. In both situations, the model predictions were validated with experimental data that corresponded to previous research by the same authors. A correct fit between the model predictions and the experimental data was observed because the modelling curves captured the major trends for the diesel distribution in each phase. The model parameters were compared to different previously reported values found in the literature. Pearson correlation coefficients were used to show the reproducibility level of the model. Copyright © 2016. Published by Elsevier B.V.

Numerical approximation abilities correlate with and predict informal but not formal mathematics abilities

PubMed Central

Libertus, Melissa E.; Feigenson, Lisa; Halberda, Justin

2013-01-01

Previous research has found a relationship between individual differences in children’s precision when nonverbally approximating quantities and their school mathematics performance. School mathematics performance emerges from both informal (e.g., counting) and formal (e.g., knowledge of mathematics facts) abilities. It remains unknown whether approximation precision relates to both of these types of mathematics abilities. In the present study we assessed the precision of numerical approximation in 85 3- to 7-year-old children four times over a span of two years. Additionally, at the last time point, we tested children’s informal and formal mathematics abilities using the Test of Early Mathematics Ability (TEMA-3; Ginsburg & Baroody, 2003). We found that children’s numerical approximation precision correlated with and predicted their informal, but not formal, mathematics abilities when controlling for age and IQ. These results add to our growing understanding of the relationship between an unlearned, non-symbolic system of quantity representation and the system of mathematical reasoning that children come to master through instruction. PMID:24076381

Numerical approximation abilities correlate with and predict informal but not formal mathematics abilities.

PubMed

Libertus, Melissa E; Feigenson, Lisa; Halberda, Justin

2013-12-01

Previous research has found a relationship between individual differences in children's precision when nonverbally approximating quantities and their school mathematics performance. School mathematics performance emerges from both informal (e.g., counting) and formal (e.g., knowledge of mathematics facts) abilities. It remains unknown whether approximation precision relates to both of these types of mathematics abilities. In the current study, we assessed the precision of numerical approximation in 85 3- to 7-year-old children four times over a span of 2years. In addition, at the final time point, we tested children's informal and formal mathematics abilities using the Test of Early Mathematics Ability (TEMA-3). We found that children's numerical approximation precision correlated with and predicted their informal, but not formal, mathematics abilities when controlling for age and IQ. These results add to our growing understanding of the relationship between an unlearned nonsymbolic system of quantity representation and the system of mathematics reasoning that children come to master through instruction. Copyright © 2013 Elsevier Inc. All rights reserved.

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)…

Visual Thinking and Gender Differences in High School Calculus

ERIC Educational Resources Information Center

Haciomeroglu, Erhan Selcuk; Chicken, Eric

2012-01-01

This study sought to examine calculus students' mathematical performances and preferences for visual or analytic thinking regarding derivative and antiderivative tasks presented graphically. It extends previous studies by investigating factors mediating calculus students' mathematical performances and their preferred modes of thinking. Data were…

Assessment Mathematics Teacher's Competencies

ERIC Educational Resources Information Center

Alnoor, A. G.; Yuanxiang, Guo; Abudhuim, F. S.

2007-01-01

This paper aimed to identifying the professional efficiencies for the intermediate schools mathematics teachers and tries to know at what level the math teachers experience those competencies. The researcher used a descriptive research approach, the study data collected from specialist educators and teacher's experts and previous studies to…

Mathematical Modelling as a Professional Task

ERIC Educational Resources Information Center

Frejd, Peter; Bergsten, Christer

2016-01-01

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

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

PubMed

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

2016-10-01

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

Differential equations with applications in cancer diseases.

PubMed

Ilea, M; Turnea, M; Rotariu, M

2013-01-01

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

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

DTIC Science & Technology

2017-08-15

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

An optimized method to calculate error correction capability of tool influence function in frequency domain

NASA Astrophysics Data System (ADS)

Wang, Jia; Hou, Xi; Wan, Yongjian; Shi, Chunyan

2017-10-01

An optimized method to calculate error correction capability of tool influence function (TIF) in certain polishing conditions will be proposed based on smoothing spectral function. The basic mathematical model for this method will be established in theory. A set of polishing experimental data with rigid conformal tool is used to validate the optimized method. The calculated results can quantitatively indicate error correction capability of TIF for different spatial frequency errors in certain polishing conditions. The comparative analysis with previous method shows that the optimized method is simpler in form and can get the same accuracy results with less calculating time in contrast to previous method.

All-optical switch using optically controlled two mode interference coupler.

PubMed

Sahu, Partha Pratim

2012-05-10

In this paper, we have introduced optically controlled two-mode interference (OTMI) coupler having silicon core and GaAsInP cladding as an all-optical switch. By taking advantage of refractive index modulation by launching optical pulse into cladding region of TMI waveguide, we have shown optically controlled switching operation. We have studied optical pulse-controlled coupling characteristics of the proposed device by using a simple mathematical model on the basis of sinusoidal modes. The device length is less than that of previous work. It is also seen that the cross talk of the OTMI switch is not significantly increased with fabrication tolerances (±δw) in comparison with previous work.

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...

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

ERIC Educational Resources Information Center

Nasser-Abu Alhija, Fadia; Amasha, Marcel

2012-01-01

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

Teachers as Managers of the Modelling Process

ERIC Educational Resources Information Center

Lingefjard, Thomas; Meier, Stephanie

2010-01-01

The work in the Comenius Network project Developing Quality in Mathematics Education II (DQME II) has a main focus on development and evaluation of modelling tasks. One reason is the gap between what mathematical modelling is and what is taught in mathematical classrooms. This article deals with one modelling task and focuses on how two teachers…

Examining the Impact of a Video Case-Based Mathematics Methods Course on Secondary Pre-Service Teachers' Skills at Analysing Students' Strategies

ERIC Educational Resources Information Center

Martinez, Mara Vanina; Superfine, Alison Castro; Carlton, Theresa; Dasgupta, Chandan

2015-01-01

This paper focuses on results from a study conducted with two cohorts of pre-service teachers (PSTs) in a video case-based mathematics methods course at a large Midwestern university in the US. The motivation for this study was to look beyond whether or not PSTs pay attention to mathematical thinking of students, as shown by previous studies when…

Generalist Genes and Learning Disabilities: A Multivariate Genetic Analysis of Low Performance in Reading, Mathematics, Language and General Cognitive Ability in a Sample of 8000 12-Year-Old Twins

ERIC Educational Resources Information Center

Haworth, Claire M. A.; Kovas, Yulia; Harlaar, Nicole; Hayiou-Thomas, Marianna E.; Petrill, Stephen A.; Dale, Philip S.; Plomin, Robert

2009-01-01

Background: Our previous investigation found that the same genes influence poor reading and mathematics performance in 10-year-olds. Here we assess whether this finding extends to language and general cognitive disabilities, as well as replicating the earlier finding for reading and mathematics in an older and larger sample. Methods: Using a…

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.

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.

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

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.

Quantitative estimation of the cost of parasitic castration in a Helisoma anceps population using a matrix population model.

PubMed

Negovetich, N J; Esch, G W

2008-10-01

Larval trematodes frequently castrate their snail intermediate hosts. When castrated, the snails do not contribute offspring to the population, yet they persist and compete with the uninfected individuals for the available food resources. Parasitic castration should reduce the population growth rate lambda, but the magnitude of this decrease is unknown. The present study attempted to quantify the cost of parasitic castration at the level of the population by mathematically modeling the population of the planorbid snail Helisoma anceps in Charlie's Pond, North Carolina. Analysis of the model identified the life-history trait that most affects lambda, and the degree to which parasitic castration can lower lambda. A period matrix product model was constructed with estimates of fecundity, survival, growth rates, and infection probabilities calculated in a previous study. Elasticity analysis was performed by increasing the values of the life-history traits by 10% and recording the percentage change in lambda. Parasitic castration resulted in a 40% decrease in lambda of H. anceps. Analysis of the model suggests that decreasing the size at maturity was more effective at reducing the cost of castration than increasing survival or growth rates of the snails. The current matrix model was the first to mathematically describe a snail population, and the predictions of the model are in agreement with published research.

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

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

ERIC Educational Resources Information Center

Unlu, Melihan; Ertekin, Erhan; Dilmac, Bulent

2017-01-01

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

Effects of septum and pericardium on heart-lung interactions in a cardiopulmonary simulation model.

PubMed

Karamolegkos, Nikolaos; Albanese, Antonio; Chbat, Nicolas W

2017-07-01

Mechanical heart-lung interactions are often overlooked in clinical settings. However, their impact on cardiac function can be quite significant. Mechanistic physiology-based models can provide invaluable insights into such cardiorespiratory interactions, which occur not only under external mechanical ventilatory support but in normal physiology as well. In this work, we focus on the cardiac component of a previously developed mathematical model of the human cardiopulmonary system, aiming to improve the model's response to the intrathoracic pressure variations that are associated with the respiratory cycle. Interventricular septum and pericardial membrane are integrated into the existing model. Their effect on the overall cardiac response is explained by means of comparison against simulation results from the original model as well as experimental data from literature.

Normal Brain-Skull Development with Hybrid Deformable VR Models Simulation.

PubMed

Jin, Jing; De Ribaupierre, Sandrine; Eagleson, Roy

2016-01-01

This paper describes a simulation framework for a clinical application involving skull-brain co-development in infants, leading to a platform for craniosynostosis modeling. Craniosynostosis occurs when one or more sutures are fused early in life, resulting in an abnormal skull shape. Surgery is required to reopen the suture and reduce intracranial pressure, but is difficult without any predictive model to assist surgical planning. We aim to study normal brain-skull growth by computer simulation, which requires a head model and appropriate mathematical methods for brain and skull growth respectively. On the basis of our previous model, we further specified suture model into fibrous and cartilaginous sutures and develop algorithm for skull extension. We evaluate the resulting simulation by comparison with datasets of cases and normal growth.

A computational modeling of semantic knowledge in reading comprehension: Integrating the landscape model with latent semantic analysis.

PubMed

Yeari, Menahem; van den Broek, Paul

2016-09-01

It is a well-accepted view that the prior semantic (general) knowledge that readers possess plays a central role in reading comprehension. Nevertheless, computational models of reading comprehension have not integrated the simulation of semantic knowledge and online comprehension processes under a unified mathematical algorithm. The present article introduces a computational model that integrates the landscape model of comprehension processes with latent semantic analysis representation of semantic knowledge. In three sets of simulations of previous behavioral findings, the integrated model successfully simulated the activation and attenuation of predictive and bridging inferences during reading, as well as centrality estimations and recall of textual information after reading. Analyses of the computational results revealed new theoretical insights regarding the underlying mechanisms of the various comprehension phenomena.

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.

Modeling the Restraint of Liquid Jets by Surface Tension in Microgravity

NASA Technical Reports Server (NTRS)

Chato, David J.; Jacqmim, David A.

2001-01-01

An axisymmetric phase field model is developed and used to model surface tension forces on liquid jets in microgravity. The previous work in this area is reviewed and a baseline drop tower experiment selected 'for model comparison. A mathematical model is developed which includes a free surface. a symmetric centerline and wall boundaries with given contact angles. The model is solved numerically with a compact fourth order stencil on a equally spaced axisymmetric grid. After grid convergence studies, a grid is selected and all drop tower tests modeled. Agreement was assessed by comparing predicted and measured free surface rise. Trend wise agreement is good but agreement in magnitude is only fair. Suspected sources of disagreement are suspected to be lack of a turbulence model and the existence of slosh baffles in the experiment which were not included in the model.

Simple Mathematical Models Do Not Accurately Predict Early SIV Dynamics

PubMed Central

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

2015-01-01

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

Level, Strength, and Facet-Specific Self-Efficacy in Mathematics Test Performance

ERIC Educational Resources Information Center

Street, Karin Elisabeth Sørlie; Malmberg, Lars-Erik; Stylianides, Gabriel J.

2017-01-01

Students' self-efficacy expectations (SEE) in mathematics are associated with their engagement and learning experiences. Going beyond previous operationalisations of SEE we propose a new instrument that takes into account not only "facet-specificity" (expectations related to particular competences or skills) and "strength"…

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

ERIC Educational Resources Information Center

Yurt, Eyüp; Sünbül, Ali Murat

2014-01-01

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

Understanding the Difficulties Faced by Engineering Undergraduates in Learning Mathematical Modelling

ERIC Educational Resources Information Center

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

2011-01-01

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

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

ERIC Educational Resources Information Center

Bal, Aytgen Pinar; Doganay, Ahmet

2014-01-01

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

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

ERIC Educational Resources Information Center

Sokolowski, Andrzej; Yalvac, Bugrahan; Loving, Cathleen

2011-01-01

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

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…