Methodology for predicting oily mixture properties in the mathematical modeling of molecular distillation

International Nuclear Information System (INIS)

Gayol, M.F.; Pramparo, M.C.; Miró Erdmann, S.M.

2017-01-01

A methodology for predicting the thermodynamic and transport properties of a multi-component oily mixture, in which the different mixture components are grouped into a small number of pseudo components is shown. This prediction of properties is used in the mathematical modeling of molecular distillation, which consists of a system of differential equations in partial derivatives, according to the principles of the Transport Phenomena and is solved by an implicit finite difference method using a computer code. The mathematical model was validated with experimental data, specifically the molecular distillation of a deodorizer distillate (DD) of sunflower oil. The results obtained were satisfactory, with errors less than 10% with respect to the experimental data in a temperature range in which it is possible to apply the proposed method. [es

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

Science.gov (United States)

Lowe, James; Carter, Merilyn; Cooper, Tom

2018-01-01

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

Mathematical model of heat transfer to predict distribution of hardness through the Jominy bar

International Nuclear Information System (INIS)

Lopez, E.; Hernandez, J. B.; Solorio, G.; Vergara, H. J.; Vazquez, O.; Garnica, F.

2013-01-01

The heat transfer coefficient was estimated at the bottom surface at Jominy bar end quench specimen by solution of the heat inverse conduction problem. A mathematical model based on the finite-difference method was developed to predict thermal paths and volume fraction of transformed phases. The mathematical model was codified in the commercial package Microsoft Visual Basic v. 6. The calculated thermal path and final phase distribution were used to evaluate the hardness distribution along the AISI 4140 Jominy bar. (Author)

Mathematical Modelling and Predictive Control of Permanent Magnet Synchronous Motor Drives

Czech Academy of Sciences Publication Activity Database

Belda, Květoslav

2013-01-01

Roč. 2, č. 4 (2013), s. 114-120 ISSN 1805-3386 R&D Projects: GA ČR(CZ) GAP102/11/0437 Institutional support: RVO:67985556 Keywords : Permanent magnet synchronous motor * mathematical modelling * discrete predictive control * multistep explicit control law * square-root optimization Subject RIV: BC - Control Systems Theory http://library.utia.cas.cz/separaty/2014/AS/belda-0422285.pdf

Outcome Prediction in Mathematical Models of Immune Response to Infection.

Directory of Open Access Journals (Sweden)

Manuel Mai

Full Text Available Clinicians need to predict patient outcomes with high accuracy as early as possible after disease inception. In this manuscript, we show that patient-to-patient variability sets a fundamental limit on outcome prediction accuracy for a general class of mathematical models for the immune response to infection. However, accuracy can be increased at the expense of delayed prognosis. We investigate several systems of ordinary differential equations (ODEs that model the host immune response to a pathogen load. Advantages of systems of ODEs for investigating the immune response to infection include the ability to collect data on large numbers of 'virtual patients', each with a given set of model parameters, and obtain many time points during the course of the infection. We implement patient-to-patient variability v in the ODE models by randomly selecting the model parameters from distributions with coefficients of variation v that are centered on physiological values. We use logistic regression with one-versus-all classification to predict the discrete steady-state outcomes of the system. We find that the prediction algorithm achieves near 100% accuracy for v = 0, and the accuracy decreases with increasing v for all ODE models studied. The fact that multiple steady-state outcomes can be obtained for a given initial condition, i.e. the basins of attraction overlap in the space of initial conditions, limits the prediction accuracy for v > 0. Increasing the elapsed time of the variables used to train and test the classifier, increases the prediction accuracy, while adding explicit external noise to the ODE models decreases the prediction accuracy. Our results quantify the competition between early prognosis and high prediction accuracy that is frequently encountered by clinicians.

Predicting the efficacy of radiotherapy in individual glioblastoma patients in vivo: a mathematical modeling approach

International Nuclear Information System (INIS)

Rockne, R; Alvord, E C Jr; Swanson, K R; Rockhill, J K; Kalet, I; Hendrickson, K; Mrugala, M; Spence, A M; Lai, A; Cloughesy, T

2010-01-01

Glioblastoma multiforme (GBM) is the most malignant form of primary brain tumors known as gliomas. They proliferate and invade extensively and yield short life expectancies despite aggressive treatment. Response to treatment is usually measured in terms of the survival of groups of patients treated similarly, but this statistical approach misses the subgroups that may have responded to or may have been injured by treatment. Such statistics offer scant reassurance to individual patients who have suffered through these treatments. Furthermore, current imaging-based treatment response metrics in individual patients ignore patient-specific differences in tumor growth kinetics, which have been shown to vary widely across patients even within the same histological diagnosis and, unfortunately, these metrics have shown only minimal success in predicting patient outcome. We consider nine newly diagnosed GBM patients receiving diagnostic biopsy followed by standard-of-care external beam radiation therapy (XRT). We present and apply a patient-specific, biologically based mathematical model for glioma growth that quantifies response to XRT in individual patients in vivo. The mathematical model uses net rates of proliferation and migration of malignant tumor cells to characterize the tumor's growth and invasion along with the linear-quadratic model for the response to radiation therapy. Using only routinely available pre-treatment MRIs to inform the patient-specific bio-mathematical model simulations, we find that radiation response in these patients, quantified by both clinical and model-generated measures, could have been predicted prior to treatment with high accuracy. Specifically, we find that the net proliferation rate is correlated with the radiation response parameter (r = 0.89, p = 0.0007), resulting in a predictive relationship that is tested with a leave-one-out cross-validation technique. This relationship predicts the tumor size post-therapy to within inter

Mathematical Model to Predict the Permeability of Water Transport in Concrete Structure

OpenAIRE

Solomon Ndubuisi Eluozo

2013-01-01

Mathematical model to predict the permeability of water transport in concrete has been established, the model is to monitor the rate of water transport in concrete structure. The process of this water transport is based on the constituent in the mixture of concrete. Permeability established a relation on the influence of the micropores on the constituent that made of concrete, the method of concrete placement determine the rate of permeability deposition in concrete structure, permeability es...

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

OpenAIRE

Frey Law, Laura A.; Shields, Richard K.

2005-01-01

Chronic spinal cord injury (SCI) induces detrimental musculoskeletal adaptations that adversely affect health status, ranging from muscle paralysis and skin ulcerations to osteoporosis. SCI rehabilitative efforts may increasingly focus on preserving the integrity of paralyzed extremities to maximize health quality using electrical stimulation for isometric training and/or functional activities. Subject-specific mathematical muscle models could prove valuable for predicting the forces necessar...

Development and evaluation of mathematical model to predict disintegration time of fast disintegrating tablets using powder characteristics.

Science.gov (United States)

Goel, H; Arora, A; Tiwary, A K; Rana, V

2011-02-01

The objective of the study was to develop a mathematical model for predicting the disintegration time of fast disintegrating tablets (FDTs) by estimating the powder characteristics of powder blend prior to compression. A combination of chitosan-alginate complex and glycine in the ratio of 50:50 was used for preparing FDTs. The developed mathematical model allowed water sorption time (WST), effective pore radius (R(eff.p)) and swelling Index (SI) of powder mixture as well as tablet crushing strength to be successfully correlated with disintegration time (DT) of FDTs. The predicted model showed that disintegration time of FDTs to be directly correlated with powder characteristics and inversely correlated with tablet crushing strength. Furthermore, a correlation of 0.97 was obtained when DT of FDTs was compared with SI/(WST * R(eff.p)). This correlation was not affected by inclusion of water soluble (ondansetron hydrochloride or metaclopramide hydrochloride) or water insoluble (domperidone) drugs in the powder blend or FDTs. These observations indicated the versatility of the mathematical model in predicting the disintegration time of FDTs by evaluating the selected characteristics of the powder blends without actually preparing the FDTs.

A Bayesian Performance Prediction Model for Mathematics Education: A Prototypical Approach for Effective Group Composition

Science.gov (United States)

Bekele, Rahel; McPherson, Maggie

2011-01-01

This research work presents a Bayesian Performance Prediction Model that was created in order to determine the strength of personality traits in predicting the level of mathematics performance of high school students in Addis Ababa. It is an automated tool that can be used to collect information from students for the purpose of effective group…

Prediction of paddy drying kinetics: A comparative study between mathematical and artificial neural network modelling

Directory of Open Access Journals (Sweden)

Beigi Mohsen

2017-01-01

Full Text Available The present study aimed at investigation of deep bed drying of rough rice kernels at various thin layers at different drying air temperatures and flow rates. A comparative study was performed between mathematical thin layer models and artificial neural networks to estimate the drying curves of rough rice. The suitability of nine mathematical models in simulating the drying kinetics was examined and the Midilli model was determined as the best approach for describing drying curves. Different feed forward-back propagation artificial neural networks were examined to predict the moisture content variations of the grains. The ANN with 4-18-18-1 topology, transfer function of hyperbolic tangent sigmoid and a Levenberg-Marquardt back propagation training algorithm provided the best results with the maximum correlation coefficient and the minimum mean square error values. Furthermore, it was revealed that ANN modeling had better performance in prediction of drying curves with lower root mean square error values.

Mathematical model predicts the elastic behavior of composite materials

Directory of Open Access Journals (Sweden)

Zoroastro de Miranda Boari

2005-03-01

Full Text Available Several studies have found that the non-uniform distribution of reinforcing elements in a composite material can markedly influence its characteristics of elastic and plastic deformation and that a composite's overall response is influenced by the physical and geometrical properties of its reinforcing phases. The finite element method, Eshelby's method and dislocation mechanisms are usually employed in formulating a composite's constitutive response. This paper discusses a composite material containing SiC particles in an aluminum matrix. The purpose of this study was to find the correlation between a composite material's particle distribution and its resistance, and to come up with a mathematical model to predict the material's elastic behavior. The proposed formulation was applied to establish the thermal stress field in the aluminum-SiC composite resulting from its fabrication process, whereby the mixture is prepared at 600 °C and the composite material is used at room temperature. The analytical results, which are presented as stress probabilities, were obtained from the mathematical model proposed herein. These results were compared with the numerical ones obtained by the FEM method. A comparison of the results of the two methods, analytical and numerical, reveals very similar average thermal stress values. It is also shown that Maxwell-Boltzmann's distribution law can be applied to identify the correlation between the material's particle distribution and its resistance, using Eshelby's thermal stresses.

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

Science.gov (United States)

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

2009-08-31

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

Investigation of Predictive Power of Mathematics Anxiety on Mathematics Achievement in Terms of Gender and Class Variables

Directory of Open Access Journals (Sweden)

Mustafa İLHAN

2013-12-01

Full Text Available This research aims to explore predictive power of mathematics anxiety in terms of gender and class variables. For this purpose relational model was used in the study. Working group of the research consists of 348 secondary school second stage students, 175 of whom are girls and 175 are boys, having education in four elementary schools in central district of Diyarbakır province, during 2011-2012 Academic Year, first Semester. “Math Anxiety Scale for Primary School Students” to determine students’ mathematics anxiety was used. Averages of students’ mathematics notes in the first term of 2011- 2012 academic year are taken as the achievement scores of mathematics. The collected data has been analyzed by SPSS 17.0. The relationship between mathematics achievement and math anxiety was analyzed with pearson correlation. The predictor power of math anxiety for mathematics achievement was determined by the regression analysis. According the research findings %17 of the total variance of mathematics achievement can be explained by math anxiety. It has been determined that predictive power of mathematics anxiety on mathematics success is higher in girls than boys. Furthermore, it has been determined in the research that predictive power of mathematics anxiety on mathematics success increases, as students proceed towards the next grade.

Applying mathematical models to predict resident physician performance and alertness on traditional and novel work schedules.

Science.gov (United States)

Klerman, Elizabeth B; Beckett, Scott A; Landrigan, Christopher P

2016-09-13

In 2011 the U.S. Accreditation Council for Graduate Medical Education began limiting first year resident physicians (interns) to shifts of ≤16 consecutive hours. Controversy persists regarding the effectiveness of this policy for reducing errors and accidents while promoting education and patient care. Using a mathematical model of the effects of circadian rhythms and length of time awake on objective performance and subjective alertness, we quantitatively compared predictions for traditional intern schedules to those that limit work to ≤ 16 consecutive hours. We simulated two traditional schedules and three novel schedules using the mathematical model. The traditional schedules had extended duration work shifts (≥24 h) with overnight work shifts every second shift (including every third night, Q3) or every third shift (including every fourth night, Q4) night; the novel schedules had two different cross-cover (XC) night team schedules (XC-V1 and XC-V2) and a Rapid Cycle Rotation (RCR) schedule. Predicted objective performance and subjective alertness for each work shift were computed for each individual's schedule within a team and then combined for the team as a whole. Our primary outcome was the amount of time within a work shift during which a team's model-predicted objective performance and subjective alertness were lower than that expected after 16 or 24 h of continuous wake in an otherwise rested individual. The model predicted fewer hours with poor performance and alertness, especially during night-time work hours, for all three novel schedules than for either the traditional Q3 or Q4 schedules. Three proposed schedules that eliminate extended shifts may improve performance and alertness compared with traditional Q3 or Q4 schedules. Predicted times of worse performance and alertness were at night, which is also a time when supervision of trainees is lower. Mathematical modeling provides a quantitative comparison approach with potential to aid

Can a mathematical model predict an individual's trait-like response to both total and partial sleep loss?

Science.gov (United States)

Ramakrishnan, Sridhar; Lu, Wei; Laxminarayan, Srinivas; Wesensten, Nancy J; Rupp, Tracy L; Balkin, Thomas J; Reifman, Jaques

2015-06-01

Humans display a trait-like response to sleep loss. However, it is not known whether this trait-like response can be captured by a mathematical model from only one sleep-loss condition to facilitate neurobehavioural performance prediction of the same individual during a different sleep-loss condition. In this paper, we investigated the extent to which the recently developed unified mathematical model of performance (UMP) captured such trait-like features for different sleep-loss conditions. We used the UMP to develop two sets of individual-specific models for 15 healthy adults who underwent two different sleep-loss challenges (order counterbalanced; separated by 2-4 weeks): (i) 64 h of total sleep deprivation (TSD) and (ii) chronic sleep restriction (CSR) of 7 days of 3 h nightly time in bed. We then quantified the extent to which models developed using psychomotor vigilance task data under TSD predicted performance data under CSR, and vice versa. The results showed that the models customized to an individual under one sleep-loss condition accurately predicted performance of the same individual under the other condition, yielding, on average, up to 50% improvement over non-individualized, group-average model predictions. This finding supports the notion that the UMP captures an individual's trait-like response to different sleep-loss conditions. © 2014 European Sleep Research Society.

Mathematical approaches for complexity/predictivity trade-offs in complex system models : LDRD final report.

Energy Technology Data Exchange (ETDEWEB)

Goldsby, Michael E.; Mayo, Jackson R.; Bhattacharyya, Arnab (Massachusetts Institute of Technology, Cambridge, MA); Armstrong, Robert C.; Vanderveen, Keith

2008-09-01

The goal of this research was to examine foundational methods, both computational and theoretical, that can improve the veracity of entity-based complex system models and increase confidence in their predictions for emergent behavior. The strategy was to seek insight and guidance from simplified yet realistic models, such as cellular automata and Boolean networks, whose properties can be generalized to production entity-based simulations. We have explored the usefulness of renormalization-group methods for finding reduced models of such idealized complex systems. We have prototyped representative models that are both tractable and relevant to Sandia mission applications, and quantified the effect of computational renormalization on the predictive accuracy of these models, finding good predictivity from renormalized versions of cellular automata and Boolean networks. Furthermore, we have theoretically analyzed the robustness properties of certain Boolean networks, relevant for characterizing organic behavior, and obtained precise mathematical constraints on systems that are robust to failures. In combination, our results provide important guidance for more rigorous construction of entity-based models, which currently are often devised in an ad-hoc manner. Our results can also help in designing complex systems with the goal of predictable behavior, e.g., for cybersecurity.

The Prediction of the Students' Academic Underachievement in Mathematics Using the DEA Model: A Developing Country Case Study

Science.gov (United States)

Moradi, Fatemeh; Amiripour, Parvaneh

2017-01-01

In this study, an attempt was made to predict the students' mathematical academic underachievement at the Islamic Azad University-Yadegare-Imam branch and the appropriate strategies in mathematical academic achievement to be applied using the Data Envelopment Analysis (DEA) model. Survey research methods were used to select 91 students from the…

Critical velocity and anaerobic paddling capacity determined by different mathematical models and number of predictive trials in canoe slalom.

Science.gov (United States)

Messias, Leonardo H D; Ferrari, Homero G; Reis, Ivan G M; Scariot, Pedro P M; Manchado-Gobatto, Fúlvia B

2015-03-01

The purpose of this study was to analyze if different combinations of trials as well as mathematical models can modify the aerobic and anaerobic estimates from critical velocity protocol applied in canoe slalom. Fourteen male elite slalom kayakers from Brazilian canoe slalom team (K1) were evaluated. Athletes were submitted to four predictive trials of 150, 300, 450 and 600 meters in a lake and the time to complete each trial was recorded. Critical velocity (CV-aerobic parameter) and anaerobic paddling capacity (APC-anaerobic parameter) were obtained by three mathematical models (Linear1=distance-time; Linear 2=velocity-1/time and Non-Linear = time-velocity). Linear 1 was chosen for comparison of predictive trials combinations. Standard combination (SC) was considered as the four trials (150, 300, 450 and 600 m). High fits of regression were obtained from all mathematical models (range - R² = 0.96-1.00). Repeated measures ANOVA pointed out differences of all mathematical models for CV (p = 0.006) and APC (p = 0.016) as well as R² (p = 0.033). Estimates obtained from the first (1) and the fourth (4) predictive trials (150 m = lowest; and 600 m = highest, respectively) were similar and highly correlated (r=0.98 for CV and r = 0.96 for APC) with the SC. In summary, methodological aspects must be considered in critical velocity application in canoe slalom, since different combinations of trials as well as mathematical models resulted in different aerobic and anaerobic estimates. Key pointsGreat attention must be given for methodological concerns regarding critical velocity protocol applied on canoe slalom, since different estimates were obtained depending on the mathematical model and the predictive trials used.Linear 1 showed the best fits of regression. Furthermore, to the best of our knowledge and considering practical applications, this model is the easiest one to calculate the estimates from critical velocity protocol. Considering this, the abyss between science

Mathematical model to predict temperature profile and air–fuel equivalence ratio of a downdraft gasification process

International Nuclear Information System (INIS)

Jaojaruek, Kitipong

2014-01-01

Highlights: • A mathematical model based on finite computation analysis was developed. • Model covers all zones of gasification process which will be useful to improve gasifier design. • Model can predict temperature profile, feedstock consumption rate and reaction equivalent ratio (ϕ). • Model-predicted parameters fitted well with experimental values. - Abstract: A mathematical model for the entire length of a downdraft gasifier was developed using thermochemical principles to derive energy and mass conversion equations. Analysis of heat transfer (conduction, convection and radiation) and chemical kinetic technique were applied to predict the temperature profile, feedstock consumption rate (FCR) and reaction equivalence ratio (RER). The model will be useful for designing gasifiers, estimating output gas composition and gas production rate (GPR). Implicit finite difference method solved the equations on the considered reactor length (50 cm) and diameter (20 cm). Conversion criteria for calculation of temperature and feedstock consumption rate were 1 × 10 −6 °C and 1 × 10 −6 kg/h, respectively. Experimental validation showed that model outputs fitted well with experimental data. Maximum deviation between model and experimental data of temperature, FCR and RER were 52 °C at combustion temperature 663 °C, 0.7 kg/h at the rate 8.1 kg/h and 0.03 at the RER 0.42, respectively. Experimental uncertainty of temperature, FCR and RER were 24.4 °C, 0.71 kg/h and 0.04, respectively, on confidence level of 95%

Mathematical Models of Tuberculosis Reactivation and Relapse

Directory of Open Access Journals (Sweden)

Robert Steven Wallis

2016-05-01

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

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

Science.gov (United States)

Fox, William

2012-01-01

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

Mathematical modeling for novel cancer drug discovery and development.

Science.gov (United States)

Zhang, Ping; Brusic, Vladimir

2014-10-01

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

Mathematical modelling

DEFF Research Database (Denmark)

Blomhøj, Morten

2004-01-01

Developing competences for setting up, analysing and criticising mathematical models are normally seen as relevant only from and above upper secondary level. The general belief among teachers is that modelling activities presuppose conceptual understanding of the mathematics involved. Mathematical...... roots for the construction of important mathematical concepts. In addition competences for setting up, analysing and criticising modelling processes and the possible use of models is a formative aim in this own right for mathematics teaching in general education. The paper presents a theoretical...... modelling, however, can be seen as a practice of teaching that place the relation between real life and mathematics into the centre of teaching and learning mathematics, and this is relevant at all levels. Modelling activities may motivate the learning process and help the learner to establish cognitive...

Competence with fractions predicts gains in mathematics achievement.

Science.gov (United States)

Bailey, Drew H; Hoard, Mary K; Nugent, Lara; Geary, David C

2012-11-01

Competence with fractions predicts later mathematics achievement, but the codevelopmental pattern between fractions knowledge and mathematics achievement is not well understood. We assessed this codevelopment through examination of the cross-lagged relation between a measure of conceptual knowledge of fractions and mathematics achievement in sixth and seventh grades (N=212). The cross-lagged effects indicated that performance on the sixth grade fractions concepts measure predicted 1-year gains in mathematics achievement (ß=.14, pmathematics achievement did not predict gains on the fractions concepts measure (ß=.03, p>.50). In a follow-up assessment, we demonstrated that measures of fluency with computational fractions significantly predicted seventh grade mathematics achievement above and beyond the influence of fluency in computational whole number arithmetic, performance on number fluency and number line tasks, central executive span, and intelligence. Results provide empirical support for the hypothesis that competence with fractions underlies, in part, subsequent gains in mathematics achievement. Copyright © 2012 Elsevier Inc. All rights reserved.

The Development of Mathematical Prediction Model to Predict Resilient Modulus for Natural Soil Stabilized by Pofa-Opc Additive for the Use in Unpaved Road Design

Science.gov (United States)

Gamil, Y. M. R.; Bakar, I. H.

2016-07-01

Resilient Modulus (Mr) is considered one of the most important parameters in the design of road structure. This paper describes the development of the mathematical model to predict resilient modulus of organic soil stabilized by the mix of Palm Oil Fuel Ash - Ordinary Portland Cement (POFA-OPC) soil stabilization additives. It aims to optimize the use of the use of POFA in soil stabilization. The optimization models enable to eliminate the arbitrary selection and its associated disadvantages in determination of the optimum additive proportion. The model was developed based on Scheffe regression theory. The mix proportions of the samples in the experiment were adopted from similar studies reported in the literature Twenty five samples were designed, prepared and then characterized for each mix proportion based on the MR in 28 days curing. The results are used to develop the mathematical prediction model. The model was statistically analyzed and verified for its adequacy and validity using F-test.

Mathematical modeling of dissolved oxygen in fish ponds ...

African Journals Online (AJOL)

Mathematical modeling of dissolved oxygen in fish ponds. WJS Mwegoha, ME Kaseva, SMM Sabai. Abstract. A mathematical model was developed to predict the effects of wind speed, light, pH, Temperature, dissolved carbon dioxide and chemical oxygen demand (COD) on Dissolved Oxygen (DO) in fish ponds. The effects ...

Studies on Mathematical Models of Wet Adhesion and Lifetime Prediction of Organic Coating/Steel by Grey System Theory.

Science.gov (United States)

Meng, Fandi; Liu, Ying; Liu, Li; Li, Ying; Wang, Fuhui

2017-06-28

A rapid degradation of wet adhesion is the key factor controlling coating lifetime, for the organic coatings under marine hydrostatic pressure. The mathematical models of wet adhesion have been studied by Grey System Theory (GST). Grey models (GM) (1, 1) of epoxy varnish (EV) coating/steel and epoxy glass flake (EGF) coating/steel have been established, and a lifetime prediction formula has been proposed on the basis of these models. The precision assessments indicate that the established models are accurate, and the prediction formula is capable of making precise lifetime forecasting of the coatings.

Mathematical modelling of flooding at Magela Creek

International Nuclear Information System (INIS)

Vardavas, I.

1989-01-01

The extent and frequency of the flooding at Magela Creek can be predicted from a mathematical/computer model describing the hydrological phases of surface runoff. Surface runoff involves complex water transfer processes over very inhomogeneous terrain. A simple mathematical model of these has been developed which includes the interception of rainfall by the plant canopy, evapotranspiration, infiltration of surface water into the soil, the storage of water in surface depressions, and overland and subsurface water flow. The rainfall-runoff model has then been incorporated into a more complex computer model to predict the amount of water that enters and leaves the Magela Creek flood plain, downstream of the mine. 2 figs., ills

Mathematical modelling of two-phase flows

International Nuclear Information System (INIS)

Komen, E.M.J.; Stoop, P.M.

1992-11-01

A gradual shift from methods based on experimental correlations to methods based on mathematical models to study 2-phase flows can be observed. The latter can be used to predict dynamical behaviour of 2-phase flows. This report discusses various mathematical models for the description of 2-phase flows. An important application of these models can be found in thermal-hydraulic computer codes used for analysis of the thermal-hydraulic behaviour of water cooled nuclear power plants. (author). 17 refs., 7 figs., 6 tabs

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

Science.gov (United States)

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.

Roll paper pilot. [mathematical model for predicting pilot rating of aircraft in roll task

Science.gov (United States)

Naylor, F. R.; Dillow, J. D.; Hannen, R. A.

1973-01-01

A mathematical model for predicting the pilot rating of an aircraft in a roll task is described. The model includes: (1) the lateral-directional aircraft equations of motion; (2) a stochastic gust model; (3) a pilot model with two free parameters; and (4) a pilot rating expression that is a function of rms roll angle and the pilot lead time constant. The pilot gain and lead time constant are selected to minimize the pilot rating expression. The pilot parameters are then adjusted to provide a 20% stability margin and the adjusted pilot parameters are used to compute a roll paper pilot rating of the aircraft/gust configuration. The roll paper pilot rating was computed for 25 aircraft/gust configurations. A range of actual ratings from 2 to 9 were encountered and the roll paper pilot ratings agree quite well with the actual ratings. In addition there is good correlation between predicted and measured rms roll angle.

Predicting tensile strength of friction stir welded AA6061 aluminium alloy joints by a mathematical model

International Nuclear Information System (INIS)

Elangovan, K.; Balasubramanian, V.; Babu, S.

2009-01-01

AA6061 aluminium alloy (Al-Mg-Si alloy) has gathered wide acceptance in the fabrication of light weight structures requiring a high strength-to weight ratio and good corrosion resistance. Compared to the fusion welding processes that are routinely used for joining structural aluminium alloys, friction stir welding (FSW) process is an emerging solid state joining process in which the material that is being welded does not melt and recast. This process uses a non-consumable tool to generate frictional heat in the abutting surfaces. The welding parameters such as tool rotational speed, welding speed, axial force etc., and tool pin profile play a major role in deciding the joint strength. An attempt has been made to develop a mathematical model to predict tensile strength of the friction stir welded AA6061 aluminium alloy by incorporating FSW process parameters. Four factors, five levels central composite design has been used to minimize number of experimental conditions. Response surface method (RSM) has been used to develop the model. Statistical tools such as analysis of variance (ANOVA), student's t-test, correlation co-efficient etc. have been used to validate the developed model. The developed mathematical model can be effectively used to predict the tensile strength of FSW joints at 95% confidence level

Why do early mathematics skills predict later reading? The role of mathematical language.

Science.gov (United States)

Purpura, David J; Logan, Jessica A R; Hassinger-Das, Brenna; Napoli, Amy R

2017-09-01

A growing body of evidence indicates that the development of mathematics and literacy skills is highly related. The importance of literacy skills-specifically language-for mathematics development has been well rationalized. However, despite several prominent studies indicating that mathematics skills are highly predictive of literacy development, the reason for this relation is not well understood. The purpose of this study was to identify how and why early mathematics is predictive of early literacy development. Participants included 125 preschool children 3-5 years old (M = 4 years 3 months). Participants were assessed on mathematics, literacy, and cognitive measures in both the fall and spring of their preschool year. Mediation analyses indicated that the relation between early mathematics and literacy skills is mediated by children's mathematical language skills. These findings suggest that, in prior research identifying mathematical performance as a significant predictor of later literacy skills, mathematical performance may have acted only as a proxy measure for more complex language skills such as those assessed on a mathematical language measure. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Mathematical modelling and numerical simulation of forces in milling process

Science.gov (United States)

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

2018-04-01

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

Mathematical modeling for prediction and optimization of TIG welding pool geometry

Directory of Open Access Journals (Sweden)

U. Esme

2009-04-01

Full Text Available In this work, nonlinear and multi-objective mathematical models were developed to determine the process parameters corresponding to optimum weld pool geometry. The objectives of the developed mathematical models are to maximize tensile load (TL, penetration (P, area of penetration (AP and/or minimize heat affected zone (HAZ, upper width (UW and upper height (UH depending upon the requirements.

A mathematical model for predicting lane changes using the steering wheel angle.

Science.gov (United States)

Schmidt, Kim; Beggiato, Matthias; Hoffmann, Karl Heinz; Krems, Josef F

2014-06-01

Positive safety effects of advanced driver assistance systems can only become effective if drivers accept and use these systems. Early detection of driver's intention would allow for selective system activation and therefore reduce false alarms. This driving simulator study aims at exploring early predictors of lane changes. In total, 3111 lane changes of 51 participants on a simulated highway track were analyzed. Results show that drivers stopped their engagement in a secondary task about 7s before crossing the lane, which indicates a first planning phase of the maneuver. Subsequently, drivers start moving toward the lane, marking a mean steering wheel angle of 2.5°. Steering wheel angle as a directly measurable vehicle parameter appears as a promising early predictor of a lane change. A mathematical model of the steering wheel angle is presented, which is supposed to contribute for predicting lane change maneuvers. The mathematical model will be part of a further predictor of lane changes. This predictor can be a new advanced driver assistance system able to recognize a driver's intention. With this knowledge, other systems can be activated or deactivated so drivers get no annoying and exhausting alarm signals. This is one way how we can increase the acceptance of assistance systems. Copyright © 2014 Elsevier Ltd. All rights reserved.

Fuzzy logic, artificial neural network and mathematical model for prediction of white mulberry drying kinetics

Science.gov (United States)

Jahedi Rad, Shahpour; Kaveh, Mohammad; Sharabiani, Vali Rasooli; Taghinezhad, Ebrahim

2018-05-01

The thin-layer convective- infrared drying behavior of white mulberry was experimentally studied at infrared power levels of 500, 1000 and 1500 W, drying air temperatures of 40, 55 and 70 °C and inlet drying air speeds of 0.4, 1 and 1.6 m/s. Drying rate raised with the rise of infrared power levels at a distinct air temperature and velocity and thus decreased the drying time. Five mathematical models describing thin-layer drying have been fitted to the drying data. Midlli et al. model could satisfactorily describe the convective-infrared drying of white mulberry fruit with the values of the correlation coefficient (R 2=0.9986) and root mean square error of (RMSE= 0.04795). Artificial neural network (ANN) and fuzzy logic methods was desirably utilized for modeling output parameters (moisture ratio (MR)) regarding input parameters. Results showed that output parameters were more accurately predicted by fuzzy model than by the ANN and mathematical models. Correlation coefficient (R 2) and RMSE generated by the fuzzy model (respectively 0.9996 and 0.01095) were higher than referred values for the ANN model (0.9990 and 0.01988 respectively).

Mathematical Modeling and Pure Mathematics

Science.gov (United States)

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…

Developing mathematical models to predict tensile properties of pulsed current gas tungsten arc welded Ti-6Al-4V alloy

International Nuclear Information System (INIS)

Balasubramanian, M.; Jayabalan, V.; Balasubramanian, V.

2008-01-01

Titanium (Ti-6Al-4V) alloy has gathered wide acceptance in the fabrication of light weight structures requiring a high strength-to-weight ratio, such as transportable bridge girders, military vehicles, road tankers and railway transport systems. The preferred welding process of titanium alloy is frequently gas tungsten arc (GTA) welding due to its comparatively easier applicability and better economy. In the case of single pass GTA welding of thinner section of this alloy, the pulsed current has been found beneficial due to its advantages over the conventional continuous current process. Many considerations come into the picture and one need to carefully balance various pulse current parameters to arrive at an optimum combination. Hence, in this investigation an attempt has been made to develop mathematical models to predict tensile properties of pulsed current GTA welded titanium alloy weldments. Four factors, five level, central composite, rotatable design matrix is used to optimise the required number of experiments. The mathematical models have been developed by response surface method (RSM). The adequacy of the models has been checked by ANOVA technique. By using the developed mathematical models, the tensile properties of the joints can be predicted with 99% confidence level

Developing mathematical models to predict tensile properties of pulsed current gas tungsten arc welded Ti-6Al-4V alloy

Energy Technology Data Exchange (ETDEWEB)

Balasubramanian, M. [Department of Production Engineering, Sathyabama University, Old Mamallapuram Road, Chennai 600 119 (India)], E-mail: manianmb@rediffmail.com; Jayabalan, V. [Department of Manufacturing Engineering, Anna University, Guindy, Chennai 600 025 (India)], E-mail: jbalan@annauniv.edu; Balasubramanian, V. [Department of Manufacturing Engineering, Annamalai University, Annamalai Nagar 608 002 (India)], E-mail: visvabalu@yahoo.com

2008-07-01

Titanium (Ti-6Al-4V) alloy has gathered wide acceptance in the fabrication of light weight structures requiring a high strength-to-weight ratio, such as transportable bridge girders, military vehicles, road tankers and railway transport systems. The preferred welding process of titanium alloy is frequently gas tungsten arc (GTA) welding due to its comparatively easier applicability and better economy. In the case of single pass GTA welding of thinner section of this alloy, the pulsed current has been found beneficial due to its advantages over the conventional continuous current process. Many considerations come into the picture and one need to carefully balance various pulse current parameters to arrive at an optimum combination. Hence, in this investigation an attempt has been made to develop mathematical models to predict tensile properties of pulsed current GTA welded titanium alloy weldments. Four factors, five level, central composite, rotatable design matrix is used to optimise the required number of experiments. The mathematical models have been developed by response surface method (RSM). The adequacy of the models has been checked by ANOVA technique. By using the developed mathematical models, the tensile properties of the joints can be predicted with 99% confidence level.

Mathematical Modelling Approach in Mathematics Education

Science.gov (United States)

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…

Prediction of bakery products nutritive value based on mathematical modeling of biochemical reactions

Directory of Open Access Journals (Sweden)

E. I. Ponomareva

2013-01-01

Full Text Available Researches are devoted to identifying changes in the chemical composition of whole-grain wheat bread during baking and to forecasting of food value of bakery products by mathematical modeling of biochemical transformations. The received model represents the invariant composition, considering speed of biochemical reactions at a batch of bakery products, and allowing conduct virtual experiments to develop new types of bread for various categories of the population, including athletes. The offered way of modeling of biochemical transformations at a stage of heat treatment allows to predict food value of bakery products, without spending funds for raw materials and large volume of experiment that will provide possibility of economy of material resources at a stage of development of new types of bakery products and possibility of production efficiency increase.

Mathematical modelling

CERN Document Server

2016-01-01

This book provides a thorough introduction to the challenge of applying mathematics in real-world scenarios. Modelling tasks rarely involve well-defined categories, and they often require multidisciplinary input from mathematics, physics, computer sciences, or engineering. In keeping with this spirit of modelling, the book includes a wealth of cross-references between the chapters and frequently points to the real-world context. The book combines classical approaches to modelling with novel areas such as soft computing methods, inverse problems, and model uncertainty. Attention is also paid to the interaction between models, data and the use of mathematical software. The reader will find a broad selection of theoretical tools for practicing industrial mathematics, including the analysis of continuum models, probabilistic and discrete phenomena, and asymptotic and sensitivity analysis.

Mathematical modeling of a new satellite thermal architecture system connecting the east and west radiator panels and flight performance prediction

International Nuclear Information System (INIS)

Torres, Alejandro; Mishkinis, Donatas; Kaya, Tarik

2014-01-01

An entirely novel satellite thermal architecture, connecting the east and west radiators of a geostationary telecommunications satellite via loop heat pipes (LHPs), is proposed. The LHP operating temperature is regulated by using pressure regulating valves (PRVs). A transient numerical model is developed to simulate the thermal dynamic behavior of the proposed system. The details of the proposed architecture and mathematical model are presented. The model is used to analyze a set of critical design cases to identify potential failure modes prior to the qualification and in-orbit tests. The mathematical model results for critical cases are presented and discussed. The model results demonstrated the robustness and versatility of the proposed architecture under the predicted worst-case conditions. - Highlights: •We developed a mathematical model of a novel satellite thermal architecture. •We provided the dimensioning cases to design the thermal architecture. •We provided the failure mode cases to verify the thermal architecture. •We provided the results of the corresponding dimensioning and failure cases

Mathematical models in marketing a collection of abstracts

CERN Document Server

Funke, Ursula H

1976-01-01

Mathematical models can be classified in a number of ways, e.g., static and dynamic; deterministic and stochastic; linear and nonlinear; individual and aggregate; descriptive, predictive, and normative; according to the mathematical technique applied or according to the problem area in which they are used. In marketing, the level of sophistication of the mathe­ matical models varies considerably, so that a nurnber of models will be meaningful to a marketing specialist without an extensive mathematical background. To make it easier for the nontechnical user we have chosen to classify the models included in this collection according to the major marketing problem areas in which they are applied. Since the emphasis lies on mathematical models, we shall not as a rule present statistical models, flow chart models, computer models, or the empirical testing aspects of these theories. We have also excluded competitive bidding, inventory and transportation models since these areas do not form the core of ·the market...

Predicting Relationships between Mathematics Anxiety, Mathematics Teaching Anxiety, Self-Efficacy Beliefs towards Mathematics and Mathematics Teaching

Science.gov (United States)

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…

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

Science.gov (United States)

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…

Predicting Relationships between Mathematics Anxiety, Mathematics Teaching Anxiety, Self-efficacy Beliefs towards Mathematics and Mathematics Teaching

OpenAIRE

Unlu, Melihan; Ertekin, Erhan; Dilmac, Bulent

2017-01-01

The purpose of the research is to investigate the relationships betweenself-efficacy beliefs toward mathematics, mathematics anxiety and self-efficacybeliefs toward mathematics teaching, mathematics teaching anxiety variables andtesting the relationships between these variables with structural equationmodel. The sample of the research, which was conducted in accordance withrelational survey model, consists of 380 university students, who studied atthe department of Elementary Mathematics Educ...

Using Prediction to Promote Mathematical Understanding and Reasoning

Science.gov (United States)

Kasmer, Lisa; Kim, Ok-Kyeong

2011-01-01

Research has shown that prediction has the potential to promote the teaching and learning of mathematics because it can be used to enhance students' thinking and reasoning at all grade levels in various topics. This article addresses the effectiveness of using prediction on students' understanding and reasoning of mathematical concepts in a middle…

Mathematical models for therapeutic approaches to control HIV disease transmission

CERN Document Server

Roy, Priti Kumar

2015-01-01

The book discusses different therapeutic approaches based on different mathematical models to control the HIV/AIDS disease transmission. It uses clinical data, collected from different cited sources, to formulate the deterministic as well as stochastic mathematical models of HIV/AIDS. It provides complementary approaches, from deterministic and stochastic points of view, to optimal control strategy with perfect drug adherence and also tries to seek viewpoints of the same issue from different angles with various mathematical models to computer simulations. The book presents essential methods and techniques for students who are interested in designing epidemiological models on HIV/AIDS. It also guides research scientists, working in the periphery of mathematical modeling, and helps them to explore a hypothetical method by examining its consequences in the form of a mathematical modelling and making some scientific predictions. The model equations, mathematical analysis and several numerical simulations that are...

Mathematical modeling of optical glazing performance

NARCIS (Netherlands)

Nijnatten, van P.A.; Wittwer, V.; Granqvist, C.G.; Lampert, C.M.

1994-01-01

Mathematical modelling can be a powerful tool in the design and optimalization of glazing. By calculation, the specifications of a glazing design and the optimal design parameters can be predicted without building costly prototypes first. Furthermore, properties which are difficult to measure, like

Mathematical modelling of tissue formation in chondrocyte filter cultures.

Science.gov (United States)

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

2011-12-17

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

Mathematical models of information and stochastic systems

CERN Document Server

Kornreich, Philipp

2008-01-01

From ancient soothsayers and astrologists to today's pollsters and economists, probability theory has long been used to predict the future on the basis of past and present knowledge. Mathematical Models of Information and Stochastic Systems shows that the amount of knowledge about a system plays an important role in the mathematical models used to foretell the future of the system. It explains how this known quantity of information is used to derive a system's probabilistic properties. After an introduction, the book presents several basic principles that are employed in the remainder of the t

Mathematical modeling of biological processes

CERN Document Server

Friedman, Avner

2014-01-01

This book on mathematical modeling of biological processes includes a wide selection of biological topics that demonstrate the power of mathematics and computational codes in setting up biological processes with a rigorous and predictive framework. Topics include: enzyme dynamics, spread of disease, harvesting bacteria, competition among live species, neuronal oscillations, transport of neurofilaments in axon, cancer and cancer therapy, and granulomas. Complete with a description of the biological background and biological question that requires the use of mathematics, this book is developed for graduate students and advanced undergraduate students with only basic knowledge of ordinary differential equations and partial differential equations; background in biology is not required. Students will gain knowledge on how to program with MATLAB without previous programming experience and how to use codes in order to test biological hypothesis.

Mathematical modeling of the flash converting process

Energy Technology Data Exchange (ETDEWEB)

Sohn, H.Y.; Perez-Tello, M.; Riihilahti, K.M. [Utah Univ., Salt Lake City, UT (United States)

1996-12-31

An axisymmetric mathematical model for the Kennecott-Outokumpu flash converting process for converting solid copper matte to copper is presented. The model is an adaptation of the comprehensive mathematical model formerly developed at the University of Utah for the flash smelting of copper concentrates. The model incorporates the transport of momentum, heat, mass, and reaction kinetics between gas and particles in a particle-laden turbulent gas jet. The standard k-{epsilon} model is used to describe gas-phase turbulence in an Eulerian framework. The particle-phase is treated from a Lagrangian viewpoint which is coupled to the gas-phase via the source terms in the Eulerian gas-phase governing equations. Matte particles were represented as Cu{sub 2}S yFeS, and assumed to undergo homogeneous oxidation to Cu{sub 2}O, Fe{sub 3}O{sub 4}, and SO{sub 2}. A reaction kinetics mechanism involving both external mass transfer of oxygen gas to the particle surface and diffusion of oxygen through the porous oxide layer is proposed to estimate the particle oxidation rate Predictions of the mathematical model were compared with the experimental data collected in a bench-scale flash converting facility. Good agreement between the model predictions and the measurements was obtained. The model was used to study the effect of different gas-injection configurations on the overall fluid dynamics in a commercial size flash converting shaft. (author)

Mathematical modeling of the flash converting process

Energy Technology Data Exchange (ETDEWEB)

Sohn, H Y; Perez-Tello, M; Riihilahti, K M [Utah Univ., Salt Lake City, UT (United States)

1997-12-31

An axisymmetric mathematical model for the Kennecott-Outokumpu flash converting process for converting solid copper matte to copper is presented. The model is an adaptation of the comprehensive mathematical model formerly developed at the University of Utah for the flash smelting of copper concentrates. The model incorporates the transport of momentum, heat, mass, and reaction kinetics between gas and particles in a particle-laden turbulent gas jet. The standard k-{epsilon} model is used to describe gas-phase turbulence in an Eulerian framework. The particle-phase is treated from a Lagrangian viewpoint which is coupled to the gas-phase via the source terms in the Eulerian gas-phase governing equations. Matte particles were represented as Cu{sub 2}S yFeS, and assumed to undergo homogeneous oxidation to Cu{sub 2}O, Fe{sub 3}O{sub 4}, and SO{sub 2}. A reaction kinetics mechanism involving both external mass transfer of oxygen gas to the particle surface and diffusion of oxygen through the porous oxide layer is proposed to estimate the particle oxidation rate Predictions of the mathematical model were compared with the experimental data collected in a bench-scale flash converting facility. Good agreement between the model predictions and the measurements was obtained. The model was used to study the effect of different gas-injection configurations on the overall fluid dynamics in a commercial size flash converting shaft. (author)

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

Science.gov (United States)

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.

Mathematical model of gluconic acid fermentation by Aspergillus niger

Energy Technology Data Exchange (ETDEWEB)

Takamatsu, T.; Shioya, S.; Furuya, T.

1981-11-01

A mathematical model for the study of gluconic acid fermentation by Aspergillus niger has been developed. The model has been deduced from the basic biological concept of multicellular filamentous microorganisms, i.e. cell population balance. It can be used to explain the behaviour of both batch and continuous cultures, even when in a lag phase. A new characteristic, involving the existence of dual equilibrium stages during fermentation, has been predicted using this mathematical model. (Refs. 6).

Mathematical modelling of thermal storage systems for the food industry

Energy Technology Data Exchange (ETDEWEB)

Lopez, A.; Lacarra, G. [Universidad Publica de Navarra Campus Arrosadia, Pamplona (Spain). Area de Tecnologia de Alimentos

1999-07-01

Dynamic mathematical models of two thermal storage systems used in the food industry to produce chilled water are presented; an ice-bank system and a holding tank system. The variability of the refrigeration demand with time was taken into account in the model. A zoned approach using mass and energy balances was applied. Heat transfer phenomena in the evaporator were modelled using empirical correlations. The experimental validation of the mathematical models on an ice-bank system at pilot plant scale, and a centralized refrigeration system with a holding tank in a winery, showed accurate prediction. Simple models are adequate to predict the dynamic behaviour of these refrigeration systems under variable heat loads. (Author)

Teaching Mathematical Modeling in Mathematics Education

Science.gov (United States)

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…

Understanding Experimental LCMV Infection of Mice: The Role of Mathematical Models

Directory of Open Access Journals (Sweden)

Gennady Bocharov

2015-01-01

Full Text Available Virus infections represent complex biological systems governed by multiple-level regulatory processes of virus replication and host immune responses. Understanding of the infection means an ability to predict the systems behaviour under various conditions. Such predictions can only rely upon quantitative mathematical models. The model formulations should be tightly linked to a fundamental step called “coordinatization” (Hermann Weyl, that is, the definition of observables, parameters, and structures that enable the link with a biological phenotype. In this review, we analyse the mathematical modelling approaches to LCMV infection in mice that resulted in quantification of some fundamental parameters of the CTL-mediated virus control including the rates of T cell turnover, infected target cell elimination, and precursor frequencies. We show how the modelling approaches can be implemented to address diverse aspects of immune system functioning under normal conditions and in response to LCMV and, importantly, make quantitative predictions of the outcomes of immune system perturbations. This may highlight the notion that data-driven applications of meaningful mathematical models in infection biology remain a challenge.

A mathematical model of steam-drum dynamics

International Nuclear Information System (INIS)

Moeck, E.O.; Hinds, H.W.

1976-12-01

Mathematical equations describing the dynamic behaviour of pressure, water mass, etc. in a steam drum are derived from basic principles. The resultant model includes such effects as steam superheating and water subcooling as well as spontaneous flashing of liquid and condensation of vapour. Experimental data from a pressurizer are adequately predicted by the model. The pressure rise following a turbine trip can be predicted by the isentropic-compression model but not by the thermodynamic-equilibrium model. The equations are individually linearized and implemented on an analog computer in such a way that their non-linear behaviour is retained for small-perturbation studies. (author)

Use of mathematical modelling to assess the impact of vaccines on antibiotic resistance.

Science.gov (United States)

Atkins, Katherine E; Lafferty, Erin I; Deeny, Sarah R; Davies, Nicholas G; Robotham, Julie V; Jit, Mark

2017-11-13

Antibiotic resistance is a major global threat to the provision of safe and effective health care. To control antibiotic resistance, vaccines have been proposed as an essential intervention, complementing improvements in diagnostic testing, antibiotic stewardship, and drug pipelines. The decision to introduce or amend vaccination programmes is routinely based on mathematical modelling. However, few mathematical models address the impact of vaccination on antibiotic resistance. We reviewed the literature using PubMed to identify all studies that used an original mathematical model to quantify the impact of a vaccine on antibiotic resistance transmission within a human population. We reviewed the models from the resulting studies in the context of a new framework to elucidate the pathways through which vaccination might impact antibiotic resistance. We identified eight mathematical modelling studies; the state of the literature highlighted important gaps in our understanding. Notably, studies are limited in the range of pathways represented, their geographical scope, and the vaccine-pathogen combinations assessed. Furthermore, to translate model predictions into public health decision making, more work is needed to understand how model structure and parameterisation affects model predictions and how to embed these predictions within economic frameworks. Copyright © 2017 Elsevier Ltd. All rights reserved.

Mathematical modelling techniques

CERN Document Server

Aris, Rutherford

1995-01-01

""Engaging, elegantly written."" - Applied Mathematical ModellingMathematical modelling is a highly useful methodology designed to enable mathematicians, physicists and other scientists to formulate equations from a given nonmathematical situation. In this elegantly written volume, a distinguished theoretical chemist and engineer sets down helpful rules not only for setting up models but also for solving the mathematical problems they pose and for evaluating models.The author begins with a discussion of the term ""model,"" followed by clearly presented examples of the different types of mode

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

Science.gov (United States)

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…

Outlooks for mathematical modelling of the glass melting process

Energy Technology Data Exchange (ETDEWEB)

Waal, H. de [TNO Institute of Applied Physics, Delft (Netherlands)

1997-12-31

Mathematical modelling is nowadays a standard tool for major producers of float glass, T.V. glass and fiberglass. Also for container glass furnaces, glass tank modelling proves to be a valuable method to optimize process conditions. Mathematical modelling is no longer just a way to visualize the flow patterns and to provide data on heat transfer. It can also predict glass quality in relation to process parameters, because all chemical and physical phenomena are included in the latest generation of models, based on experimental and theoretical research on these phenomena.

Mathematical Modeling in Mathematics Education: Basic Concepts and Approaches

Science.gov (United States)

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…

MATHEMATICAL MODEL MANIPULATOR ROBOTS

Directory of Open Access Journals (Sweden)

O. N. Krakhmalev

2015-12-01

Full Text Available A mathematical model to describe the dynamics of manipulator robots. Mathematical model are the implementation of the method based on the Lagrange equation and using the transformation matrices of elastic coordinates. Mathematical model make it possible to determine the elastic deviations of manipulator robots from programmed motion trajectories caused by elastic deformations in hinges, which are taken into account in directions of change of the corresponding generalized coordinates. Mathematical model is approximated and makes it possible to determine small elastic quasi-static deviations and elastic vibrations. The results of modeling the dynamics by model are compared to the example of a two-link manipulator system. The considered model can be used when performing investigations of the mathematical accuracy of the manipulator robots.

Nitrite-Mediated Hypoxic Vasodilation Predicted from Mathematical Modeling and Quantified from in Vivo Studies in Rat Mesentery

Directory of Open Access Journals (Sweden)

Donald G. Buerk

2017-12-01

Full Text Available Nitric oxide (NO generated from nitrite through nitrite reductase activity in red blood cells has been proposed to play a major role in hypoxic vasodilation. However, we have previously predicted from mathematical modeling that much more NO can be derived from tissue nitrite reductase activity than from red blood cell nitrite reductase activity. Evidence in the literature suggests that tissue nitrite reductase activity is associated with xanthine oxidoreductase (XOR and/or aldehyde oxidoreductase (AOR. We investigated the role of XOR and AOR in nitrite-mediated vasodilation from computer simulations and from in vivo exteriorized rat mesentery experiments. Vasodilation responses to nitrite in the superfusion medium bathing the mesentery equilibrated with 5% O2 (normoxia or zero O2 (hypoxia at either normal or acidic pH were quantified. Experiments were also conducted following intraperitoneal (IP injection of nitrite before and after inhibiting XOR with allopurinol or inhibiting AOR with raloxifene. Computer simulations for NO and O2 transport using reaction parameters reported in the literature were also conducted to predict nitrite-dependent NO production from XOR and AOR activity as a function of nitrite concentration, PO2 and pH. Experimentally, the largest arteriolar responses were found with nitrite >10 mM in the superfusate, but no statistically significant differences were found with hypoxic and acidic conditions in the superfusate. Nitrite-mediated vasodilation with IP nitrite injections was reduced or abolished after inhibiting XOR with allopurinol (p < 0.001. Responses to IP nitrite before and after inhibiting AOR with raloxifene were not as consistent. Our mathematical model predicts that under certain conditions, XOR and AOR nitrite reductase activity in tissue can significantly elevate smooth muscle cell NO and can serve as a compensatory pathway when endothelial NO production is limited by hypoxic conditions. Our theoretical and

Which Preschool Mathematics Competencies Are Most Predictive of Fifth Grade Achievement?

Science.gov (United States)

Nguyen, Tutrang; Watts, Tyler W.; Duncan, Greg J.; Clements, Douglas H.; Sarama, Julie S.; Wolfe, Christopher; Spitler, Mary Elaine

2016-01-01

In an effort to promote best practices regarding mathematics teaching and learning at the preschool level, national advisory panels and organizations have emphasized the importance of children’s emergent counting and related competencies, such as the ability to verbally count, maintain one-to-one correspondence, count with cardinality, subitize, and count forward or backward from a given number. However, little research has investigated whether the kind of mathematical knowledge promoted by the various standards documents actually predict later mathematics achievement. The present study uses longitudinal data from a primarily low-income and minority sample of children to examine the extent to which preschool mathematical competencies, specifically basic and advanced counting, predict fifth grade mathematics achievement. Using regression analyses, we find early numeracy abilities to be the strongest predictors of later mathematics achievement, with advanced counting competencies more predictive than basic counting competencies. Our results highlight the significance of preschool mathematics knowledge for future academic achievement. PMID:27057084

Predictive factors of user acceptance on the primary educational mathematics aids product

Science.gov (United States)

Hidayah, I.; Margunani; Dwijanto

2018-03-01

Mathematics learning in primary schools requires instructional media. According to Piaget's theory, students are still in the concrete operational stage. For this reason, the development of the primary level mathematics aids is needed to support the development of successful mathematics learning. The stages of this research are the stages of commercialization with preparatory, marketing, and measurement analysis procedures. Promotion as part of marketing is done by doing a demonstration to the teacher. Measurements were performed to explore the predictive factors of user feasibility in adopting the product. Measurements were conducted using the concept of Technology Acceptance Model (TAM). Measurement variables include external variables, perceived usefulness, perceived ease of use, attitude, intention to use, and actual use. The result of this research shows that the contribution of predictive factors of mathematics teachers on the teaching aids product as follows: the external variable and perceived ease of use at 74%, perceived usefulness at 72%, intention to use (behavioral) at 58%, attitude at 52%, and the consequence factor (actual use) at 42%.

Thermoregulation in premature infants: A mathematical model.

Science.gov (United States)

Pereira, Carina Barbosa; Heimann, Konrad; Czaplik, Michael; Blazek, Vladimir; Venema, Boudewijn; Leonhardt, Steffen

2016-12-01

In 2010, approximately 14.9 million babies (11.1%) were born preterm. Because preterm infants suffer from an immature thermoregulatory system they have difficulty maintaining their core body temperature at a constant level. Therefore, it is essential to maintain their temperature at, ideally, around 37°C. For this, mathematical models can provide detailed insight into heat transfer processes and body-environment interactions for clinical applications. A new multi-node mathematical model of the thermoregulatory system of newborn infants is presented. It comprises seven compartments, one spherical and six cylindrical, which represent the head, thorax, abdomen, arms and legs, respectively. The model is customizable, i.e. it meets individual characteristics of the neonate (e.g. gestational age, postnatal age, weight and length) which play an important role in heat transfer mechanisms. The model was validated during thermal neutrality and in a transient thermal environment. During thermal neutrality the model accurately predicted skin and core temperatures. The difference in mean core temperature between measurements and simulations averaged 0.25±0.21°C and that of skin temperature averaged 0.36±0.36°C. During transient thermal conditions, our approach simulated the thermoregulatory dynamics/responses. Here, for all infants, the mean absolute error between core temperatures averaged 0.12±0.11°C and that of skin temperatures hovered around 0.30°C. The mathematical model appears able to predict core and skin temperatures during thermal neutrality and in case of a transient thermal conditions. Copyright © 2016 Elsevier Ltd. All rights reserved.

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

Science.gov (United States)

Popilski, Hen; Stepensky, David

2015-05-01

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

Developing mathematical modelling competence

DEFF Research Database (Denmark)

Blomhøj, Morten; Jensen, Tomas Højgaard

2003-01-01

In this paper we introduce the concept of mathematical modelling competence, by which we mean being able to carry through a whole mathematical modelling process in a certain context. Analysing the structure of this process, six sub-competences are identified. Mathematical modelling competence...... cannot be reduced to these six sub-competences, but they are necessary elements in the development of mathematical modelling competence. Experience from the development of a modelling course is used to illustrate how the different nature of the sub-competences can be used as a tool for finding...... the balance between different kinds of activities in a particular educational setting. Obstacles of social, cognitive and affective nature for the students' development of mathematical modelling competence are reported and discussed in relation to the sub-competences....

Mathematical model and simulations of radiation fluxes from buried radionuclides

International Nuclear Information System (INIS)

Ahmad Saat

1999-01-01

A mathematical model and a simple Monte Carlo simulations were developed to predict radiation fluxes from buried radionuclides. The model and simulations were applied to measured (experimental) data. The results of the mathematical model showed good acceptable order of magnitude agreement. A good agreement was also obtained between the simple simulations and the experimental results. Thus, knowing the radionuclide distribution profiles in soil from a core sample, it can be applied to the model or simulations to estimate the radiation fluxes emerging from the soil surface. (author)

Mathematical Modeling of Column-Base Connections under Monotonic Loading

Directory of Open Access Journals (Sweden)

Gholamreza Abdollahzadeh

2014-12-01

Full Text Available Some considerable damage to steel structures during the Hyogo-ken Nanbu Earthquake occurred. Among them, many exposed-type column bases failed in several consistent patterns, such as brittle base plate fracture, excessive bolt elongation, unexpected early bolt failure, and inferior construction work, etc. The lessons from these phenomena led to the need for improved understanding of column base behavior. Joint behavior must be modeled when analyzing semi-rigid frames, which is associated with a mathematical model of the moment–rotation curve. The most accurate model uses continuous nonlinear functions. This article presents three areas of steel joint research: (1 analysis methods of semi-rigid joints; (2 prediction methods for the mechanical behavior of joints; (3 mathematical representations of the moment–rotation curve. In the current study, a new exponential model to depict the moment–rotation relationship of column base connection is proposed. The proposed nonlinear model represents an approach to the prediction of M–θ curves, taking into account the possible failure modes and the deformation characteristics of the connection elements. The new model has three physical parameters, along with two curve-fitted factors. These physical parameters are generated from dimensional details of the connection, as well as the material properties. The M–θ curves obtained by the model are compared with published connection tests and 3D FEM research. The proposed mathematical model adequately comes close to characterizing M–θ behavior through the full range of loading/rotations. As a result, modeling of column base connections using the proposed mathematical model can give crucial beforehand information, and overcome the disadvantages of time consuming workmanship and cost of experimental studies.

A mathematical model of crevice and pitting corrosion

International Nuclear Information System (INIS)

Sharland, S.M.; Tasker, P.W.

1985-09-01

A predictive and self-consistent mathematical model incorporating the electrochemical, chemical and ionic migration processes characterising crevice and pitting corrosion is described. The model predicts full details of the steady-state solution chemistry and electrode kinetics (and hence metal penetration rates) within the corrosion cavities as functions of the many parameters on which these depend such as external electrode potential and crevice dimensions. The crevice is modelled as a parallel-sided slot filled with a dilute sodium chloride solution. Corrosion in both one and two directions is considered. The model includes a solid hydroxide precipitation reaction and assesses the effect on the corrosion rates of consequent changes in the chemical and physical environment within the crevice. A time stepping method is developed for the study of the progression of the corrosion with a precipitation reaction included and is applied to a restricted range of parameters. The applicability of this method is justified in relation to the physical and mathematical approximations made during the construction of the model. (author)

Comparison of mathematical models and artificial neural networks for prediction of drying kinetics of mushroom in microwave vacuum dryer

Directory of Open Access Journals (Sweden)

Ghaderi A.

2012-01-01

Full Text Available Drying characteristics of button mushroom slices were determined using microwave vacuum drier at various powers (130, 260, 380, 450 W and absolute pressures (200, 400, 600, 800 mbar. To select a suitable mathematical model, 6 thin-layer drying models were fitted to the experimental data. The fitting rates of models were assessed based on three parameters; highest R2, lowest chi square ( and root mean square error (RMSE. In addition, using the experimental data, an ANN trained by standard back-propagation algorithm, was developed in order to predict moisture ratio (MR and drying rate (DR values based on the three input variables (drying time, absolute pressure, microwave power. Different activation functions and several rules were used to assess percentage error between the desired and the predicted values. According to our findings, Midilli et al. model showed a reasonable fitting with experimental data. While, the ANN model showed its high capability to predict the MR and DR quite well with determination coefficients (R2 of 0.9991, 0.9995 and 0.9996 for training, validation and testing, respectively. Furthermore, their predictions Mean Square Error were 0.00086, 0.00042 and 0.00052, respectively.

A Mathematical Model Development for the Lateral Collapse of Octagonal Tubes

Science.gov (United States)

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

2018-04-01

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

Evaluating the Predictive Value of Growth Prediction Models

Science.gov (United States)

Murphy, Daniel L.; Gaertner, Matthew N.

2014-01-01

This study evaluates four growth prediction models--projection, student growth percentile, trajectory, and transition table--commonly used to forecast (and give schools credit for) middle school students' future proficiency. Analyses focused on vertically scaled summative mathematics assessments, and two performance standards conditions (high…

Validation of mathematical models for the prediction of organs-at-risk dosimetric metrics in high-dose-rate gynecologic interstitial brachytherapy

Energy Technology Data Exchange (ETDEWEB)

Damato, Antonio L.; Viswanathan, Akila N.; Cormack, Robert A. [Dana-Farber Cancer Institute and Brigham and Women' s Hospital, Boston, Massachusetts 02115 (United States)

2013-10-15

Purpose: Given the complicated nature of an interstitial gynecologic brachytherapy treatment plan, the use of a quantitative tool to evaluate the quality of the achieved metrics compared to clinical practice would be advantageous. For this purpose, predictive mathematical models to predict the D{sub 2cc} of rectum and bladder in interstitial gynecologic brachytherapy are discussed and validated.Methods: Previous plans were used to establish the relationship between D2cc and the overlapping volume of the organ at risk with the targeted area (C0) or a 1-cm expansion of the target area (C1). Three mathematical models were evaluated: D{sub 2cc}=α*C{sub 1}+β (LIN); D{sub 2cc}=α– exp(–β*C{sub 0}) (EXP); and a mixed approach (MIX), where both C{sub 0} and C{sub 1} were inputs of the model. The parameters of the models were optimized on a training set of patient data, and the predictive error of each model (predicted D{sub 2cc}− real D{sub 2cc}) was calculated on a validation set of patient data. The data of 20 patients were used to perform a K-fold cross validation analysis, with K = 2, 4, 6, 8, 10, and 20.Results: MIX was associated with the smallest mean prediction error <6.4% for an 18-patient training set; LIN had an error <8.5%; EXP had an error <8.3%. Best case scenario analysis shows that an error ≤5% can be achieved for a ten-patient training set with MIX, an error ≤7.4% for LIN, and an error ≤6.9% for EXP. The error decreases with the increase in training set size, with the most marked decrease observed for MIX.Conclusions: The MIX model can predict the D{sub 2cc} of the organs at risk with an error lower than 5% with a training set of ten patients or greater. The model can be used in the development of quality assurance tools to identify treatment plans with suboptimal sparing of the organs at risk. It can also be used to improve preplanning and in the development of real-time intraoperative planning tools.

The epidemiological impact of antiretroviral use predicted by mathematical models: a review

Directory of Open Access Journals (Sweden)

Ferguson Neil M

2005-09-01

Full Text Available Abstract This review summarises theoretical studies attempting to assess the population impact of antiretroviral therapy (ART use on mortality and HIV incidence. We describe the key parameters that determine the impact of therapy, and argue that mathematical models of disease transmission are the natural framework within which to explore the interaction between antiviral use and the dynamics of an HIV epidemic. Our review focuses on the potential effects of ART in resource-poor settings. We discuss choice of model type and structure, the potential for risk behaviour change following widespread introduction of ART, the importance of the stage of HIV infection at which treatment is initiated, and the potential for spread of drug resistance. These issues are illustrated with results from models of HIV transmission. We demonstrate that HIV transmission models predicting the impact of ART use should incorporate a realistic progression through stages of HIV infection in order to capture the effect of the timing of treatment initiation on disease spread. The realism of existing models falls short of properly reproducing patterns of diagnosis timing, incorporating heterogeneity in sexual behaviour, and describing the evolution and transmission of drug resistance. The uncertainty surrounding certain effects of ART, such as changes in sexual behaviour and transmission of ART-resistant HIV strains, demands exploration of best and worst case scenarios in modelling, but this must be complemented by surveillance and behavioural surveys to quantify such effects in settings where ART is implemented.

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

Science.gov (United States)

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.

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

Science.gov (United States)

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.

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

Directory of Open Access Journals (Sweden)

Hanna Mulder

2017-10-01

Full Text Available 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.

Designing Prediction Tasks in a Mathematics Software Environment

Science.gov (United States)

Brunström, Mats; Fahlgren, Maria

2015-01-01

There is a recognised need in mathematics teaching for new kinds of tasks which exploit the affordances provided by new technology. This paper focuses on the design of prediction tasks to foster student reasoning about exponential functions in a mathematics software environment. It draws on the first iteration of a design based research study…

Mathematical modeling of flow-injection techniques and their applications for environmental monitoring

International Nuclear Information System (INIS)

Begum, N.N.; Ahmed, J.

2006-01-01

A classification of the existing mathematical models of flow-injection (FI) manifolds based on the main principles on which they are built, have been proposed. Numerous mathematical models of FI systems employing ideas from different scientific areas (e.g. mathematical statistics, chemical engineering, chromatography) have been developed so far. The models have been compared with respect to their predictive power, the complexity of their mathematical treatment, and the requirements for computation time when applied to single-line, multi-channel and conjugated two-line FI systems. It is concluded that the axially dispersed plug flow model deserves special attention because it offers an acceptable compromise between the conflicting requirements for maximal possible mathematical simplicity and maximal possible precision. Applicability of these existing flow-injection models to single-line, multi-channel and conjugated two-line systems for environmental monitoring have been discussed. (author)

Mathematical and computational modeling simulation of solar drying Systems

Science.gov (United States)

Mathematical modeling of solar drying systems has the primary aim of predicting the required drying time for a given commodity, dryer type, and environment. Both fundamental (Fickian diffusion) and semi-empirical drying models have been applied to the solar drying of a variety of agricultural commo...

Mathematical model of an optically pumped molecular laser

CSIR Research Space (South Africa)

Botha, LR

2009-07-01

Full Text Available A mathematical model was developed that accurately predicts the performance of an optically pumped HBr laser. Relatively high conversion efficiency was achieved. Tm pumped Ho:YLF is a viable source for pumping HBr laser, while HBr can be scaled...

Neuro-fuzzy modeling in bankruptcy prediction

Directory of Open Access Journals (Sweden)

Vlachos D.

2003-01-01

Full Text Available For the past 30 years the problem of bankruptcy prediction had been thoroughly studied. From the paper of Altman in 1968 to the recent papers in the '90s, the progress of prediction accuracy was not satisfactory. This paper investigates an alternative modeling of the system (firm, combining neural networks and fuzzy controllers, i.e. using neuro-fuzzy models. Classical modeling is based on mathematical models that describe the behavior of the firm under consideration. The main idea of fuzzy control, on the other hand, is to build a model of a human control expert who is capable of controlling the process without thinking in a mathematical model. This control expert specifies his control action in the form of linguistic rules. These control rules are translated into the framework of fuzzy set theory providing a calculus, which can stimulate the behavior of the control expert and enhance its performance. The accuracy of the model is studied using datasets from previous research papers.

Mathematical Modeling Using MATLAB

National Research Council Canada - National Science Library

Phillips, Donovan

1998-01-01

.... Mathematical Modeling Using MA MATLAB acts as a companion resource to A First Course in Mathematical Modeling with the goal of guiding the reader to a fuller understanding of the modeling process...

Mathematical models to predict rheological parameters of lateritic hydromixtures

OpenAIRE

Gabriel Hernández-Ramírez; Arístides A. Legrá-Lobaina; Beatriz Ramírez-Serrano; Liudmila Pérez-García

2017-01-01

The present work had as objective to establish mathematical models that allow the prognosis of the rheological parameters of the lateritic pulp at concentrations of solids from 35% to 48%, temperature of the preheated hydromixture superior to 82 ° C and number of mineral between 3 and 16. Four samples of lateritic pulp were used in the study at different process locations. The results allowed defining that the plastic properties of the lateritic pulp in the conditions of this study conform to...

Mathematical modeling of infectious disease dynamics

Science.gov (United States)

Siettos, Constantinos I.; Russo, Lucia

2013-01-01

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

A three-dimensional mathematical model to predict air-cooling flow and temperature distribution of wire loops in the Stelmor air-cooling system

International Nuclear Information System (INIS)

Hong, Lingxiang; Wang, Bo; Feng, Shuai; Yang, Zhiliang; Yu, Yaowei; Peng, Wangjun; Zhang, Jieyu

2017-01-01

Highlights: • A 3-dimentioanl mathematical models for complex wire loops was set up in Stelmor. • The air flow field in the cooling process was simulated. • The convective heat transfer coefficient was simulated coupled with air flow field. • The temperature distribution with distances was predicted. - Abstract: Controlling the forced air cooling conditions in the Stelmor conveyor line is important for improving the microstructure and mechanical properties of steel wire rods. A three-dimensional mathematical model incorporating the turbulent flow of the cooling air and heat transfer of the wire rods was developed to predict the cooling process in the Stelmor air-cooling line of wire rolling mills. The distribution of cooling air from the plenum chamber and the forced convective heat transfer coefficient for the wire loops were simulated at the different locations over the conveyor. The temperature profiles and cooling curves of the wire loops in Stelmor conveyor lines were also calculated by considering the convective heat transfer, radiative heat transfer as well as the latent heat during transformation. The calculated temperature results using this model agreed well with the available measured results in the industrial tests. Thus, it was demonstrated that this model can be useful for studying the air-cooling process and predicting the temperature profile and microstructure evolution of the wire rods.

A mathematical model for describing the mechanical behaviour of root canal instruments.

Science.gov (United States)

Zhang, E W; Cheung, G S P; Zheng, Y F

2011-01-01

The purpose of this study was to establish a general mathematical model for describing the mechanical behaviour of root canal instruments by combining a theoretical analytical approach with a numerical finite-element method. Mathematical formulas representing the longitudinal (taper, helical angle and pitch) and cross-sectional configurations and area, the bending and torsional inertia, the curvature of the boundary point and the (geometry of) loading condition were derived. Torsional and bending stresses and the resultant deformation were expressed mathematically as a function of these geometric parameters, modulus of elasticity of the material and the applied load. As illustrations, three brands of NiTi endodontic files of different cross-sectional configurations (ProTaper, Hero 642, and Mani NRT) were analysed under pure torsion and pure bending situation by entering the model into a finite-element analysis package (ANSYS). Numerical results confirmed that mathematical models were a feasible method to analyse the mechanical properties and predict the stress and deformation for root canal instruments during root canal preparation. Mathematical and numerical model can be a suitable way to examine mechanical behaviours as a criterion of the instrument design and to predict the stress and strain experienced by the endodontic instruments during root canal preparation. © 2010 International Endodontic Journal.

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

Science.gov (United States)

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

2014-08-28

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

Prognosis of Cs 137 dynamics in Pripyat river using mathematical modeling

International Nuclear Information System (INIS)

Ris, T.V.

2010-01-01

The analysis of measured and predicted data of Cs 137 dynamics in the water of Pripyat River are given using mathematical models developed by J. Smith (AQUASCOPE), L. Hakanson, and proposed transport model. (authors)

Mathematical Modeling: A Structured Process

Science.gov (United States)

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…

Predictive models for PEM-electrolyzer performance using adaptive neuro-fuzzy inference systems

Energy Technology Data Exchange (ETDEWEB)

Becker, Steffen [University of Tasmania, Hobart 7001, Tasmania (Australia); Karri, Vishy [Australian College of Kuwait (Kuwait)

2010-09-15

Predictive models were built using neural network based Adaptive Neuro-Fuzzy Inference Systems for hydrogen flow rate, electrolyzer system-efficiency and stack-efficiency respectively. A comprehensive experimental database forms the foundation for the predictive models. It is argued that, due to the high costs associated with the hydrogen measuring equipment; these reliable predictive models can be implemented as virtual sensors. These models can also be used on-line for monitoring and safety of hydrogen equipment. The quantitative accuracy of the predictive models is appraised using statistical techniques. These mathematical models are found to be reliable predictive tools with an excellent accuracy of {+-}3% compared with experimental values. The predictive nature of these models did not show any significant bias to either over prediction or under prediction. These predictive models, built on a sound mathematical and quantitative basis, can be seen as a step towards establishing hydrogen performance prediction models as generic virtual sensors for wider safety and monitoring applications. (author)

Executive functioning predicts reading, mathematics, and theory of mind during the elementary years.

Science.gov (United States)

Cantin, Rachelle H; Gnaedinger, Emily K; Gallaway, Kristin C; Hesson-McInnis, Matthew S; Hund, Alycia M

2016-06-01

The goal of this study was to specify how executive functioning components predict reading, mathematics, and theory of mind performance during the elementary years. A sample of 93 7- to 10-year-old children completed measures of working memory, inhibition, flexibility, reading, mathematics, and theory of mind. Path analysis revealed that all three executive functioning components (working memory, inhibition, and flexibility) mediated age differences in reading comprehension, whereas age predicted mathematics and theory of mind directly. In addition, reading mediated the influence of executive functioning components on mathematics and theory of mind, except that flexibility also predicted mathematics directly. These findings provide important details about the development of executive functioning, reading, mathematics, and theory of mind during the elementary years. Copyright © 2016 Elsevier Inc. All rights reserved.

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

Science.gov (United States)

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…

Use of mathematic modeling to compare and predict hemodynamic effects of the modified Blalock-Taussig and right ventricle-pulmonary artery shunts for hypoplastic left heart syndrome.

Science.gov (United States)

Bove, Edward L; Migliavacca, Francesco; de Leval, Marc R; Balossino, Rossella; Pennati, Giancarlo; Lloyd, Thomas R; Khambadkone, Sachin; Hsia, Tain-Yen; Dubini, Gabriele

2008-08-01

Stage one reconstruction (Norwood operation) for hypoplastic left heart syndrome can be performed with either a modified Blalock-Taussig shunt or a right ventricle-pulmonary artery shunt. Both methods have certain inherent characteristics. It is postulated that mathematic modeling could help elucidate these differences. Three-dimensional computer models of the Blalock-Taussig shunt and right ventricle-pulmonary artery shunt modifications of the Norwood operation were developed by using the finite volume method. Conduits of 3, 3.5, and 4 mm were used in the Blalock-Taussig shunt model, whereas conduits of 4, 5, and 6 mm were used in the right ventricle-pulmonary artery shunt model. The hydraulic nets (lumped resistances, compliances, inertances, and elastances) were identical in the 2 models. A multiscale approach was adopted to couple the 3-dimensional models with the circulation net. Computer simulations were compared with postoperative catheterization data. Good correlation was found between predicted and observed data. For the right ventricle-pulmonary artery shunt modification, there was higher aortic diastolic pressure, decreased pulmonary artery pressure, lower Qp/Qs ratio, and higher coronary perfusion pressure. Mathematic modeling predicted minimal regurgitant flow in the right ventricle-pulmonary artery shunt model, which correlated with postoperative Doppler measurements. The right ventricle-pulmonary artery shunt demonstrated lower stroke work and a higher mechanical efficiency (stroke work/total mechanical energy). The close correlation between predicted and observed data supports the use of mathematic modeling in the design and assessment of surgical procedures. The potentially damaging effects of a systemic ventriculotomy in the right ventricle-pulmonary artery shunt modification of the Norwood operation have not been analyzed.

Mathematical model insights into arsenic detoxification

Directory of Open Access Journals (Sweden)

Nijhout H Frederik

2011-08-01

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

Mathematical Modelling of Surfactant Self-assembly at Interfaces

KAUST Repository

Morgan, C. E.

2015-01-01

© 2015 Society for Industrial and Applied Mathematics. We present a mathematical model to describe the distribution of surfactant pairs in a multilayer structure beneath an adsorbed monolayer. A mesoscopic model comprising a set of ordinary differential equations that couple the rearrangement of surfactant within the multilayer to the surface adsorption kinetics is first derived. This model is then extended to the macroscopic scale by taking the continuum limit that exploits the typically large number of surfactant layers, which results in a novel third-order partial differential equation. The model is generalized to allow for the presence of two adsorbing boundaries, which results in an implicit free-boundary problem. The system predicts physically observed features in multilayer systems such as the initial formation of smaller lamellar structures and the typical number of layers that form in equilibrium.

Models for predicting compressive strength and water absorption of ...

African Journals Online (AJOL)

This work presents a mathematical model for predicting the compressive strength and water absorption of laterite-quarry dust cement block using augmented Scheffe's simplex lattice design. The statistical models developed can predict the mix proportion that will yield the desired property. The models were tested for lack of ...

Social-geographic approaches to application of economic-mathematical modeling in predicting the place of Ukrainian farming economies in food market commoditization

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Valeriy Rudenko

2017-11-01

Full Text Available Social-geographic analysis of farmery with application of economic-mathematical modeling allowed for prediction of farming economies’ role in food market commoditization. The equation of potential demand was suggested. Actual consumption and its recommended rates with respect to meat and meat products, milk and milk products, eggs, fish and fish products, bread and cereal products, potatoes, vegetables, fruits and berries, etc, were compared. Cartographic model of Ukrainian domestic food market’s potential capacity (within good-money relations was developed. The low level of purchasing power, especially in rural population, makes a high percentage of foodstuffs be beyond the goods-money relations. In rural areas, they (inclusive of farmers produce and consume a significant portion of foodstuffs that escaped the goods-money relations, or such foodstuffs were given to them by the relatives. We regard that in the process of assessment of the capacity of domestic food market, this share of products should also be taken into account. The assessment also necessitates consideration of the number of urban and rural population in Ukrainian regions; manufacturing of certain types of agricultural production; needs in this or that type of product as prescribed by minimal and rational consumption rates. When predicting, with the use of economic-mathematical modeling, the places of farming economies in commoditization of food market, it is reasonable to apply the parameters of time series of the number of farming economies and the areas of lands used by them with consideration of the dynamics of population number and the level of its (population self-provision with agricultural production. Application of predictive linear models shows that the share of production manufactured by farming economies will be most essential before 2020 on the market of potatoes and vegetables (reaching 15 %. Despite the predicted double increase in animal production, its share

Mathematical Modelling to Predict Oxidative Behaviour of Conjugated Linoleic Acid in the Food Processing Industry

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Aitziber Ojanguren

2013-06-01

Full Text Available Industrial processes that apply high temperatures in the presence of oxygen may compromise the stability of conjugated linoleic acid (CLA bioactive isomers. Statistical techniques are used in this study to model and predict, on a laboratory scale, the oxidative behaviour of oil with high CLA content, controlling the limiting factors of food processing. This modelling aims to estimate the impact of an industrial frying process (140 °C, 7 L/h air on the oxidation of CLA oil for use as frying oil instead of sunflower oil. A factorial design was constructed within a temperature (80–200 °C and air flow (7–20 L/h range. Oil stability index (Rancimat method was used as a measure of oxidation. Three-level full factorial design was used to obtain a quadratic model for CLA oil, enabling the oxidative behaviour to be predicted under predetermined process conditions (temperature and air flow. It is deduced that temperatures applied in food processes affect the oxidation of CLA to a greater extent than air flow. As a result, it is estimated that the oxidative stability of CLA oil is less resistant to industrial frying than sunflower oil. In conclusion, thanks to the mathematical model, a good choice of the appropriate industrial food process can be selected to avoid the oxidation of the bioactive isomers of CLA, ensuring its functionality in novel applications.

Mathematical Model for Multicomponent Adsorption Equilibria Using Only Pure Component Data

DEFF Research Database (Denmark)

Marcussen, Lis

2000-01-01

A mathematical model for nonideal adsorption equilibria in multicomponent mixtures is developed. It is applied with good results for pure substances and for prediction of strongly nonideal multicomponent equilibria using only pure component data. The model accounts for adsorbent...

Mathematical modeling of a convective textile drying process

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G. Johann

2014-12-01

Full Text Available This study aims to develop a model that accurately represents the convective drying process of textile materials. The mathematical modeling was developed from energy and mass balances and, for the solution of the mathematical model, the technique of finite differences, in Cartesian coordinates, was used. It transforms the system of partial differential equations into a system of ordinary equations, with the unknowns, the temperature and humidity of both the air and the textile material. The simulation results were compared with experimental data obtained from the literature. In the statistical analysis the Shapiro-Wilk test was used to validate the model and, in all cases simulated, the results were p-values greater than 5 %, indicating normality of the data. The R-squared values were above 0.997 and the ratios Fcalculated/Fsimulated, at the 95 % confidence level, higher than five, indicating that the modeling was predictive in all simulations.

Finite mathematics models and applications

CERN Document Server

Morris, Carla C

2015-01-01

Features step-by-step examples based on actual data and connects fundamental mathematical modeling skills and decision making concepts to everyday applicability Featuring key linear programming, matrix, and probability concepts, Finite Mathematics: Models and Applications emphasizes cross-disciplinary applications that relate mathematics to everyday life. The book provides a unique combination of practical mathematical applications to illustrate the wide use of mathematics in fields ranging from business, economics, finance, management, operations research, and the life and social sciences.

Modeling eBook acceptance: A study on mathematics teachers

Science.gov (United States)

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

2014-12-01

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

Prediction of Basic Math Course Failure Rate in the Physics, Meteorology, Mathematics, Actuarial Sciences and Pharmacy Degree Programs

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Luis Rojas-Torres

2014-09-01

Full Text Available This paper summarizes a study conducted in 2013 with the purpose of predicting the failure rate of math courses taken by Pharmacy, Mathematics, Actuarial Science, Physics and Meteorology students at Universidad de Costa Rica (UCR. Using the Logistics Regression statistical techniques applied to the 2010 cohort, failure rates were predicted of students in the aforementioned programs in one of their Math introductory courses (Calculus 101 for Physics and Meteorology, Math Principles for Mathematics and Actuarial Science and Applied Differential Equations for Pharmacy. For these models, the UCR admission average, the student’s genre, and the average correct answers in the Quantitative Skills Test were used as predictor variables. The most important variable for all models was the Quantitative Skills Test, and the model with the highest correct classification rate was the Logistics Regression. For the estimated Physics-Meteorology, Pharmacy and Mathematics-Actuarial Science models, correct classifications were 89.8%, 73.6%, and 93.9%, respectively.

The 24-Hour Mathematical Modeling Challenge

Science.gov (United States)

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…

Experimental and Mathematical Modeling for Prediction of Tool Wear on the Machining of Aluminium 6061 Alloy by High Speed Steel Tools

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Okokpujie Imhade Princess

2017-12-01

Full Text Available In recent machining operation, tool life is one of the most demanding tasks in production process, especially in the automotive industry. The aim of this paper is to study tool wear on HSS in end milling of aluminium 6061 alloy. The experiments were carried out to investigate tool wear with the machined parameters and to developed mathematical model using response surface methodology. The various machining parameters selected for the experiment are spindle speed (N, feed rate (f, axial depth of cut (a and radial depth of cut (r. The experiment was designed using central composite design (CCD in which 31 samples were run on SIEG 3/10/0010 CNC end milling machine. After each experiment the cutting tool was measured using scanning electron microscope (SEM. The obtained optimum machining parameter combination are spindle speed of 2500 rpm, feed rate of 200 mm/min, axial depth of cut of 20 mm, and radial depth of cut 1.0mm was found out to achieved the minimum tool wear as 0.213 mm. The mathematical model developed predicted the tool wear with 99.7% which is within the acceptable accuracy range for tool wear prediction.

Experimental and Mathematical Modeling for Prediction of Tool Wear on the Machining of Aluminium 6061 Alloy by High Speed Steel Tools

Science.gov (United States)

Okokpujie, Imhade Princess; Ikumapayi, Omolayo M.; Okonkwo, Ugochukwu C.; Salawu, Enesi Y.; Afolalu, Sunday A.; Dirisu, Joseph O.; Nwoke, Obinna N.; Ajayi, Oluseyi O.

2017-12-01

In recent machining operation, tool life is one of the most demanding tasks in production process, especially in the automotive industry. The aim of this paper is to study tool wear on HSS in end milling of aluminium 6061 alloy. The experiments were carried out to investigate tool wear with the machined parameters and to developed mathematical model using response surface methodology. The various machining parameters selected for the experiment are spindle speed (N), feed rate (f), axial depth of cut (a) and radial depth of cut (r). The experiment was designed using central composite design (CCD) in which 31 samples were run on SIEG 3/10/0010 CNC end milling machine. After each experiment the cutting tool was measured using scanning electron microscope (SEM). The obtained optimum machining parameter combination are spindle speed of 2500 rpm, feed rate of 200 mm/min, axial depth of cut of 20 mm, and radial depth of cut 1.0mm was found out to achieved the minimum tool wear as 0.213 mm. The mathematical model developed predicted the tool wear with 99.7% which is within the acceptable accuracy range for tool wear prediction.

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

Science.gov (United States)

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…

A mathematical model in charactering chloride diffusivity in unsaturated cementitious material

NARCIS (Netherlands)

Zhang, Y.; Ye, G.; Pecur, I.B.; Baricevic, A.; Stirmer, N; Bjegovic, D.

2017-01-01

In this paper, a new analytic model for predicting chloride diffusivity in unsaturated cementitious materials is developed based on conductivity theory and Nernst-Einstein equation. The model specifies that chloride diffusivity in unsaturated cementitious materials can be mathematically described as

Mathematical modeling of dissolved oxygen in fish ponds

African Journals Online (AJOL)

TUOYO

A mathematical model was developed to predict the effects of wind speed, light, pH, Temperature, dissolved carbon dioxide .... chlorophyll, the energy obtained splits water, and oxygen ... is a function of temperature T, light L, substrate, and pH as shown in ..... plants and its relation to the concentration of carbon dioxide and.

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

Science.gov (United States)

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…

Mathematical modeling of the Phoenix Rising pathway.

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Chad Liu

2014-02-01

Full Text Available Apoptosis is a tightly controlled process in mammalian cells. It is important for embryogenesis, tissue homoeostasis, and cancer treatment. Apoptosis not only induces cell death, but also leads to the release of signals that promote rapid proliferation of surrounding cells through the Phoenix Rising (PR pathway. To quantitatively understand the kinetics of interactions of different molecules in this pathway, we developed a mathematical model to simulate the effects of various changes in the PR pathway on the secretion of prostaglandin E2 (PGE2, a key factor for promoting cell proliferation. These changes include activation of caspase 3 (C3, caspase 7 (C7, and nuclear factor κB (NFκB. In addition, we simulated the effects of cyclooxygenase-2 (COX2 inhibition and C3 knockout on the level of secreted PGE2. The model predictions on PGE2 in MEF and 4T1 cells at 48 hours after 10-Gray radiation were quantitatively consistent with the experimental data in the literature. Compared to C7, the model predicted that C3 activation was more critical for PGE2 production. The model also predicted that PGE2 production could be significantly reduced when COX2 expression was blocked via either NFκB inactivation or treatment of cells with exogenous COX2 inhibitors, which led to a decrease in the rate of conversion from arachidonic acid to prostaglandin H2 in the PR pathway. In conclusion, the mathematical model developed in this study yielded new insights into the process of tissue regrowth stimulated by signals from apoptotic cells. In future studies, the model can be used for experimental data analysis and assisting development of novel strategies/drugs for improving cancer treatment or normal tissue regeneration.

Mathematical model for prediction of droplet sizes and distribution associated with impact of liquid-containing projectile

International Nuclear Information System (INIS)

Shelke, Ashish V.; Gera, B.; Maheshwari, N.K.; Singh, R.K.

2018-01-01

After the events of 9/11, the impact of fast flying commercial aircraft is considered as major hazard threatening the Nuclear Power Plant's (NPP) safety. The study of fuel spillage phenomenon and fireball formation is important to understand fire hazards due to burning of dispersed aviation fuel. The detailed analysis of fuel dispersion is very difficult to deliberate because both, large NPP structures and the large size of commercial aircrafts. Sandia National Laboratories, USA conducted impact tests using cylindrical projectiles filled with water to measure the associated parameters. Due to combustion properties and volatile nature of hydrocarbon fuels, the obtained parameters from impact studies using water are incomplete in fire analysis of flammable droplet clouds. A mathematical model is developed for prediction of droplet sizes and distribution associated with the impact of a liquid-containing projectile. The model can predict the transient behavior of droplet cloud. It is validated with experimental data available in literature. In the present study, the analysis has been performed using water and kerosene. The data obtained can be utilized as boundary and initial condition for CFD analysis. This information is useful for fire hazard analysis of aircraft impacts on NPP structures.

Study on China’s Earthquake Prediction by Mathematical Analysis and its Application in Catastrophe Insurance

Science.gov (United States)

Jianjun, X.; Bingjie, Y.; Rongji, W.

2018-03-01

The purpose of this paper was to improve catastrophe insurance level. Firstly, earthquake predictions were carried out using mathematical analysis method. Secondly, the foreign catastrophe insurances’ policies and models were compared. Thirdly, the suggestions on catastrophe insurances to China were discussed. The further study should be paid more attention on the earthquake prediction by introducing big data.

Biological-Mathematical Modeling of Chronic Toxicity.

Science.gov (United States)

1981-07-22

34Mathematical Model of Uptake and Distribution," Uptake and Distribution of Anesthetic Agents, E. M. Papper and R. J. Kitz (Editors, McGraw-Hill Book Co., Inc...distribution, In: Papper , E.M. and Kltz, R.J.(eds.) Uptake and distribution of anesthetic agents, McGraw- Hill, New York, p. 72 3. Plpleson, W.W...1963) Quantitative prediction of anesthetic concentrations. In: Papper , E.M. and Kitz, R.J. (eds.) Uptake and distribution of anesthetic agents, McGraw

Modeling life the mathematics of biological systems

CERN Document Server

Garfinkel, Alan; Guo, Yina

2017-01-01

From predator-prey populations in an ecosystem, to hormone regulation within the body, the natural world abounds in dynamical systems that affect us profoundly. This book develops the mathematical tools essential for students in the life sciences to describe these interacting systems and to understand and predict their behavior. Complex feedback relations and counter-intuitive responses are common in dynamical systems in nature; this book develops the quantitative skills needed to explore these interactions. Differential equations are the natural mathematical tool for quantifying change, and are the driving force throughout this book. The use of Euler’s method makes nonlinear examples tractable and accessible to a broad spectrum of early-stage undergraduates, thus providing a practical alternative to the procedural approach of a traditional Calculus curriculum. Tools are developed within numerous, relevant examples, with an emphasis on the construction, evaluation, and interpretation of mathematical models ...

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

Science.gov (United States)

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

2017-01-01

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

Mathematical modeling with multidisciplinary applications

CERN Document Server

Yang, Xin-She

2013-01-01

Features mathematical modeling techniques and real-world processes with applications in diverse fields Mathematical Modeling with Multidisciplinary Applications details the interdisciplinary nature of mathematical modeling and numerical algorithms. The book combines a variety of applications from diverse fields to illustrate how the methods can be used to model physical processes, design new products, find solutions to challenging problems, and increase competitiveness in international markets. Written by leading scholars and international experts in the field, the

Applied impulsive mathematical models

CERN Document Server

Stamova, Ivanka

2016-01-01

Using the theory of impulsive differential equations, this book focuses on mathematical models which reflect current research in biology, population dynamics, neural networks and economics. The authors provide the basic background from the fundamental theory and give a systematic exposition of recent results related to the qualitative analysis of impulsive mathematical models. Consisting of six chapters, the book presents many applicable techniques, making them available in a single source easily accessible to researchers interested in mathematical models and their applications. Serving as a valuable reference, this text is addressed to a wide audience of professionals, including mathematicians, applied researchers and practitioners.

Fluid reasoning predicts future mathematics among children and adolescents

Science.gov (United States)

Green, Chloe T.; Bunge, Silvia A.; Chiongbian, Victoria Briones; Barrow, Maia; Ferrer, Emilio

2017-01-01

The aim of this longitudinal study was to determine whether fluid reasoning (FR) plays a significant role in the acquisition of mathematics skills, above and beyond the effects of other cognitive and numerical abilities. Using a longitudinal cohort sequential design, we examined how FR measured at three assessment occasions, spaced approximately 1.5 years apart, predicted math outcomes for a group of 69 participants between ages 6 and 21 across all three assessment occasions. We used structural equation modeling (SEM) to examine the direct and indirect relations between children's prior cognitive abilities and their future math achievement. A model including age, FR, vocabulary, and spatial skills accounted for 90% of the variance in future math achievement. In this model, FR was the only significant predictor of future math achievement; neither age, vocabulary, nor spatial skills were significant predictors. Thus, FR was the only predictor of future math achievement across a wide age range that spanned primary and secondary school. These findings build on Cattell's conceptualization of FR (Cattell, 1987) as a scaffold for learning, showing that this domain-general ability supports the acquisition of rudimentary math skills as well as the ability to solve more complex mathematical problems. PMID:28152390

A novel mathematical model for controllable near-field electrospinning

Science.gov (United States)

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

2014-01-01

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

A novel mathematical model for controllable near-field electrospinning

International Nuclear Information System (INIS)

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

2014-01-01

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

A novel mathematical model for controllable near-field electrospinning

Energy Technology Data Exchange (ETDEWEB)

Ru, Changhai, E-mail: rchhai@gmail.com, E-mail: luojun@shu.edu.cn [College of Automation, Harbin Engineering University, Harbin 150001 (China); Robotics and Microsystems Center, Soochow University, Suzhou 215021 (China); Chen, Jie; Shao, Zhushuai [Robotics and Microsystems Center, Soochow University, Suzhou 215021 (China); Pang, Ming [College of Automation, Harbin Engineering University, Harbin 150001 (China); Luo, Jun, E-mail: rchhai@gmail.com, E-mail: luojun@shu.edu.cn [School of Mechatronics Engineering and Automation, Shanghai University, Shanghai 200072 (China)

2014-01-15

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

A Primer for Mathematical Modeling

Science.gov (United States)

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…

New Application of Bioelectrical Impedance Analysis by the Back Propagation Artificial Neural Network Mathematically Predictive Model of Tissue Composition in the Lower Limbs of Elderly People

Directory of Open Access Journals (Sweden)

Tsang-Pai Liu

2012-03-01

Conclusion: In summary, the greater predictive accuracy and precision made the application of BIA with the BP–ANN mathematical model more feasible for the clinical measurement of FM and FFM in the lower limbs of elderly people.

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

Science.gov (United States)

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…

Methodology and Results of Mathematical Modelling of Complex Technological Processes

Science.gov (United States)

Mokrova, Nataliya V.

2018-03-01

The methodology of system analysis allows us to draw a mathematical model of the complex technological process. The mathematical description of the plasma-chemical process was proposed. The importance the quenching rate and initial temperature decrease time was confirmed for producing the maximum amount of the target product. The results of numerical integration of the system of differential equations can be used to describe reagent concentrations, plasma jet rate and temperature in order to achieve optimal mode of hardening. Such models are applicable both for solving control problems and predicting future states of sophisticated technological systems.

Factors Predicting Mathematics Achievement of 8th Graders in TIMSS 2015

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Mehmet Hayri SARI

2017-09-01

Full Text Available In the study, it is aimed to investigate the student, teacher and school factors predicting mathematics achievement of Turkish 8th grade students in TIMSS 2015. The group of the study consists of 6079 students and 220 teachers who attended TIMSS from Turkey. The data of the study was obtained from student and teacher questionnaires and mathematics cognitive test scores. In the data analysis, multilevel regression analysis was used in which dependent variables were plausible mathematics scores and independent variables were student, teacher and school scale scores. According to results, 34% percent of student-level variance was explained by student-level variables. It was found that self-confidence level of students was the most important predictor of mathematics achievement among student-level variables. Additionally, educational resources at home variable was also among the important predictors of mathematics achievement. Teacher and school factors explained 29% of between school variance. Among these variables, school emphasis on academic success and teaching limited by student needs were two significant variables that could predict mathematics achievement of students.

Mathematical modelling of membrane separation

DEFF Research Database (Denmark)

Vinther, Frank

This thesis concerns mathematical modelling of membrane separation. The thesis consists of introductory theory on membrane separation, equations of motion, and properties of dextran, which will be the solute species throughout the thesis. Furthermore, the thesis consist of three separate mathemat......This thesis concerns mathematical modelling of membrane separation. The thesis consists of introductory theory on membrane separation, equations of motion, and properties of dextran, which will be the solute species throughout the thesis. Furthermore, the thesis consist of three separate...... mathematical models, each with a different approach to membrane separation. The first model is a statistical model investigating the interplay between solute shape and the probability of entering the membrane. More specific the transition of solute particles from being spherical to becoming more elongated...

Mathematical modeling of a thermovoltaic cell

Science.gov (United States)

White, Ralph E.; Kawanami, Makoto

1992-01-01

A new type of battery named 'Vaporvolt' cell is in the early stage of its development. A mathematical model of a CuO/Cu 'Vaporvolt' cell is presented that can be used to predict the potential and the transport behavior of the cell during discharge. A sensitivity analysis of the various transport and electrokinetic parameters indicates which parameters have the most influence on the predicted energy and power density of the 'Vaporvolt' cell. This information can be used to decide which parameters should be optimized or determined more accurately through further modeling or experimental studies. The optimal thicknesses of electrodes and separator, the concentration of the electrolyte, and the current density are determined by maximizing the power density. These parameter sensitivities and optimal design parameter values will help in the development of a better CuO/Cu 'Vaporvolt' cell.

Mathematical modeling of a mixed flow spray dryer

International Nuclear Information System (INIS)

Kasiri, N.; Delkhan, F.

2001-01-01

In this paper a mathematical model has been developed to simulate the behavior of spray dryers with an up-flowing spray. The model is based on mass, energy and momentum balance on a single droplet , and mass and energy balances on the drying gas. The system of nonlinear differential equations thus obtained is solved to predict the changes in temperature, humidity, diameter, velocity components and the density of the droplets as well as the temperature and the humidity changes of the drying gas. The predicted results were then compared with an industrially available set of results. A good degree of proximity between the two is reported

Personalizing oncology treatments by predicting drug efficacy, side-effects, and improved therapy: mathematics, statistics, and their integration.

Science.gov (United States)

Agur, Zvia; Elishmereni, Moran; Kheifetz, Yuri

2014-01-01

Despite its great promise, personalized oncology still faces many hurdles, and it is increasingly clear that targeted drugs and molecular biomarkers alone yield only modest clinical benefit. One reason is the complex relationships between biomarkers and the patient's response to drugs, obscuring the true weight of the biomarkers in the overall patient's response. This complexity can be disentangled by computational models that integrate the effects of personal biomarkers into a simulator of drug-patient dynamic interactions, for predicting the clinical outcomes. Several computational tools have been developed for personalized oncology, notably evidence-based tools for simulating pharmacokinetics, Bayesian-estimated tools for predicting survival, etc. We describe representative statistical and mathematical tools, and discuss their merits, shortcomings and preliminary clinical validation attesting to their potential. Yet, the individualization power of mathematical models alone, or statistical models alone, is limited. More accurate and versatile personalization tools can be constructed by a new application of the statistical/mathematical nonlinear mixed effects modeling (NLMEM) approach, which until recently has been used only in drug development. Using these advanced tools, clinical data from patient populations can be integrated with mechanistic models of disease and physiology, for generating personal mathematical models. Upon a more substantial validation in the clinic, this approach will hopefully be applied in personalized clinical trials, P-trials, hence aiding the establishment of personalized medicine within the main stream of clinical oncology. © 2014 Wiley Periodicals, Inc.

Preschoolers' precision of the approximate number system predicts later school mathematics performance.

Science.gov (United States)

Mazzocco, Michèle M M; Feigenson, Lisa; Halberda, Justin

2011-01-01

The Approximate Number System (ANS) is a primitive mental system of nonverbal representations that supports an intuitive sense of number in human adults, children, infants, and other animal species. The numerical approximations produced by the ANS are characteristically imprecise and, in humans, this precision gradually improves from infancy to adulthood. Throughout development, wide ranging individual differences in ANS precision are evident within age groups. These individual differences have been linked to formal mathematics outcomes, based on concurrent, retrospective, or short-term longitudinal correlations observed during the school age years. However, it remains unknown whether this approximate number sense actually serves as a foundation for these school mathematics abilities. Here we show that ANS precision measured at preschool, prior to formal instruction in mathematics, selectively predicts performance on school mathematics at 6 years of age. In contrast, ANS precision does not predict non-numerical cognitive abilities. To our knowledge, these results provide the first evidence for early ANS precision, measured before the onset of formal education, predicting later mathematical abilities.

Number sense in infancy predicts mathematical abilities in childhood.

Science.gov (United States)

Starr, Ariel; Libertus, Melissa E; Brannon, Elizabeth M

2013-11-05

Human infants in the first year of life possess an intuitive sense of number. This preverbal number sense may serve as a developmental building block for the uniquely human capacity for mathematics. In support of this idea, several studies have demonstrated that nonverbal number sense is correlated with mathematical abilities in children and adults. However, there has been no direct evidence that infant numerical abilities are related to mathematical abilities later in childhood. Here, we provide evidence that preverbal number sense in infancy predicts mathematical abilities in preschool-aged children. Numerical preference scores at 6 months of age correlated with both standardized math test scores and nonsymbolic number comparison scores at 3.5 years of age, suggesting that preverbal number sense facilitates the acquisition of numerical symbols and mathematical abilities. This relationship held even after controlling for general intelligence, indicating that preverbal number sense imparts a unique contribution to mathematical ability. These results validate the many prior studies purporting to show number sense in infancy and support the hypothesis that mathematics is built upon an intuitive sense of number that predates language.

Mathematical Modeling: Challenging the Figured Worlds of Elementary Mathematics

Science.gov (United States)

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

Science.gov (United States)

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…

An introduction to mathematical modeling

CERN Document Server

Bender, Edward A

2000-01-01

Employing a practical, ""learn by doing"" approach, this first-rate text fosters the development of the skills beyond the pure mathematics needed to set up and manipulate mathematical models. The author draws on a diversity of fields - including science, engineering, and operations research - to provide over 100 reality-based examples. Students learn from the examples by applying mathematical methods to formulate, analyze, and criticize models. Extensive documentation, consisting of over 150 references, supplements the models, encouraging further research on models of particular interest. The

Mathematical models of cancer and their use in risk assessment. Technical report No. 27

International Nuclear Information System (INIS)

Whittemore, A.S.

1979-08-01

The sensitivity of risk predictions to certain assumptions in the underlying mathematical model is illustrated. To avoid the misleading and erroneous predictions that can result from the use of models incorporating assumptions whose validity is questionable, the following steps should be taken. First, state the assumptions used in a proposed model in terms that are clear to all who will use the model to assess risk. Second, assess the sensitivity of predictions to changes in model assumptions. Third, scrutinize pivotal assumptions in light of the best available human and animal data. Fourth, stress inconsistencies between model assumptions and experimental or epidemiological observations. The model fitting procedure will yield the most information when the data discriminates between theories because of their inconsistency with one or more assumptions. In this sense, mathematical theories are most successful when they fail. Finally, exclude value judgments from the quantitative procedures used to assess risk; instead include them explicitly in that part of the decision process concerned with cost-benefit analysis

A mathematical model of aerosol holding chambers

DEFF Research Database (Denmark)

Zak, M; Madsen, J; Berg, E

1999-01-01

A mathematical model of aerosol delivery from holding chambers (spacers) was developed incorporating tidal volume (VT), chamber volume (Vch), apparatus dead space (VD), effect of valve insufficiency and other leaks, loss of aerosol by immediate impact on the chamber wall, and fallout of aerosol...... in the chamber with time. Four different spacers were connected via filters to a mechanical lung model, and aerosol delivery during "breathing" was determined from drug recovery from the filters. The formula correctly predicted the delivery of budesonide aerosol from the AeroChamber (Trudell Medical, London...

Mathematical Modeling in the Undergraduate Curriculum

Science.gov (United States)

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

Science.gov (United States)

Gould, Heather

2013-01-01

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

Mathematical model for spreading dynamics of social network worms

International Nuclear Information System (INIS)

Sun, Xin; Liu, Yan-Heng; Han, Jia-Wei; Liu, Xue-Jie; Li, Bin; Li, Jin

2012-01-01

In this paper, a mathematical model for social network worm spreading is presented from the viewpoint of social engineering. This model consists of two submodels. Firstly, a human behavior model based on game theory is suggested for modeling and predicting the expected behaviors of a network user encountering malicious messages. The game situation models the actions of a user under the condition that the system may be infected at the time of opening a malicious message. Secondly, a social network accessing model is proposed to characterize the dynamics of network users, by which the number of online susceptible users can be determined at each time step. Several simulation experiments are carried out on artificial social networks. The results show that (1) the proposed mathematical model can well describe the spreading dynamics of social network worms; (2) weighted network topology greatly affects the spread of worms; (3) worms spread even faster on hybrid social networks

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

Science.gov (United States)

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

2017-03-07

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

Mathematical Modelling of Predatory Prokaryotes

NARCIS (Netherlands)

Wilkinson, Michael H.F.

2006-01-01

Predator–prey models have a long history in mathematical modelling of ecosystem dynamics and evolution. In this chapter an introduction to the methodology of mathematical modelling is given, with emphasis on microbial predator–prey systems, followed by a description of variants of the basic

Central Pressure Appraisal: Clinical Validation of a Subject-Specific Mathematical Model.

Directory of Open Access Journals (Sweden)

Francesco Tosello

Full Text Available Current evidence suggests that aortic blood pressure has a superior prognostic value with respect to brachial pressure for cardiovascular events, but direct measurement is not feasible in daily clinical practice.The aim of the present study is the clinical validation of a multiscale mathematical model for non-invasive appraisal of central blood pressure from subject-specific characteristics.A total of 51 young male were selected for the present study. Aortic systolic and diastolic pressure were estimated with a mathematical model and were compared to the most-used non-invasive validated technique (SphygmoCor device, AtCor Medical, Australia. SphygmoCor was calibrated through diastolic and systolic brachial pressure obtained with a sphygmomanometer, while model inputs consist of brachial pressure, height, weight, age, left-ventricular end-systolic and end-diastolic volumes, and data from a pulse wave velocity study.Model-estimated systolic and diastolic central blood pressures resulted to be significantly related to SphygmoCor-assessed central systolic (r = 0.65 p <0.0001 and diastolic (r = 0.84 p<0.0001 blood pressures. The model showed a significant overestimation of systolic pressure (+7.8 (-2.2;14 mmHg, p = 0.0003 and a significant underestimation of diastolic values (-3.2 (-7.5;1.6, p = 0.004, which imply a significant overestimation of central pulse pressure. Interestingly, model prediction errors mirror the mean errors reported in large meta-analysis characterizing the use of the SphygmoCor when non-invasive calibration is performed.In conclusion, multi-scale mathematical model predictions result to be significantly related to SphygmoCor ones. Model-predicted systolic and diastolic aortic pressure resulted in difference of less than 10 mmHg in the 51% and 84% of the subjects, respectively, when compared with SphygmoCor-obtained pressures.

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

Science.gov (United States)

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.

On determining the prediction limits of mathematical models for time series

International Nuclear Information System (INIS)

Peluso, E.; Gelfusa, M.; Lungaroni, M.; Talebzadeh, S.; Gaudio, P.; Murari, A.; Contributors, JET

2016-01-01

Prediction is one of the main objectives of scientific analysis and it refers to both modelling and forecasting. The determination of the limits of predictability is an important issue of both theoretical and practical relevance. In the case of modelling time series, reached a certain level in performance in either modelling or prediction, it is often important to assess whether all the information available in the data has been exploited or whether there are still margins for improvement of the tools being developed. In this paper, an information theoretic approach is proposed to address this issue and quantify the quality of the models and/or predictions. The excellent properties of the proposed indicator have been proved with the help of a systematic series of numerical tests and a concrete example of extreme relevance for nuclear fusion.

Mathematical Modeling: A Bridge to STEM Education

Science.gov (United States)

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…

BEHAVE: fire behavior prediction and fuel modeling system-BURN Subsystem, part 1

Science.gov (United States)

Patricia L. Andrews

1986-01-01

Describes BURN Subsystem, Part 1, the operational fire behavior prediction subsystem of the BEHAVE fire behavior prediction and fuel modeling system. The manual covers operation of the computer program, assumptions of the mathematical models used in the calculations, and application of the predictions.

Wind tunnel modeling of roadways: Comparison with mathematical models

International Nuclear Information System (INIS)

Heidorn, K.; Davies, A.E.; Murphy, M.C.

1991-01-01

The assessment of air quality impacts from roadways is a major concern to urban planners. In order to assess future road and building configurations, a number of techniques have been developed including mathematical models, which simulate traffic emissions and atmospheric dispersion through a series of mathematical relationships and physical models. The latter models simulate emissions and dispersion through scaling of these processes in a wind tunnel. Two roadway mathematical models, HIWAY-2 and CALINE-4, were applied to a proposed development in a large urban area. Physical modeling procedures developed by Rowan Williams Davies and Irwin Inc. (RWDI) in the form of line source simulators were also applied, and the resulting carbon monoxide concentrations were compared. The results indicated a factor of two agreement between the mathematical and physical models. The physical model, however, reacted to change in building massing and configuration. The mathematical models did not, since no provision for such changes was included in the mathematical models. In general, the RWDI model resulted in higher concentrations than either HIWAY-2 or CALINE-4. Where there was underprediction, it was often due to shielding of the receptor by surrounding buildings. Comparison of these three models with the CALTRANS Tracer Dispersion Experiment showed good results although concentrations were consistently underpredicted

Mathematical modeling and hydrodynamics of Electrochemical deburring process

Science.gov (United States)

Prabhu, Satisha; Abhishek Kumar, K., Dr

2018-04-01

The electrochemical deburring (ECD) is a variation of electrochemical machining is considered as one of the efficient methods for deburring of intersecting features and internal parts. Since manual deburring costs are comparatively high one can potentially use this method in both batch production and flow production. The other advantage of this process is that time of deburring as is on the order of seconds as compared to other methods. In this paper, the mathematical modeling of Electrochemical deburring is analysed from its deburring time and base metal removal point of view. Simultaneously material removal rate is affected by electrolyte temperature and bubble formation. The mathematical model and hydrodynamics of the process throw limelight upon optimum velocity calculations which can be theoretically determined. The analysis can be the powerful tool for prediction of the above-mentioned parameters by experimentation.

Predicting Alkylate Yield and its Hydrocarbon Composition for Sulfuric Acid Catalyzed Isobutane Alkylation with Olefins Using the Method of Mathematical Modeling

OpenAIRE

Nurmakanova, А. Е.; Ivashkina, Elena Nikolaevna; Ivanchina, Emilia Dmitrievna; Dolganov, I. A.; Boychenko, S. S.

2015-01-01

The article provides the results of applied mathematical model of isobutane alkylation with olefins catalyzed by sulfuric acid to predict yield and hydrocarbon composition of alkylate caused by the changes in the feedstock composition and process parameters. It is shown that the alkylate produced from feedstock with less mass fraction of isobutane has lower octane value. Wherein the difference in composition of the feedstock contributes to antiknock index by the amount of 1.0-2.0 points.

Mathematical models for plant-herbivore interactions

Science.gov (United States)

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.

Leaching of saltstone: Laboratory and field testing and mathematical modeling

International Nuclear Information System (INIS)

Grant, M.W.; Langton, C.A.; Oblath, S.B.; Pepper, D.W.; Wallace, R.M.; Wilhite, E.L.; Yau, W.W.F.

1987-01-01

A low-level alkaline salt solution will be a byproduct in the processing of high-level waste at the Savannah River Plant (SRP). This solution will be incorporated into a wasteform, saltstone, and disposed of in surface vaults. Laboratory and field leach testing and mathematical modeling have demonstrated the predictability of contaminant release from cement wasteforms. Saltstone disposal in surface vaults will meet the design objective, which is to meet drinking water standards in shallow groundwater at the disposal area boundary. Diffusion is the predominant mechanism for release of contaminants to the environment. Leach testing in unsaturated soil, at soil moisture levels above 1 wt %, has shown no difference in leach rate compared to leaching in distilled water. Field leach testing of three thirty-ton blocks of saltstone in lysimeters has been underway since January 1984. Mathematical models were applied to assess design features for saltstone disposal. One dimensional infinite-composite and semi-infinite analytical models were developed for assessing diffusion of nitrate from saltstone through a cement barrier. Numerical models, both finite element and finite difference, were validated by comparison of model predictions with the saltstone lysimeter results. Validated models were used to assess the long-term performance of the saltstone stored in surface vaults. The maximum concentrations of all contaminants released from saltstone to shallow groundwater are predicted to be below drinking water standards at the disposal area boundary. 5 refs., 11 figs., 5 tabs

A mathematical prediction model incorporating molecular subtype for risk of non-sentinel lymph node metastasis in sentinel lymph node-positive breast cancer patients: a retrospective analysis and nomogram development.

Science.gov (United States)

Wang, Na-Na; Yang, Zheng-Jun; Wang, Xue; Chen, Li-Xuan; Zhao, Hong-Meng; Cao, Wen-Feng; Zhang, Bin

2018-04-25

Molecular subtype of breast cancer is associated with sentinel lymph node status. We sought to establish a mathematical prediction model that included breast cancer molecular subtype for risk of positive non-sentinel lymph nodes in breast cancer patients with sentinel lymph node metastasis and further validate the model in a separate validation cohort. We reviewed the clinicopathologic data of breast cancer patients with sentinel lymph node metastasis who underwent axillary lymph node dissection between June 16, 2014 and November 16, 2017 at our hospital. Sentinel lymph node biopsy was performed and patients with pathologically proven sentinel lymph node metastasis underwent axillary lymph node dissection. Independent risks for non-sentinel lymph node metastasis were assessed in a training cohort by multivariate analysis and incorporated into a mathematical prediction model. The model was further validated in a separate validation cohort, and a nomogram was developed and evaluated for diagnostic performance in predicting the risk of non-sentinel lymph node metastasis. Moreover, we assessed the performance of five different models in predicting non-sentinel lymph node metastasis in training cohort. Totally, 495 cases were eligible for the study, including 291 patients in the training cohort and 204 in the validation cohort. Non-sentinel lymph node metastasis was observed in 33.3% (97/291) patients in the training cohort. The AUC of MSKCC, Tenon, MDA, Ljubljana, and Louisville models in training cohort were 0.7613, 0.7142, 0.7076, 0.7483, and 0.671, respectively. Multivariate regression analysis indicated that tumor size (OR = 1.439; 95% CI 1.025-2.021; P = 0.036), sentinel lymph node macro-metastasis versus micro-metastasis (OR = 5.063; 95% CI 1.111-23.074; P = 0.036), the number of positive sentinel lymph nodes (OR = 2.583, 95% CI 1.714-3.892; P model based on the results of multivariate analysis was established to predict the risk of non

Mathematical biology

CERN Document Server

Murray, James D

1993-01-01

The book is a textbook (with many exercises) giving an in-depth account of the practical use of mathematical modelling in the biomedical sciences. The mathematical level required is generally not high and the emphasis is on what is required to solve the real biological problem. The subject matter is drawn, e.g. from population biology, reaction kinetics, biological oscillators and switches, Belousov-Zhabotinskii reaction, reaction-diffusion theory, biological wave phenomena, central pattern generators, neural models, spread of epidemics, mechanochemical theory of biological pattern formation and importance in evolution. Most of the models are based on real biological problems and the predictions and explanations offered as a direct result of mathematical analysis of the models are important aspects of the book. The aim is to provide a thorough training in practical mathematical biology and to show how exciting and novel mathematical challenges arise from a genuine interdisciplinary involvement with the biosci...

Mathematical Modelling, Simulation, and Optimal Control of the 2014 Ebola Outbreak in West Africa

Directory of Open Access Journals (Sweden)

Amira Rachah

2015-01-01

it is crucial to modelize the virus and simulate it. In this paper, we begin by studying a simple mathematical model that describes the 2014 Ebola outbreak in Liberia. Then, we use numerical simulations and available data provided by the World Health Organization to validate the obtained mathematical model. Moreover, we develop a new mathematical model including vaccination of individuals. We discuss different cases of vaccination in order to predict the effect of vaccination on the infected individuals over time. Finally, we apply optimal control to study the impact of vaccination on the spread of the Ebola virus. The optimal control problem is solved numerically by using a direct multiple shooting method.

Mathematical modeling of microbial growth in milk

Directory of Open Access Journals (Sweden)

Jhony Tiago Teleken

2011-12-01

Full Text Available A mathematical model to predict microbial growth in milk was developed and analyzed. The model consists of a system of two differential equations of first order. The equations are based on physical hypotheses of population growth. The model was applied to five different sets of data of microbial growth in dairy products selected from Combase, which is the most important database in the area with thousands of datasets from around the world, and the results showed a good fit. In addition, the model provides equations for the evaluation of the maximum specific growth rate and the duration of the lag phase which may provide useful information about microbial growth.

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

Science.gov (United States)

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.

Avoiding reification. Heuristic effectiveness of mathematics and the prediction of the Ω- particle

Science.gov (United States)

Ginammi, Michele

2016-02-01

According to Steiner (1998), in contemporary physics new important discoveries are often obtained by means of strategies which rely on purely formal mathematical considerations. In such discoveries, mathematics seems to have a peculiar and controversial role, which apparently cannot be accounted for by means of standard methodological criteria. M. Gell-Mann and Y. Ne'eman's prediction of the Ω- particle is usually considered a typical example of application of this kind of strategy. According to Bangu (2008), this prediction is apparently based on the employment of a highly controversial principle-what he calls the "reification principle". Bangu himself takes this principle to be methodologically unjustifiable, but still indispensable to make the prediction logically sound. In the present paper I will offer a new reconstruction of the reasoning that led to this prediction. By means of this reconstruction, I will show that we do not need to postulate any "reificatory" role of mathematics in contemporary physics and I will contextually clarify the representative and heuristic role of mathematics in science.

A predictive mathematical model for the calculation of the final mass of Graves' disease thyroids treated with 131I

Science.gov (United States)

Traino, Antonio C.; Di Martino, Fabio; Grosso, Mariano; Monzani, Fabio; Dardano, Angela; Caraccio, Nadia; Mariani, Giuliano; Lazzeri, Mauro

2005-05-01

Substantial reductions in thyroid volume (up to 70-80%) after radioiodine therapy of Graves' hyperthyroidism are common and have been reported in the literature. A relationship between thyroid volume reduction and outcome of 131I therapy of Graves' disease has been reported by some authors. This important result could be used to decide individually the optimal radioiodine activity A0 (MBq) to administer to the patient, but a predictive model relating the change in gland volume to A0 is required. Recently, a mathematical model of thyroid mass reduction during the clearance phase (30-35 days) after 131I administration to patients with Graves' disease has been published and used as the basis for prescribing the therapeutic thyroid absorbed dose. It is well known that the thyroid volume reduction goes on until 1 year after therapy. In this paper, a mathematical model to predict the final mass of Graves' diseased thyroids submitted to 131I therapy is presented. This model represents a tentative explanation of what occurs macroscopically after the end of the clearance phase of radioiodine in the gland (the so-called second-order effects). It is shown that the final thyroid mass depends on its basal mass, on the radiation dose absorbed by the gland and on a constant value α typical of thyroid tissue. α has been evaluated based on a set of measurements made in 15 reference patients affected by Graves' disease and submitted to 131I therapy. A predictive equation for the calculation of the final mass of thyroid is presented. It is based on macroscopic parameters measurable after a diagnostic 131I capsule administration (0.37-1.85 MBq), before giving the therapy. The final mass calculated using this equation is compared to the final mass of thyroid measured 1 year after therapy administration in 22 Graves' diseased patients. The final masses calculated and measured 1 year after therapy are in fairly good agreement (R = 0.81). The possibility, for the physician, to decide a

A predictive mathematical model for the calculation of the final mass of Graves' disease thyroids treated with 131I

International Nuclear Information System (INIS)

Traino, Antonio C; Martino, Fabio Di; Grosso, Mariano; Monzani, Fabio; Dardano, Angela; Caraccio, Nadia; Mariani, Giuliano; Lazzeri, Mauro

2005-01-01

Substantial reductions in thyroid volume (up to 70-80%) after radioiodine therapy of Graves' hyperthyroidism are common and have been reported in the literature. A relationship between thyroid volume reduction and outcome of 131 I therapy of Graves' disease has been reported by some authors. This important result could be used to decide individually the optimal radioiodine activity A 0 (MBq) to administer to the patient, but a predictive model relating the change in gland volume to A 0 is required. Recently, a mathematical model of thyroid mass reduction during the clearance phase (30-35 days) after 131 I administration to patients with Graves' disease has been published and used as the basis for prescribing the therapeutic thyroid absorbed dose. It is well known that the thyroid volume reduction goes on until 1 year after therapy. In this paper, a mathematical model to predict the final mass of Graves' diseased thyroids submitted to 131 I therapy is presented. This model represents a tentative explanation of what occurs macroscopically after the end of the clearance phase of radioiodine in the gland (the so-called second-order effects). It is shown that the final thyroid mass depends on its basal mass, on the radiation dose absorbed by the gland and on a constant value α typical of thyroid tissue. α has been evaluated based on a set of measurements made in 15 reference patients affected by Graves' disease and submitted to 131 I therapy. A predictive equation for the calculation of the final mass of thyroid is presented. It is based on macroscopic parameters measurable after a diagnostic 131 I capsule administration (0.37-1.85 MBq), before giving the therapy. The final mass calculated using this equation is compared to the final mass of thyroid measured 1 year after therapy administration in 22 Graves' diseased patients. The final masses calculated and measured 1 year after therapy are in fairly good agreement (R = 0.81). The possibility, for the physician, to

Mathematical model of heat transfer to predict distribution of hardness through the Jominy bar; Modelo matematico de la transferencia de calor para predecir el perfil de durezas en probetas Jominy

Energy Technology Data Exchange (ETDEWEB)

Lopez, E.; Hernandez, J. B.; Solorio, G.; Vergara, H. J.; Vazquez, O.; Garnica, F.

2013-06-01

The heat transfer coefficient was estimated at the bottom surface at Jominy bar end quench specimen by solution of the heat inverse conduction problem. A mathematical model based on the finite-difference method was developed to predict thermal paths and volume fraction of transformed phases. The mathematical model was codified in the commercial package Microsoft Visual Basic v. 6. The calculated thermal path and final phase distribution were used to evaluate the hardness distribution along the AISI 4140 Jominy bar. (Author)

Mathematical Modelling of Immune Parameters in the Evolution of Severe Dengue

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M. K. Premaratne

2017-01-01

Full Text Available Aims. Predicting the risk of severity at an early stage in an individual patient will be invaluable in preventing morbidity and mortality caused by dengue. We hypothesized that such predictions are possible by analyzing multiple parameters using mathematical modeling. Methodology. Data from 11 adult patients with dengue fever (DF and 25 patients with dengue hemorrhagic fever (DHF were analyzed. Multivariate statistical analysis was performed to study the characteristics and interactions of parameters using dengue NS1 antigen levels, dengue IgG antibody levels, platelet counts, and lymphocyte counts. Fuzzy logic fundamentals were used to map the risk of developing severe forms of dengue. The cumulative effects of the parameters were incorporated using the Hamacher and the OWA operators. Results. The operator classified the patients according to the severity level during the time period of 96 hours to 120 hours after the onset of fever. The accuracy ranged from 53% to 89%. Conclusion. The results show a robust mathematical model that explains the evolution from dengue to its serious forms in individual patients. The model allows prediction of severe cases of dengue which could be useful for optimal management of patients during a dengue outbreak. Further analysis of the model may also deepen our understanding of the pathways towards severe illness.

A mathematical model of reservoir sediment quality prediction based on land-use and erosion processes in watershed

Science.gov (United States)

Junakova, N.; Balintova, M.; Junak, J.

2017-10-01

The aim of this paper is to propose a mathematical model for determining of total nitrogen (N) and phosphorus (P) content in eroded soil particles with emphasis on prediction of bottom sediment quality in reservoirs. The adsorbed nutrient concentrations are calculated using the Universal Soil Loss Equation (USLE) extended by the determination of the average soil nutrient concentration in top soils. The average annual vegetation and management factor is divided into five periods of the cropping cycle. For selected plants, the average plant nutrient uptake divided into five cropping periods is also proposed. The average nutrient concentrations in eroded soil particles in adsorbed form are modified by sediment enrichment ratio to obtain the total nutrient content in transported soil particles. The model was designed for the conditions of north-eastern Slovakia. The study was carried out in the agricultural basin of the small water reservoir Klusov.

Causal Bayes Model of Mathematical Competence in Kindergarten

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Božidar Tepeš

2016-06-01

Full Text Available In this paper authors define mathematical competences in the kindergarten. The basic objective was to measure the mathematical competences or mathematical knowledge, skills and abilities in mathematical education. Mathematical competences were grouped in the following areas: Arithmetic and Geometry. Statistical set consisted of 59 children, 65 to 85 months of age, from the Kindergarten Milan Sachs from Zagreb. The authors describe 13 variables for measuring mathematical competences. Five measuring variables were described for the geometry, and eight measuring variables for the arithmetic. Measuring variables are tasks which children solved with the evaluated results. By measuring mathematical competences the authors make causal Bayes model using free software Tetrad 5.2.1-3. Software makes many causal Bayes models and authors as experts chose the model of the mathematical competences in the kindergarten. Causal Bayes model describes five levels for mathematical competences. At the end of the modeling authors use Bayes estimator. In the results, authors describe by causal Bayes model of mathematical competences, causal effect mathematical competences or how intervention on some competences cause other competences. Authors measure mathematical competences with their expectation as random variables. When expectation of competences was greater, competences improved. Mathematical competences can be improved with intervention on causal competences. Levels of mathematical competences and the result of intervention on mathematical competences can help mathematical teachers.

Evaluation of Mathematical Models for Tankers’ Maneuvering Motions

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Erhan AKSU

2017-03-01

Full Text Available In this study, the maneuvering performance of two tanker ships, KVLCC1 and KVLCC2 which have different stern forms are predicted using a system-based method. Two different 3 DOF (degrees of freedom mathematical models based on the MMG(Maneuvering Modeling Group concept areappliedwith the difference in representing lateral force and yawing moment by second and third order polynomials respectively. Hydrodynamic coefficients and related parameters used in the mathematical models of the same scale models of KVLCC1 and KVLCC2 ships are estimated by using experimental data of NMRI (National Maritime Research Institute. The simulations of turning circle with rudder angle ±35o , zigzag(±10o /±10o and zigzag (±20o /±20o maneuvers are carried out and compared with free running model test data of MARIN (Maritime Research Institute Netherlands in this study. As a result of the analysis, it can be summarised that MMG model based on the third order polynomial is superior to the one based on the second order polynomial in view of estimation accuracy of lateral hull force and yawing moment.

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

Science.gov (United States)

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

2018-01-01

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

Mathematical models in medicine: Diseases and epidemics

International Nuclear Information System (INIS)

Witten, M.

1987-01-01

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

Mathematical modeling and visualization of functional neuroimages

DEFF Research Database (Denmark)

Rasmussen, Peter Mondrup

This dissertation presents research results regarding mathematical modeling in the context of the analysis of functional neuroimages. Specifically, the research focuses on pattern-based analysis methods that recently have become popular within the neuroimaging community. Such methods attempt...... sets are characterized by relatively few data observations in a high dimensional space. The process of building models in such data sets often requires strong regularization. Often, the degree of model regularization is chosen in order to maximize prediction accuracy. We focus on the relative influence...... be carefully selected, so that the model and its visualization enhance our ability to interpret the brain. The second part concerns interpretation of nonlinear models and procedures for extraction of ‘brain maps’ from nonlinear kernel models. We assess the performance of the sensitivity map as means...

Mathematical modeling and visualization of functional neuroimages

DEFF Research Database (Denmark)

Rasmussen, Peter Mondrup

This dissertation presents research results regarding mathematical modeling in the context of the analysis of functional neuroimages. Specifically, the research focuses on pattern-based analysis methods that recently have become popular analysis tools within the neuroimaging community. Such methods...... neuroimaging data sets are characterized by relatively few data observations in a high dimensional space. The process of building models in such data sets often requires strong regularization. Often, the degree of model regularization is chosen in order to maximize prediction accuracy. We focus on the relative...... be carefully selected, so that the model and its visualization enhance our ability to interpret brain function. The second part concerns interpretation of nonlinear models and procedures for extraction of ‘brain maps’ from nonlinear kernel models. We assess the performance of the sensitivity map as means...

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

Science.gov (United States)

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.

Strong inference in mathematical modeling: a method for robust science in the 21st century

Directory of Open Access Journals (Sweden)

Vitaly V. Ganusov

2016-07-01

Full Text Available 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 [1], 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 [2], 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 21st century.

A fuzzy mathematical model of West Java population with logistic growth model

Science.gov (United States)

Nurkholipah, N. S.; Amarti, Z.; Anggriani, N.; Supriatna, A. K.

2018-03-01

In this paper we develop a mathematics model of population growth in the West Java Province Indonesia. The model takes the form as a logistic differential equation. We parameterize the model using several triples of data, and choose the best triple which has the smallest Mean Absolute Percentage Error (MAPE). The resulting model is able to predict the historical data with a high accuracy and it also able to predict the future of population number. Predicting the future population is among the important factors that affect the consideration is preparing a good management for the population. Several experiment are done to look at the effect of impreciseness in the data. This is done by considering a fuzzy initial value to the crisp model assuming that the model propagates the fuzziness of the independent variable to the dependent variable. We assume here a triangle fuzzy number representing the impreciseness in the data. We found that the fuzziness may disappear in the long-term. Other scenarios also investigated, such as the effect of fuzzy parameters to the crisp initial value of the population. The solution of the model is obtained numerically using the fourth-order Runge-Kutta scheme.

Robust multi-model predictive control of multi-zone thermal plate system

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Poom Jatunitanon

2018-02-01

Full Text Available A modern controller was designed by using the mathematical model of a multi–zone thermal plate system. An important requirement for this type of controller is that it must be able to keep the temperature set-point of each thermal zone. The mathematical model used in the design was determined through a system identification process. The results showed that when the operating condition is changed, the performance of the controller may be reduced as a result of the system parameter uncertainties. This paper proposes a weighting technique of combining the robust model predictive controller for each operating condition into a single robust multi-model predictive control. Simulation and experimental results showed that the proposed method performed better than the conventional multi-model predictive control in rise time of transient response, when used in a system designed to work over a wide range of operating conditions.

A Mathematical Model for Cisplatin Cellular Pharmacodynamics

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Ardith W. El-Kareh

2003-03-01

Full Text Available A simple theoretical model for the cellular pharmacodynamics of cisplatin is presented. The model, which takes into account the kinetics of cisplatin uptake by cells and the intracellular binding of the drug, can be used to predict the dependence of survival (relative to controls on the time course of extracellular exposure. Cellular pharmacokinetic parameters are derived from uptake data for human ovarian and head and neck cancer cell lines. Survival relative to controls is assumed to depend on the peak concentration of DNA-bound intracellular platinum. Model predictions agree well with published data on cisplatin cytotoxicity for three different cancer cell lines, over a wide range of exposure times. In comparison with previously published mathematical models for anticancer drug pharmacodynamics, the present model provides a better fit to experimental data sets including long exposure times (∼100 hours. The model provides a possible explanation for the fact that cell kill correlates well with area under the extracellular concentration-time curve in some data sets, but not in others. The model may be useful for optimizing delivery schedules and for the dosing of cisplatin for cancer therapy.

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

Science.gov (United States)

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

Mathematical Modeling and Computational Thinking

Science.gov (United States)

Sanford, John F.; Naidu, Jaideep T.

2017-01-01

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

Summer Camp of Mathematical Modeling in China

Science.gov (United States)

Tian, Xiaoxi; Xie, Jinxing

2013-01-01

The Summer Camp of Mathematical Modeling in China is a recently created experience designed to further Chinese students' academic pursuits in mathematical modeling. Students are given more than three months to research on a mathematical modeling project. Researchers and teams with outstanding projects are invited to the Summer Camp to present…

Strategies to Support Students' Mathematical Modeling

Science.gov (United States)

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 Model and Analysis of Negative Skin Friction of Pile Group in Consolidating Soil

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Gangqiang Kong

2013-01-01

Full Text Available In order to calculate negative skin friction (NSF of pile group embedded in a consolidating soil, the dragload calculating formulas of single pile were established by considering Davis one-dimensional nonlinear consolidation soils settlement and hyperbolic load-transfer of pile-soil interface. Based on effective influence area theory, a simple semiempirical mathematical model of analysis for predicting the group effect of pile group under dragload was described. The accuracy and reliability of mathematical models built in this paper were verified by practical engineering comparative analysis. Case studies were studied, and the prediction values were found to be in good agreement with those of measured values. Then, the influences factors, such as, soil consolidation degree, the initial volume compressibility coefficient, and the stiffness of bearing soil, were analyzed and discussed. The results show that the mathematical models considering nonlinear soil consolidation and group effect can reflect the practical NSF of pile group effectively and accurately. The results of this paper can provide reference for practical pile group embedded in consolidating soil under NSF design and calculation.

Explorations in Elementary Mathematical Modeling

Science.gov (United States)

Shahin, Mazen

2010-01-01

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

models for predicting compressive strength and water absorption

African Journals Online (AJOL)

user

presents a mathematical model for predicting the compressive strength and water absorption of laterite-quarry dust cement block using ... building and construction of new infrastructure and .... In (6), R is a vector containing the real ratios of the.

Mathematical Modeling of Diverse Phenomena

Science.gov (United States)

Howard, J. C.

1979-01-01

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

Predicting the scanning branches of hysteretic soil water-retention capacity with use of the method of mathematical modeling

Science.gov (United States)

Terleev, V.; Ginevsky, R.; Lazarev, V.; Nikonorov, A.; Togo, I.; Topaj, A.; Moiseev, K.; Abakumov, E.; Melnichuk, A.; Dunaieva, I.

2017-10-01

A mathematical model of the hysteresis of the water-retention capacity of the soil is proposed. The parameters of the model are interpreted within the framework of physical concepts of the structure and capillary properties of soil pores. On the basis of the model, a computer program with an interface that allows for dialogue with the user is developed. The program has some of options: visualization of experimental data; identification of the model parameters with use of measured data by means of an optimizing algorithm; graphical presentation of the hysteresis loop with application of the assigned parameters. Using the program, computational experiments were carried out, which consisted in verifying the identifiability of the model parameters from data on the main branches, and also in testing the ability to predict the scanning branches of the hysteresis loop. For the experiments, literature data on two sandy soils were used. The absence of an “artificial pump effect” is proved. A sufficiently high accuracy of the prediction of the scanning branches of the hysteresis loop has been achieved in comparison with the three models of the precursors. The practical importance of the proposed model and computer program, which is developed on its basis, is to ensure the calculation of precision irrigation rates. The application of such rates in irrigation farming will help to prevent excess moisture from flowing beyond the root layer of the soil and, thus, minimize the unproductive loss of irrigation water and agrochemicals, as well as reduce the risk of groundwater contamination and natural water eutrophication.

Mathematical model for the power generation from arbitrarily oriented photovoltaic panel

Directory of Open Access Journals (Sweden)

Hassan Qusay

2017-01-01

Full Text Available In this paper, a mathematical model for modelling the solar radiation components and photovoltaic arrays power outputs from arbitrarily oriented photovoltaic panel has been presented. Base on the model electrical power prediction of the photovoltaic system in realistic local condition has been presented and compared with experimental measurement. The results show the effectiveness of the proposed model, which provides tools to better understand the performance and reliability as well as decision-making tool in designing of a hybrid renewable energy base power generation system. It has been shown that base on the model prediction, the efficiency and possible failures of the system can be found which are important from the technical and economical point of view.

An introduction to mathematical modeling of infectious diseases

CERN Document Server

Li, Michael Y

2018-01-01

This text provides essential modeling skills and methodology for the study of infectious diseases through a one-semester modeling course or directed individual studies.  The book includes mathematical descriptions of epidemiological concepts, and uses classic epidemic models to introduce different mathematical methods in model analysis.  Matlab codes are also included for numerical implementations. It is primarily written for upper undergraduate and beginning graduate students in mathematical sciences who have an interest in mathematical modeling of infectious diseases.  Although written in a rigorous mathematical manner, the style is not unfriendly to non-mathematicians.

An aqueous physical and mathematical modelling of ultrasonic degassing of molten metals

International Nuclear Information System (INIS)

Meidani, A.R.N.; Hasan, M.

1999-01-01

A comprehensive mathematical model, combined with an aqueous physical modelling, have been developed to simulate the ultrasonic degassing of a gassy liquid. The mathematical model forms a set of coupled, highly nonlinear and stiff differential equations. Therefore, the modified Gear method, which is a good numerical scheme for solving extremely fast moving boundary problems is applied. The threshold pressure and the effects of ultrasonic specifications on rectified diffusion of the dissolved air in water with different initial concentrations are studied. The results show that the air bubble grows when the ultrasonic pressure amplitude is more than the threshold pressure. In this case, the bubble volume reaches several times of its initial value in a fraction of second and the gas bubble may float to the surface due to the buoyancy force. A parametric study on the present model is carried out. The results of aqueous physical modelling for bubble growth are compared to the results of the mathematical model which show a reasonable agreement between the experiments and the predictions. (author)

Principles of mathematical modeling

CERN Document Server

Dym, Clive

2004-01-01

Science and engineering students depend heavily on concepts of mathematical modeling. In an age where almost everything is done on a computer, author Clive Dym believes that students need to understand and "own" the underlying mathematics that computers are doing on their behalf. His goal for Principles of Mathematical Modeling, Second Edition, is to engage the student reader in developing a foundational understanding of the subject that will serve them well into their careers. The first half of the book begins with a clearly defined set of modeling principles, and then introduces a set of foundational tools including dimensional analysis, scaling techniques, and approximation and validation techniques. The second half demonstrates the latest applications for these tools to a broad variety of subjects, including exponential growth and decay in fields ranging from biology to economics, traffic flow, free and forced vibration of mechanical and other systems, and optimization problems in biology, structures, an...

Implicit Theories, Expectancies, and Values Predict Mathematics Motivation and Behavior across High School and College.

Science.gov (United States)

Priess-Groben, Heather A; Hyde, Janet Shibley

2017-06-01

Mathematics motivation declines for many adolescents, which limits future educational and career options. The present study sought to identify predictors of this decline by examining whether implicit theories assessed in ninth grade (incremental/entity) predicted course-taking behaviors and utility value in college. The study integrated implicit theory with variables from expectancy-value theory to examine potential moderators and mediators of the association of implicit theories with college mathematics outcomes. Implicit theories and expectancy-value variables were assessed in 165 American high school students (47 % female; 92 % White), who were then followed into their college years, at which time mathematics courses taken, course-taking intentions, and utility value were assessed. Implicit theories predicted course-taking intentions and utility value, but only self-concept of ability predicted courses taken, course-taking intentions, and utility value after controlling for prior mathematics achievement and baseline values. Expectancy for success in mathematics mediated associations between self-concept of ability and college outcomes. This research identifies self-concept of ability as a stronger predictor than implicit theories of mathematics motivation and behavior across several years: math self-concept is critical to sustained engagement in mathematics.

A hybrid discrete-continuum mathematical model of pattern prediction in the developing retinal vasculature.

Science.gov (United States)

McDougall, S R; Watson, M G; Devlin, A H; Mitchell, C A; Chaplain, M A J

2012-10-01

Pathological angiogenesis has been extensively explored by the mathematical modelling community over the past few decades, specifically in the contexts of tumour-induced vascularisation and wound healing. However, there have been relatively few attempts to model angiogenesis associated with normal development, despite the availability of animal models with experimentally accessible and highly ordered vascular topologies: for example, growth and development of the vascular plexus layers in the murine retina. The current study aims to address this issue through the development of a hybrid discrete-continuum mathematical model of the developing retinal vasculature in neonatal mice that is closely coupled with an ongoing experimental programme. The model of the functional vasculature is informed by a range of morphological and molecular data obtained over a period of several days, from 6 days prior to birth to approximately 8 days after birth. The spatio-temporal formation of the superficial retinal vascular plexus (RVP) in wild-type mice occurs in a well-defined sequence. Prior to birth, astrocytes migrate from the optic nerve over the surface of the inner retina in response to a chemotactic gradient of PDGF-A, formed at an earlier stage by migrating retinal ganglion cells (RGCs). Astrocytes express a variety of chemotactic and haptotactic proteins, including VEGF and fibronectin (respectively), which subsequently induce endothelial cell sprouting and modulate growth of the RVP. The developing RVP is not an inert structure; however, the vascular bed adapts and remodels in response to a wide variety of metabolic and biomolecular stimuli. The main focus of this investigation is to understand how these interacting cellular, molecular, and metabolic cues regulate RVP growth and formation. In an earlier one-dimensional continuum model of astrocyte and endothelial migration, we showed that the measured frontal velocities of the two cell types could be accurately reproduced

Concepts of mathematical modeling

CERN Document Server

Meyer, Walter J

2004-01-01

Appropriate for undergraduate and graduate students, this text features independent sections that illustrate the most important principles of mathematical modeling, a variety of applications, and classic models. Students with a solid background in calculus and some knowledge of probability and matrix theory will find the material entirely accessible. The range of subjects includes topics from the physical, biological, and social sciences, as well as those of operations research. Discussions cover related mathematical tools and the historical eras from which the applications are drawn. Each sec

Mathematical modelling of ionospheric TEC from Turkish permanent GNSS Network (TPGN) observables during 2009-2017 and predictability of NeQuick and Kriging models

Science.gov (United States)

Ansari, Kutubuddin; Panda, Sampad Kumar; Corumluoglu, Ozsen

2018-03-01

The present study examines the ionospheric Total Electron Content (TEC) variations in the lower mid-latitude Turkish region from the Turkish permanent GNSS network (TPGN) and International GNSS Services (IGS) observations during the years 2009 to 2017. The corresponding vertical TEC (VTEC) predicted by Kriging and NeQuick-2 models are evaluated to realize their efficacy over the country. We studied the diurnal, seasonal and spatial pattern of VTEC variation and tried to estimate by a new mathematical model using the long term of 9 years VTEC data. The diurnal variation of VTEC demonstrates a normal trend with its gradual enhancement from dawn to attain a peak around 09:00-14.00 UT and reaching the minimum level after 22.00 UT. The seasonal behavior of VTEC indicates a strong semi-annual variation of VTEC with maxima in September equinox followed by March equinox and minima in June solstice followed by December solstice. Also, the spatial variation in VTEC depicts a meaningful longitudinal/latitudinal pattern altering with seasons. It decreases longitudinally from the west to the east during March equinox and June solstice increases with latitude. The comparative analysis among the GNSS-VTEC, Kriging, NeQuick and the proposed mathematical model are evaluated with the help one way ANOVA test. The analysis shows that the null hypothesis of the models during storm and quiet days are accepted and suggesting that all models are statistically significantly equivalent from each other. We believe the outcomes from this study would complement towards a relatively better understanding of the lower mid-latitude VTEC variation over the Turkish region and analogous latitudes over the globe.

Prediction of moisture variation during composting process: A comparison of mathematical models.

Science.gov (United States)

Wang, Yongjiang; Ai, Ping; Cao, Hongliang; Liu, Zhigang

2015-10-01

This study was carried out to develop and compare three models for simulating the moisture content during composting. Model 1 described changes in water content using mass balance, while Model 2 introduced a liquid-gas transferred water term. Model 3 predicted changes in moisture content without complex degradation kinetics. Average deviations for Model 1-3 were 8.909, 7.422 and 5.374 kg m(-3) while standard deviations were 10.299, 8.374 and 6.095, respectively. The results showed that Model 1 is complex and involves more state variables, but can be used to reveal the effect of humidity on moisture content. Model 2 tested the hypothesis of liquid-gas transfer and was shown to be capable of predicting moisture content during composting. Model 3 could predict water content well without considering degradation kinetics. Copyright © 2015 Elsevier Ltd. All rights reserved.

Modeling Students' Problem Solving Performance in the Computer-Based Mathematics Learning Environment

Science.gov (United States)

Lee, Young-Jin

2017-01-01

Purpose: The purpose of this paper is to develop a quantitative model of problem solving performance of students in the computer-based mathematics learning environment. Design/methodology/approach: Regularized logistic regression was used to create a quantitative model of problem solving performance of students that predicts whether students can…

Teaching mathematical modelling through project work

DEFF Research Database (Denmark)

Blomhøj, Morten; Kjeldsen, Tinne Hoff

2006-01-01

are reported in manners suitable for internet publication for colleagues. The reports and the related discussions reveal interesting dilemmas concerning the teaching of mathematical modelling and how to cope with these through “setting the scene” for the students modelling projects and through dialogues......The paper presents and analyses experiences from developing and running an in-service course in project work and mathematical modelling for mathematics teachers in the Danish gymnasium, e.g. upper secondary level, grade 10-12. The course objective is to support the teachers to develop, try out...... in their own classes, evaluate and report a project based problem oriented course in mathematical modelling. The in-service course runs over one semester and includes three seminars of 3, 1 and 2 days. Experiences show that the course objectives in general are fulfilled and that the course projects...

Mathematical modelling of scour: A review

DEFF Research Database (Denmark)

Sumer, B. Mutlu

2007-01-01

A review is presented of mathematical modelling of scour around hydraulic and marine structures. Principal ideas, general features and procedures are given. The paper is organized in three sections: the first two sections deal with the mathematical modelling of scour around piers....../piles and pipelines, respectively, the two benchmark cases, while the third section deals with the mathematical modelling of scour around other structures such as groins, breakwaters and sea walls. A section is also added to discuss potential future research areas. Over one hundred references are included...

Mathematical modeling a chemical engineer's perspective

CERN Document Server

Rutherford, Aris

1999-01-01

Mathematical modeling is the art and craft of building a system of equations that is both sufficiently complex to do justice to physical reality and sufficiently simple to give real insight into the situation. Mathematical Modeling: A Chemical Engineer's Perspective provides an elementary introduction to the craft by one of the century's most distinguished practitioners.Though the book is written from a chemical engineering viewpoint, the principles and pitfalls are common to all mathematical modeling of physical systems. Seventeen of the author's frequently cited papers are reprinted to illus

Mathematical prediction of core body temperature from environment, activity, and clothing: The heat strain decision aid (HSDA).

Science.gov (United States)

Potter, Adam W; Blanchard, Laurie A; Friedl, Karl E; Cadarette, Bruce S; Hoyt, Reed W

2017-02-01

Physiological models provide useful summaries of complex interrelated regulatory functions. These can often be reduced to simple input requirements and simple predictions for pragmatic applications. This paper demonstrates this modeling efficiency by tracing the development of one such simple model, the Heat Strain Decision Aid (HSDA), originally developed to address Army needs. The HSDA, which derives from the Givoni-Goldman equilibrium body core temperature prediction model, uses 16 inputs from four elements: individual characteristics, physical activity, clothing biophysics, and environmental conditions. These inputs are used to mathematically predict core temperature (T c ) rise over time and can estimate water turnover from sweat loss. Based on a history of military applications such as derivation of training and mission planning tools, we conclude that the HSDA model is a robust integration of physiological rules that can guide a variety of useful predictions. The HSDA model is limited to generalized predictions of thermal strain and does not provide individualized predictions that could be obtained from physiological sensor data-driven predictive models. This fully transparent physiological model should be improved and extended with new findings and new challenging scenarios. Published by Elsevier Ltd.

A Mathematical Model for the Prediction of Injectivity Decline | Odeh ...

African Journals Online (AJOL)

Injectivity impairment due to invasion of solid suspensions has been studied by several investigators and some modelling approaches have also been reported. Worthy of note is the development of analytical models for internal and external filtration coupled with transition time concept for predicting the overall decline in ...

Development and Validation of a Mathematical Model for Olive Oil Oxidation

Science.gov (United States)

Rahmouni, K.; Bouhafa, H.; Hamdi, S.

2009-03-01

A mathematical model describing the stability or the susceptibility to oxidation of extra virgin olive oil has been developed. The model has been resolved by an iterative method using differential finite method. It was validated by experimental data of extra virgin olive oil (EVOO) oxidation. EVOO stability was tested by using a Rancimat at four different temperatures 60, 70, 80 and 90° C until peroxide accumulation reached 20 [meq/kg]. Peroxide formation is speed relatively slow; fits zero order reaction with linear regression coefficients varying from 0, 98 to 0, 99. The mathematical model was used to predict the shelf life of bulk conditioned olive oil. This model described peroxide accumulation inside a container in excess of oxygen as a function of time at various positions from the interface air/oil. Good correlations were obtained between theoretical and experimental values.

Mathematical model of a PEMFC using a PBI membrane

International Nuclear Information System (INIS)

Cheddie, Denver; Munroe, Norman

2006-01-01

Proton exchange membrane fuel cells (PEMFC) operating with Nafion[reg] membranes have encountered numerous problems associated with water management and CO poisoning because of their low temperature of operation. Alternative high temperature membranes have been investigated, one such membrane being polybenzimidazole (PBI). This paper presents a one dimensional mathematical model, which predicts the polarization performance of a PEMFC using a PBI membrane. Peak power densities in the same order as Nafion[reg] are predicted. Results indicate that the greatest scope for improving PBI PEMFC performance is increasing the membrane conductivity and improving the catalyst performance as it interfaces with the PBI membrane

Opinions of Secondary School Mathematics Teachers on Mathematical Modelling

Science.gov (United States)

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…

Specific Type of Knowledge Map: Mathematical Model

OpenAIRE

Milan, Houška; Martina, Beránková

2005-01-01

The article deals with relationships between mathematical models and knowledge maps. The goal of the article is to suggest how to use the mathematical model as a knowledge map and/or as a part (esp. the inference mechanism) of the knowledge system. The results are demonstrated on the case study, when the knowledge from a story is expressed by mathematical model. The model is used for both knowledge warehousing and inferencing new artificially derived knowledge.

Fermentation process diagnosis using a mathematical model

Energy Technology Data Exchange (ETDEWEB)

Yerushalmi, L; Volesky, B; Votruba, J

1988-09-01

Intriguing physiology of a solvent-producing strain of Clostridium acetobutylicum led to the synthesis of a mathematical model of the acetone-butanol fermentation process. The model presented is capable of describing the process dynamics and the culture behavior during a standard and a substandard acetone-butanol fermentation. In addition to the process kinetic parameters, the model includes the culture physiological parameters, such as the cellular membrane permeability and the number of membrane sites for active transport of sugar. Computer process simulation studies for different culture conditions used the model, and quantitatively pointed out the importance of selected culture parameters that characterize the cell membrane behaviour and play an important role in the control of solvent synthesis by the cell. The theoretical predictions by the new model were confirmed by experimental determination of the cellular membrane permeability.

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

Science.gov (United States)

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…

Mathematical modeling of hot air/electrohydrodynamic (EHD) drying kinetics of mushroom slices

International Nuclear Information System (INIS)

Taghian Dinani, Somayeh; Hamdami, Nasser; Shahedi, Mohammad; Havet, Michel

2014-01-01

Highlights: • Hot air/EHD drying behavior of thin layer mushroom slices was evaluated. • A new empirical model was proposed for drying kinetics modeling of mushroom slices. • The new model presents excellent predictions for hot air/EHD drying of mushroom. - Abstract: Researches about mathematical modeling of electrohydrodynamic (EHD) drying are rare. In this study, hot air combined with electrohydrodynamic (EHD) drying behavior of thin layer mushroom slices was evaluated in a laboratory scale dryer at voltages of 17, 19, and 21 kV and electrode gaps of 5, 6, and 7 cm. The drying curves were fitted to ten different mathematical models (Newton, Page, Modified Page, Henderson and Pabis, Logarithmic, Two-term exponential, Midilli and Kucuk, Wang and Singh, Weibull and Parabolic models) and a proposed new empirical model to select a suitable drying equation for drying mushroom slices in a hot air combined with EHD dryer. Coefficients of the models were determined by non-linear regression analysis and the models were compared based on their coefficient of determination (R 2 ), sum of square errors (SSE) and root mean square error (RMSE) between experimental and predicted moisture ratios. According to the results, the proposed model that contains only three parameters provided the best fit with the experimental data. It was closely followed by the Midilli and Kucuk model that contains four parameters. Therefore, the proposed model can present comfortable usage and excellent predictions for the moisture content changes of mushroom slices in the hot air combined with EHD drying system

Mathematical modeling of porosity formation in die cast A356 wheels

International Nuclear Information System (INIS)

Maijer, D.; Cockcroft, S.L.; Wells, M.A.; Luciuk, T.; Hermesmann, C.

2000-01-01

In an effort to leverage recent advances in modeling and process simulation tools, a mathematical model has been developed to predict porosity formation in die cast A356 wheels as part of a collaborative research agreement between researchers at the University of British Columbia and Canadian Autoparts Toyota Incorporated. The heat transfer model represents a three-dimensional, 30 o , slice of the wheel and die and is based on the commercial finite element code ABAQUS. Extensive temperature measurements in the die and in the wheel taken over several cycles in the casting process were used to fine tune and validate the model. Initial work on predicting porosity formation has focused on using the Niyama parameter as a measure of the probability of porosity. To date Niyama porosity predictions agree well with plant experience and show promise for reducing losses associated with porosity. (author)

Predictive ability of boiler production models | Ogundu | Animal ...

African Journals Online (AJOL)

The weekly body weight measurements of a growing strain of Ross broiler were used to compare the of ability of three mathematical models (the multi, linear, quadratic and Exponential) to predict 8 week body weight from early body measurements at weeks I, II, III, IV, V, VI and VII. The results suggest that the three models ...

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

Science.gov (United States)

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…

Long-term response to recombinant human growth hormone treatment: a new predictive mathematical method.

Science.gov (United States)

Migliaretti, G; Ditaranto, S; Guiot, C; Vannelli, S; Matarazzo, P; Cappello, N; Stura, I; Cavallo, F

2018-07-01

Recombinant GH has been offered to GH-deficient (GHD) subjects for more than 30 years, in order to improve height and growth velocity in children and to enhance metabolic effects in adults. The aim of our work is to describe the long-term effect of rhGH treatment in GHD pediatric patients, suggesting a growth prediction model. A homogeneous database is defined for diagnosis and treatment modalities, based on GHD patients afferent to Hospital Regina Margherita in Turin (Italy). In this study, 232 GHD patients are selected (204 idiopathic GHD and 28 organic GHD). Each measure is shown in terms of mean with relative standard deviations (SD) and 95% confidence interval (95% CI). To estimate the final height of each patient on the basis of few measures, a mathematical growth prediction model [based on Gompertzian function and a mixed method based on the radial basis functions (RBFs) and the particle swarm optimization (PSO) models] was performed. The results seem to highlight the benefits of an early start of treatment, further confirming what is suggested by the literature. Generally, the RBF-PSO method shows a good reliability in the prediction of the final height. Indeed, RMSE is always lower than 4, i.e., in average the forecast will differ at most of 4 cm to the real value. In conclusion, the large and accurate database of Italian GHD patients allowed us to assess the rhGH treatment efficacy and compare the results with those obtained in other Countries. Moreover, we proposed and validated a new mathematical model forecasting the expected final height after therapy which was validated on our cohort.

Using a Prediction Model to Manage Cyber Security Threats

Directory of Open Access Journals (Sweden)

Venkatesh Jaganathan

2015-01-01

Full Text Available Cyber-attacks are an important issue faced by all organizations. Securing information systems is critical. Organizations should be able to understand the ecosystem and predict attacks. Predicting attacks quantitatively should be part of risk management. The cost impact due to worms, viruses, or other malicious software is significant. This paper proposes a mathematical model to predict the impact of an attack based on significant factors that influence cyber security. This model also considers the environmental information required. It is generalized and can be customized to the needs of the individual organization.

Using a Prediction Model to Manage Cyber Security Threats.

Science.gov (United States)

Jaganathan, Venkatesh; Cherurveettil, Priyesh; Muthu Sivashanmugam, Premapriya

2015-01-01

Cyber-attacks are an important issue faced by all organizations. Securing information systems is critical. Organizations should be able to understand the ecosystem and predict attacks. Predicting attacks quantitatively should be part of risk management. The cost impact due to worms, viruses, or other malicious software is significant. This paper proposes a mathematical model to predict the impact of an attack based on significant factors that influence cyber security. This model also considers the environmental information required. It is generalized and can be customized to the needs of the individual organization.

Using a Prediction Model to Manage Cyber Security Threats

Science.gov (United States)

Muthu Sivashanmugam, Premapriya

2015-01-01

Cyber-attacks are an important issue faced by all organizations. Securing information systems is critical. Organizations should be able to understand the ecosystem and predict attacks. Predicting attacks quantitatively should be part of risk management. The cost impact due to worms, viruses, or other malicious software is significant. This paper proposes a mathematical model to predict the impact of an attack based on significant factors that influence cyber security. This model also considers the environmental information required. It is generalized and can be customized to the needs of the individual organization. PMID:26065024

A mathematical model for predicting photo-induced voltage and photostriction of PLZT with coupled multi-physics fields and its application

International Nuclear Information System (INIS)

Huang, J H; Wang, X J; Wang, J

2016-01-01

The primary purpose of this paper is to propose a mathematical model of PLZT ceramic with coupled multi-physics fields, e.g. thermal, electric, mechanical and light field. To this end, the coupling relationships of multi-physics fields and the mechanism of some effects resulting in the photostrictive effect are analyzed theoretically, based on which a mathematical model considering coupled multi-physics fields is established. According to the analysis and experimental results, the mathematical model can explain the hysteresis phenomenon and the variation trend of the photo-induced voltage very well and is in agreement with the experimental curves. In addition, the PLZT bimorph is applied as an energy transducer for a photovoltaic–electrostatic hybrid actuated micromirror, and the relation of the rotation angle and the photo-induced voltage is discussed based on the novel photostrictive mathematical model. (paper)

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

Science.gov (United States)

Khusna, H.; Heryaningsih, N. Y.

2018-01-01

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

Mathematical Modelling as a Professional Task

Science.gov (United States)

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…

A mathematical model of a lithium/thionyl chloride primary cell

Science.gov (United States)

Evans, T. I.; Nguyen, T. V.; White, R. E.

1987-08-01

A 1-D mathematical model for the lithium/thionyl chloride primary cell was developed to investigate methods of improving its performance and safety. The model includes many of the components of a typical lithium/thionyl chloride cell such as the porous lithium chloride film which forms on the lithium anode surface. The governing equations are formulated from fundamental conservation laws using porous electrode theory and concentrated solution theory. The model is used to predict 1-D, time dependent profiles of concentration, porosity, current, and potential as well as cell temperature and voltage. When a certain discharge rate is required, the model can be used to determine the design criteria and operating variables which yield high cell capacities. Model predictions can be used to establish operational and design limits within which the thermal runaway problem, inherent in these cells, can be avoided.

Mathematical models for atmospheric pollutants. Final report

International Nuclear Information System (INIS)

Drake, R.L.; Barrager, S.M.

1979-08-01

The present and likely future roles of mathematical modeling in air quality decisions are described. The discussion emphasizes models and air pathway processes rather than the chemical and physical behavior of specific anthropogenic emissions. Summarized are the characteristics of various types of models used in the decision-making processes. Specific model subclasses are recommended for use in making air quality decisions that have site-specific, regional, national, or global impacts. The types of exposure and damage models that are currently used to predict the effects of air pollutants on humans, other animals, plants, ecosystems, property, and materials are described. The aesthetic effects of odor and visibility and the impact of pollutants on weather and climate are also addressed. Technical details of air pollution meteorology, chemical and physical properties of air pollutants, solution techniques, and air quality models are discussed in four appendices bound in separate volumes

Mathematical models of hysteresis

International Nuclear Information System (INIS)

1998-01-01

The ongoing research has largely been focused on the development of mathematical models of hysteretic nonlinearities with nonlocal memories. The distinct feature of these nonlinearities is that their current states depend on past histories of input variations. It turns out that memories of hysteretic nonlinearities are quite selective. Indeed, experiments show that only some past input extrema (not the entire input variations) leave their marks upon future states of hysteretic nonlinearities. Thus special mathematical tools are needed in order to describe nonlocal selective memories of hysteretic nonlinearities. The origin of such tools can be traced back to the landmark paper of Preisach. Their research has been primarily concerned with Preisach-type models of hysteresis. All these models have a common generic feature; they are constructed as superpositions of simplest hysteretic nonlinearities-rectangular loops. During the past four years, the study has been by and large centered around the following topics: (1) further development of Scalar and vector Preisach-type models of hysteresis; (2) experimental testing of Preisach-type models of hysteresis; (3) development of new models for viscosity (aftereffect) in hysteretic systems; (4) development of mathematical models for superconducting hysteresis in the case of gradual resistive transitions; (5) software implementation of Preisach-type models of hysteresis; and (6) development of new ideas which have emerged in the course of the research work. The author briefly describes the main scientific results obtained in the areas outlined above

Mathematical models of hysteresis

Energy Technology Data Exchange (ETDEWEB)

NONE

1998-08-01

The ongoing research has largely been focused on the development of mathematical models of hysteretic nonlinearities with nonlocal memories. The distinct feature of these nonlinearities is that their current states depend on past histories of input variations. It turns out that memories of hysteretic nonlinearities are quite selective. Indeed, experiments show that only some past input extrema (not the entire input variations) leave their marks upon future states of hysteretic nonlinearities. Thus special mathematical tools are needed in order to describe nonlocal selective memories of hysteretic nonlinearities. The origin of such tools can be traced back to the landmark paper of Preisach. Their research has been primarily concerned with Preisach-type models of hysteresis. All these models have a common generic feature; they are constructed as superpositions of simplest hysteretic nonlinearities-rectangular loops. During the past four years, the study has been by and large centered around the following topics: (1) further development of Scalar and vector Preisach-type models of hysteresis; (2) experimental testing of Preisach-type models of hysteresis; (3) development of new models for viscosity (aftereffect) in hysteretic systems; (4) development of mathematical models for superconducting hysteresis in the case of gradual resistive transitions; (5) software implementation of Preisach-type models of hysteresis; and (6) development of new ideas which have emerged in the course of the research work. The author briefly describes the main scientific results obtained in the areas outlined above.

Mathematical modelling of metabolism

DEFF Research Database (Denmark)

Gombert, Andreas Karoly; Nielsen, Jens

2000-01-01

Mathematical models of the cellular metabolism have a special interest within biotechnology. Many different kinds of commercially important products are derived from the cell factory, and metabolic engineering can be applied to improve existing production processes, as well as to make new processes...... availability of genomic information and powerful analytical techniques, mathematical models also serve as a tool for understanding the cellular metabolism and physiology....... available. Both stoichiometric and kinetic models have been used to investigate the metabolism, which has resulted in defining the optimal fermentation conditions, as well as in directing the genetic changes to be introduced in order to obtain a good producer strain or cell line. With the increasing...

Using Covariation Reasoning to Support Mathematical Modeling

Science.gov (United States)

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…

The many faces of the mathematical modeling cycle

NARCIS (Netherlands)

Perrenet, J.C.; Zwaneveld, B.

2012-01-01

In literature about mathematical modeling a diversity can be seen in ways of presenting the modeling cycle. Every year, students in the Bachelor’s program Applied Mathematics of the Eindhoven University of Technology, after having completed a series of mathematical modeling projects, have been

Mathematical concepts for mechanical engineering design

CERN Document Server

Asli, Kaveh Hariri; Aliyev, Soltan Ali Ogli

2013-01-01

PrefaceIntroductionHeat Flow: From Theory to PracticeDispersed Fluid and Ideal Fluid MechanicsModeling for Pressure Wave into Water PipelineHeat Transfer and Vapor BubbleMathematical Concepts and Computational Approaches on Hydrodynamics InstabilityMathematical Concepts and Dynamic ModelingModeling for Predictions of Air Entrance into Water PipelineIndex

Modelling sexual transmission of HIV: testing the assumptions, validating the predictions

Science.gov (United States)

Baggaley, Rebecca F.; Fraser, Christophe

2010-01-01

Purpose of review To discuss the role of mathematical models of sexual transmission of HIV: the methods used and their impact. Recent findings We use mathematical modelling of “universal test and treat” as a case study to illustrate wider issues relevant to all modelling of sexual HIV transmission. Summary Mathematical models are used extensively in HIV epidemiology to deduce the logical conclusions arising from one or more sets of assumptions. Simple models lead to broad qualitative understanding, while complex models can encode more realistic assumptions and thus be used for predictive or operational purposes. An overreliance on model analysis where assumptions are untested and input parameters cannot be estimated should be avoided. Simple models providing bold assertions have provided compelling arguments in recent public health policy, but may not adequately reflect the uncertainty inherent in the analysis. PMID:20543600

Mathematical models for lymphatic filariasis transmission and control: Challenges and prospects

Directory of Open Access Journals (Sweden)

Kaliannagounder Krishnamoorthy

2008-02-01

Full Text Available Abstract Background Mathematical models developed for describing the dynamics of transmission, infection, disease and control of lymphatic filariasis (LF gained momentum following the 1997 World Health Assembly resolution and the launching of the Global Programme to Eliminate Lymphatic Filariasis (GPELF in 2000. Model applications could provide valuable inputs for making decisions while implementing large scale programmes. However these models need to be evaluated at different epidemiological settings for optimization and fine-tuning with new knowledge and understanding on infection/disease dynamics. Discussion EPIFIL and LYMFASIM are the two mathematical simulation models currently available for lymphatic filariasis transmission and control. Both models have been used for prediction and evaluation of control programmes under research settings. Their widespread application in evaluating large-scale elimination programmes warrants validation of assumptions governing the dynamics of infection and disease in different epidemiological settings. Furthermore, the predictive power of the models for decision support can be enhanced by generating knowledge on some important issues that pose challenges and incorporating such knowledge into the models. We highlight factors related to the efficacy of the drugs of choice, their mode of action, and the possibility that drug resistance may develop; the role of vector-parasite combinations; the magnitude of transmission thresholds; host-parasite interactions and their effects on the dynamics of infection and immunity; parasite biology, and progression to LF-associated disease. Summary The two mathematical models developed offer potential decision making tools for transmission and control of LF. In view of the goals of the GPELF, the predictive power of these models needs to be enhanced for their wide-spread application in large scale programmes. Assimilation and translation of new information into the models is

Mathematical models in radiogeochronology

International Nuclear Information System (INIS)

Abril, J.M.; Garcia Leon, M.

1991-01-01

The study of activity vs. depth profiles in sediment cores of some man-made and natural ocurring radionuclides have shown to be a poweful tool for dating purposes. Nevertheless, in most cases, an adecuate interpretation of such profiles requires mathematical models. In this paper, by considering the sediment as a continuum, a general equation for diffusion of radionuclides through it is obtained. Consequentely, some previously published dating models are found to be particular solutions of such general advenction-diffusion problem. Special emphasis is given to the mathematical treatment of compactation effect and time dependent problems. (author)

Mathematical model for biomolecular quantification using large-area surface-enhanced Raman spectroscopy mapping

DEFF Research Database (Denmark)

Palla, Mirkó; Bosco, Filippo; Yang, Jaeyoung

2015-01-01

Surface-enhanced Raman spectroscopy (SERS) based on nanostructured platforms is a promising technique for quantitative and highly sensitive detection of biomolecules in the field of analytical biochemistry. Here, we report a mathematical model to predict experimental SERS signal (or hotspot) inte...

Mathematical modelling a case studies approach

CERN Document Server

Illner, Reinhard; McCollum, Samantha; Roode, Thea van

2004-01-01

Mathematical modelling is a subject without boundaries. It is the means by which mathematics becomes useful to virtually any subject. Moreover, modelling has been and continues to be a driving force for the development of mathematics itself. This book explains the process of modelling real situations to obtain mathematical problems that can be analyzed, thus solving the original problem. The presentation is in the form of case studies, which are developed much as they would be in true applications. In many cases, an initial model is created, then modified along the way. Some cases are familiar, such as the evaluation of an annuity. Others are unique, such as the fascinating situation in which an engineer, armed only with a slide rule, had 24 hours to compute whether a valve would hold when a temporary rock plug was removed from a water tunnel. Each chapter ends with a set of exercises and some suggestions for class projects. Some projects are extensive, as with the explorations of the predator-prey model; oth...

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

Science.gov (United States)

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

2017-01-05

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

Engaging Elementary Students in the Creative Process of Mathematizing Their World through Mathematical Modeling

Directory of Open Access Journals (Sweden)

Jennifer M. Suh

2017-06-01

Full Text Available This paper examines the experiences of two elementary teachers’ implementation of mathematical modeling in their classrooms and how the enactment by the teachers and the engagement by students exhibited their creativity, critical thinking, collaboration and communication skills. In particular, we explore the questions: (1 How can phases of mathematical modeling as a process serve as a venue for exhibiting students’ critical 21st century skills? (2 What were some effective pedagogical practices teachers used as they implemented mathematical modeling with elementary students and how did these promote students’ 21st century skills? We propose that mathematical modeling provides space for teachers and students to have a collective experience through the iterative process of making sense of and building knowledge of important mathematical ideas while engaging in the critical 21st century skills necessary in our complex modern world.

A mathematical model to predict the effect of heat recovery on the wastewater temperature in sewers.

Science.gov (United States)

Dürrenmatt, David J; Wanner, Oskar

2014-01-01

Raw wastewater contains considerable amounts of energy that can be recovered by means of a heat pump and a heat exchanger installed in the sewer. The technique is well established, and there are approximately 50 facilities in Switzerland, many of which have been successfully using this technique for years. The planning of new facilities requires predictions of the effect of heat recovery on the wastewater temperature in the sewer because altered wastewater temperatures may cause problems for the biological processes used in wastewater treatment plants and receiving waters. A mathematical model is presented that calculates the discharge in a sewer conduit and the spatial profiles and dynamics of the temperature in the wastewater, sewer headspace, pipe, and surrounding soil. The model was implemented in the simulation program TEMPEST and was used to evaluate measured time series of discharge and temperatures. It was found that the model adequately reproduces the measured data and that the temperature and thermal conductivity of the soil and the distance between the sewer pipe and undisturbed soil are the most sensitive model parameters. The temporary storage of heat in the pipe wall and the exchange of heat between wastewater and the pipe wall are the most important processes for heat transfer. The model can be used as a tool to determine the optimal site for heat recovery and the maximal amount of extractable heat. Copyright © 2013 Elsevier Ltd. All rights reserved.

Mathematical (Disabilities Within the Opportunity-Propensity Model: The Choice of Math Test Matters

Directory of Open Access Journals (Sweden)

Elke Baten

2018-05-01

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

Comprehensive applied mathematical modeling in the natural and engineering sciences theoretical predictions compared with data

CERN Document Server

Wollkind, David J

2017-01-01

This text demonstrates the process of comprehensive applied mathematical modeling through the introduction of various case studies.  The case studies are arranged in increasing order of complexity based on the mathematical methods required to analyze the models. The development of these methods is also included, providing a self-contained presentation. To reinforce and supplement the material introduced, original problem sets are offered involving case studies closely related to the ones presented.  With this style, the text’s perspective, scope, and completeness of the subject matter are considered unique. Having grown out of four self-contained courses taught by the authors, this text will be of use in a two-semester sequence for advanced undergraduate and beginning graduate students, requiring rudimentary knowledge of advanced calculus and differential equations, along with a basic understanding of some simple physical and biological scientific principles. .

Mathematical psychology.

Science.gov (United States)

Batchelder, William H

2010-09-01

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

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

Science.gov (United States)

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

2014-01-01

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

Developmental gains in visuospatial memory predict gains in mathematics achievement.

Directory of Open Access Journals (Sweden)

Yaoran Li

Full Text Available Visuospatial competencies are related to performance in mathematical domains in adulthood, but are not consistently related to mathematics achievement in children. We confirmed the latter for first graders and demonstrated that children who show above average first-to-fifth grade gains in visuospatial memory have an advantage over other children in mathematics. The study involved the assessment of the mathematics and reading achievement of 177 children in kindergarten to fifth grade, inclusive, and their working memory capacity and processing speed in first and fifth grade. Intelligence was assessed in first grade and their second to fourth grade teachers reported on their in-class attentive behavior. Developmental gains in visuospatial memory span (d = 2.4 were larger than gains in the capacity of the central executive (d = 1.6 that in turn were larger than gains in phonological memory span (d = 1.1. First to fifth grade gains in visuospatial memory and in speed of numeral processing predicted end of fifth grade mathematics achievement, as did first grade central executive scores, intelligence, and in-class attentive behavior. The results suggest there are important individual differences in the rate of growth of visuospatial memory during childhood and that these differences become increasingly important for mathematics learning.

Developmental gains in visuospatial memory predict gains in mathematics achievement.

Science.gov (United States)

Li, Yaoran; Geary, David C

2013-01-01

Visuospatial competencies are related to performance in mathematical domains in adulthood, but are not consistently related to mathematics achievement in children. We confirmed the latter for first graders and demonstrated that children who show above average first-to-fifth grade gains in visuospatial memory have an advantage over other children in mathematics. The study involved the assessment of the mathematics and reading achievement of 177 children in kindergarten to fifth grade, inclusive, and their working memory capacity and processing speed in first and fifth grade. Intelligence was assessed in first grade and their second to fourth grade teachers reported on their in-class attentive behavior. Developmental gains in visuospatial memory span (d = 2.4) were larger than gains in the capacity of the central executive (d = 1.6) that in turn were larger than gains in phonological memory span (d = 1.1). First to fifth grade gains in visuospatial memory and in speed of numeral processing predicted end of fifth grade mathematics achievement, as did first grade central executive scores, intelligence, and in-class attentive behavior. The results suggest there are important individual differences in the rate of growth of visuospatial memory during childhood and that these differences become increasingly important for mathematics learning.

Developmental Gains in Visuospatial Memory Predict Gains in Mathematics Achievement

Science.gov (United States)

Li, Yaoran; Geary, David C.

2013-01-01

Visuospatial competencies are related to performance in mathematical domains in adulthood, but are not consistently related to mathematics achievement in children. We confirmed the latter for first graders and demonstrated that children who show above average first-to-fifth grade gains in visuospatial memory have an advantage over other children in mathematics. The study involved the assessment of the mathematics and reading achievement of 177 children in kindergarten to fifth grade, inclusive, and their working memory capacity and processing speed in first and fifth grade. Intelligence was assessed in first grade and their second to fourth grade teachers reported on their in-class attentive behavior. Developmental gains in visuospatial memory span (d = 2.4) were larger than gains in the capacity of the central executive (d = 1.6) that in turn were larger than gains in phonological memory span (d = 1.1). First to fifth grade gains in visuospatial memory and in speed of numeral processing predicted end of fifth grade mathematics achievement, as did first grade central executive scores, intelligence, and in-class attentive behavior. The results suggest there are important individual differences in the rate of growth of visuospatial memory during childhood and that these differences become increasingly important for mathematics learning. PMID:23936154

Mathematical Modeling in the High School Curriculum

Science.gov (United States)

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…

Mathematical Modeling Approaches in Plant Metabolomics.

Science.gov (United States)

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

2018-01-01

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

Students’ mathematical learning in modelling activities

DEFF Research Database (Denmark)

Kjeldsen, Tinne Hoff; Blomhøj, Morten

2013-01-01

Ten years of experience with analyses of students’ learning in a modelling course for first year university students, led us to see modelling as a didactical activity with the dual goal of developing students’ modelling competency and enhancing their conceptual learning of mathematical concepts i...... create and help overcome hidden cognitive conflicts in students’ understanding; that reflections within modelling can play an important role for the students’ learning of mathematics. These findings are illustrated with a modelling project concerning the world population....

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

Science.gov (United States)

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…

The sensitivity research of multiparameter biosensors based on HEMT by the mathematic modeling method

Science.gov (United States)

Tikhomirov, V. G.; Gudkov, A. G.; Agasieva, S. V.; Gorlacheva, E. N.; Shashurin, V. D.; Zybin, A. A.; Evseenkov, A. S.; Parnes, Y. M.

2017-11-01

The numerical impact modeling of some external effects on the CVC of biosensors based on AlGaN/GaN heterostructures (HEMT) was carried out. The mathematical model was created that allowed to predict the behavior of the drain current depending on condition changes on the heterostructure surface in the gate region and to start the process of directed construction optimization of the biosensors based on AlGaN/GaN HEMT with the aim of improving their performance. The calculation of the drain current of the biosensor construction was carried out to confirm the reliability of the developed mathematical model and obtained results.

Modelling and predicting growth of psychrotolerant pseudomonads in milk and cottage cheese

DEFF Research Database (Denmark)

Martinez Rios, Veronica; Østergaard, Nina Bjerre; Rosshaug, Per Sand

.43. The acceptable simulation zone method showed the new model for cottage cheese to successfully predict growth of psychrotolerant pseudomonads at both constant and dynamic temperature storage conditions. The new models can be used together with the Food Spoilage and Safety Predictor (FSSP) software to predict......Mathematical models were developed and evaluated for growth of psychrotolerant pseudomonads in chilled milk and cottage cheese with cultured cream dressing. The mathematical models include the effect of temperature, pH, NaCl, lactic acid and sorbic acid. A simplified cardinal parameter growth model...... was developed based on growth in broth. Subsequently, the reference growth rate parameter (μref at 25 °C) was fitted to a total of 35 growth rates from cottage cheese with cultured cream dressing. Growth rate models for milk and cottage cheese were evaluated by comparison with data from literature and new...

A Mathematical model to predict the US Airlines operation costs and airports charges per route per passenger

NARCIS (Netherlands)

Carmona Benitez, R.B.; Lodewijiks, G.

2010-01-01

A mathematical model to estimate the average airlines operational costs and airports charges per route is important for airlines companies trying to open new routes and for data generation for other purpose such as transport modeling, simulation modeling, investment analyses for airlines and

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

Science.gov (United States)

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.

A survey on computational intelligence approaches for predictive modeling in prostate cancer

OpenAIRE

Cosma, G; Brown, D; Archer, M; Khan, M; Pockley, AG

2017-01-01

Predictive modeling in medicine involves the development of computational models which are capable of analysing large amounts of data in order to predict healthcare outcomes for individual patients. Computational intelligence approaches are suitable when the data to be modelled are too complex forconventional statistical techniques to process quickly and eciently. These advanced approaches are based on mathematical models that have been especially developed for dealing with the uncertainty an...

Mathematical modelling of fracture hydrology

International Nuclear Information System (INIS)

Herbert, A.W.; Hodgkindon, D.P.; Lever, D.A.; Robinson, P.C.; Rae, J.

1985-01-01

This report reviews work carried out between January 1983 and December 1984 for the CEC/DOE contract 'Mathematical Modelling of Fracture Hydrology' which forms part of the CEC Mirage project (CEC 1984. Come 1985. Bourke et. al. 1983). It describes the development and use of a variety of mathematical models for the flow of water and transport of radionuclides in flowing groundwater. These models have an important role to play in assessing the long-term safety of radioactive waste burial, and in the planning and interpretation of associated experiments. The work is reported under five headings, namely 1) Statistical fracture network modelling, 2) Continuum models of flow and transport, 3) Simplified models, 4) Analysis of laboratory experiments, 5) Analysis of field experiments

Mathematical modeling of laser lipolysis

Directory of Open Access Journals (Sweden)

Reynaud Jean

2008-02-01

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

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

Science.gov (United States)

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.

Mathematical modelling of pasta dough dynamic viscosity, thermal conductivity and diffusivity

Directory of Open Access Journals (Sweden)

Andrei Ionuţ SIMION

2015-08-01

Full Text Available This work aimed to study the mathematical variation of three main thermodynamic properties (dynamic viscosity, thermal conductivity and thermal diffusivity of pasta dough obtained by mixing wheat semolina and water with dough humidity and deformation speed (for dynamic viscosity, respectively with dough humidity and temperature (for thermal diffusivity and conductivity. The realized regression analysis of existing graphical data led to the development of mathematical models with a high degree of accuracy. The employed statistical tests (least squares, relative error and analysis of variance revealed that the obtained equations are able to describe and predict the tendency of the dough thermodynamic properties.

Multi-band effective mass approximations advanced mathematical models and numerical techniques

CERN Document Server

Koprucki, Thomas

2014-01-01

This book addresses several mathematical models from the most relevant class of kp-Schrödinger systems. Both mathematical models and state-of-the-art numerical methods for adequately solving the arising systems of differential equations are presented. The operational principle of modern semiconductor nano structures, such as quantum wells, quantum wires or quantum dots, relies on quantum mechanical effects. The goal of numerical simulations using quantum mechanical models in the development of semiconductor nano structures is threefold: First they are needed for a deeper understanding of experimental data and of the operational principle. Secondly, they allow us to predict and optimize in advance the qualitative and quantitative properties of new devices in order to minimize the number of prototypes needed. Semiconductor nano structures are embedded as an active region in semiconductor devices. Thirdly and finally, the results of quantum mechanical simulations of semiconductor nano structures can be used wit...

Mathematical modeling of diphtheria transmission in Thailand.

Science.gov (United States)

Sornbundit, Kan; Triampo, Wannapong; Modchang, Charin

2017-08-01

In this work, a mathematical model for describing diphtheria transmission in Thailand is proposed. Based on the course of diphtheria infection, the population is divided into 8 epidemiological classes, namely, susceptible, symptomatic infectious, asymptomatic infectious, carrier with full natural-acquired immunity, carrier with partial natural-acquired immunity, individual with full vaccine-induced immunity, and individual with partial vaccine-induced immunity. Parameter values in the model were either directly obtained from the literature, estimated from available data, or estimated by means of sensitivity analysis. Numerical solutions show that our model can correctly describe the decreasing trend of diphtheria cases in Thailand during the years 1977-2014. Furthermore, despite Thailand having high DTP vaccine coverage, our model predicts that there will be diphtheria outbreaks after the year 2014 due to waning immunity. Our model also suggests that providing booster doses to some susceptible individuals and those with partial immunity every 10 years is a potential way to inhibit future diphtheria outbreaks. Copyright © 2017 Elsevier Ltd. All rights reserved.

Mathematical models of human paralyzed muscle after long-term training

OpenAIRE

Frey Law, L.A.; Shields, R.K.

2007-01-01

Spinal cord injury (SCI) results in major musculoskeletal adaptations, including muscle atrophy, faster contractile properties, increased fatigability, and bone loss. The use of functional electrical stimulation (FES) provides a method to prevent paralyzed muscle adaptations in order to sustain force-generating capacity. Mathematical muscle models may be able to predict optimal activation strategies during FES, however muscle properties further adapt with long-term training. The purpose of th...

Mathematical modeling of the energy consumption of heated swimming pools

Energy Technology Data Exchange (ETDEWEB)

Le Bel, C.; Millette, J. [LTE Shawinigan, Shawinigan, PQ (Canada)

2007-07-01

A mathematical model was developed to estimate the water temperature of a residential swimming pool. The model can compare 2 different situations and, if local climatic conditions are known, it can accurately predict energy costs of the pool relative to the total energy consumption of the house. When used with the appropriate energy transfer coefficient and weather file, the model can estimate the water temperature of a residential swimming pool having specific characteristics, such as in-ground, above-ground, heated or non-heated. The model is suitable for determining residential loads. It can be applied to different pool types and sizes, for different water heating scenarios and different climatic regions. Data obtained from the monitoring of water temperature and electricity use of 57 residential swimming pools was used to validate the model. In addition, 5 above-ground pools were installed on the property of LTE Shawinigan to allow for a more detailed study of the parameters involved in the thermal balance of a pool. The mathematical model, based on a global heat transfer coefficient, can determine the effect of a solar blanket and the effect of water volume. 14 refs., 5 tabs., 11 figs.

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

Science.gov (United States)

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

2017-09-01

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

Exploring Yellowstone National Park with Mathematical Modeling

Science.gov (United States)

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…

Mathematical modelling of the combustion of a single wood particle

Energy Technology Data Exchange (ETDEWEB)

Porteiro, J.; Miguez, J.L.; Granada, E.; Moran, J.C. [Departamento de Ingenieria Mecanica, Maquinas y Motores Termicos y Fluidos. Universidad de Vigo, Lagoas Marcosende 9 36200 Vigo (Spain)

2006-01-15

A mathematical model describing the thermal degradation of densified biomass particles is presented here. The model uses a novel discretisation scheme and combines intra-particle combustion processes with extra-particle transport processes, thereby including thermal and diffusional control mechanisms. The influence of structural changes on the physical-thermal properties of wood in its different stages is studied together with shrinkage of the particle during its degradation. The model is used to compare the predicted data with data on the mass loss dynamics and internal temperature of several particles from previous works and relevant literature, with good agreement. (author)

PENGEMBANGAN MODEL COMPREHENSIVE MATHEMATICS INSTRUCTION (CMI DALAM MEMBANGUN KEMAMPUAN MATHEMATICAL THINKING SISWA

Directory of Open Access Journals (Sweden)

Nita Delima

2017-03-01

Full Text Available Kesetaraan dalam pendidikan merupakan elemen penting dari beberapa standar visi NCTM dalam pendidikan matematika. Kesetaraan yang dimaksud, tidak berarti bahwa setiap siswa harus menerima pembelajaran yang identik dari guru; sebaliknya, menuntut sebuah pembelajaran yang mengakomodasi sebuah akses dalam mencapai kemampuan setiap siswa. Selain itu, NCTM juga mengemukakan bahwa dalam pembelajaran matematika terdapat lima standar proses yang harus terpenuhi, yakni problem solving, reasoning and proof, connections, communication, dan representation. Sementara itu, kemampuan problem solving yang dimiliki oleh seseorang akan mempengaruhi pada fleksibilitas proses berpikir mereka. Proses berpikir yang dimaksud dapat berupa proses dinamik yang memuat kompleksitas ide–ide matematik yang dimiliki serta dapat mengekspansi pemahaman tentang matematika yang disebut sebagai mathematical thinking. Dengan demikian, diperlukan sebuah model pembelajaran yang dapat berfungsi sebagai alat pedagogis guru, baik sebelum, selama dan setelah pembelajaran, terutama dalam membangun mathematical thinking siswa. Kerangka Comprehensive Mathematics Instruction (CMI merupakan sebuah kerangka prinsip – prinsip praktek pembelajaran yang bertujuan untuk menciptakan pengalaman matematika yang seimbang, sehingga siswa dapat memiliki pemikiran dan pemahaman matematika secara mendalam, kerangka CMI memiliki semua kriteria sebuah model pembelajaran. Adapun syntax untuk model CMI terdiri dari develop, solidify dan practice. Dalam penerapannya, setiap syntax tersebut meliputi tiga tahapan, yakni tujuan (purpose, peran guru (teacher role dan peran siswa (student role. Berdasarkan hasil analisis eksploratif yang telah dilakukan, dapat disimpulkan bahwa model pembelajaran CMI ini dapat menjadi sebuah alat pedagogis yang baru bagi guru yang dapat digunakan, baik sebelum, selama dan setelah pembelajaran dalam membangun kemampuan mathematical thinking siswa.    Kata Kunci: Comprehensive

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

Science.gov (United States)

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…

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

Science.gov (United States)

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

2013-11-18

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

A spatially-averaged mathematical model of kidney branching morphogenesis

KAUST Repository

Zubkov, V.S.

2015-08-01

© 2015 Published by Elsevier Ltd. Kidney development is initiated by the outgrowth of an epithelial ureteric bud into a population of mesenchymal cells. Reciprocal morphogenetic responses between these two populations generate a highly branched epithelial ureteric tree with the mesenchyme differentiating into nephrons, the functional units of the kidney. While we understand some of the mechanisms involved, current knowledge fails to explain the variability of organ sizes and nephron endowment in mice and humans. Here we present a spatially-averaged mathematical model of kidney morphogenesis in which the growth of the two key populations is described by a system of time-dependant ordinary differential equations. We assume that branching is symmetric and is invoked when the number of epithelial cells per tip reaches a threshold value. This process continues until the number of mesenchymal cells falls below a critical value that triggers cessation of branching. The mathematical model and its predictions are validated against experimentally quantified C57Bl6 mouse embryonic kidneys. Numerical simulations are performed to determine how the final number of branches changes as key system parameters are varied (such as the growth rate of tip cells, mesenchyme cells, or component cell population exit rate). Our results predict that the developing kidney responds differently to loss of cap and tip cells. They also indicate that the final number of kidney branches is less sensitive to changes in the growth rate of the ureteric tip cells than to changes in the growth rate of the mesenchymal cells. By inference, increasing the growth rate of mesenchymal cells should maximise branch number. Our model also provides a framework for predicting the branching outcome when ureteric tip or mesenchyme cells change behaviour in response to different genetic or environmental developmental stresses.

A spatially-averaged mathematical model of kidney branching morphogenesis

KAUST Repository

Zubkov, V.S.; Combes, A.N.; Short, K.M.; Lefevre, J.; Hamilton, N.A.; Smyth, I.M.; Little, M.H.; Byrne, H.M.

2015-01-01

© 2015 Published by Elsevier Ltd. Kidney development is initiated by the outgrowth of an epithelial ureteric bud into a population of mesenchymal cells. Reciprocal morphogenetic responses between these two populations generate a highly branched epithelial ureteric tree with the mesenchyme differentiating into nephrons, the functional units of the kidney. While we understand some of the mechanisms involved, current knowledge fails to explain the variability of organ sizes and nephron endowment in mice and humans. Here we present a spatially-averaged mathematical model of kidney morphogenesis in which the growth of the two key populations is described by a system of time-dependant ordinary differential equations. We assume that branching is symmetric and is invoked when the number of epithelial cells per tip reaches a threshold value. This process continues until the number of mesenchymal cells falls below a critical value that triggers cessation of branching. The mathematical model and its predictions are validated against experimentally quantified C57Bl6 mouse embryonic kidneys. Numerical simulations are performed to determine how the final number of branches changes as key system parameters are varied (such as the growth rate of tip cells, mesenchyme cells, or component cell population exit rate). Our results predict that the developing kidney responds differently to loss of cap and tip cells. They also indicate that the final number of kidney branches is less sensitive to changes in the growth rate of the ureteric tip cells than to changes in the growth rate of the mesenchymal cells. By inference, increasing the growth rate of mesenchymal cells should maximise branch number. Our model also provides a framework for predicting the branching outcome when ureteric tip or mesenchyme cells change behaviour in response to different genetic or environmental developmental stresses.

Mathematical modeling courses for Media technology students

DEFF Research Database (Denmark)

Timcenko, Olga

2009-01-01

This paper addresses curriculum development for Mathematical Modeling course at Medialogy education. Medialogy as a study line was established in 2002 at Faculty for Engineering and Natural Sciences at Aalborg University, and mathematics curriculum has already been revised three times, Mathematic...

Teaching Mathematical Modelling for Earth Sciences via Case Studies

Science.gov (United States)

Yang, Xin-She

2010-05-01

Mathematical modelling is becoming crucially important for earth sciences because the modelling of complex systems such as geological, geophysical and environmental processes requires mathematical analysis, numerical methods and computer programming. However, a substantial fraction of earth science undergraduates and graduates may not have sufficient skills in mathematical modelling, which is due to either limited mathematical training or lack of appropriate mathematical textbooks for self-study. In this paper, we described a detailed case-study-based approach for teaching mathematical modelling. We illustrate how essential mathematical skills can be developed for students with limited training in secondary mathematics so that they are confident in dealing with real-world mathematical modelling at university level. We have chosen various topics such as Airy isostasy, greenhouse effect, sedimentation and Stokes' flow,free-air and Bouguer gravity, Brownian motion, rain-drop dynamics, impact cratering, heat conduction and cooling of the lithosphere as case studies; and we use these step-by-step case studies to teach exponentials, logarithms, spherical geometry, basic calculus, complex numbers, Fourier transforms, ordinary differential equations, vectors and matrix algebra, partial differential equations, geostatistics and basic numeric methods. Implications for teaching university mathematics for earth scientists for tomorrow's classroom will also be discussed. Refereces 1) D. L. Turcotte and G. Schubert, Geodynamics, 2nd Edition, Cambridge University Press, (2002). 2) X. S. Yang, Introductory Mathematics for Earth Scientists, Dunedin Academic Press, (2009).

Mathematical Modeling and Dynamic Simulation of Metabolic Reaction Systems Using Metabolome Time Series Data

Directory of Open Access Journals (Sweden)

Kansuporn eSriyudthsak

2016-05-01

Full Text Available The high-throughput acquisition of metabolome data is greatly anticipated for the complete understanding of cellular metabolism in living organisms. A variety of analytical technologies have been developed to acquire large-scale metabolic profiles under different biological or environmental conditions. Time series data are useful for predicting the most likely metabolic pathways because they provide important information regarding the accumulation of metabolites, which implies causal relationships in the metabolic reaction network. Considerable effort has been undertaken to utilize these data for constructing a mathematical model merging system properties and quantitatively characterizing a whole metabolic system in toto. However, there are technical difficulties between benchmarking the provision and utilization of data. Although hundreds of metabolites can be measured, which provide information on the metabolic reaction system, simultaneous measurement of thousands of metabolites is still challenging. In addition, it is nontrivial to logically predict the dynamic behaviors of unmeasurable metabolite concentrations without sufficient information on the metabolic reaction network. Yet, consolidating the advantages of advancements in both metabolomics and mathematical modeling remain to be accomplished. This review outlines the conceptual basis of and recent advances in technologies in both the research fields. It also highlights the potential for constructing a large-scale mathematical model by estimating model parameters from time series metabolome data in order to comprehensively understand metabolism at the systems level.

Mathematical Modeling and Dynamic Simulation of Metabolic Reaction Systems Using Metabolome Time Series Data.

Science.gov (United States)

Sriyudthsak, Kansuporn; Shiraishi, Fumihide; Hirai, Masami Yokota

2016-01-01

The high-throughput acquisition of metabolome data is greatly anticipated for the complete understanding of cellular metabolism in living organisms. A variety of analytical technologies have been developed to acquire large-scale metabolic profiles under different biological or environmental conditions. Time series data are useful for predicting the most likely metabolic pathways because they provide important information regarding the accumulation of metabolites, which implies causal relationships in the metabolic reaction network. Considerable effort has been undertaken to utilize these data for constructing a mathematical model merging system properties and quantitatively characterizing a whole metabolic system in toto. However, there are technical difficulties between benchmarking the provision and utilization of data. Although, hundreds of metabolites can be measured, which provide information on the metabolic reaction system, simultaneous measurement of thousands of metabolites is still challenging. In addition, it is nontrivial to logically predict the dynamic behaviors of unmeasurable metabolite concentrations without sufficient information on the metabolic reaction network. Yet, consolidating the advantages of advancements in both metabolomics and mathematical modeling remain to be accomplished. This review outlines the conceptual basis of and recent advances in technologies in both the research fields. It also highlights the potential for constructing a large-scale mathematical model by estimating model parameters from time series metabolome data in order to comprehensively understand metabolism at the systems level.

Rival approaches to mathematical modelling in immunology

Science.gov (United States)

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

2007-08-01

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

Mathematical modelling of demineralisation of high sulphur coal by bioleaching

Energy Technology Data Exchange (ETDEWEB)

Weerasekara, N.S.; Frutos, F.J.G.; Cara, J.; Lockwood, F.C. [University of London Imperial College of Science Technology & Medicine, London (United Kingdom)

2008-02-15

During coal combustion various toxic compounds are generated from its sulphur content. Their environmental impacts are considered to be very important. While there are various conventional preparation methods to remove the sulphur in the fuel, recent work reveals that newly-isolated micro-organisms, naturally present in coal, have the ability to reduce its sulphur content. The removal of sulphur using biological leaching involving acidophilic iron oxidising bacteria like Acidithiobacillus ferrooxidans and Leptospirillum ferrooxidans are examined and a computational technique based on computational fluid dynamics is developed to model the biological leaching of sulphur from coal. The model was validated against a pack-column experiment carried out for iron separation during 60 days. The mathematical model predicted iron separation over time is similar to experimental measurements, with an average difference of 5.5%. According to the experimental results, there was an overall reduction of 33% of pyrite, whereas the model prediction was 32%. The model results shows overall good agreement with pack-column experimental data.

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

Science.gov (United States)

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.

Mathematical models of human behavior

DEFF Research Database (Denmark)

Møllgaard, Anders Edsberg

at the Technical University of Denmark. The data set includes face-to-face interaction (Bluetooth), communication (calls and texts), mobility (GPS), social network (Facebook), and general background information including a psychological profile (questionnaire). This thesis presents my work on the Social Fabric...... data set, along with work on other behavioral data. The overall goal is to contribute to a quantitative understanding of human behavior using big data and mathematical models. Central to the thesis is the determination of the predictability of different human activities. Upper limits are derived....... Evidence is provided, which implies that the asymmetry is caused by a self-enhancement in the initiation dynamics. These results have implications for the formation of social networks and the dynamics of the links. It is shown that the Big Five Inventory (BFI) representing a psychological profile only...

Mathematical model for cross-flow-induced vibrations of tube rows

International Nuclear Information System (INIS)

Chen, S.S.

1976-09-01

A mathematical model for flow-induced vibrations in heat exchanger tube banks is presented which includes the effects of vortex shedding, fluidelastic coupling, drag force, and fluid inertia coupling. Once the fluid forces are known, the model can predict the details of complex tube-fluid interactions: (1) natural frequencies and mode shapes of coupled vibrations; (2) critical flow velocities; (3) responses to vortex shedding, drag force, and other types of excitations; and (4) the dominant excitation mechanism at a given flow velocity. The analytical results are in good agreement with the published experimental results

Assessment of Primary 5 Students' Mathematical Modelling Competencies

Science.gov (United States)

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

2012-01-01

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

Mathematical models of human paralyzed muscle after long-term training.

Science.gov (United States)

Law, L A Frey; Shields, R K

2007-01-01

Spinal cord injury (SCI) results in major musculoskeletal adaptations, including muscle atrophy, faster contractile properties, increased fatigability, and bone loss. The use of functional electrical stimulation (FES) provides a method to prevent paralyzed muscle adaptations in order to sustain force-generating capacity. Mathematical muscle models may be able to predict optimal activation strategies during FES, however muscle properties further adapt with long-term training. The purpose of this study was to compare the accuracy of three muscle models, one linear and two nonlinear, for predicting paralyzed soleus muscle force after exposure to long-term FES training. Further, we contrasted the findings between the trained and untrained limbs. The three models' parameters were best fit to a single force train in the trained soleus muscle (N=4). Nine additional force trains (test trains) were predicted for each subject using the developed models. Model errors between predicted and experimental force trains were determined, including specific muscle force properties. The mean overall error was greatest for the linear model (15.8%) and least for the nonlinear Hill Huxley type model (7.8%). No significant error differences were observed between the trained versus untrained limbs, although model parameter values were significantly altered with training. This study confirmed that nonlinear models most accurately predict both trained and untrained paralyzed muscle force properties. Moreover, the optimized model parameter values were responsive to the relative physiological state of the paralyzed muscle (trained versus untrained). These findings are relevant for the design and control of neuro-prosthetic devices for those with SCI.

Influence of biodiesel blending on physicochemical properties and importance of mathematical model for predicting the properties of biodiesel blend

International Nuclear Information System (INIS)

Wakil, M.A.; Kalam, M.A.; Masjuki, H.H.; Atabani, A.E.; Rizwanul Fattah, I.M.

2015-01-01

Highlights: • Short identification of selected biodiesel feedstock. • Review of physicochemical properties for blended biodiesel. • Mathematical model for predicting properties of various biodiesel blends. - Abstract: The growing demand for green world serves as one of the most significant challenges of modernization. Requirements like largest usage of energy for modern society as well as demand for friendly milieu create a deep concern in field of research. Biofuels are placed at the peak of the research arena for their underlying benefits as mentioned by multiple researches. Out of a number of vegetable oils, only a few are used commercially for biodiesel production. Due to various limitations of edible oil, non-edible oils are becoming a profitable choice. Till today, very little percentage of biodiesel is used successfully in engine. The research is still continuing for improving the biodiesel usage level. Recently, it is found that the blended biodiesel from more than one feedstock provides better performance in engine. This paper reviews the physicochemical properties of different biodiesel blends obtained from various feedstocks with a view to properly understand the fuel quality. Moreover, a short description of each feedstock is given along with graphical presentation of important properties for various blend percentages from B0 to B100. Finally, mathematical model is formed for predicting various properties of biodiesel blend with the help of different research data by using polynomial curve fitting method. The results obtained from a number of literature based on this work shows that the heating value of biodiesel is about 11% lower than diesel except coconut (14.5% lower) whereas kinematic viscosity is in the range of 4–5.4 mm 2 /s. Flash point of all biodiesels are more than 150 °C, except neem and coconut. Cold flow properties of calophyllum, palm, jatropha, moringa are inferior to others. This would help to determine important properties of

Estimating confidence intervals in predicted responses for oscillatory biological models.

Science.gov (United States)

St John, Peter C; Doyle, Francis J

2013-07-29

The dynamics of gene regulation play a crucial role in a cellular control: allowing the cell to express the right proteins to meet changing needs. Some needs, such as correctly anticipating the day-night cycle, require complicated oscillatory features. In the analysis of gene regulatory networks, mathematical models are frequently used to understand how a network's structure enables it to respond appropriately to external inputs. These models typically consist of a set of ordinary differential equations, describing a network of biochemical reactions, and unknown kinetic parameters, chosen such that the model best captures experimental data. However, since a model's parameter values are uncertain, and since dynamic responses to inputs are highly parameter-dependent, it is difficult to assess the confidence associated with these in silico predictions. In particular, models with complex dynamics - such as oscillations - must be fit with computationally expensive global optimization routines, and cannot take advantage of existing measures of identifiability. Despite their difficulty to model mathematically, limit cycle oscillations play a key role in many biological processes, including cell cycling, metabolism, neuron firing, and circadian rhythms. In this study, we employ an efficient parameter estimation technique to enable a bootstrap uncertainty analysis for limit cycle models. Since the primary role of systems biology models is the insight they provide on responses to rate perturbations, we extend our uncertainty analysis to include first order sensitivity coefficients. Using a literature model of circadian rhythms, we show how predictive precision is degraded with decreasing sample points and increasing relative error. Additionally, we show how this method can be used for model discrimination by comparing the output identifiability of two candidate model structures to published literature data. Our method permits modellers of oscillatory systems to confidently

a mathematical model for predicting output in an oilfield in the niger

African Journals Online (AJOL)

eobe

resultant model was found to have greater utility in predicting oil field output as it produced less residual. The ... decision making by the oilfield manager is facilitated by reliable ... Scaling laws from percolation theory was used to predict oilfield ...

Reducing the scan time in gastric emptying scintigraphy by using mathematical models

Energy Technology Data Exchange (ETDEWEB)

Yoon, Min Ki; Hwang, Kyung Hoon; Choe, Won Sick [Gachon Medical School Gil Medical Center, Incheon (Korea, Republic of); Lee, Byeong Il; Lee, Jae Sung [Seoul National University College of Medicine, Seoul (Korea, Republic of)

2005-08-15

Gastric emptying scan (GES) is usually acquired up to 2 hours. Our study investigated whether a fraction of meal-retention in the stomach at 120 minutes (FR120) was predicted from the data measured for 90 minutes by using non-linear curve fitting. We aimed at saving the delayed imaging by utilizing mathematical models. Ninety-six patients underwent GES immediately after taking a boiled egg with 74 MBq (2 mCi) Tc-99m DTPA. The patients were divided into Group I (T{sub 1/2} {<=} 90 min) and Group II (90 minpredicted FR120 was calculated from the acquired functional formulas. A correlation coefficient between the measured FR120 and the predicted FR120 was computed (MedCalc 6.0). Correlation coefficients(r) between the measured FR120 and the predicted FRA120 of each mathematical functions were as follows: simple exponential function (Group I: 0.8858, Group II: 0.5982, {rho} < 0.0001), power exponential function (Group I: 0.8755, Group II: 0.6008, {rho} < 0.0001), modified power exponential function (Group I: 0.8892, Group II: 0.5882, {rho} < 0.0001), and simple exponential function at the late times (Group I: 0.9085, Group II: 0.6832, {rho} < 0.0001). In all the fitting models, the predicted FR120 were significantly correlated with the measured FR120 in Group I but not in Group II. There was no statistically significant difference in correlation among the 4 mathematical models. In the cases with T{sub 1/2} {<=} 90 min, the predicted FR120 is significantly

Plant control using embedded predictive models

International Nuclear Information System (INIS)

Godbole, S.S.; Gabler, W.E.; Eschbach, S.L.

1990-01-01

B and W recently undertook the design of an advanced light water reactor control system. A concept new to nuclear steam system (NSS) control was developed. The concept, which is called the Predictor-Corrector, uses mathematical models of portions of the controlled NSS to calculate, at various levels within the system, demand and control element position signals necessary to satisfy electrical demand. The models give the control system the ability to reduce overcooling and undercooling of the reactor coolant system during transients and upsets. Two types of mathematical models were developed for use in designing and testing the control system. One model was a conventional, comprehensive NSS model that responds to control system outputs and calculates the resultant changes in plant variables that are then used as inputs to the control system. Two other models, embedded in the control system, were less conventional, inverse models. These models accept as inputs plant variables, equipment states, and demand signals and predict plant operating conditions and control element states that will satisfy the demands. This paper reports preliminary results of closed-loop Reactor Coolant (RC) pump trip and normal load reduction testing of the advanced concept. Results of additional transient testing, and of open and closed loop stability analyses will be reported as they are available

Mathematical modeling and computational intelligence in engineering applications

CERN Document Server

Silva Neto, Antônio José da; Silva, Geraldo Nunes

2016-01-01

This book brings together a rich selection of studies in mathematical modeling and computational intelligence, with application in several fields of engineering, like automation, biomedical, chemical, civil, electrical, electronic, geophysical and mechanical engineering, on a multidisciplinary approach. Authors from five countries and 16 different research centers contribute with their expertise in both the fundamentals and real problems applications based upon their strong background on modeling and computational intelligence. The reader will find a wide variety of applications, mathematical and computational tools and original results, all presented with rigorous mathematical procedures. This work is intended for use in graduate courses of engineering, applied mathematics and applied computation where tools as mathematical and computational modeling, numerical methods and computational intelligence are applied to the solution of real problems.

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

Science.gov (United States)

Baten, Elke; Desoete, Annemie

2018-01-01

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

The (Mathematical) Modeling Process in Biosciences.

Science.gov (United States)

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.

A Fuzzy mathematical model to estimate the effects of global warming on the vitality of Laelia purpurata orchids.

Science.gov (United States)

Putti, Fernando Ferrari; Filho, Luis Roberto Almeida Gabriel; Gabriel, Camila Pires Cremasco; Neto, Alfredo Bonini; Bonini, Carolina Dos Santos Batista; Rodrigues Dos Reis, André

2017-06-01

This study aimed to develop a fuzzy mathematical model to estimate the impacts of global warming on the vitality of Laelia purpurata growing in different Brazilian environmental conditions. In order to develop the mathematical model was considered as intrinsic factors the parameters: temperature, humidity and shade conditions to determine the vitality of plants. Fuzzy model results could accurately predict the optimal conditions for cultivation of Laelia purpurata in several sites of Brazil. Based on fuzzy model results, we found that higher temperatures and lacking of properly shading can reduce the vitality of orchids. Fuzzy mathematical model could precisely detect the effect of higher temperatures causing damages on vitality of plants as a consequence of global warming. Copyright © 2017 Elsevier Inc. All rights reserved.

Continuum mechanics the birthplace of mathematical models

CERN Document Server

Allen, Myron B

2015-01-01

Continuum mechanics is a standard course in many graduate programs in engineering and applied mathematics as it provides the foundations for the various differential equations and mathematical models that are encountered in fluid mechanics, solid mechanics, and heat transfer.  This book successfully makes the topic more accessible to advanced undergraduate mathematics majors by aligning the mathematical notation and language with related courses in multivariable calculus, linear algebra, and differential equations; making connections with other areas of applied mathematics where parial differe

Mathematical modelling of the electrostatic pendulum in school and undergraduate education

International Nuclear Information System (INIS)

Forjan, Matej; Marhl, Marko; Grubelnik, Vladimir

2014-01-01

The electrostatic pendulum, also known as the electrostatic ping-pong, is an exciting experiment in school as well as in undergraduate education. We can easily demonstrate how the frequency of the electrostatic pendulum depends on the voltage across the capacitor. In this paper, we develop a simple mathematical model describing the dynamics of this experiment. In a step-wise manner, we introduce the external forces influencing the dynamics of the electrostatic pendulum. First, we take into account the electric force only. Then, we add air resistance and the non-elasticity of ball collisions with the capacitor plates. The model predictions show that the non-elastic collisions have greater effect on the pendulum dynamics than air resistance; in particular, this is true for higher frequencies of the pendulum. For lower frequencies, however, gravity is of crucial importance. The mathematical model is implemented in a graphic-oriented computer program, which gives the possibility of using this theoretical analysis also at the secondary school level. (paper)

Drying of semicrystalline polymers: Mathematical modeling and experimental characterization of poly(vinyl alcohol) films

OpenAIRE

Wong, Sim-Siong; Altınkaya, Sacide; Mallapragada, Surya K.

2004-01-01

A mathematical model was developed to predict the drying mechanism of semicrystalline polymers involving multiple solvents. Since drying of semicrystalline polymers can be accompanied by changes in polymer degree of crystallinity, the model integrates crystallization kinetics and the Vrentas-Duda diffusion model to provide a better understanding of the mechanism. The model considers the effect of external conditions such as temperature, film shrinkage and diffusion and evaporation of multiple...

Modelling and Optimizing Mathematics Learning in Children

Science.gov (United States)

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

2013-01-01

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

A mathematical model for supplying air-cooling for a building using a packed bed

Energy Technology Data Exchange (ETDEWEB)

Marewo, G.T. [Zimbabwe Univ., Mathematics Dept., Harare (Zimbabwe); Henwood, D.J. [School of Computing and Mathematical Sciences, Brighton (United Kingdom)

2006-01-15

The cooling system at the Harare International School uses a packed bed system for storing the coldness of the night-time to be used later for day-time air-conditioning. A two-phase mathematical model is described for the packed bed which includes heat dispersion in the fluid, and heat loss to the environment. This is in contrast to other studies, where at least one of these terms is neglected to simplify the mathematical model. A numerical method for obtaining a solution is proposed and implemented. Using measured inlet temperatures, the measured and predicted outlet temperatures of the bed show good trend agreement. The differences in detail are examined through sensitivity analyses for both the heat convection transfer and air velocity. It is apparent that adjusting these parameters can increase the agreement between the predicted and measured data. A parametric study for heat storage with various materials and bed sizes is given, which indicates how the code may be used as a tool for improving design and operational parameters. Practical application: A mathematical model of a packed bed is described; the bed is made up of fluid flowing over solid material with heat interchange between the two. The solid material is idealized as spheres and the fluid temperature is assumed uniform in a cross-section of the bed. The model includes heat interchange between the bed and its surrounding environment and allows for time varying fluid velocity. The input data is the inlet temperature to the bed, which may be measured. The comparison with measured data may be helpful to anyone attempting to develop and test a similar model. The sensitivity tests give an understanding of the significance of some of the parameters involved. The Appendix gives a mathematical statement of the problem and an outline of an approach to developing computer code for a numerical solution. (Author)

Mathematical modeling of a process the rolling delivery

Science.gov (United States)

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.

A mathematical model of the spread of the AIDS virus

Energy Technology Data Exchange (ETDEWEB)

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

1987-01-01

A mathematical computer model of the spread of the AIDS epidemic in the US is being developed at Los Alamos National Laboratory. This model predicts the spreading of the HIV infection, and subsequent development of clinical AIDS in various population groups. These groups are chosen according to age, frequency and type of sexual contact, population density, and region of the country. Type of sexual contact includes not only the heterosexual, homosexual differentiation but also repeated contacts with such primary partners as spouses. In conjunction with the computer model, we are developing a database containing relevant information on the natural history of the viral infection, the prevalence of the infection and of clinical AIDS in the population, the distribution of people into sexual behavior groups as a function of age and information on interregional contacts. The effects of variable infectiousness and sexual activity during the long period from infection to disease are found to have a major impact on the predictions of the model. 24 refs., 5 figs.

Numerical approximation abilities correlate with and predict informal but not formal mathematics abilities.

Science.gov (United States)

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.

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

Science.gov (United States)

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.

Modelling Mathematical Reasoning in Physics Education

Science.gov (United States)

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

2012-04-01

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

Complex versus simple models: ion-channel cardiac toxicity prediction.

Science.gov (United States)

Mistry, Hitesh B

2018-01-01

There is growing interest in applying detailed mathematical models of the heart for ion-channel related cardiac toxicity prediction. However, a debate as to whether such complex models are required exists. Here an assessment in the predictive performance between two established large-scale biophysical cardiac models and a simple linear model B net was conducted. Three ion-channel data-sets were extracted from literature. Each compound was designated a cardiac risk category using two different classification schemes based on information within CredibleMeds. The predictive performance of each model within each data-set for each classification scheme was assessed via a leave-one-out cross validation. Overall the B net model performed equally as well as the leading cardiac models in two of the data-sets and outperformed both cardiac models on the latest. These results highlight the importance of benchmarking complex versus simple models but also encourage the development of simple models.

Complex versus simple models: ion-channel cardiac toxicity prediction

Directory of Open Access Journals (Sweden)

Hitesh B. Mistry

2018-02-01

Full Text Available There is growing interest in applying detailed mathematical models of the heart for ion-channel related cardiac toxicity prediction. However, a debate as to whether such complex models are required exists. Here an assessment in the predictive performance between two established large-scale biophysical cardiac models and a simple linear model Bnet was conducted. Three ion-channel data-sets were extracted from literature. Each compound was designated a cardiac risk category using two different classification schemes based on information within CredibleMeds. The predictive performance of each model within each data-set for each classification scheme was assessed via a leave-one-out cross validation. Overall the Bnet model performed equally as well as the leading cardiac models in two of the data-sets and outperformed both cardiac models on the latest. These results highlight the importance of benchmarking complex versus simple models but also encourage the development of simple models.

An introduction to mathematical modeling a course in mechanics

CERN Document Server

Oden, Tinsley J

2011-01-01

A modern approach to mathematical modeling, featuring unique applications from the field of mechanics An Introduction to Mathematical Modeling: A Course in Mechanics is designed to survey the mathematical models that form the foundations of modern science and incorporates examples that illustrate how the most successful models arise from basic principles in modern and classical mathematical physics. Written by a world authority on mathematical theory and computational mechanics, the book presents an account of continuum mechanics, electromagnetic field theory, quantum mechanics, and statistical mechanics for readers with varied backgrounds in engineering, computer science, mathematics, and physics. The author streamlines a comprehensive understanding of the topic in three clearly organized sections: Nonlinear Continuum Mechanics introduces kinematics as well as force and stress in deformable bodies; mass and momentum; balance of linear and angular momentum; conservation of energy; and constitutive equation...

Mathematical models and accuracy of radioisotope gauges

International Nuclear Information System (INIS)

Urbanski, P.

1989-01-01

Mathematical expressions relating the variance and mean value of the intrinsic error with the parameters of one and multi-dimensional mathematical models of radioisotope gauges are given. Variance of the intrinsic error at the model's output is considered as a sum of the variances of the random error which is created in the first stages of the measuring chain and the random error of calibration procedure. The mean value of the intrinsic error (systematic error) appears always for nonlinear models. It was found that the optimal model of calibration procedure not always corresponds to the minimal value of the intrinsic error. The derived expressions are applied for the assessment of the mathematical models of some of the existing gauges (radioisotope belt weigher, XRF analyzer and coating thickness gauge). 7 refs., 5 figs., 1 tab. (author)

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

Science.gov (United States)

Sinha, Ashok

2016-03-01

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

Leading Undergraduate Research Projects in Mathematical Modeling

Science.gov (United States)

Seshaiyer, Padmanabhan

2017-01-01

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

Scaffolding Mathematical Modelling with a Solution Plan

Science.gov (United States)

Schukajlow, Stanislaw; Kolter, Jana; Blum, Werner

2015-01-01

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

Programme of research into the management and storage of radioactive waste. Mathematical modelling

International Nuclear Information System (INIS)

Rae, J.

1984-01-01

Progress in work on the importance of fractures in rocks to waste disposal studies is reported. The permeability of the fracture system is predicted. Computer programmes are used to solve problems of ground water flow and radionuclide transport, and a new 'dual porosity' mathematical model is assessed for radionuclide transportation. (U.K.)

Modeling interdisciplinary activities involving Mathematics

DEFF Research Database (Denmark)

Iversen, Steffen Møllegaard

2006-01-01

In this paper a didactical model is presented. The goal of the model is to work as a didactical tool, or conceptual frame, for developing, carrying through and evaluating interdisciplinary activities involving the subject of mathematics and philosophy in the high schools. Through the terms...... of Horizontal Intertwining, Vertical Structuring and Horizontal Propagation the model consists of three phases, each considering different aspects of the nature of interdisciplinary activities. The theoretical modelling is inspired by work which focuses on the students abilities to concept formation in expanded...... domains (Michelsen, 2001, 2005a, 2005b). Furthermore the theoretical description rest on a series of qualitative interviews with teachers from the Danish high school (grades 9-11) conducted recently. The special case of concrete interdisciplinary activities between mathematics and philosophy is also...

The Spectrum of Mathematical Models.

Science.gov (United States)

Karplus, Walter J.

1983-01-01

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

Mathematical model in economic environmental problems

Energy Technology Data Exchange (ETDEWEB)

Nahorski, Z. [Polish Academy of Sciences, Systems Research Inst. (Poland); Ravn, H.F. [Risoe National Lab. (Denmark)

1996-12-31

The report contains a review of basic models and mathematical tools used in economic regulation problems. It starts with presentation of basic models of capital accumulation, resource depletion, pollution accumulation, and population growth, as well as construction of utility functions. Then the one-state variable model is discussed in details. The basic mathematical methods used consist of application of the maximum principle and phase plane analysis of the differential equations obtained as the necessary conditions of optimality. A summary of basic results connected with these methods is given in appendices. (au) 13 ills.; 17 refs.

Dynamic mathematical modeling of IL13-induced signaling in Hodgkin and primary mediastinal B-cell lymphoma allows prediction of therapeutic targets.

Science.gov (United States)

Raia, Valentina; Schilling, Marcel; Böhm, Martin; Hahn, Bettina; Kowarsch, Andreas; Raue, Andreas; Sticht, Carsten; Bohl, Sebastian; Saile, Maria; Möller, Peter; Gretz, Norbert; Timmer, Jens; Theis, Fabian; Lehmann, Wolf-Dieter; Lichter, Peter; Klingmüller, Ursula

2011-02-01

Primary mediastinal B-cell lymphoma (PMBL) and classical Hodgkin lymphoma (cHL) share a frequent constitutive activation of JAK (Janus kinase)/STAT signaling pathway. Because of complex, nonlinear relations within the pathway, key dynamic properties remained to be identified to predict possible strategies for intervention. We report the development of dynamic pathway models based on quantitative data collected on signaling components of JAK/STAT pathway in two lymphoma-derived cell lines, MedB-1 and L1236, representative of PMBL and cHL, respectively. We show that the amounts of STAT5 and STAT6 are higher whereas those of SHP1 are lower in the two lymphoma cell lines than in normal B cells. Distinctively, L1236 cells harbor more JAK2 and less SHP1 molecules per cell than MedB-1 or control cells. In both lymphoma cell lines, we observe interleukin-13 (IL13)-induced activation of IL4 receptor α, JAK2, and STAT5, but not of STAT6. Genome-wide, 11 early and 16 sustained genes are upregulated by IL13 in both lymphoma cell lines. Specifically, the known STAT-inducible negative regulators CISH and SOCS3 are upregulated within 2 hours in MedB-1 but not in L1236 cells. On the basis of this detailed quantitative information, we established two mathematical models, MedB-1 and L1236 model, able to describe the respective experimental data. Most of the model parameters are identifiable and therefore the models are predictive. Sensitivity analysis of the model identifies six possible therapeutic targets able to reduce gene expression levels in L1236 cells and three in MedB-1. We experimentally confirm reduction in target gene expression in response to inhibition of STAT5 phosphorylation, thereby validating one of the predicted targets.

Development of a Multidisciplinary Middle School Mathematics Infusion Model

Science.gov (United States)

Russo, Maria; Hecht, Deborah; Burghardt, M. David; Hacker, Michael; Saxman, Laura

2011-01-01

The National Science Foundation (NSF) funded project "Mathematics, Science, and Technology Partnership" (MSTP) developed a multidisciplinary instructional model for connecting mathematics to science, technology and engineering content areas at the middle school level. Specifically, the model infused mathematics into middle school curriculum…

Mathematical models in biology bringing mathematics to life

CERN Document Server

Ferraro, Maria; Guarracino, Mario

2015-01-01

This book presents an exciting collection of contributions based on the workshop “Bringing Maths to Life” held October 27-29, 2014 in Naples, Italy.  The state-of-the art research in biology and the statistical and analytical challenges facing huge masses of data collection are treated in this Work. Specific topics explored in depth surround the sessions and special invited sessions of the workshop and include genetic variability via differential expression, molecular dynamics and modeling, complex biological systems viewed from quantitative models, and microscopy images processing, to name several. In depth discussions of the mathematical analysis required to extract insights from complex bodies of biological datasets, to aid development in the field novel algorithms, methods and software tools for genetic variability, molecular dynamics, and complex biological systems are presented in this book. Researchers and graduate students in biology, life science, and mathematics/statistics will find the content...

Ocular hemodynamics and glaucoma: the role of mathematical modeling.

Science.gov (United States)

Harris, Alon; Guidoboni, Giovanna; Arciero, Julia C; Amireskandari, Annahita; Tobe, Leslie A; Siesky, Brent A

2013-01-01

To discuss the role of mathematical modeling in studying ocular hemodynamics, with a focus on glaucoma. We reviewed recent literature on glaucoma, ocular blood flow, autoregulation, the optic nerve head, and the use of mathematical modeling in ocular circulation. Many studies suggest that alterations in ocular hemodynamics play a significant role in the development, progression, and incidence of glaucoma. Although there is currently a limited number of studies involving mathematical modeling of ocular blood flow, regulation, and diseases (such as glaucoma), preliminary modeling work shows the potential of mathematical models to elucidate the mechanisms that contribute most significantly to glaucoma progression. Mathematical modeling is a useful tool when used synergistically with clinical and laboratory data in the study of ocular blood flow and glaucoma. The development of models to investigate the relationship between ocular hemodynamic alterations and glaucoma progression will provide a unique and useful method for studying the pathophysiology of glaucoma.

Dealing with dissatisfaction in mathematical modelling to integrate QFD and Kano’s model

Science.gov (United States)

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.

Modified Mathematical Model For Neutralization System In Stirred Tank Reactor

Directory of Open Access Journals (Sweden)

Ahmmed Saadi Ibrehem

2011-05-01

Full Text Available A modified model for the neutralization process of Stirred Tank Reactors (CSTR reactor is presented in this study. The model accounts for the effect of strong acid [HCL] flowrate and strong base [NaOH] flowrate with the ionic concentrations of [Cl-] and [Na+] on the Ph of the system. In this work, the effect of important reactor parameters such as ionic concentrations and acid and base flowrates on the dynamic behavior of the CSTR is investigated and the behavior of mathematical model is compared with the reported models for the McAvoy model and Jutila model. Moreover, the results of the model are compared with the experimental data in terms of pH dynamic study. A good agreement is observed between our model prediction and the actual plant data. © 2011 BCREC UNDIP. All rights reserved(Received: 1st March 2011, Revised: 28th March 2011; Accepted: 7th April 2011[How to Cite: A.S. Ibrehem. (2011. Modified Mathematical Model For Neutralization System In Stirred Tank Reactor. Bulletin of Chemical Reaction Engineering & Catalysis, 6(1: 47-52. doi:10.9767/bcrec.6.1.825.47-52][How to Link / DOI: http://dx.doi.org/10.9767/bcrec.6.1.825.47-52 || or local:  http://ejournal.undip.ac.id/index.php/bcrec/article/view/825 ] | View in 

Mathematical modeling of left ventricular dimensional changes in mice during aging

Directory of Open Access Journals (Sweden)

Yang Tianyi

2012-12-01

Full Text Available Abstract Cardiac aging is characterized by diastolic dysfunction of the left ventricle (LV, which is due in part to increased LV wall stiffness. In the diastolic phase, myocytes are relaxed and extracellular matrix (ECM is a critical determinant to the changes of LV wall stiffness. To evaluate the effects of ECM composition on cardiac aging, we developed a mathematical model to predict LV dimension and wall stiffness changes in aging mice by integrating mechanical laws and our experimental results. We measured LV dimension, wall thickness, LV mass, and collagen content for wild type (WT C57/BL6J mice of ages ranging from 7.3 months to those of 34.0 months. The model was established using the thick wall theory and stretch-induced tissue growth to an isotropic and homogeneous elastic composite with mixed constituents. The initial conditions of the simulation were set based on the data from the young mice. Matlab simulations of this mathematical model demonstrated that the model captured the major features of LV remodeling with age and closely approximated experimental results. Specifically, the temporal progression of the LV interior and exterior dimensions demonstrated the same trend and order-of-magnitude change as our experimental results. In conclusion, we present here a validated mathematical model of cardiac aging that applies the thick-wall theory and stretch-induced tissue growth to LV remodeling with age.

Predictive modelling of complex agronomic and biological systems.

Science.gov (United States)

Keurentjes, Joost J B; Molenaar, Jaap; Zwaan, Bas J

2013-09-01

Biological systems are tremendously complex in their functioning and regulation. Studying the multifaceted behaviour and describing the performance of such complexity has challenged the scientific community for years. The reduction of real-world intricacy into simple descriptive models has therefore convinced many researchers of the usefulness of introducing mathematics into biological sciences. Predictive modelling takes such an approach another step further in that it takes advantage of existing knowledge to project the performance of a system in alternating scenarios. The ever growing amounts of available data generated by assessing biological systems at increasingly higher detail provide unique opportunities for future modelling and experiment design. Here we aim to provide an overview of the progress made in modelling over time and the currently prevalent approaches for iterative modelling cycles in modern biology. We will further argue for the importance of versatility in modelling approaches, including parameter estimation, model reduction and network reconstruction. Finally, we will discuss the difficulties in overcoming the mathematical interpretation of in vivo complexity and address some of the future challenges lying ahead. © 2013 John Wiley & Sons Ltd.

Clinical implications of in silico mathematical modeling for glioblastoma: a critical review.

Science.gov (United States)

Protopapa, Maria; Zygogianni, Anna; Stamatakos, Georgios S; Antypas, Christos; Armpilia, Christina; Uzunoglu, Nikolaos K; Kouloulias, Vassilis

2018-01-01

Glioblastoma remains a clinical challenge in spite of years of extensive research. Novel approaches are needed in order to integrate the existing knowledge. This is the potential role of mathematical oncology. This paper reviews mathematical models on glioblastoma from the clinical doctor's point of view, with focus on 3D modeling approaches of radiation response of in vivo glioblastomas based on contemporary imaging techniques. As these models aim to provide a clinically useful tool in the era of personalized medicine, the integration of the latest advances in molecular and imaging science and in clinical practice by the in silico models is crucial for their clinical relevance. Our aim is to indicate areas of GBM research that have not yet been addressed by in silico models and to point out evidence that has come up from in silico experiments, which may be worth considering in the clinic. This review examines how close these models have come in predicting the outcome of treatment protocols and in shaping the future of radiotherapy treatments.

Mathematical Modelling of Surfactant Self-assembly at Interfaces

KAUST Repository

Morgan, C. E.; Breward, C. J. W.; Griffiths, I. M.; Howell, P. D.

2015-01-01

© 2015 Society for Industrial and Applied Mathematics. We present a mathematical model to describe the distribution of surfactant pairs in a multilayer structure beneath an adsorbed monolayer. A mesoscopic model comprising a set of ordinary

a Discrete Mathematical Model to Simulate Malware Spreading

Science.gov (United States)

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

2012-10-01

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

Use of mathematical modeling in nuclear measurements projects

International Nuclear Information System (INIS)

Toubon, H.; Menaa, N.; Mirolo, L.; Ducoux, X.; Khalil, R. A.; Chany, P.; Devita, A.

2011-01-01

Mathematical modeling of nuclear measurement systems is not a new concept. The response of the measurement system is described using a pre-defined mathematical model that depends on a set of parameters. These parameters are determined using a limited set of experimental measurement points e.g. efficiency curve, dose rates... etc. The model that agrees with the few experimental points is called an experimentally validated model. Once these models have been validated, we use mathematical interpolation to find the parameters of interest. Sometimes, when measurements are not practical or are impossible extrapolation is implemented but with care. CANBERRA has been extensively using mathematical modeling for the design and calibration of large and sophisticated systems to create and optimize designs that would be prohibitively expensive with only experimental tools. The case studies that will be presented here are primarily performed with MCNP, CANBERRA's MERCURAD/PASCALYS and ISOCS (In Situ Object Counting Software). For benchmarking purposes, both Monte Carlo and ray-tracing based codes are inter-compared to show models consistency and add a degree of reliability to modeling results. (authors)

Mathematical Models of the Use of Caffeine as a Counter Measure to the Deterioration of Neurobehaviorial Functioning During Sleep Deprivation

National Research Council Canada - National Science Library

Jewett, Megan

2000-01-01

The specific aims are to refine mathematical models that predict homeostatic and circadian regulation of human alertness and short-term memory during sleep deprivation, and to validate these models...

Mathematical modelling and TMCP simulation for optimisation of steel behaviour

International Nuclear Information System (INIS)

Siwecki, T.

2001-01-01

Physically based mathematical models for prediction of steel behaviour and microstructure evolution in connection with thermal and thermomechanical controlled processing (TMCP) development in Swedish Institute for Metals Research are discussed. The models can be used for computer predictions of recrystallization and grain growth of austenite after deformation, precipitation or dissolution of microalloying carbonitride in austenite, flow stress during hot working, phase transformation behaviour during accelerated cooling as well as the final microstructure and mechanical properties. The database, which contains information about steel behaviour for a large number of HSLA steels, is also presented. Optimization of TMCP parameters for improving the properties of the steel are discussed in relation to the microstructure and mechanical properties. The effect of TMCP parameters (reheating temperature, rolling schedules and finish rolling temperature as well as accelerated control cooling) on steel properties was studied in laboratory scale. (author)

Mathematical modelling of fracture hydrology

International Nuclear Information System (INIS)

Herbert, A.W.; Hodgkinson, D.P.; Lever, D.A.; Robinson, P.C.; Rae, J.

1985-06-01

This report summarises the work performed between January 1983 and December 1984 for the CEC/DOE contract 'Mathematical Modelling of Fracture Hydrology', under the following headings: 1) Statistical fracture network modelling, 2) Continuum models of flow and transport, 3) Simplified models, 4) Analysis of laboratory experiments and 5) Analysis of field experiments. (author)

A design of mathematical modelling for the mudharabah scheme in shariah insurance

Science.gov (United States)

Cahyandari, R.; Mayaningsih, D.; Sukono

2017-01-01

Indonesian Shariah Insurance Association (AASI) believes that 2014 is the year of Indonesian Shariah insurance, since its growth was above the conventional insurance. In December 2013, 43% growth was recorded for shariah insurance, while the conventional insurance was only hit 20%. This means that shariah insurance has tremendous potential to remain growing in the future. In addition, the growth can be predicted from the number of conventional insurance companies who open sharia division, along with the development of Islamic banking development which automatically demand the role of shariah insurance to protect assets and banking transactions. The development of shariah insurance should be accompanied by the development of premium fund management mechanism, in order to create innovation on shariah insurance products which beneficial for the society. The development of premium fund management model shows a positive progress through the emergence of Mudharabah, Wakala, Hybrid (Mudharabah-Wakala), and Wakala-Waqf. However, ‘model’ term that referred in this paper is regarded as an operational model in form of a scheme of management mechanism. Therefore, this paper will describe a mathematical modeling for premium fund management scheme, especially for Mudharabah concept. Mathematical modeling is required for an analysis process that can be used to predict risks that could be faced by a company in the future, so that the company could take a precautionary policy to minimize those risks.

Mathematical Modelling Plant Signalling Networks

KAUST Repository

Muraro, D.; Byrne, H.M.; King, J.R.; Bennett, M.J.

2013-01-01

methods for modelling gene and signalling networks and their application in plants. We then describe specific models of hormonal perception and cross-talk in plants. This mathematical analysis of sub-cellular molecular mechanisms paves the way for more

Mathematical modeling and applications in nonlinear dynamics

CERN Document Server

Merdan, Hüseyin

2016-01-01

The book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear discrete equations and hybrid equations. Such modeling can be effectively applied to the wide spectrum of nonlinear physical problems, including the KAM (Kolmogorov-Arnold-Moser (KAM)) theory, singular differential equations, impulsive dichotomous linear systems, analytical bifurcation trees of periodic motions, and almost or pseudo- almost periodic solutions in nonlinear dynamical systems. Provides methods for mathematical models with switching, thresholds, and impulses, each of particular importance for discontinuous processes Includes qualitative analysis of behaviors on Tumor-Immune Systems and methods of analysis for DNA, neural networks and epidemiology Introduces...

Mathematical modeling of CA125 kinetics in recurrent ovarian cancer (ROC) patients treated with chemotherapy and predictive value of early modeled kinetic parameters in CALYPSO trial: A GCIG study

DEFF Research Database (Denmark)

You, Benoit; Colomban, Olivier; Heywood, Mark

2011-01-01

Background: Although CA125 kinetic profiles may be related with relapse risk in ovarian cancer patients treated with chemotherapy, no reliable kinetic parameters have been reported. Mathematical modeling may help describe CA125 decline dynamically and determine parameters predictive of relapse....... Methods: Data from CALYPSO phase III trial data comparing 2 carboplatin-based regimens in ROC patients were analyzed. Based on population kinetic approach (Monolix software), a semi-mechanistic model was used to fit serum log (CA125) concentration-time profiles with following parameters: tumor growth rate...... the first 50 treatment days were tested regarding progression free survival (PFS) against other reported prognostic factors using Cox-models: treatment arm; platinum-free interval (PFI), metastatic site number, largest tumor size, elevated WBC and measurable disease. Results: The CA125 kinetics from 898...

ANALYSIS MUSIC CONCERTS ADOPTING THE MATHEMATICAL MODEL OF HIT PHENOMENA

OpenAIRE

Kawahata Yasuko; Genda Etsuo; Ishii Akira

2013-01-01

A mathematical model for the hit phenomenon in entertainment within a society is presented as a stochastic process of interactions of human dynamics. In this paper, we analyzed music to the concert.Knowing the cost of advertising the concert is difficult. But exposure to the media of the artist can be seen. We tried to analysis of music concert itself by performing a prediction of reputation of artists during the concert tour from this exposure.In this paper, The world most pop...

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

Science.gov (United States)

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

FEMME, a flexible environment for mathematically modelling the environment

NARCIS (Netherlands)

Soetaert, K.E.R.; DeClippele, V.; Herman, P.M.J.

2002-01-01

A new, FORTRAN-based, simulation environment called FEMME (Flexible Environment for Mathematically Modelling the Environment), designed for implementing, solving and analysing mathematical models in ecology is presented. Three separate phases in ecological modelling are distinguished: (1) the model

Model-free prediction and regression a transformation-based approach to inference

CERN Document Server

Politis, Dimitris N

2015-01-01

The Model-Free Prediction Principle expounded upon in this monograph is based on the simple notion of transforming a complex dataset to one that is easier to work with, e.g., i.i.d. or Gaussian. As such, it restores the emphasis on observable quantities, i.e., current and future data, as opposed to unobservable model parameters and estimates thereof, and yields optimal predictors in diverse settings such as regression and time series. Furthermore, the Model-Free Bootstrap takes us beyond point prediction in order to construct frequentist prediction intervals without resort to unrealistic assumptions such as normality. Prediction has been traditionally approached via a model-based paradigm, i.e., (a) fit a model to the data at hand, and (b) use the fitted model to extrapolate/predict future data. Due to both mathematical and computational constraints, 20th century statistical practice focused mostly on parametric models. Fortunately, with the advent of widely accessible powerful computing in the late 1970s, co...

mathematical models for estimating radio channels utilization

African Journals Online (AJOL)

2017-08-08

Aug 8, 2017 ... Mathematical models for radio channels utilization assessment by real-time flows transfer in ... data transmission networks application having dynamic topology ..... Journal of Applied Mathematics and Statistics, 56(2): 85–90.

Mathematical Modelling of a Friction Stir Welding Process to Predict the Joint Strength of Two Dissimilar Aluminium Alloys Using Experimental Data and Genetic Programming

Directory of Open Access Journals (Sweden)

Mohammed Yunus

2018-01-01

Full Text Available Friction stir welding (FSW is the most popular and efficient method of solid-state joining for similar as well as dissimilar metals and alloys. It is mostly used in applications for aerospace, rail, automotive, and marine industries. Many researchers are currently working with different perspectives on this FSW process for various combinations of materials. The general input process parameters are the thickness of the plate, axial load, rotational speed, welding speed, and tilt angle. The output parameters are joint hardness, % of elongation, and impact and yield strengths. Genetic programming (GP is a relatively new method of evolutionary computing with the principal advantage of this approach being to evaluate efficacious predictive mathematical models or equations without any prior assumption regarding the possible form of the functional relationship. This paper both defines and illustrates how GP can be applied to the FSW process to derive precise relationships between the output and input parameters in order to obtain a generalized prediction model. A GP model will assist engineers in quantifying the performance of FSW, and the results from this study can then be utilized to estimate future requirements based on the historical data to provide a robust solution. The obtained results from the GP models showed good agreement with experimental and target data at an average prediction error of 0.72%.

Safety of nuclear reactors - Part A - unsteady state temperature history mathematical model

International Nuclear Information System (INIS)

El-Shayeb, M.; Yusoff, M.Z.; Boosroh, M.H.; Ideris, F.; Hasmady Abu Hassan, S.; Bondok, A.

2004-01-01

A nuclear reactor structure under abnormal operations of near meltdown will be exposed to a tremendous amount of heat flux in addition to the stress field applied under normal operation. Temperature encountered in such case is assumed to be beyond 1000 Celsius degrees. A 2-dimensional mathematical model based on finite difference methods, has been developed for the fire resistance calculation of a concrete-filled square steel column with respect to its temperature history. Effects due to nuclear radiation and mechanical vibrations will be explored in a later future model. The temperature rise in each element can be derived from its heat balance by applying the parabolic unsteady state, partial differential equation and numerical solution into the steel region. Calculation of the temperature of the elementary regions needs to satisfy the symmetry conditions and the relevant material properties. The developed mathematical model is capable to predict the temperature history in the column and on the surface with respect to time. (authors)

Optimising the anaerobic co-digestion of urban organic waste using dynamic bioconversion mathematical modelling

DEFF Research Database (Denmark)

Fitamo, Temesgen Mathewos; Boldrin, Alessio; Dorini, G.

2016-01-01

Mathematical anaerobic bioconversion models are often used as a convenient way to simulate the conversion of organic materials to biogas. The aim of the study was to apply a mathematical model for simulating the anaerobic co-digestion of various types of urban organic waste, in order to develop...... in a continuously stirred tank reactor. The model's outputs were validated with experimental results obtained in thermophilic conditions, with mixed sludge as a single substrate and urban organic waste as a co-substrate at hydraulic retention times of 30, 20, 15 and 10 days. The predicted performance parameter...... (methane productivity and yield) and operational parameter (concentration of ammonia and volatile fatty acid) values were reasonable and displayed good correlation and accuracy. The model was later applied to identify optimal scenarios for an urban organic waste co-digestion process. The simulation...

Energy models for commercial energy prediction and substitution of renewable energy sources

International Nuclear Information System (INIS)

Iniyan, S.; Suganthi, L.; Samuel, Anand A.

2006-01-01

In this paper, three models have been projected namely Modified Econometric Mathematical (MEM) model, Mathematical Programming Energy-Economy-Environment (MPEEE) model, and Optimal Renewable Energy Mathematical (OREM) model. The actual demand for coal, oil and electricity is predicted using the MEM model based on economic, technological and environmental factors. The results were used in the MPEEE model, which determines the optimum allocation of commercial energy sources based on environmental limitations. The gap between the actual energy demand from the MEM model and optimal energy use from the MPEEE model, has to be met by the renewable energy sources. The study develops an OREM model that would facilitate effective utilization of renewable energy sources in India, based on cost, efficiency, social acceptance, reliability, potential and demand. The economic variations in solar energy systems and inclusion of environmental constraint are also analyzed with OREM model. The OREM model will help policy makers in the formulation and implementation of strategies concerning renewable energy sources in India for the next two decades

Mathematical modelling in solid mechanics

CERN Document Server

Sofonea, Mircea; Steigmann, David

2017-01-01

This book presents new research results in multidisciplinary fields of mathematical and numerical modelling in mechanics. The chapters treat the topics: mathematical modelling in solid, fluid and contact mechanics nonconvex variational analysis with emphasis to nonlinear solid and structural mechanics numerical modelling of problems with non-smooth constitutive laws, approximation of variational and hemivariational inequalities, numerical analysis of discrete schemes, numerical methods and the corresponding algorithms, applications to mechanical engineering numerical aspects of non-smooth mechanics, with emphasis on developing accurate and reliable computational tools mechanics of fibre-reinforced materials behaviour of elasto-plastic materials accounting for the microstructural defects definition of structural defects based on the differential geometry concepts or on the atomistic basis interaction between phase transformation and dislocations at nano-scale energetic arguments bifurcation and post-buckling a...

One-dimensional chain of quantum molecule motors as a mathematical physics model for muscle fibers

International Nuclear Information System (INIS)

Si Tie-Yan

2015-01-01

A quantum chain model of multiple molecule motors is proposed as a mathematical physics theory for the microscopic modeling of classical force-velocity relation and tension transients in muscle fibers. The proposed model was a quantum many-particle Hamiltonian to predict the force-velocity relation for the slow release of muscle fibers, which has not yet been empirically defined and was much more complicated than the hyperbolic relationships. Using the same Hamiltonian model, a mathematical force-velocity relationship was proposed to explain the tension observed when the muscle was stimulated with an alternative electric current. The discrepancy between input electric frequency and the muscle oscillation frequency could be explained physically by the Doppler effect in this quantum chain model. Further more, quantum physics phenomena were applied to explore the tension time course of cardiac muscle and insect flight muscle. Most of the experimental tension transient curves were found to correspond to the theoretical output of quantum two- and three-level models. Mathematical modeling electric stimulus as photons exciting a quantum three-level particle reproduced most of the tension transient curves of water bug Lethocerus maximus. (special topic)

Interfacial Fluid Mechanics A Mathematical Modeling Approach

CERN Document Server

Ajaev, Vladimir S

2012-01-01

Interfacial Fluid Mechanics: A Mathematical Modeling Approach provides an introduction to mathematical models of viscous flow used in rapidly developing fields of microfluidics and microscale heat transfer. The basic physical effects are first introduced in the context of simple configurations and their relative importance in typical microscale applications is discussed. Then,several configurations of importance to microfluidics, most notably thin films/droplets on substrates and confined bubbles, are discussed in detail.  Topics from current research on electrokinetic phenomena, liquid flow near structured solid surfaces, evaporation/condensation, and surfactant phenomena are discussed in the later chapters. This book also:  Discusses mathematical models in the context of actual applications such as electrowetting Includes unique material on fluid flow near structured surfaces and phase change phenomena Shows readers how to solve modeling problems related to microscale multiphase flows Interfacial Fluid Me...

Mathematical model of the Savannah River Site waste tank farm

International Nuclear Information System (INIS)

Smith, F.G. III.

1991-01-01

A mathematical model has been developed to simulate operation of the waste tank farm and the associated evaporator systems at the Savannah River Site. The model solves material balance equations to predict the volumes of liquid waste, salt, and sludge for all of the tanks within each of the evaporator systems. Additional logic is included to model the behavior of waste tanks not directly associated with the evaporators. Input parameters include the Material Management Plan forecast of canyon operations, specification of other waste sources for the evaporator systems, evaporator operating characteristics, and salt and sludge removal schedules. The model determines how the evaporators will operate, when waste transfers can be made, and waste accumulation rates. Output from the model includes waste tank contents, summaries of systems operations, and reports of space gain and the remaining capacity to store waste materials within the tank farm. Model simulations can be made to predict waste tank capacities on a daily basis for up to 20 years. The model is coded as a set of three computer programs designed to run on either IBM compatible or Apple Macintosh II personal computers

Mathematical Formulation Requirements and Specifications for the Process Models

Energy Technology Data Exchange (ETDEWEB)

Steefel, C.; Moulton, D.; Pau, G.; Lipnikov, K.; Meza, J.; Lichtner, P.; Wolery, T.; Bacon, D.; Spycher, N.; Bell, J.; Moridis, G.; Yabusaki, S.; Sonnenthal, E.; Zyvoloski, G.; Andre, B.; Zheng, L.; Davis, J.

2010-11-01

The Advanced Simulation Capability for Environmental Management (ASCEM) is intended to be a state-of-the-art scientific tool and approach for understanding and predicting contaminant fate and transport in natural and engineered systems. The ASCEM program is aimed at addressing critical EM program needs to better understand and quantify flow and contaminant transport behavior in complex geological systems. It will also address the long-term performance of engineered components including cementitious materials in nuclear waste disposal facilities, in order to reduce uncertainties and risks associated with DOE EM's environmental cleanup and closure activities. Building upon national capabilities developed from decades of Research and Development in subsurface geosciences, computational and computer science, modeling and applied mathematics, and environmental remediation, the ASCEM initiative will develop an integrated, open-source, high-performance computer modeling system for multiphase, multicomponent, multiscale subsurface flow and contaminant transport. This integrated modeling system will incorporate capabilities for predicting releases from various waste forms, identifying exposure pathways and performing dose calculations, and conducting systematic uncertainty quantification. The ASCEM approach will be demonstrated on selected sites, and then applied to support the next generation of performance assessments of nuclear waste disposal and facility decommissioning across the EM complex. The Multi-Process High Performance Computing (HPC) Simulator is one of three thrust areas in ASCEM. The other two are the Platform and Integrated Toolsets (dubbed the Platform) and Site Applications. The primary objective of the HPC Simulator is to provide a flexible and extensible computational engine to simulate the coupled processes and flow scenarios described by the conceptual models developed using the ASCEM Platform. The graded and iterative approach to assessments

Mathematical Formulation Requirements and Specifications for the Process Models

International Nuclear Information System (INIS)

Steefel, C.; Moulton, D.; Pau, G.; Lipnikov, K.; Meza, J.; Lichtner, P.; Wolery, T.; Bacon, D.; Spycher, N.; Bell, J.; Moridis, G.; Yabusaki, S.; Sonnenthal, E.; Zyvoloski, G.; Andre, B.; Zheng, L.; Davis, J.

2010-01-01

The Advanced Simulation Capability for Environmental Management (ASCEM) is intended to be a state-of-the-art scientific tool and approach for understanding and predicting contaminant fate and transport in natural and engineered systems. The ASCEM program is aimed at addressing critical EM program needs to better understand and quantify flow and contaminant transport behavior in complex geological systems. It will also address the long-term performance of engineered components including cementitious materials in nuclear waste disposal facilities, in order to reduce uncertainties and risks associated with DOE EM's environmental cleanup and closure activities. Building upon national capabilities developed from decades of Research and Development in subsurface geosciences, computational and computer science, modeling and applied mathematics, and environmental remediation, the ASCEM initiative will develop an integrated, open-source, high-performance computer modeling system for multiphase, multicomponent, multiscale subsurface flow and contaminant transport. This integrated modeling system will incorporate capabilities for predicting releases from various waste forms, identifying exposure pathways and performing dose calculations, and conducting systematic uncertainty quantification. The ASCEM approach will be demonstrated on selected sites, and then applied to support the next generation of performance assessments of nuclear waste disposal and facility decommissioning across the EM complex. The Multi-Process High Performance Computing (HPC) Simulator is one of three thrust areas in ASCEM. The other two are the Platform and Integrated Toolsets (dubbed the Platform) and Site Applications. The primary objective of the HPC Simulator is to provide a flexible and extensible computational engine to simulate the coupled processes and flow scenarios described by the conceptual models developed using the ASCEM Platform. The graded and iterative approach to assessments naturally

A mathematical model for predicting glucose levels in critically-ill patients: the PIGnOLI model

Directory of Open Access Journals (Sweden)

Zhongheng Zhang

2015-06-01

Full Text Available Background and Objectives. Glycemic control is of paramount importance in the intensive care unit. Presently, several BG control algorithms have been developed for clinical trials, but they are mostly based on experts’ opinion and consensus. There are no validated models predicting how glucose levels will change after initiating of insulin infusion in critically ill patients. The study aimed to develop an equation for initial insulin dose setting.Methods. A large critical care database was employed for the study. Linear regression model fitting was employed. Retested blood glucose was used as the independent variable. Insulin rate was forced into the model. Multivariable fractional polynomials and interaction terms were used to explore the complex relationships among covariates. The overall fit of the model was examined by using residuals and adjusted R-squared values. Regression diagnostics were used to explore the influence of outliers on the model.Main Results. A total of 6,487 ICU admissions requiring insulin pump therapy were identified. The dataset was randomly split into two subsets at 7 to 3 ratio. The initial model comprised fractional polynomials and interactions terms. However, this model was not stable by excluding several outliers. I fitted a simple linear model without interaction. The selected prediction model (Predicting Glucose Levels in ICU, PIGnOLI included variables of initial blood glucose, insulin rate, PO volume, total parental nutrition, body mass index (BMI, lactate, congestive heart failure, renal failure, liver disease, time interval of BS recheck, dextrose rate. Insulin rate was significantly associated with blood glucose reduction (coefficient: −0.52, 95% CI [−1.03, −0.01]. The parsimonious model was well validated with the validation subset, with an adjusted R-squared value of 0.8259.Conclusion. The study developed the PIGnOLI model for the initial insulin dose setting. Furthermore, experimental study is

Exploring the Relationship between Mathematical Modelling and Classroom Discourse

Science.gov (United States)

Redmond, Trevor; Sheehy, Joanne; Brown, Raymond

2010-01-01

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